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 Reason, thought, and language: or The m 
 
 olin 
 
 3 1924 029 149 354 
 
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REASON, THOUGHT 
 AND LANGUAGE 
 
 OR 
 
 THE MANY AND THE ONE 
 
 A REVISED SYSTEM OF LOGICAL DOCTRINE 
 
 IN RELATION TO THE FORMS OF 
 
 IDIOMATIC DISCOURSE 
 
 BY 
 
 DOUGLAS MACLEANE, M.A. 
 
 SOMETIME FELLOW, LECTURER AND CHAPLAIN 
 OF PEMBROKE COLLEGE, OXFORD 
 
 LONDON 
 HENRY FROWDE 
 
 OXFORD UNIVERSITY PRESS WAREHOUSE 
 AMEN CORNER, E.C, 
 
 1906 
 
^,H6H1%5' 
 
 oxford: HORACE HART 
 PRINTER TO THE UNIVERSITY 
 
PREFACE 
 
 Specialists in what is sometimes spoken of disparag- 
 ingly as Formal Logic have of late been almost as scarce 
 as canonists or line-engravers. I therefore deem myself 
 very fortunate to have been allowed to submit the first 
 draft of this book to the expert criticisms of my friend, 
 Mr. St. George Stock, M.A., of Oxford, who went through 
 it in manuscript with his usual acute vigilance. If any 
 errors, other than those of judgement, be detected in it, 
 they have probably crept in during the rewriting of the 
 work. 
 
 These pages represent an effort to strengthen and 
 revivify Formal Logic — though I do not admit that Logic 
 can be anything but formal — by bringing it into closer 
 connexion with the living facts of thought and speech. 
 I have been bold enough also to think that both ancient 
 and recent views upon various parts of logical theory 
 require examination, and that the entire subject can be 
 with advantage rehandled. The shield which I have 
 especially desired to touch by way of challenge is that of 
 the ' new logicians ' who hold that there can be reasons 
 without Reason, as well as that of the traditional Logic 
 which makes the implicit expUcit without the help of 
 a middle term. Except in the light of what is universal 
 thought cannot exist. 
 
 Although I have assumed some acquaintance with the 
 elements of Logic, I hope the exposition here presented 
 
iv Preface 
 
 will not prove too technical for any intelligent reader. 
 The historical aspects of the subject are ably treated of 
 in established philosophical works, and are here merely 
 glanced at. If an occasional repetition be complained 
 of, I would plead that no one reads a treatise of this kind 
 straight through — stans pede, as I may say, in uno. If 
 on the other hand some lacunae are noticed, let it be 
 remembered that, in Voltaire's phrase, ' le secret d'ennuyer 
 est celui de tout dire.' I have exposed quite a large 
 enough surface to the arrows of criticism, and cannot 
 feel confident that none will find their way home. If any 
 penetrate, I trust, at least, that they will have pierced, not 
 a skeleton of dry bones, but flesh and blood. 
 
 CoDFORD St. Peter, Wilts. 
 
CONTENTS 
 
 CHAPTER I 
 
 PAGE 
 
 Introductory 1-14 
 
 Aim in view, § i. What Logic is and is not, §§ 2-4. Logic 
 cannot but be ' formal ' ; yet it should not stand aloof from the 
 complexities of thought and language, §§ 5-7. Even a purely 
 symbolic Logic, while unconcerned with the content of Terms, 
 has to take account of the grammatical elements of predication, 
 §§ 8-14. It is only when we go outside the data that our 
 reasoning ceases to be formal, § 15. 'Pormal' Logic accused 
 of narrowness and rigidity, § 16. An unlimited field before it 
 in the living facts of idiomatic expression, §§ 17, 18. This field 
 scarcely known to the ancients, and neglected by the moderns 
 for other objects of inquiry, §§ 19, 20. On the other hand, the 
 law of Rationality is throughout one, §§ 21-3. 
 
 CHAPTER II 
 The Justification of any Thought .... 15-30 
 
 The subject of Logic is rational Consequence in Thought. 
 Some analysis of the Thinking act is therefore required, § 24. 
 But Logic is not Psychology, § 25. It investigates the justifica- 
 tion of our thoughts. Every thought must have a mediating 
 ground ; to think is to interpret, §| 26, 27. The assigning of 
 a ground constitutes Syllogism, §§ 28, 29. Logic combats 
 fallacy, not falsity, §§ 30, 31. Varieties of ways in which a 
 ground may be assigned, § 32. Inadequate grounds, §§ 33, 34. 
 Logic, then, is more directly concerned with Judgements (which 
 can be mistaken) than with Concepts (which cannot), §§ 35, 36. 
 Objection, that some consecutions in thought do not require a 
 middle term. Immediate consequence and immediate confliction 
 alleged to be possible, in and between both Concepts and Judge- 
 ments, § 37. The objection met. The mind can never work from 
 one point to another except through a universal. Illustrations, 
 §§ 38-49. The Aristotelian Logic not consistently formal, being 
 blended with' metaphysics and with natural philosophy, S 50. 
 The view of Logic as an Organon to the Sciences, 9 Ji. 
 Baconianism, § 52. Induction is only the ordinary Logic applied 
 in a particular way, §§ 53, 54. Logic cannot supply rules for 
 comparing and judging, §§ 55-7. On its theoretic side Logic 
 is an exact science ; but in its connexion with human Thought 
 and Speech it presents many problems and admits of progress, 
 §58. 
 
vi Contents 
 
 PAGE 
 
 CHAPTER III 
 
 The One sought in the Many 31-9 
 
 Beginnings of logical curiosity, § 59. The mind's conscious- 
 ness of self, § 60. Yet Philosophy's first questionings were about 
 God and the World, § 61. The groping after unity and law in 
 nature and in conduct led to the establishment of General Con- 
 ceptions and Definitions. Morality and Truth defended against 
 sophistical challenge, §§ 62-5. Necessities of argumentation 
 gave birth to a practical- and eristic Logic of the open air. 
 Aristotle's scientific system thought out later, §§ 66-70. There 
 must be a science of Reasoning as Reasoning, § 71. Logic is 
 not simply Mental Science, §§ 72-4. 
 
 CHAPTER IV 
 Immutability of Rational Law 40-59 
 
 Reason an immutable standard and law, prior to all others, 
 §§ 75, 76. Denial by the Empirical School, §§ 77-9. This Law 
 is outside of, and above, proof, §§ 80, 81. Postulate of Truth, 
 §§ 82, 83. Reason and Thought distinguished, §§ 84-9. We 
 partake of Reason, § 90. We do not reason wrongly, but think 
 wrongly, §§ 91-3. Not our Reason, but our Understanding, is 
 deceived and darkened, §§ 94-6. Ambiguity of Middle Terms, 
 §§ 97, 98. Other sources of Fallacy, §§ 99, 100. Petiiio 
 ■principii, § loi. Fallacies, material and formal, §§ 102-5. 
 Can we be too logical ? §§ 106-11. Note. Raymond Lull. 
 
 CHAPTER V 
 
 Reason regulates Thought 60-81 
 
 Rational compulsion laid on Thought, § 112. Thought 
 human and divine, §§ 113-15- Law of Rationality supreme and 
 ultimate, § 116. Twofold, prohibitive and imperative, § 117 
 Axiom of Consistency : its double aspect, §§ 118, 119. Principle 
 of Contradiction, §§ 120-3. Hegehan view, §§ 124-31. Popular 
 objections to the Principle, §§ 132-4. How applied to quanti- 
 fied judgements, §§ 135-42. If applied only to singular judge- 
 ments, contradictory and contrary apt to be confused, 55 uv-o 
 Prmciple of Excluded Middle, §§ 150-5. Challenged as only 
 true within a certain 'universe of discourse', §§ 156-60 Applied 
 to quantified judgements, § 161. A metaphysical difficulty raised 
 SS 162, 163. Fallacy of Many Questions, and question-beggin? 
 Epithets, §§ 164-7. The Dilemma, §§ 168-70. ^ 
 
 CHAPTER VI 
 
 Axiom of Persistency ... »„ 
 
 . 02-93 
 
 Positive and compulsive side of the Law of Rationality, S 171 
 
 Complementary to Axiom of Consistency, §S 172-4 Thesarn^ 
 
 as the Principle of Identity, § 175, which il „L merely tau^o! 
 
 logous, §§ 176-8. All assertion is an amplification, 6S 170 ,80 
 
 Identity perdunng through differences, § 181. A unity ^ 
 
Contents vii 
 
 > PAGE 
 
 plurality even in identifying judgements, §§ 182, 183. The 
 pure Concrete is unnameable and unknowable, §§ 184, 185. 
 Basis of Syllogism, § 186. Question about 'Identical' or 
 Analytic Judgements irrelevant, §§ 187, 188. Subjects regarded 
 primarily in extension, predicates in intension, §§ 189-93. 
 Search for the one in the many the meaning of Induction. 
 § 194. Mill on the Dictum de omni, § 195. Everything abides 
 as it is till some cause of change occurs, §§ 196-9. 
 
 CHAPTER VII 
 
 Sufficient Reason 94-107 
 
 A logical principle. Every thought requires justification, 
 §§ 200-5. Ultimate elements of belief, § 206. Authority as a 
 ground,8§ 207. Will, §§ 208-10. Hov/ ? Sind Wky ? §^ 211-13. 
 Cause and Ground, § 214. Ratio essendi and ratio cognoscendi, 
 § 215. Sign a priori and a posteriori, §§ 216-18. Sign and 
 Formal Cause, § 219. Plurality of Causes, § 220. Cause and 
 Because, § 221. Where in a judgement does the Cause reside? 
 § 222. Logic scrutinizes the sufficiency, not of any Reason, but, 
 of any Reasoning, §§ 223, 224. Consideration of the Form of 
 Thinking necessary, § 225. Note. Narrative Judgements. 
 
 CHAPTER VIII 
 Whatever is Rational is Syllogistic . . 108-20 
 
 Thought, its Form and Matter, § 226. Modality, § 227. To 
 think is to judge, § 228. Are there three Forms of Thought ? 
 § 229. Syllogism is on a different footing from Conception and 
 Judgement, §§ 230-1. Conception and Judgement, as such, 
 exhibit no ration^ character. The subject considered. Illustra- 
 tions, §§ 232-42. No idea can be denied or predicated of itself, 
 §§ 243, 244. Inconsistencies, §§ 245, 246. Opposition of Judge- 
 ments, § 247. There are not three kinds of Comparison, 
 §§ 248-52. Ratiocination, as employed upon human Thought, 
 is discursive, but is concerned with the operations of Thought, 
 not the properties of Things, § 253. Is Syllogism a judgement ? 
 §254. 
 
 CHAPTER IX 
 Conception . . . . . . . . 121-42 
 
 Analysis of the Form of Thought, §§ 255, 256. Conditions 
 of Thought, §§ 257, 258. All human Thought is Conceptual, 
 §§ 259-62. But Concepts resolvable ultimately into Presenta- 
 tions to Consciousness combined by the Intellect, § 263. 
 Abstraction, §§ 264, 265. Perception and Reflexion, §§ 266, 267. 
 Ideational activity of the Understanding in combining sense- 
 impressions, §§ 268-71. Unity in diversity, § 272. Conscious- 
 ness demands transition, § 273; but also persistence, § 274. 
 Apprehension of Universals, § 275. Does Abstraction precede 
 Generalization? §§ 276-8. Classification and Naming, §§ 279-85. 
 The Concrete cannot be conceived. Place and Time. Tense, 
 §§ 286, 287. Every Judgement has some abstract character. 
 
viii Contents 
 
 PAGE 
 
 §§ 288, 289. Nothing can be conceived which has not been 
 experienced, and so cannot be imaged, § 290. Conversely, 
 Images are of individuals, § 291. Common Names, §§ 292-4. 
 Every Concept a complex, § 295. Qualifying (or Determmmg) 
 and Descriptive (or Epithetical) Adjectives, §§ 296, 297. How 
 the Concept develops as the Judgement, §§ 298, 299. Counter- 
 implication of Sub-Contraries, §§ 300-2. 
 
 CHAPTER X 
 
 Inter-relation of Concepts 143"^^ 
 
 Elements of the Concept, § 303. Definition, §§ 304-6. Inter- 
 section of spheres, §§ 307, 308. Genus, Species, and Differentia, 
 §§ 3091 31°- Inverse variation of Extension and Intension : how 
 to be understood, §§ 311-19. Logical Whole and Part, § 320. 
 Natural subordination of Concepts extra-logical, §§ 321, 322. 
 Summum Genus, §§ 323-5. Infima Species, §§ 326-30. Sub- 
 alternation, § 331. Conceptual Matter and Form, §§ 332-8. 
 Matter and Form in Reasoning, §§ 339-43- ' Formal Thinking ', 
 §§ 344-6. Reasoning is for Logic the only formal process, 
 §§ 347-9- The Matter of Reasoning is Judgements ; The Form 
 is the Illation, §§ 350, 351. 
 
 CHAPTER XI 
 
 Division and Definition 162-96 
 
 Division of a Concept's Extension, § 352. Dichotomy, § 353. 
 Any ground of Division logically admissible, § 354. To serve 
 a practical purpose, however, th&fundamentufft divisionis must 
 be given, § 355. Cross-division, §§ 356-8. Rules, §§ 359-61. 
 Seeming exceptions, § 362. Only Common Names divisible, 
 § 363. Ideal Partition, §§ 364-6. Material Partition, § 367. 
 Logic only supplies Negative Safeguards, § 368. Dichotomy 
 criticized by Aristotle, § 369. 
 
 Definition the counterpart of Division, §§ 370-6. What 
 names are definable ? §§ 377, 378. Defining by Negatives, § 379. 
 Good and bad Definition, §§ 380-4. Can Logic recognize 
 Definition? § 385. Definition is subjective, since the meaning 
 or intension of a name is so, §§ 386-g. There can be no defi- 
 nitio ret, §§ 390-2. All Definition is Notional, §§ 393-5. 
 Definition by Cause, §§ 396-8. English dislike of Definition, 
 § 399. Definition of Substances and of Attributes, § 400. 
 Definition /«r effectum, §§ 401, 402. 'Analytic ' and ' Synthetic ' 
 Definition, § 403. Which comes first. Definition or Division ? 
 §§ 404-7- 
 
 Predicables, how far recognized by Logic, §§ 408-10. Pro- 
 perty, §§ 411, 412. Accident, §§ 413-16. The usual treatment 
 of the Predicables belongs to a Realistic system, not to Logic, 
 §§417,418. Species subiicibilis axiA^raedicabilis,^ 419. Logic 
 concerned with all predicates, §§ 420, 421. 
 
 Force of Negative Sign attached to Concepts, § 422. The 
 entire Concept cannot be negated, §§ 423-6. Emphasis laid 
 on negated element, § 427. 
 
Contents ix 
 
 PAGE 
 
 CHAPTER XII 
 
 Judgement 197-204 
 
 Should discussion of Judgement have preceded that of Con- 
 cept ? §§ 428-33. Rudiments of Thinking, §§ 434, 435. The 
 question psychological, not logical, § 436. Assertion of reality 
 the essence of Judgement, § 437. Concepts are Judgements in 
 fosse, §§ 438, 439. How is Quantification implicit in Concepts ? 
 §§ 440-3. Does assertion of reality involve the actual existence 
 of the Subject ? §§ 444, 445. The subject of all judgement is the 
 Real, §§ 446-8. The ultimate 'Universe of Discourse' is the 
 Real conditioned in this or that way, §§ 449-51. 
 
 CHAPTER XIII 
 
 Import of the Proposition 205-19 
 
 Import of ' is ', §§ 452, 453. Cannot be a mere Copula, 
 §§ 454-6. Always predicates existence ; but in what sense ? 
 § 457. Illustrations, §§ 458, 459. Further criticism of the 
 usual doctrine, §§ 460-3. Secundi adiacentis, § 464. ' Copula ' 
 often omitted, § 465. Existence predicated not absolutely but 
 as qualified, §§ 466, 467. Denial of existence, § 468. Interest 
 of every statement resides in its predicate, § 469. Existence 
 hypothesized and assumed, § 470. Existence of subject deter- 
 mined not by the ' Copula ' but by the form of the proposition, 
 §§ 471, 472. It is not a question of quantity and quality, but 
 of abstract and concrete, §§ 473-6. Singular judgements, § 477. 
 Categorical and Hypothetical, § 478. Further discussion of 
 existential import of A, E, J, and O propositions, §§ 479-83. 
 What is meant by judged existence? § 484. Existence of 
 predicate class, §§ 485, 486. 
 
 CHAPTER XIV 
 
 Import of the Proposition {contmued) . . . 220-9 
 
 Every judgement is within an assumed sphere of discourse — 
 ultimately Reality, § 487 ; which is the same in Predicate as 
 in Subject, §§ 488, 489. Coinherence in Reality either notional 
 or phenomenal, § 490. Sometimes expressed by ' and ', § 491. 
 But Subject and Predicate are not on an equal footing, § 492. 
 In one sense the Predicate comes first, § 493. All judgement 
 brings Object under Concept, T/tai under What, § 494. The 
 Subject may be simply pointed to, § 495. The Subject is 
 essentially substantival, the Predicate adjectival, §§ 496, 497. 
 But what is attributed is an Attribute, § 498. Hamilton's 
 doctrine of the Proposition criticized, § 499. ' Congruence ' and 
 ' Confliction ', § 500. Does not account for A propositions, 
 § 501. His doctrine assumes a classified scheme of inter- 
 ordinated Notions, § 502. 'Agreement of Notions ' ; Hamilton 
 treats all judgement as Analytic, §§ 503-5. Logical schools. 
 §506, 
 
X Contents 
 
 PAGE 
 
 CHAPTER XV 
 Analytic Judgements 230-47 
 
 Judgements Explicative and Informative, § 507. 'Verbal', 
 § 508. ' Identical ', § 509. Such judgements in common use. 
 Their purpose. Illustrations, §§ 510, 511. 'Contradictions in 
 terms', § 512. Locke on 'frivolous' judgements, §§ SI3> Si4- 
 Appeal to an assumed agreement, § S'S- AH propositions are 
 instructive, § 516. Definitions, § 517. Locke's view really a 
 Realist one, § 518. Reflective and expository judgements, 
 § 519. An Analytic Judgement must claim to be such, § 520. 
 The content of names is not fixed, § 521. Yet definitions do not 
 change with every increase of knowledge, § 522. Our notion of 
 a thing is not all we know about it, §f 523, 524. Analytic 
 judgements go below the surface, § 525. View that all judge- 
 ments are analytical, § 526. View that all are synthetic, § 527. 
 Particular propositions synthetic, § 528. Analytic Judgements 
 do not analyse, but base themselves on the analysis of, an idea, 
 §§ 529-31. Analytic Judgements not ' immediate '. Pure reason 
 cannot say what is in a notion, § 532. ' Synthetic Judgements 
 apriorV, § 533. Appealing Vocatives, § 534. 
 
 CHAPTER XVI 
 
 General and Concrete Judgements . . . 248-61 
 
 Every Abstract Judgement implies a Cause or Law, § 535. 
 Concrete Judgements state a fact, § 536. The cause not always 
 indicated in the judgement, §§ 537-40. Every General Proposi- 
 tion involves both an 'if and a 'because', § 541. Metaphysical 
 aspects of predication extra-logical, §§ 542-6. Hypothetical 
 and Categorical, §§ 547, 548. Abstract character of some 
 seemingly Particular judgements, §§ 549, 550. Different mean- 
 ings of 'air, § 551. Mixture of abstract and concrete, § 552. 
 Past tense, § 553. Mark of quantity when part of predicate, 
 § 554. Particular judgements obtained by generalization, §§ 555, 
 556. Invariableness of connexion between antecedent and 
 consequent, § 557. Appeal to experience, § 558. Connexion 
 expressed by ' and ', § 559. Predictive, § 560. Reciprocative 
 judgements, § 561. Purely concrete statement impossible, § 562. 
 Yet the distinction of abstract and concrete important, § 563. 
 Clearer in English than in more synthetic languages, § 564. 
 A point of space or of time may have an abstract interest, § 565. 
 
 CHAPTER XVn 
 
 Quantification 262-75 
 
 Quantity of Judgements. The major premiss must be definite, 
 § 566. Hamilton's scheme of Quantity, § 567. Suggested 
 classification of Judgements, §§ 568, 569. ' All ' and ' all the ', 
 §570. Quantity as part of Subject or Predicate, § 571. Marks 
 of a Particular Judgement, § 572. Examples, § 573. Plural 
 Judgements, § 574. Singular Judgements, § 575. How to be 
 classed, §§ 576-8. Uniqueness, § 579. Individual Judgements, 
 
Contents xi 
 
 . PAGE 
 
 § 580. General Propositions about 'one'. Examples, § 581. 
 Sigwart on Particular and Universal Judgements, §§ 582, 583. 
 ' Always ' and ' sometimes ' relative expressions, § 584. Quantity 
 not a determination of the subject, § 585. A, E, I, and O 
 Judgements, § 586. / and O, § 587. ' Some only ', § 588. 
 Opposition of Disjunctives, § 589. Omnis X and nullus noti-X, 
 § 590. Interrogations, § 591. Particular Negatives, § 592. 
 
 CHAPTER XVIII 
 Negation and Modality 276-85 
 
 Denial of Quantification, § S93- Denial falls where the 
 interest lies, § 594. Place of ' not ' in a sentence, § 595. Doctrine 
 that Negation implies a tentative Assertion, § 596. No such 
 thing as a negative, but only a negated, ' Copula,' § 597. Is 
 Negation a severance ? § 598. Objection to the view that 
 Negation is a judgement concerning a judgement, § 599. Nega- 
 tive and Privative Conception, § 600. ' Not ' as part of the 
 subject, § 601. Summing up, § 602. Denial of an idea aflfects 
 its whole extension, but part only of its intension, § 603. Sup- 
 posed difficulty of proving a Negative, § 604. Modals — 
 Modality when an element of the Predicate, §§ 605, 606. When 
 affecting the entire Judgement, does it 'modify the Copula'? 
 § 607. Assertiveness admits of no degrees, § 608. Problematic 
 Judgement, § 609. Every judgement is a necessary inference, 
 § 610. Probability, § 611. Do Tense and Mood modify the 
 assertion? § 612. Negation, § 613. 
 
 CHAPTER XIX 
 Implication of Judgements 286-97 
 
 Conversion, § 614. Simple and /«rat«rf««j, § 615. Opposi- 
 tion of Judgements, § 616. Obversion ; Conversion of Particular 
 Negatives, § 617. Non-X is non- Y. Examples, § 618. ' Only ', 
 §619. Is Implication illative ?§ 620. Conversion of ^ judge- 
 ments, §§ 621, 622. Neither Conversion nor Obversion an 
 inferential process, § 623. The A judgement completed, § 624. 
 Differs from /, §§ 625, 626. Diagrams exhibiting implication 
 of Judgements, § 627. Consequent and Antecedent, § 628. 
 Opposition of Singulars, § 629. From denial of Antecedent or 
 affirmation of Consequent nothing follows, § 630. Judgements 
 expanded in conjunctive form, § 631. Concessive antecedents, 
 § 632. Consequent and Consequence, § 633. Added Deter- 
 minants and Equipollence, §§ 634-6. 
 
 CHAPTER XX 
 Extension and Intension 298-309 
 
 In Predication, § 637. Extension of Subject governs Predicate, 
 § 638. Unless the quantification is relative, § 639. Intension, 
 S 640. Subject-term's empirical extension, apart from quantifica- 
 tion, § 641. Extensions identified, not equated, § 642. Conver- 
 
xii Contents 
 
 PAGE 
 
 sion of Judgements viewed in Intension, § 643. Extension and 
 Intension inseparable, § 644. Proper and Common Names, 
 § 645. Hamilton's ' discovery', § 646. ' Containing ' and ' Con- 
 tained ', § 647. Notional Inclusion, § 648. How to be applied 
 to Particular Judgements? § 649. Intensive Conversion only 
 possible in analytic E judgements, § 650. Confused analysis, 
 § 651. Class-inclusion and Attribution, § 652. Judgements 
 expressed in Extension. Examples, § 653. ' Major ' and ' Minor ', 
 § 654. Numbers, § 655. 
 
 The Categories, § 656. Limited interest for the logician, § 657. 
 Grammatical significance, § 658. Adverbial predicates, § 659. 
 Other irregular predications, § 660. Conversion of such propo- 
 sitions. Imperatives, Interrogatives and Interjections, §661. 
 
 CHAPTER XXI 
 
 Quantification of Predicate .... 310-26 
 
 Ignores Intension, § 662. Hamilton's attack on ' the common 
 doctrine ', §§ 663, 664. A ' discovery' ? § 665. Or a paradoxical 
 innovation ? § 666. Defended by Veitch, § 667. ' Enounce as 
 you think', § 668. How far arguable? § 669. Implied Extension 
 of Predicates, § 670. Distributive and Collective Assertion, 
 §§671,672. Will any formula combine both? § 673. 'All X 
 is all Y' ; ' Some X is all F', § 674. Ambiguity of ' all ', § 675. 
 What is asserted of wholes is not in the same formula asserted 
 of objects severally, § 676. Unnatural formulas. Hamilton 
 inconsistent, § 677. Violence to the natural import of predica- 
 tion, § 678. A twofold quaesitum, § 679. ' Every X is every 
 F', § 680. Subject and Predicate levelled, § 681. Examples of 
 Reciprocating Judgements, § 682. Complicated new Proposi- 
 tional Forms, § 683. Hamilton's doctrine applied to Negative 
 Judgements, § 684. 'Non-equation', § 685. Rather an equation 
 of Negated Terms, § 686. Hamilton's own doubt, § 687. Facts 
 of common speech and syntax alleged in support, § 688. The 
 plea examined, § 689. Exponibles, §§ 690, 691. Definitions, 
 I 692. Predicates of E and O; oil and E, § 693. Predication 
 is not algebra, § 694. A subsidiary scheme of implied exten- 
 sional equation might have been of interest, § 695. But predica- 
 tion is not merely adding and subtracting, § 696. Hamilton's 
 doctrine applied to Syllogism ; consideration deferred, § 697. 
 Plurality of Causes criticized from an equational standpoint, 
 §§ 698, 699. Difference between Condition and Conditioned 
 destroyed, § 700. Irrelevant elements, §§ 701, 702. Judgement 
 itself abolished, §§ 703,704. And Logic also, §705. Plural Causes : 
 Examples, § 706. A Conclusion can be reached through more 
 than one Middle Term. We thus come to Syllogism, § 707. 
 
 CHAPTER XXn 
 
 Syllogism 327-38 
 
 Why it has been necessary to analyse Conception and Judge- 
 ment, § 708. Will a combination of Notion and Proposition 
 yield an inference? §§ 709, 710. Premisses may be either or 
 both hypothetic. Demonstrative reasoning, § 711. The latter 
 
Contents xiii 
 
 PAGE 
 
 extra-logical, § 712. Syllogism regarded as a single act of 
 thought, § 713. Hamilton's general Formula of Syllogism, § 714. 
 Implies Notional Inclusion, § 715. Inclusive spheres: do they 
 enable us to dispense with middle terms? § 716. Mill's view, 
 § 717. His own formula faulty, § 718. 'Coexistence' and 
 'Agreement', §§ 719, 720. Particular Inferences, § 721. Con- 
 ditions of Valid Inference : Case and Rule ; Laws and Cautions, 
 §§ 722-31. Proof that a true Conclusion may be drawn from 
 false premisses, §§ 732-6. 
 
 CHAPTER XXIII 
 
 Mood and Figure 339-66 
 
 Valid and invalid combinations, §§ 737-40. Can be arrived at 
 also apriori, § 741. Persistency and Consistency the double basis 
 of Syllogism. Figures I and II. Direct and Indirect Moods, 
 |§ 742-53. Figure I has no real supremacy over Figure III, 
 P 7S4~62. Mnemonics for reduction to the First Figure, 
 §§ 763-8. Reduction to the Second Figure as easy, §§ 769- 
 72. Cross-reduction, § 773. ' Major ', ' Minor ' and ' Middle ', 
 §§ 774-6. A hierarchy of Concepts, § "JT]. Special features 
 of the Four Figures. Figure I, §§ 778-80. Figure II, §§ 781, 
 782. Figure III, §§ 783-7. Figure IV, j§ 788-94. Distinc- 
 tion of Figures attacked by Kant, § 795. 
 
 CHAPTER XXIV 
 Mood and Figure {continued) .... 367-86 
 
 Semi-conjunctive Reasoning, § 796. Conspectus of figured 
 Forms, §§ 797, 798. Possible combinations, § 799. Implied 
 judgements about non-/", § 800. And about non-5, § 801. 
 Scheme of Moods with quality abolished, §§ 802, 803. Negative 
 and Privative Conception, § 804. Reduction on this basis, § 805. 
 A proposed simplification, §§ 806-8. A revised Mnemonic, 
 §§ 809-11. Distinction between Major and Minor essential, 
 §§ 812, 813. Order of Premisses. Indian Syllogism, §§ 814-20. 
 Hamilton's Intensive Syllogism, §§ 821, 822. Sumption and 
 Subsumption, § 823. Veitch's criticism, §§ 824-8. Negation 
 of Intension, § 829. 'Part of and 'involved in', § 830. Is 
 Extension or Intension uppermost in thought ? § 831. 
 
 CHAPTER XXV 
 Unfigured Syllogism 387-409 
 
 Hamilton's equational system no real simplification, §§ 832- 
 44. Ultra-dimidiate Quantification, §§ 845-7. Mathematics 
 applied to Logic, §§ 848-61. Bearing on the inter-relation of 
 Premisses and Conclusion, §§ 862-5. Inter-relation of the 
 Extensions of three Terms, § 866. Proposed notation, §§ 867-9. 
 
xiv Contents 
 
 PAGE 
 
 CHAPTER XXVI 
 
 Elliptical Reasonings 410-31 
 
 Sorites, §§ 870-83. Enthymeme, §§ 884-8. Other elliptical 
 reasonings, §§ 889-98. Syllogism in one proposition, §§ 899- 
 901. Formulas for the four Figures, §§ 902-5. The ground 
 as a separate clause, §§ 906, 907. Epicheirema, § 908. 
 
 CHAPTER XXVn 
 
 Conditional Reasonings 432-52 
 
 How divided, § 909. Do they differ from Categorical? 
 §§ 910-12. Abstract and Hypothetical, § 913. Nature of 
 minor premiss, § 914. ' Krug's view, §§ 9x5-17. 'Broken- 
 backed sequences', § 918. Temporal and spatial conjunctions, 
 §§ 919) 920. We are not concerned with metaphysical or gram- 
 matical questions, § 921. Reason and Consequent and the 
 Principle of Identity, §§ 922, 923. Equational view of Logic, 
 § 924. How applied by Hamilton to Hypotheticals, § 925. His 
 Canon, § 926. Hypotheticals ignored by Aristotle. Such forms 
 more needed in some languages than in others, § 927. Only 
 preparations for argumentation, § 928. Sigwart's view, § 929. 
 How many terms in a hypothetical judgement ? § 930. Is there 
 any 'immediate inference'? § 931. Antecedent affirmed and 
 Consequent denied, '§§ 932, 933. Modus ponens and Modus 
 tollens, §§ 934, 935. Negative predicates, § 936. Phrasing of 
 hypothetical judgements, § 937. How contradicted, §§ 938, 939. 
 Particular minor premiss, §§ 940, 941. Minor premiss may be 
 itself hypothetic, § 942. This shown in the four Figures, 
 §§ 943~5- Pre-eminence of First and Second Figures clearly 
 seen, § 946. Adversative 'if, § 947. 
 
 CHAPTER XXVni 
 
 Disjunctive Reasonings 453-73 
 
 Various Forms of Disjunction, §§ 948, 949. How contradicted, 
 §950. Exclusive or only alternative? §§ 951, 952. Disiunctio 
 ambigui, §§ 953, 954. Choice between contradictories, § 955. 
 Disjunctions with many members, § 956. Material incompati- 
 bility, § 957. Modus ponendo tollens and modus tollendo panens, 
 §§ 958, 959- Disjunction of contradictories does not require 
 syllogizing, § 960. Conjunctive-disjunctive judgement, § 961. 
 As major premiss, § 962. Constructive and Destructive, § 963. 
 Double disjunction, §§ 964, 965. Dilemma, §§ 966-74. Danger 
 in rebutting, §§ 975-7. Hypothetico-disjunctive, § 978. Be- 
 tween Hypothetical and Abstract Categorical Judgements no 
 logical distinction, §§ 979-81. 
 
 CHAPTER XXIX 
 
 Attacks on the Syllogism 474-97 
 
 Modern anti-scientific School, § 982. Denial of a single type 
 of Inference, § 983. Synthetic activity of Thought, § 984. 
 
Contents xv 
 
 PAGE 
 
 What is to take the place of Syllogism ? § 985. Dr. Bradley's 
 indictment, § 986. Charge of ■petitio frincijiii, § 987, Major 
 premisses unnecessary, § 988. Reasoning without reasons, § 989. 
 'Private inspiration' suggested as a substitute, § 990. Or 
 inspection, § 991. An emancipated Logic, § 992. A point of 
 connexion all that is demanded, § 993. Rule against quaternio 
 terminorum repudiated, § 994. Mill's Reasoning without univer- 
 sals examined, §§ 995-1011. The difficulty a psychological one 
 only, §§ 1012-14. The major premiss in Substitutional Inference, 
 § 1015. And in arithmetical reasonings, § 1016. 
 
 CHAPTER XXX 
 
 Is Syllogism a Petitio Principii ? . . . 498-508 
 
 The Charge examined, §§ 1017-31. Another criticism 
 suggested and rejected, §§ 1032-7. 
 
 CHAPTER XXXI 
 
 Universale, how obtained? 509-20 
 
 How are General Propositions arrived at? § 1038. By a 
 formal process exercised upon the data of experience, §§ 1039- 
 42. All inference is at bottom the same, §§ 1043, 1044. In- 
 duction is only the application of logical law to a particular 
 principle, that of Causality, §§ 1045, X046. Canons of Induction, 
 §§ 1047-61. 'Search for Form', or, in logical language, for 
 the Middle Term, §§ 1062, 1063. 
 
 CHAPTER XXXII 
 
 Principle of Causality 521-49 
 
 'Uniformity of Nature', an ambiguous phrase, §§ 1064-6. 
 Causality, § 1067. Cosmic stability a truth given by experience, 
 §§ 1068, io6q. Not so the axiom that causes are always followed 
 by their effects, §§ X070, 1071. Induction applies this axiom to 
 phenomena, § 1072. Is the Axiom of Induction itself an induc- 
 tion? §§ 107.3, 1074. Induction a union of ratiocination with 
 intelligence, §§ 1075-7. Aristotelian 'Perfect' Induction, §§ 1078- 
 80. Methods|of true scientific Induction, § 1081. Need, however, 
 of insight and imagination, § 1082. Induction explains all facts, 
 not physical phenomena only, §§ 1083, 1084. Disciplinary value 
 of Inductive and Deductive Methods compared, § 1085. Logic 
 is not Methodology, § 1086. Nor does it supply a Criterion of 
 Truth, § 1087. Reason is not Judgement, § 1088. Reason can- 
 not frame bonae noHones, § 1089. Illustrations, §§ 1090, 1091. 
 Analogy, §§ 1092-1101. 
 
 Appendices 550 
 
ERRATA 
 
 Page 72, note i, line 11, for say truly read I say truly 
 
 P. 95, page-heading, ybr a Necessary read b.s Necessary 
 
 P. 134, n. I, last line, for f^a read (^a 
 
 P. 152, § 324, 1. 3, insert comma after richest 
 
 P. 157, 11. 3, last line, yby corregiosity read correggiosity 
 
 P- ^^78, § 389, 1. 7, y&rLotze ji?arfLotze 
 
 P. 216, 11. I, last line, for II a read II y a 
 
 P- 357) n. Ji, 1. 4, for preicdated reorf predicated 
 
 P. 366, I. 10, for Dimasis read Dimaris 
 
 P. 480, 1. I2,^>- dominate rearf dominant 
 
CHAPTER I 
 
 INTRODUCTION 
 
 § I. If it be the case, as an eminent logician of the new school 
 complains, that throughout the modern textbooks Logic is in 
 a chaotic condition, exhibiting an astonishing diversity of opinion 
 about its province and methods, there may be room for yet 
 another treatise, which shall at least attempt to work out in 
 detail a single and consistent view. The ideal which I set 
 before me is that of a Logic which shall be more consistently 
 formal than the Aristotelian and scholastic tradition, yet in 
 intimate touch with the realities of human thought and language. 
 
 § 2. 'Logic,' observes Dr. Bosanquet, 'has a hard task to 
 hold its own against Metaphysics and Psychology.'^ It starts 
 from the assumption of Reality and moves in the sphere of 
 Mind. Nevertheless its conclusions are the same whatever 
 view we take of the nature of Being and by whatever faculties 
 we perceive and think. The older logicians mingled ontological 
 conceptions with the science. The recent tendency has been to 
 confuse it with epistemology, 'tracing the evolution of Knowledge 
 in the light of its value and import,' from the first glimmer of 
 awaking consciousness to the ordered hierarchy of the sciences, 
 the greater and lesser thrones of Wisdom. Now the basis and 
 presupposition of Logic, no doubt, is metaphysical — that funda- 
 mental nature of Reality, that imperativeness of Truth, which 
 imposes upon Thought the obligation of self-consistency. Still, 
 this obligation is postulated by the logician, not proved.^ He 
 does not try to pierce the veil to a knowledge of the ultimate 
 Real. And with other questions connected with Being, such 
 as essences and accidents, the relations of substance and quality, 
 the meaning of causality, of necessity, of good and evil, of space 
 and time, of personality — what God is and what man is — , he 
 
 ^ Logic, i. 247. 
 
 " ' Logic does not investigate the truth, trustworthiness, or validity of its 
 own principles. This task belongs to Metaphysics.'— Sidgwick, Use of 
 Words in Reasoning, p. 8. 
 
 B 
 
2 Introduction 
 
 is not at all, or only incidentally, concerned. Similarly, while 
 tracing the rational connexions of Thought, Logic is bound, 
 indeed, to accept help from outside in taking the thinking act, 
 to some extent, to pieces. It is only interested in the concept 
 and the judgement as products; yet, to understand these 
 products, it must scrutinize conceiving and judging as processes. 
 On the other hand. Logic does not concern itself with mental, 
 any more than with physical, phenomena as such, as contingently 
 thus or thus. The constitution of Mind is for the psychologist 
 to determine, as the nature of Existence is for the metaphysician. 
 § 3. Nor yet again must Logic be confused with Method. 
 Dr. Bosanquet, for instance, contends that 
 
 ' The subject matter of logic is Knowledge qua Knowledge, 
 or the form of knowledge. It is quite essential to distinguish 
 the form of knowledge in this sense from its matter or content. 
 The " matter " of knowledge is the whole region of facts dealt 
 with by science and perception . . . The phrase "Science of 
 Sciences" does not mean that Logic is a Science which com- 
 prises all the special sciences, but that Logic is a Science dealing 
 with those general properties and relations which all sciences 
 qua sciences have in common. . . . Thus, not the nature and 
 affinities of the plant-world, but classification, explanation, 
 observation, experiment, theory, are the pihenomena in virtue 
 of which the organized structure of botanical science participates 
 in the form of knowledge, and its objects become, in these 
 respects, objects of logical theory.' * -'^ 
 
 Accordingly he maintains that the form of knowledge (identified 
 with logical form) 'depends in some degree upon its matter'. 
 The employment of symbols to represent logical processes is 
 therefore, he considers, of very limited utility. 
 
 § 4. Except that reasoning supposes a universal element in 
 thought, I hold that Logic is no more Science than it is the 
 sciences. Classification, explanation, observation, experiment, 
 theory, are governed by logical laws. But Logic cannot tell us 
 how to observe, theorize, and so forth, successfully. Or if it 
 can do so, it must be some other branch of inquiry which 
 analyses the purely formal relations of thought as connected 
 rationally. Why should the new Logic, the ' Logic of Truth ', 
 treat the old Logic with contemptuous toleration as a humble 
 relative who has seen better days, when the two inquiries have 
 
 ^ Essentials of Logic, Lecture III. 
 
A 'Purely Formal' Logic 3 
 
 really nothing to do with one another?* The hedge-sparrow 
 squeezed into a corner is not related to the cuckoo, its intrusive 
 guest, nor under any obligation to drudge for it. 
 
 § 5. And yet there may be something worth weighing in 
 the 'opposition to Formal Logic' announced by writers like 
 Mr. Alfred Sidgwick. He tells us that 'formal logicians assume 
 that the logical character of a word, or of an assertion, belongs 
 to it quite independently of its context '. They seem to think 
 that 'a sentence which is intended to express an assertion is 
 the same thing as the assertion which that sentence is intended 
 to express',' and that 'forms of sentence have some peculiar 
 virtue which binds assertor and audience equally to a single 
 indisputable meaning'; whereas 'the most effective source of 
 fallacy and dispute is always the failure to get our meaning 
 clear'.' To ask for the precise interpretation of a sentence, 
 which is only the assertion's outer husk, ought not, he urges, to 
 be regarded as going outside Logic. We must not be forbidden, 
 then, to examine the matter asserted. We must not hfead off 
 and starve inquiry by prohibiting excursions into the domain 
 of psychology or of metaphysics, lest we so ' cramp Logic that 
 it becomes a mere collection of misleading formulas, coupled 
 with a little elementary grammar '.* ' The traditional conception 
 of a reasoning process as something separate from its subject 
 matter sterilizes the inquiry into the nature of good and bad 
 reasoning.' ^ 
 
 § 6. There appears to be some confusion here between 
 ascertaining the meaning of a proposition and inquiring into 
 the objective nature and actual relations of the subject matter.' 
 
 ' Mr. A. Sidgwick, while advocating ' that larger and deeper study of 
 Logic which is sometimes called the Theory of Knowledge ', confesses that 
 it is 'to a great extent incompatible with the objects of the formal 
 logician '. No doubt, until we reach the ultimate facts of consciousness, 
 the ^tmum cognitum, every judgement, as having a ground, is partly an 
 inference. But the separation of the inferential form from the judged 
 content is the very object of Logic, and is a wholly different inquiry from 
 an investigation of the bases, conditions, processes and faculties involved 
 in Cognition. If the logician has not to inquire what the world is in 
 itself, neither has he to ask how we perceive it, nor in what way we can 
 best arrange our knowledge of it. 
 
 ''■ The Use of Words in Reasoning, p. 17. 
 
 ° Ibid. p. 19. * Ibid. p. 9. ° Ibid. p. 10. 
 
 ° For the Matter of reasoning as contrasted with its Form, see 
 below, § 3S0. 
 
 B 2 
 
4 Introduction 
 
 Invalid reasoning, says Mr. Sidgwiclc, 'lies in the subject matter. 
 It is no use considering the form alone.' ^ But he will not, 
 I think, deny that the argument, 'Cats are dogs, dogs are 
 animals, therefore cats are animals,' is perfectly valid reasoning, 
 and leads to a conclusion not merely correct but true.^ What 
 he intends, no doubt, is that we must look to the meaning 
 of a proposition and not simply to its verbal expression. The 
 textbooks, he says, 'keep alive the notion that formality is 
 the strength of Logic instead of its weakness.' ' 
 
 § 7. Now, the strictest formalist even of 'the childish or 
 mediaeval Logic' knew very well that he had to deal with 
 thoughts rather than sounds or marks upon paper, and that, 
 if a pound is sixteen ounces and stray pigs are kept in a pound, 
 it does not follow that stray pigs are kept in sixteen ounces. 
 But we have all met the pedantic stickler in common life who 
 informs us that an argument is illogical, through some trifling 
 irregularity ; as when we are not allowed to say that bad 
 workmen complain of their tools, and that therefore, since 
 X does so, he must be a bad workman — where no doubt we 
 have been technically guilty of ' undistributed middle ' ; but 
 we meant ' bad workmen, and only they, complain '. And 
 certainly the older Logic, taking little notice of such sub- 
 auditions, was somewhat wooden and unpractical. Still, one of 
 the uses of Logic is to make men express themselves accurately, 
 affording them the opportunity of restating their reasoning if 
 necessary. Logic and common sense have to help one another. 
 The former shows the latter, when puzzled, what tests to apply 
 to any reasoning. The latter suggests to the former what the 
 real import is of the materials supplied to it. Again, we often 
 instinctively see the bearing of a complicated point while the 
 
 ^ Op. cit. p. 12. 
 
 '^ All reasoning is formal, not because it exhibits a form or because it 
 excludes matter, but because, in Hansel's words, the reasoning act ' is based 
 on the form only of the preliminary data without reference to the par- 
 ticular matter. ... So long as the formal relation of the data remains 
 the same, the matter may be changed as we please, without affecting the 
 logical value of the thought. . . . For this reason, all examples of logical 
 thinking are better expressed by means of arbitrary symbols than of 
 significant terms : not that it is in any case possible to think without some 
 matter or other, but because it is wholly indifferent what matter we may 
 at the time be thinking about' {Prolegomena Logica, 1st ed. pp. 242-4). 
 
 ' Op. cit. p. 7. 
 
Formal, but not simply Symbolic . 5 
 
 formula 'All -^ is Y' and its three blind brothers are hobbling 
 a long way behind. 
 
 Again, apply the syllogistic formula, 'AH Y's are Z; .X" is a Y; 
 then X is Z,' to the following example — ' All dogs come into the 
 world blind. Ponto is a dog. Then Ponto comes into the world 
 blind.' We want came not comes. It has to be pointed out, 
 then, that a General Proposition is such, either as . making 
 a concrete statement about the members of a class generally — 
 as in the illustration just given — , or as making a general state- 
 ment about a concretely designated object or objects — e.g., 
 'My three houses always let easily' — , or as making a general 
 statement about a class generally^ — e. g., ' all cats (always) lap.' 
 The conventional formula for syllogism fits general predication 
 in the second and the third sense only. Nor will 'X is always, 
 or invariably, Y' suit no. i any better. We seem to want some- 
 thing like — ' It is the nature of X to be Y' 
 
 Here is an argument — ' Bibamus, moriendum est.' And here 
 a universal A proposition — ' Me duce, tutus eris.' And here, 
 though imperative, an E judgement — ' Ne sua Minervam.' 
 
 § 8. So long as Logic remains in a symbolic shape, no question, 
 of course, can arise about the content of the terms of any pro- 
 position, though many difiBculties and ambiguities may attach, 
 as we shall see, to the verbal signs of quantity and quality and 
 to the various phrases by which the attribution of y to ^ can 
 be expressed. 'A term is any name or combination of names 
 and words describing the qualities and circumstances of a 
 thing' (Jevons). It ranges from a bare individual indication or 
 pronoun — 'that object': ' she ' — to the most complicated bundle 
 of grammatical clauses within one conception. A purely sym- 
 bolic Logic not only leaves the content of the propositional 
 terms empty of significance, but requires the great variety of 
 relations between the terms, in which relations the form of the 
 thought consists, to be given in one or other of four moulds, 
 usually expressed in the forms — All ^'s are Y, some ^'s are Y, 
 no X's are Y, some ^'s are not Y. A very useful Logic, like 
 Dean Aldrich's, may be constructed within these limits; and 
 it was indeed an immense philosophic achievement when 'the 
 master of them that know ' first excogitated the bare skeleton 
 forms into which all argumentation in every language can be 
 thrown, displajdng the laws of rational consecution between 
 
6 Introduction 
 
 thought and thought. It was much to enable men to challenge 
 an opponent to bring into the light the hidden ground of any 
 assertion, to complete his syllogism, to exhibit his reasoning 
 in one of the regular analyses, and, thus dissected, to submit 
 it to formal tests. A simple norm of ratiocination demands 
 for its elements simple norms of judgement. And these the 
 ' traditional Logic ' framed, and built up into an inexpugnable 
 system. >< 
 
 § 9. But, in the first place, while undoubtedly there is such 
 a thing as an abstract form of thinking, no syntactical type 
 of sentence — such as '^'s are Y' — has an absolute right to 
 be regarded as its representative. The same thought is equally 
 well expressed by ' V-ness is predicable of X things ' ; or by, 
 'The possession oiX quality carries with it the possession of 
 Y quality ' ; or by, ' Where X is found Y is found ' ; or in other 
 ways. For the marks of quantity, all, some, not any, not all, we 
 may substitute always, sometimes, never, not always {sometimes 
 not), or other modes of expression, more or less complicated. 
 'All ^'s are Y' is the same mental judgement as ' only ys are X ', 
 and the following pair of syllogisms are identical in reasoning : — 
 
 Every M is P 
 Some S's are M 
 Therefore soine S's are P 
 
 None but P's are M 
 S is in some cases M 
 Therefore S is in some cases P. 
 If the latter type were adopted, the usual scheme of moods and 
 figures would seem at first sight dislocated ; ^ but this syllogism 
 comes out in the second Figure, in the mood Festino with a 
 negative subject- term — 
 
 No not-P's are M. 
 S is sometimes M 
 
 Therefore 5 is sometimes not not-/*. 
 Now, ' None but the brave deserve the fair ' expresses what is 
 meant at least as simply as ' Every one who deserves the fair is 
 brave ', and ' Only the industrious will be relieved ' is at least as 
 intelligible as ' All who will be relieved are industrious '. 
 
 The missing premiss of 'It is Jehu, the son of Nimshi, 
 for he driveth furiously', is more naturally expressed in the 
 form, 'Only Jehu drives furiously,' than in the form, 'All who 
 drive furiously are Jehu.' 
 
 * See Appendix H. 
 
Complexities of Actual Thought 7 
 
 § 10. The laws of ratiocination are the same, whatever type 
 of propositional formula we select. But it is more obvious, to 
 take an example, that in ' All X's are Y' Y is undistributed 
 than it is in ' None but Y's are X ', which is rationally the same 
 judgement. Again, ' Only the wise are free ' is equivalent to ' All 
 who are free are wise'; but "Tis only noble to be good' is 
 tantamount to saying, 'All who are noble are good', not 'AH 
 who are good are noble.' 
 
 § II. Secondly, no set of logical formulas will enable us 
 to analyse the complexities of actual thought and speech, or to 
 expose without further help any but the simplest fallacies. The 
 symbolic Syllogism is unequal to the subtilty not only of nature 
 but of thought.^ In such an argument as Montaigne's 'Je 
 I'aimais parceque c'etait lui, parceque c'^tait moi ', a real process 
 of reasoning is concealed; but it is not easy to exhibit it 
 formally. Even 'Here am I, for thou didst call me' is not 
 quite so simple as it looks. Nor ' Be ye holy, for I am holy '. 
 Or take the following syllogism : — 
 
 Hoc ita iustum est si est voluntarium. 
 
 lustum est. Ergo est voluntarium. 
 This is really in Figure I, the major premiss being equivalent 
 to ' Omne iustum voluntarium est '. Or take this : — 
 Nemo fere saltat sobrius nisi forte insanit. 
 iV sobrius est et saltat. Ergo insanit. 
 More fully— 
 
 Nemo non-insaniens sobrius est et saltat. • 
 
 N sobrius est et saltat. 
 
 Ergo non est non-insaniens (i. e. insanit). 
 Symbolically — 
 
 No non- F is X and also Z (no non-YX is Z). 
 
 N is X and also Z. Therefore N is not non-Y. 
 
 ^ Here is a sentence taken at random from a letter written by Laud to 
 Sir Kenelm Digby : — ' It is not your-change {A) that-can-change-me 
 {B) ; who (C) never yet left (D) but where-I-was-first-forsaken {E), 
 and not always there (E).' The sentence contains three propositions — 
 no 5 is A; no non-^C is D ; some EC is not D. The thing that can 
 change me is not your change : no case where I was not first forsaken 
 was ever a case of my leaving ; and some cases where I was first for- 
 saken are not cases of my leaving (in the past). And here is a familiar 
 concept : — ' God {X ) without-whom (non-X) nothing is strong ( Y), nothing 
 is holy (Z) '=an X of whom it is the case that no non- A!" is Y and no 
 non--Sr is Z ;=a (non-JC is non- Y) (non-^ is non-Z) X ! 
 
8 Introduction 
 
 More simply— 
 
 Every XZ is Y (Every sober dancer is mad) 
 N is XZ. Therefore N is Y. 
 Sobrius means non-ebrius, not tipsy : and, if we represent it by 
 non-^ instead of X, the syllogism will have a still more com- 
 plicated and artificial look. Nevertheless the reasoning is 
 transparent and usual. 
 
 § 12. The following seems to follow rule, yet it is absurdly 
 vicious : — 'All Cabinet ministers are human. Just nineteen 
 politicians are Cabinet ministers. Just nineteen politicians, 
 then, are human.' In the following the major term has the 
 appearance of being less extensive than the middle, and the 
 middle than the minor — '20 pennyweights are an ounce troy; 
 an ounce troy is ^^ of a pound ; then 20 dwts are j^ lb.' 
 
 § 13. Miss Trotwood's ' Donkeys ! ' implied a complete syllo- 
 gism. On the other hand, many reasonings seem to have four 
 terms. ' You must be quick with your letter, for the postman is 
 waiting.' ' As the wind is so cold, I shall wrap up.' We shall 
 have also to examine numerical, and what Hamilton calls ultra- 
 dimidiate, inferences. De Morgan declares plausibly that any one 
 who sticks close to Aristotle's rules will be unable to prove that, 
 if most men have coats and most have waistcoats, some men 
 have both. Jevons's wooden toy for getting and testing con- 
 clusions from premisses could better deal with this class of 
 arguments, however, than with many others. 
 
 § 14. The ' mere logician ' is certainly not bound to interpret 
 and arrange men's thoughts for them, or to point out the defect 
 in any confused piece of reasoning as it stands. The interpreta- 
 tion of language is a necessary preliminary to his examination 
 of the connexion of the thought. He can claim to have the 
 argument enounced in full before giving his verdict upon it. 
 Thus the following lament of Lord Burleigh is a syllogism in 
 the Second Figure — 
 
 Ease and pleasure quake to hear of death ; 
 But my life desireth to be dissolved. 
 (It follows that) my life is full of cares of miseries. 
 
 But we can demand that the expressions shall be formalized. 
 I agree, however, that a logic in vacuo, wholly unrelated to 
 actual difficulties and complexities of reasoning, what Sidgwick 
 calls a fair weather Logic, applicable where no doubt or difference 
 
Thought dealt with through Language 9 
 
 of opinion has entered but helpless just at the point where ques- 
 tion arises, needs to be supplemented, or rather illustrated, by 
 an analysis of actual arguments and forms of speech. Reason 
 in itself is absolute and universal ; yet being for human beings 
 intimately connected with human thought, it must exhibit its 
 unity in and through the varying structure of thoughts/ The 
 practising logician, ever seeking behind the accidental parlance 
 the necessary sequence of idea, studies the idiomatic expression 
 of thought, with which, however, and not with the expression, 
 his concern truly lies. 
 
 § 15. This necessity of dealing with thought through language 
 does not destroy the essentially formal nature of logical inquiry. 
 Logic is formal because the validity of an argument does not 
 depend on what we happen to know, outside the data, of the actual 
 properties of the objects about which we are speaking, but on the 
 rational connexion between premisses and conclusion. It is the 
 same thing to the logician whether he is presented with such 
 a proposition as, ' It never rains but it pours,' or such as, ' It 
 never thaws but it freezes' — until he is told that thawing and 
 freezing are contraries. He does not care whether the con- 
 clusion that Socrates is mortal is reached by affirming that 
 Socrates is a man and all men are mortal, or from the premisses 
 that Socrates is a fish and all fish are mortal. If, on being told 
 that water is nothing but HjO, I go on to conclude that Thames 
 water is nothing but HjO, he will check me with a caution about 
 dicta simpliciter and dicta secundum quid) but not because he 
 happens to know that Thames water when analysed is found 
 to be that and a great deal more. He declines to disallow 
 concepts such as 'Greek kalends', 'fricass6 dans la neige', 
 ' strawberries in the sea and herrings in the wood ', or proposi- 
 tions like Proudhon's 'The true form of State is anarchy', or 
 'She had been vexed if vexed she had not been', until the 
 incompatibilities which may exist in them are formally presented. 
 Directly we go outside our data, we are appealing to the matter 
 
 ' The anti-scientific school now fashionable denies the unity. ' Our 
 main principle will have as many forms as there happen to be categories 
 or kinds of relation ' (Bradley, Logic, p. 242). This school seizes trium- 
 phantly on reasonings like this — ' Ten were killed and five wounded ; so 
 that twice as many were killed as were wounded ' — to expose the sacer- 
 dotal pretensions and exploded tyranny of the Major Premiss. 
 
10 Introduction 
 
 not to the form, to external experience not to internal rational 
 necessity. Logic, in a word, is concerned with the necessary 
 validity of consequences rather than with the contingent truth 
 of assertions, with proofs rather than with circumstances. 
 
 § i6. ' Formal ' Logic is, then, the only Logic. Such a science 
 is often disparaged as narrow and narrowing.' To be sure, 
 a river which has broken its banks and flooded the country- 
 side has acquired breadth by such expansion; yet it is good 
 engineering to coerce it within its proper channel. We have 
 nothing to do with broad and narrow in philosophy. The 
 inquiry what it is gives the inferential connexions of thought 
 their legitimate force and right may conceivably be not worth 
 undertaking. But if it is to be undertaken it must be kept 
 scrupulously apart from investigation and co-ordination of the 
 laws, however general, of phenomena, and from the grouping 
 of them under the categories of human sensibility and under- 
 standing. 
 
 § 17. But a fertile field lies before the logician in the 
 daedalian richness of human thought and speech — which is 
 not only thought's expression but its mould. The foot shapes 
 the shoe, and the shoe shapes the foot. We speak as we think ; 
 but also, to a great extent, we think as we speak : that is to say, 
 our thinkings run in the moulds prescribed by inherited syntax. 
 Language implies Conception, and reacts on our conceptional 
 powers, to develop and shape them. 
 
 § 18. The question whether Language is necessary to Thought 
 hinges on the possibility of framing general conceptions which 
 are not fixed in a representative sign — words, or other significant 
 marks, being, as Sir William Hamilton felicitously says, the 
 entrenched and fortified positions which enable Thought, its 
 spadework done, to advance into new territory. The question 
 about the connexion between Thought and Language is for Logic, 
 however, less about the content of terms than about the formal 
 relations of terms in the proposition. It is not names that give 
 
 ' Not, however, it should be observed, by Mill, who says : — ' I know of 
 nothing, in my education, to which I think myself more indebted for 
 whatever capacity of thinking I have attained, than early practical famili- 
 arity with the school logic. I am persuaded that nothing in modern 
 education tends so much, when properly used, to form exact thinkers. 
 The boasted influence of mathematical studies is nothing to it' (Auto- 
 biography, p. 19). 
 
The Traditional Forms Inelastic ii 
 
 the logician most trouble. He could construct a very living 
 science with the help of three letters of the alphabet. But it 
 is when he tries to express the multitudinous aspects of predica- 
 tion by algebraic or other symbols, or by the bald and simple 
 forms of the ' traditional logic ', that he gets out of touch with 
 the multifarious activity of real thought. 'All X'& are Y', for 
 instance, has to stand for such propositions as, ' It never rains 
 but it pours ' (no not- y is X) j ' Everybody's business is nobody's 
 business'; 'Obstaprincipiis'; 'One good turn deserves another'; 
 ' You shall want ere I want ' ; ' Other days bring other ways ' ; 
 and a myriad other expressions, a number of which I have 
 suggested later and in an appendix. ' No ^ is Y' must repre- 
 sent such propositions as these :^ — 'Liberty is one thing and 
 licence is quite another'; 'Stemmata quid faciunt?'; 'God 
 befriend us as our cause is just'; 'Vendredi chair ne man- 
 geras ' ; and so forth. The logician has to point out that ' One 
 man (should have) one vote ' is not a singular proposition, nor 
 ' Tres faciunt collegium ' a plural one, nor ' The many fail, the 
 one succeeds ' a combination of plural and singular ' — all these 
 being general propositions, as also is 'Two's company, three's 
 none '. He has further to find room under the same formula, 
 ' Every X is Y', for general propositions (' every X' = all ^'s) 
 and for concrete universals (' every X' = all the X's). Probable 
 and Modal judgements have also to be considered. Then, 
 there are Narrative judgements ; also Added Determinants — in 
 which the knot is not always so easily untied as in, ' English- 
 men wear clothes; then old Englishmen wear old clothes' — , 
 and Exceptive and Exclusive arguments. The Swedish agent's 
 complaint, ' Only one man in England can write Latin, and 
 that man blind,' cannot without weakness be carried to the 
 conclusion, 'Then only one blind man in England can write 
 Latin.' Rules of Inductive Inference will have to tell us why, 
 ' This liquid poisoned M yesterday ; therefore it will poison N 
 to-day,' and, ' This liquid scalded M yesterday ; therefore it will 
 scald N to-day,' are not on all-fours. 
 
 § 19. A universal Logic is possible because a universal 
 Grammar is possible, the basal structure of thought being the 
 same for all mankind. But this underlying unity admits of 
 an immense variety of idiomatic peculiarities — for instance, the 
 impersonal forms of speech of the Japanese. To the Greek 
 
12 Introduction 
 
 logicians, among whom linguistic study was in its infancy, all 
 non-Hellenic tongues were barbarous. The mediaeval writers 
 on Logic wrote for the most part in Latin, with its clear-cut and 
 inelastic syntax. The comparative study of languages has now 
 made great advance j yet even in England, which has a speech 
 grammatically poor but opulent and imaginative of phrase, 
 logicians have seldom departed from the trifling round of 
 inherited illustration, based on the idea of a fixed natural 
 order of concepts, — ' Man is rational,' and the like — unless it 
 be to devise examples of the pseudo-scientific and ' useful ' kind, 
 conveying incidental information about monocotyledonous plants, 
 rhomboidal spar, mercury, carbon, and the Aryan race. The 
 form of such illustrations is usually too easy for our purpose. 
 A hundred times more exercise would be afforded to the logical 
 student by a Shakespearian comedy or the talk of two children 
 at play. The mediaevals, for all their limited range of illustra- 
 tion, were right to associate Logic in their academic Trivium 
 with Rhetoric and Grammar. It is in this direction that the 
 future of Logic as, in one sense, a progressive science should, 
 in my opinion, be looked for. 
 
 § 20. Logic has to a great extent emancipated itself from the 
 hewing of wood and drawing of water for experimental science, 
 which the sensationalist school regarded as its proper menial 
 service, though Mansel could say in 1851 :— ' The slave has 
 broken prison, but the master has not yet relinquished his claim, 
 and the fugitive still carries about him some links of his chain 
 by which ever and anon some emissary of his former tyrants 
 seeks to drag him back to the burdens and the flesh-pots of his 
 servitude.' ^ Since Kant, the opposite tendency, that of develop- 
 ing the matter of thought from its form and of identifying 
 Thought and Being, has had greater influence, but is equally 
 fatal to pure Logic. 
 
 § 21. No doubt. Logic cannot be 'formal' if Mr. Sidgwick is 
 right in his ultra- Nominalist contention that there is no abstract 
 law of rationality— no 'entity' of reasoning— distinct from 
 thought's subject matter; for, he says, 'to imagine that because 
 we can speak of things in the abstract therefore abstractions 
 have independent existence is to forget that they are, after all, 
 abstractions.' ^ He complains that ' the textbooks generally 
 
 1 N. British Rev., vol. xv, No. 29. 2 jj^g ^y i^grds, pp. 10, 20. 
 
Attacks on the Syllogism 13 
 
 assume that all the doctrines of Logic may be deduced from 
 axioms as undeniable as those of Euclid, and that unless this 
 is done the " scientific foundation " is absent '} He speaks of 
 ' the so-called laws of thought '.' ' The generalisations of Logic 
 are only roughly true.' ' He grants that the Syllogism is ' not 
 a wholly useless piece of logical lumber *. It contains a truth 
 ' which, when the proper precautions are taken, may perhaps be 
 found not entirely useless '.* Yet it is mechanical and standstill. 
 § 22. On the other hand, in view of the modern attack from 
 so many quarters upon middle terms, that is, upon reasoning 
 through universals, the ' formal logician ' cannot but be consoled 
 by the following words of Mr. Sidgwick : — 
 
 'The leading idea of the Syllogism is the recognition that 
 where any fact is produced as sufficient to prove a conclusion, 
 the suflGciency of such fact for such purpose depends on the 
 acceptance of a generalisation which covers it and connects it 
 with the conclusion. No doubt this is an extremely elementary 
 truth. It ... is part of the constitution of any mind that forms 
 a judgment about concrete affairs . . . However far we develop 
 our Logic, we cannot outgrow our early acceptance of the axiom 
 that every particular case has a general rule behind it, and the 
 corollary that proof consists in finding a general rule to cover 
 the particular case.' ° 
 
 Elsewhere the same writer remarks that, as requiring (i) a 
 principle and (2) the application of such principle, ' all rationalisa- 
 tion may be represented syllogistically.' ' 
 
 § 23. The rules of the textbooks are merely the elucidation of 
 this statement, which gives the 'formal logician' all that he 
 really asks. Having it, he may admit that the older Logic 
 insufficiently recognized the difficulty of making the framework 
 of abstract formulas fit the diversity of actual thinkings, and also 
 that the concealment of real complexity under verbal simplicity 
 is one of the most frequent sources of fallacy. We want a 
 dialectical casuistry to deal with the refinements and subtilties 
 of thought and speech. The problem which, Mr. Sidgwick 
 remarks, ' is always troubling Logic and which never troubles 
 Geometry, the difficulty of using your definition to tell you 
 precisely how some doctrine shall be interpreted in particular 
 cases,' must be grappled with. Thus arises the true applied 
 
 ^ Op. cit. p. 6. " Ibid, p. 20. ' Ibid. p. 57. * Ibid. p. 72. 
 
 ■* Ibid. p. 72. * Fallacies, p. iii. 
 
14 Introduction 
 
 Logic, the logica utens, which in no way resembles the utilitarian 
 Logic of Ramus, Locke, Stewart, Mill, and Bain. 
 
 Recently an anarchical school of logicians has established itselfj 
 which throws dirt and stones at the Syllogism, rails at rules, 
 and overthrows a philosophy in a footnote. I trust I have done 
 justice to that 'synthetic activity of Thought' by which it is sought 
 to supersede the dethroned syllogistic reasoning. But the 
 movement against major premisses is an endeavour to remove 
 the linch-pin of connected thinking — that is, of Thought itself. 
 
CHAPTER II 
 THE JUSTIFICATION OF ANY THOUGHT 
 
 § 24. The subject of Logic is Rational Consequence in Thought. 
 The consequential nexus in all thinking is Reason. Logic, then, 
 investigates the Law, or Laws, which Reason imposes upon the 
 connexions of Thought. To do this it must to some extent 
 analyse the thinking act. Is judgement an equation of values 
 — as when we say ' ten shillings are half a sovereign '? Is it 
 an identification, even when conceptually expressed — so that 
 'patience is a virtue' identifies patience with a particular 
 virtue? Or is it conceptual, the placing of ah object under 
 a conception, even when expressed as an identification — so that 
 'L'Etat c'est moi' brings the State under the idea of Louis 
 XlVth's person ? Or is it sometimes one and sometimes 
 another? Hobbes in his Computatio sive Logica makes all 
 judgement and all reasoning to be an addition or subtraction 
 sum. 
 
 § 25. An analysis of conception and judgement is therefore 
 necessary; but only so far as is required for the purpose of 
 detecting in what way the imperative of Reason is obeyed in this, 
 that and the other sequence of thought. The logician leaves it to 
 the psychologist to scrutinize further the inner mechanism of our 
 mental faculties, the secret workshop of our consciousness. He 
 is only concerned with the formal relations of thoughts regarded 
 as products.^ Once he is given the meaning of a proposition, 
 he ceases to concern himself with its history. Had it been 
 turned out by a rationalizing machine rather than by a mind, 
 the fact would be immaterial to him. Again, he is not con- 
 
 ^ Psychology, says Mr. J. N. Keynes, deals with reasoning processes in 
 the sense of observed uniformities, and investigates their genesis. Logic 
 deals with them purely as regulative and authoritative. It is ' concerned 
 with reasonings only in respect of their cogency; and with the dependence 
 of one judgment upon another only in so far as it is a dependence in 
 respect of proof ' {Studies and Exercises in Formal Logic, p. 5). 
 
i6 The Justification of any Thought 
 
 cerned directly with the elements of feehng and behef and (as 
 Descartes shows) of will which enter into all judgement. 
 
 § 26, Logic deals with thoughts as justified, as rationalized. 
 All thinking the consecution of which is shown as obeying 
 Reason— thought explicating itself as rationally inevitable — is 
 thereby justified. Every judgement must have a ground. The 
 attribution of a characteristic to an object cannot be supposed 
 unmediated, reasonless. It was arrived at somehow. In other 
 words, it is an interpretation. We view every fact in the light 
 of a theory. I may be unwilUng or unable — like him who did 
 not love Dr. Fell ^ — to say what the ground or justification of 
 my judgement is. But until the reason is assigned Logic cannot 
 test it. And the assigning it turns the judgement into a 
 syllogism.'' 
 
 § 27. To say that a judgement must have a ground is only to 
 say that it results from finding that some circumstance which 
 
 * Brown was bidden by Dean Fell, under pain of expulsion, to translate 
 straight off Martial's epigram : — 
 
 Non amo te, Sabidi, nee possum dicere quare. 
 Hoc tantum possum dicere, non amo te. 
 Compare — 
 
 ' Hunccine amas ? ' Equidem. ' Quare ? ' Quia talis habetur. 
 ' Inspice '. Quid prodest ? Intima causa latet. (Alexius.) 
 
 * ' In every judgment more or less of criticism is entangled, such 
 criticism being the element in every judgment which makes it a reasoned 
 judgment, as contrasted with what an unreasoned judgment would be if 
 such a thing could be found' (Sidgwick, Use of Words in Reasoning, 
 p. 362). Ultimately, no doubt, we are driven back to facts of immediate 
 perception. But perception is not yet judgement. Judgement begins 
 when interpretation begins. Facts cannot be inconsistent, but only 
 theories. No formed judgement, no proposition framed in language, can 
 be a bare statement of fact. A painter cannot ' paint what he sees ' till he 
 knows what it is he sees. Even a judgement of identification refers an object 
 to some category already possessed by the mind. And statements about 
 our perceptions themselves are descriptive and interpretative, and, there- 
 fore, liable to be mistaken. If I did not know it to be otherwise, I could 
 sometimes of a bright, windy night find it almost impossible not to think 
 that the moon 'was racing through the fleecy scud. There can be no 
 iniaTTifiJi of a/iea-a, only vovs. Take these two sets of statements — ' This 
 object is a revolver ; it is six-chambered ; two of the chambers are empty; 
 it is rusty ; it was made by [maker's name] '; and, ' This pistol is an 
 ingenious weapon ; two shots have been fired from it ; it has been a long 
 time in the water ; it has not been cleaned ; it is of an old-fashioned 
 make.' The latter set of assertions is highly interpretative compared 
 with the former. Yet neither is really intuitional. In fact, an intuitional 
 statement is impossible. 
 
Every Judgement has a Ground 17 
 
 we know about a subject (about all S's or some 5's) invariably 
 carries with it the characteristic P, is found in P things only, 
 though not necessarily in all P things. This circumstance is 
 the middle term, the ground of attributing P to 5. I say that 
 Dick is a bad boy, because he breaks windows, or does some- 
 thing else which I consider only bad boys do — ^though some 
 bad boys, it may be, show their badness in other ways. 
 
 § 28. The allegation of the ground of a judgement, then, 
 necessarily takes the form of two other judgements, one of 
 which contains the subject and the other the predicate of the 
 original proposition, while a third term is common to both, the 
 relation of this middle term to the other two being regulated by 
 rational laws which Logic investigates. ' A syllogism used for 
 proof,' says Sidgwick, 'is a judgment (the conclusion) expanded 
 so that the two disputable elements in it shall lie open to 
 inspection.'^ The inward connexion of the thought is macfe 
 explicit. On the other hand, in assigning a reason for a judge- 
 ment, we frequently state one premiss only, leaving the other 
 to be understood. E. g. — ' There is mercy with Thee ; there- 
 fore shalt Thou be feared ' ; ' Lightly tread ; 'tis hallowed 
 ground ' ; ' Eo immitior erat quia toleraverat * ; ' Beati mundo 
 corde, quoniam ipsi Deum videbunt'; or Cade's, 'Away with 
 him ; he speaks Latin.* 
 
 § 29. Or, to view the matter from the other end, if two 
 thoughts meet in a middle term in certain ways. Reason impels 
 the thinking activity along a determined groove and compels it 
 to draw a conclusion. Should the mind by a confusion of ideas 
 attempt to travel down a wrong groove. Logic points out that 
 there is no rational sequence of thought, that the conclusion 
 ' does not follow '. It may even have to turn the mind out of the 
 attempted inference as being incompatible with the premisses. 
 
 § 30. Logic combats not falsity but fallacy. Demonstration 
 requires an ultimate postulate both of Matter and of Form — a 
 criterion of the truth of the data, and a criterion of the validity 
 of the reasoning. But Logic is concerned with the latter only. 
 It does not ask whether a statement is true, but how it is 
 justified formally. It does not require, then, to know the con- 
 tent of terms, but only their formal inter-relation." Logic is a 
 
 1 Op. cit. 82. 
 
 ' If the content of the terms remains abstract and blank, the syllogism 
 
 c 
 
i8 The Justification of any Thought 
 
 kind of consulting physician or confessor. 'Why,' it asks, 
 ' do you say that whales are not fishes ? But, after all, you 
 need not specify your reason. It will be enough to say by what 
 rational process you arrive at that conclusion.' Answer. — 
 ' Whales are not fishes because they are something which no 
 fish is ' — the unexpressed something being ' viviparous '. Or all 
 three terms may be left blank. Inquirer. — 'Something I am 
 thinking of must have a certain characteristic because it belongs 
 to a general class of things which I know has that characteristic. 
 Is this good reasoning?' Logic signifies assent. Again, 
 ' This is that, and that is not the other. Pray, what am I to 
 conclude?' 'That this is not the other.' Again, 'il/'s are 
 always P, but 5's are never M, Can I infer that 5's are never 
 P? ' ' No, certainly not.' 
 
 § 31. If the following reasonings were put before the plain 
 man — 
 
 (a) Soldiers wear uniform. Sailors are not soldiers. There- 
 fore sailors do not wear uniform. 
 
 (6) Swans are birds. Horses are not swans. Therefore 
 horses are not birds. 
 
 (c) Slaves belong to a master. Freemen are not slaves. 
 Therefore no freeman belongs to a master — 
 he might not improbably say that any one can see through (a), 
 that (6) is a good argument, and that in (c) each of the three 
 propositions is a truism. Yet (a), (6), and (c) are similar in form 
 and all alike bad reasoning. The conclusion of (a) is false as a 
 conclusion (Sioti) and false as a proposition (oti). The conclusions 
 of (b) and (c) are true as propositions but false (i. e. without 
 justification) as conclusions. The premisses in every case are 
 true. In the syllogism, ' Pat is Irish because he is a Frenchman 
 and all Frenchmen are Irish,' the conclusion is correctly drawn 
 and true in itself, though both premisses be absurdly false.^ 
 
 which combines them is also a skeleton construction. If the tenns are 
 clothed with circumstance, the syllogistic framework is so also ; but the 
 force of the reasoning depends not on the material connexions of the 
 varying contents, but on the inward and rational connexion of the judged 
 relations of the terms, considered formally. 
 
 ^ That such elementary lessons in logic are not unnecessary is clear 
 when a serious-minded paper like the Spectator lays it down (Feb. 18, 
 1899, p. 225) that, 'Though a man may sometimes jump to a right con- 
 clusion and illogically reach firm ground, he can never by the logical 
 
Valid Forms for alleging, a Ground 19 
 
 § 32. The reasons for an assertion may be, like FalstafTs, 
 as plenty as blackberries. But what the logician is alone 
 concerned with is the limited variety of ways in which the 
 ground of a conclusion can be formally exhibited. Thus — Why 
 do you say that 5 is sometimes P? I say it because — 
 
 (i) S has been known occasionally to be M and M's, are 
 always P [Darii). Or because, 
 
 (2) M's are always both 5 and P (Darapti). Or because, 
 
 (3) M's are always S and are sometimes P (Disamis). Or 
 because, 
 
 (4) ^'s are always P and are sometimes 5 {Datisi). Or 
 because, 
 
 (5) Every P is M and M's are always 5 (Bramantip). Or 
 because, 
 
 (6) Some P's are M and M's are always S (Dimaris), 
 Again. Why do you say that no 5 is P? I say it because — 
 (i) 5 is always M, and M is never P (Celarent). Or because, 
 
 (2) P is never M, while 5 is always M (Cesare). Or because, 
 
 (3) 5 is never M, while P is always M (Camestres). Or 
 because, 
 
 (4) P is always M, and M is never 5 (Camenes). 
 
 Only one kind of reason can be given for the assertion that 
 5 is always P. But that S is not always P could be shown in 
 eight different ways. 
 
 If other modes of arriving at a conclusion were proposed they 
 would be invalid. It is the task of Logic to sort out the valid 
 from the invalid forms of reasoning, enabling us to distinguish 
 consequence from inconsequence. It has nothing to do with the 
 worth of the premisses so long as they are premisses. But 
 directly we turn our attention to them in themselves, and regard 
 them not as data but as tudicata, they too must show their 
 rational anatomy, the plan of their reasoned construction. 
 
 § 33. The most amusing sophisms are those which audaciously 
 
 process get a right conclusion from incorrect premisses.' It is really 
 safer to have both premisses wrong than one only. Whately gives, as 
 examples of a true conclusion being reached illogically from true pre- 
 misses, the following : — 
 
 Every rational agent is accountable. Brutes are not rational agents. 
 Therefore they are not accountable. 
 
 All wise legislators suit their laws to the genius of their nation. Solon 
 did this. Therefore he was a wise legislator. 
 
 c 2 
 
20 The Justification of any Thought 
 
 elude dissection, while pretending to offer a plausible reason ; 
 as when Lamb excused his coming so often late to the office by 
 saying that any rate he always left it early; or as when the 
 husband claims to be economical by making one slice of bread 
 do for both butter and jam. Sometimes the ground alleged is 
 a mere play upon words, equivoque, or even pun. George 
 Selwyn, speaking of Sir Thomas Rumbold, M.P., who had 
 begun life as a drawer at White's and was ending it as nabob 
 and millionaire, observed that everything comes to him who 
 knows how to wait. Successful equivocation among childlike 
 nations, with a great idea of the mysterious sanctity of words,^ 
 is held to bind the person deceived ; as when Lycurgus bound 
 the men of Sparta to observe his laws until his return, and never 
 returned. 
 
 § 34. The implied ground of a judgement may be so ludicrously 
 inadequate that the jest would be gone if the argument were 
 displayed in full. The Gloucestershire song, George Ridler's 
 Oven, tells us that 'Gaarge he wur the oldest brother, And 
 therevoore he would zing the beass '. When gas took the place 
 of sperm oil as an illuminant, a benevolent lady asked. What 
 will become of the poor whales ? The reasoning implies such 
 confusion of thought that the help of Logic for its exposure 
 hardly seems worth invoking. And yet if fox-hunting were to 
 go out, and some one were to ask. What will become of the poor 
 foxes ? the question would be a very pertinent one ; for if foxes 
 were not artificially preserved for the chase they would soon be 
 exterminated. 
 
 § 35. Reasoning, we have seen, is thought justifying itself 
 formally. It is the educing of a judgement from two antecedently 
 formed or given judgements. The ratiocinative act, then, has to 
 do directly with judgement, and only indirectly with conception. 
 The terms of a syllogism may be left blank, but the outlined 
 judgements of which it is composed must be stated. Conversely, 
 every conclusion is a judgement. Judgement is ' a consciousness 
 concerning the objective validity of a subjective combination of 
 ideas ' (Ueberweg). It may therefore be mistaken, and so requires 
 proof. A concept, on the other hand, does not admit of error, 
 until it is asserted of a subject. When we speak of a ' true idea ' 
 
 ^ St. Augustine defines falsehood as ' an unnatural use of words, con- 
 trary to their final causes '- 
 
A Concept needs no Justification 21 
 
 we mean that it is true in this or that predication. It cannot, 
 therefore, be called upon for its ground. Not being propounded 
 as either true or false, it needs no justification. If it is 
 (psychically) possible it is possible, and there is an end of the 
 matter. 'Truth', says Dr. Bradley, 'is not found except in 
 judgements.' There is no Why? to be asked for the notion 
 ' an unlawful desire ', but only for the same notion developed as 
 a proposition — ' Some desires are unlawful.' Nor can a notion 
 stand as premiss. If we see a picture we do not inquire, What 
 then? 
 
 § 36. It is true that a concept is often complex, and indeed all 
 except the primary notions — and can these be called notions ? — 
 are really so. No object can have one attribute only unqualified 
 by any other. Now the determining element in a concept, that 
 which specifies it in the larger class to which it belongs, may be 
 replaced by a relative clause, containing a dependent judgement. 
 A broken vase is a vase which is broken. A three-legged stool 
 is a stool which has legs which are in number three. A horse 
 is an animal which is equine. Nevertheless such a dependent 
 judgement asserts nothing categorically. It therefore needs no 
 justification. It is ideal only. 
 
 Accordingly the consideration of the Concept only enters into 
 Logic as enabling us to analyse the import of the Proposition. 
 
 § 37. But the reader is perhaps impatient to object to what is 
 said above as follows : — Rational consequence in Thought, if 
 that be the right definition of the province of Logic, need not 
 always imply mediation, the alleging of a ground for a statement. 
 Is there not such a thing, he will ask, as immediate consequence ? 
 In certain propositions, such as truistic and also analytical 
 propositions, the subject involves and necessitates the predicate. 
 And even in concepts one element of the compound may carry 
 another element with it by rational implication. Contrariwise, 
 a concept may contain formally incompatible elements, and 
 a judgement may be a contradiction in terms. In such cases 
 there is surely no need of middle terms. The concept or judge- 
 ment is self-justifying or self-condemning. 
 
 § 38. A closer consideration will, however, show that there 
 cannot be siich a thing as immediate inference, or consequence, 
 in thought. Consistency, as contrasted with bare repetition, is 
 never simple, but always complex. 
 
22 The Justification of any Thought 
 
 § 39. Both concepts and judgements, it is true, frequently 
 exhibit marks of internal implication. E.g. — 'a man and (there- 
 fore) a brother'; 'the safest because the boldest plan'. The 
 former is explicatio notionis; the latter expUcatio rei. 'A new 
 Church and therefore no Church' (Theophilus Anglicanus) is 
 probably the former. In other words ' therefore ' and ' because ' 
 point to general knowledge, to a major premiss, which is in 
 the background. A man and (since the notion of man includes 
 brotherhood) a brother. The safest plan because (boldest plans 
 being safest) the boldest. It is obvious that safest cannot be 
 be got straight out of boldest. If this is less obvious in the case 
 of brother and man, let it be considered that the entire content 
 of the notion ' man ' is not to be assumed as conveyed by 
 the name 'man', which is all that, logically, we are given to 
 start with. If the content of 'man' is given, such datum is 
 something extraneous to the concept considered objectively. 
 Again, ' a selfish, and so an unlawful, desire ' means ' a selfish 
 (which is necessarily an unlawful) desire ' — the parenthetic asser- 
 tion standing outside the concept, in apposition to one of its 
 elements. The Almighty is 'patiens quia aeternus'. Wesley 
 speaks of the Choctaws as ' the least polished, that is the least 
 corrupted, of the Indian nations '. 
 
 § 40. Another class of obviously complex notions contains an 
 adversative particle. 'Black but comely.' 'Slow but sure.' 'Advo- 
 catus et non latro.' Johnson said of Somerville that he wrote 
 very well for a gentleman. Here, again, a general proposition 
 is suggested. Advocates are (usually) robbers. Gentlemen do 
 not (usually) write well. It is only by virtue of such general 
 maxim that the notion has a rational character. This is the 
 true significance of the legal aphorism, Exceptio probat regulam. 
 Other illustrations are — 'A maiden of our century, yet most 
 meek.' ' Poor (or rich), but honest.' ' Dura lex, sed lex.' 
 
 § 41. A mark of internal implication is also found in proposi- 
 tions. E.g. — 'A quadrangle has necessarily four corners'; 
 'A native oyster cannot have been imported'; 'Vertebrate 
 creatures must needs have backbones ' ; 'To sail quite round 
 a peninsula is clearly out of the question.' In such judgements 
 there is explicatio notionis. But the internal mark of illation 
 may be found in purely synthetic propositions; e. g. 'A bishop 
 nowadays is necessarily a man with private means.' 
 
Only Syllogism exhibits Rational Character 23 
 
 § 42. The following may be given as illustrations of adversa- 
 tive propositions — 'Fiat iustitia, ruat caelum'. 'Though He slay 
 me, yet will I trust in Him'. 'Naturam expellas furca tamen 
 usque recurret'. 'Timeo Danaos et dona ferentes'. 'A vagabond 
 is not for that reason necessarily a rogue '. ' Ut desint vires, 
 tamen est laudanda voluntas '. ' Ne sit summum malum dolor, 
 malum certe est'. The Greek /a€v . . . 8e breaks up the antithesis 
 into two parallel assertions. Contrast, 'England, with all thy 
 faults, I love thee still.' 
 
 § 43. This subject will be treated of more fully under Analytical 
 Judgement (§ 507 seq.). 
 
 § 44. Next, let us take the case of concepts and propositions 
 in which, though there is no mark of internal implication, the 
 elements seem obviously to imply and involve one another, 
 either riotionally or etymologically, or even verbally. Instances 
 are such as : — 
 
 Stuck adhesive and suspended hung. 
 
 A pacific eirenicon making for peace. 
 
 A peculiar property. 
 
 A wedded wife. 
 
 Four square. 
 
 An unlucky mischance. 
 
 Semibovemque virum semivirumque bovem (Ovid). 
 
 The foolishness of fools is folly. 
 Costard says, 'We know what we know,' and Joe Gargery in 
 Great Expectations assures Pip, ' Manners is manners, but your 
 'ealth's your 'ealth.' Sarah Battle deemed cards to be cards, 
 desiring therefore the rigour of the game. When the butler 
 at. Queen's Crawley announced mouton aux navets and potage 
 de mouton a I'ecossaise, Sir Pitt Crawley observed with satisfac- 
 tion that mutton is mutton, and an uncommonly good thing 
 too — or words to that effect. We say, 'Che sara sara,' and 
 ' Let bygones be bygones,' or ' We shall see what we shall see '. 
 
 § 45. It is clear, however, that we cannot get from ' stuck ' to 
 ' adhesive ' or from ' peculiar ' to ' property ' by a formal process 
 of pure reason, without some additional explanation or some 
 knowledge of the matter, though the matter be the content of 
 a notion, or the meaning of a word, and not the properties 
 of a thing. Even where, as in the above propositions, there 
 is an actual verbal tautology, the word in the predicate has 
 
24 The Justification of any Thought 
 
 not precisely the same force as it has in the subject. The 
 subject is more denominative and the predicate more intensive 
 —drawing attention to what might otherwise escape notice in 
 the characteristics which the name implies. 
 
 § 46. In fact, every proposition has some ampliative signifi- 
 cance, otherwise it would not be worth making — would not 
 be, indeed, a proposition. ' It is ultimately one/ remarks 
 Dr. Bosanquet, 'to say that I judge and that the real world for 
 me, my real world, extends itself.' ^ ' A \% A' \s, not a judgement 
 at all unless there be some real movement and advance of 
 thought, some clearer knowledge gained by myself or imparted 
 to another. Even a platitude is an extension of thought ; and 
 moreover we often, out of a kind of moderation, couch assertions 
 in a purposely platitudinous form, especially by the use of 
 'too' — e.g. 'We ought not to attempt too much.' 
 
 § 47. Similarly, in the case of concepts, pleonasm is never 
 mere repetition, but either force is sought to be gained by 
 synonym — as, 'a poor unfortunate,' 'delightful and charming,' 
 'miserly skinflint' — , or the redundancy is humorous — as in 
 Artemus Ward's 'female woman' — , or is due to ignorance 
 or local idiom — a Scotch guide-book before me speaks of the 
 ' Episcopal bishop ' (i. e. Episcopalian) — ; or to a change in 
 the meaning of words — as, when we say ' cloth clothes ', for we 
 also speak of linen clothes, and of a fair linen cloth. 
 
 § 48. A real internal confliction of elements in concept or 
 judgement is equally impossible. We can frame with lips or 
 pen a contradiction in terms — ' bona fide imposture,' ' four-footed 
 biped,' 'most tolerable and not to be endured,* 'your full cup 
 is almost empty,' or the hke— but nothing here has been 
 conceived or judged by the mind. No doubt, we are familiar 
 with expressions in which there is apparently a self-contradiction, 
 either verbal, as lago's 'I am not that I am', ttoXis cittoXis, 
 faultily faultless, 'he is all fault that hath no fault at all,' or 
 in sense, as, 'when I am weak then I am strong,' 'plus 5a 
 change plus c'est la meme chose/ 'bourgeois gentilhomme,' 
 'black rubrick,' 'red albe.' One of Beaumont and Fletcher's 
 plays is entitled, 'A king and no king.' But in such cases we 
 have, not any real incompatibility of ideas, but rhetorical, 
 
 ^ Logic, i. 4. 
 
Aristotelian Logic not Formal enough 25 
 
 poetical, epigrammatic, or humorous trope. This will be 
 further illustrated below (§§ 133, 235 seq.). 
 
 § 49. An internal necessitation or confliction of ideas must 
 be given, then, by means of a middle term. If it is objected that 
 whoever judges must be supposed to know what his ideas 
 contain, we reply that the content must be realized by prior 
 reflexion before judgement can take place ; and though to the 
 speaker his own proposition may be a matter of course, it is not 
 so to the hearer, otherwise it would not be made. 
 
 § 50. The Aristotelian Logic is often. disparaged as merely 
 formal. But, in truth, neither in the hands of its founder nor in 
 that of his exponents, whether Peripatetic, Arabian or Scholastic, 
 was it formal enough, being blended with natural philosophy, 
 transcendental metaphysics, and divinity. The dovetailing of 
 Logic into demonstration from self-evident axioms or irreform- 
 able dogmas of faith was especially the aim of the mediaeval 
 schoolmen. A system of Logic cannot, it is true, be constructed 
 which shall be compatible with all opposing metaphysical 
 doctrines; for an extreme nominalism or atomism strikes at 
 the root of conception, of judgement, and of truth itself Logic 
 is unable tp show how ideas may be formed so as always to 
 agree with facts, but it guarantees that, if a thought is true, the 
 facts shall be found to correspond — ^which is what is meant by 
 truth. But, beyond postulating the existence and laws of truth, 
 the logician is not concerned with ontological inquiries. His 
 science, while it demands universals, can only help in a negative 
 and merely regulative way towards their formation; nor can 
 it distinguish cause and effect from any, other unexpressed 
 relation between the subject and predicate of a general proposi- 
 tion. To it the propositions, 'Cold winds come from snowy 
 regions,' 'Cold winds dry the ground,' and 'Cold winds are 
 unpleasant,' are the same in form, though to the meta- 
 physician the first expresses a cause, the second an effect, and 
 the third the inherence of a quality. ' It is slippery because 
 it has frozen ' and ' It has frozen, because it is slippery ' are 
 similar propositions for the logician's purpose ; though to 
 Thought the one is ratio essendi, the other ratio cognoscendi. 
 The subordination of ascending and descending classes, which 
 for the physical philosopher is a scheme of species and genera, 
 
26 The Justification of any Thought 
 
 and for the ontologist the reconciliation of Being and Becoming, 
 is for our purpose a relation merely of larger or narrower 
 extension and intension. 
 
 § 51. Easier than the detachment of Logic from metaphysical 
 and psychological problems should be its liberation from a 
 supposed allegiance to the sciences as their Organon. For by 
 the view of Formal Logic as an introduction or propaedeutic to 
 the Logic of ' fruit ', by the view which regards Syllogism as the 
 Law and Inductive investigation as the Gospel, a line of partition 
 is drawn between Deductive and Inductive Logic, which may 
 even form separate volumes.^ The comparative utility of these 
 two subjects of study need not here be discussed. They are 
 essentially different, and no clear conception of Logic will 
 embrace them both. They are not two' wings of the same 
 building ; still less is ' Formal Logic ' the antechamber by which 
 we enter the spacious halls of Experimental inquiry ; but it is 
 as though to a symmetrical and self-contained Doric temple we 
 built on a vast modern factory or railway station. 
 
 § 53. Baconianism did not give men an enlarged and reformed 
 Logic, but rather induced them to turn their backs on Logic as 
 useless for the enrichment of human knowledge or the improve- 
 ment of the human lot. Whether scimus ut sctamus or scimus ut 
 operemur, in either case melius est naturam secure quam abstrahere. 
 Logic offers no extension of man's empire over the universe. 
 The system which Bacon proposed to substitute for the tenm 
 deducta mathemata filo of the schoolmen — who, however must 
 be given the credit of having on certain subjects spoken almost 
 the final word— is weak and halting. It is really his superficial 
 comparisons of instances which is unequal to the subtilty of 
 nature. Laws do not leap to the comparing eye in the easy 
 way Bacon imagined. It is not by his rules that the great 
 
 1 Grote observes, however, that whereas formerly the two streams— the 
 ' Inductive and Ratiocinative halves of Logic '— ' flowed altogether apart 
 in our minds, like two parallel lines never joining nor approaching. . . . 
 Mr. Mill has performed the difficult task of overcoming the inveterate 
 repugnance between them, so as to combine the two into one homo- 
 geneous compound' (Review of J. S. Mill on Hamilton's Philosophy 
 Westminster Review, 1866). None the less, what Mill has to say about 
 formal logic is distinct from what he has to say about Induction ; whereas 
 logicis at every step liable to become entangled with questions of meta- 
 physics or of psychology. 
 
Inductive Proof 27 
 
 conquests of modern science have been achieved.^ There must 
 be ' anticipations ' — not the barren theorizing of the intelkctus 
 sibi permissus, but great and fruitful hypotheses.* On the other 
 hand, he convincingly showed that knowledge cannot advance 
 a step without materials furnished by the outer or inner experi- 
 ence. But Logic stands apart from Experience, whether inner 
 or outer. It is equally indifferent to the existence or non- 
 existence of ' innate ideas '. The properties of a triangle are 
 not more logical than the properties of salt or sugar, nor the 
 laws of beauty and goodness than the law of gravitation. 
 
 § 53. In' Induction there is, no doubt, a formal element of 
 rational necessitation, which it is the work of ' Inductive Logic ' 
 to abstract from the matter given in experience. It will be 
 found, however, that the universal, validity-bestowing principle 
 in all proof is the same, whether we are proving deductively or 
 inductively. Not only must we say with Mill that ' all reasoning 
 is resolvable into syllogisms', but with Hegel that everything 
 rational is essentially syllogistic. . 
 
 § 54. Inductive Logic is merely the regular logic applied in 
 a particular way. Postulating as a vast major premiss the 
 axioma generalissimum that Causes, uncounteracted, are always 
 followed by their Effects, it subsumes under it a number of 
 suggested explanations of a phenomenon, with a view to testing 
 them and excluding all except the right one. If this or that 
 
 ^ ' No amount of observation could detect any resemblance between the 
 bursting of a thunderstorm and the attraction of a loadstone, or between 
 the burning of charcoal and the rusting of a nail ' (A. W. Benn, Greek 
 Philosophers, i. 151). 
 
 ^ 'Modem science has substituted for the wings of Icarus a pair 
 of crutches, bearing the names of Observation and Induction, with 
 which, no doubt, she advances more securely. Nevertheless, science 
 would be wrong in attributing all her progress to method. Besides 
 the two instruments that we have named resides a free force, a sponta- 
 neous element of the human mind ' (Vinet, Metaphysics). Bacon, says 
 Dean Church, 'was so afraid of assumptions and "anticipations" and 
 prejudices, that he missed the true place of the rational and formative 
 element in his account of Induction.' His system was, therefore, 'as 
 barren of results as those deductive philosophies on which he lavished his 
 scorn ' {Bacon, p. 245). ' The verification of a great hypothesis is a kind 
 of questioning and cross-questioning of Nature. Her awful silence in the 
 presence of the unperceiving gives way before those who know how to 
 put the questions' (Wilfrid Ward, Problems and Persons, p. 141). 
 
28 The Justification of any Thought 
 
 circumstance is not always followed by the effect under considera- 
 tion, it cannot be the required cause. The minor premisses in 
 this kind of reasoning are furnished by experience ; and the 
 combination of experience with the above-mentioned axiom is 
 what enlarges our previous knowledge of the laws of things. 
 Mill tells us that he long puzzled himself 'with the great paradox 
 of the discovery of new truths by general reasoning. . . . How 
 a conclusion, being contained or implied in the premisses, could 
 be a new truth was a difficulty which no one, I thought, had 
 sufficiently felt, and which at all events no one had succeeded 
 in clearing up '} But is it not plain that the newness of the 
 truth arises either out of the novelty of the experience, or from 
 old experience being viewed in a new light ? 
 
 § 55- What is important, then, for induction is not reason 
 (raisonnement) but knowledge and judgement. The logical 
 analysis of the inductive process is of great interest. But the 
 Five Methods are employed at every moment by every man, 
 woman and child. Had they remained unformulated, the advance 
 of the sciences would not have been retarded in the smallest 
 degree.'' That advance must be ascribed to the wiser direction 
 of the thinking subject, the judicious employment of the trained 
 understanding upon the materials accumulated by observation 
 and experiment. The natural philosopher is more concerned 
 to ask what analogies are on all fours than, with the logician, to 
 inquire in the abstract why parity of reasoning rightly carries 
 conviction to the mind. 
 
 § 56. A ' general theory of the right relations of all thought 
 to its matter ', a ' reasoned theory of the rules which should 
 govern the search for objective truth',' a 'scientia dirigendi 
 facultatem cognoscitivam in cognoscenda veritate',* may be 
 much superior to Logic, to ' the faded dialectic of the schools ' ; 
 but it is not Logic. Inductive science furnishes rules for dis- 
 tinguishing relevant from irrelevant grounds of inference. The 
 trained experience of a detective, for instance, seizes on the 
 important, and dismisses the unessential, features of a case. 
 
 ^ Autobiography, p. 180. 
 
 "^ Mathematics, on the other hand, are studied both for their own sakes 
 and as a potent organon in the development of complex sciences such as 
 physics, chemistry and astronomy. 
 
 ' Mill, On Hamilton, p. 477. < Occam. 
 
Logic cannot extend our Knowledge 29 
 
 But the laying bare by Logic of the inward principle of illative 
 cogency will be of little assistance for guiding the judgement to 
 discriminate aright. 
 
 § 57. And yet one writer ailer another has confused counsel 
 proffered to the intelligence for judicious grouping of the con- 
 tingent properties of things with dissection of the fundamental 
 law of universal Reason.^ Lewes, for instance, defines Logic 
 as the ' science of philosophical tools *, ' the codification of the 
 rules of proof which the various sciences have employed and 
 must employ '.' But why ' must ' ? It is this absolutely valid 
 and compulsive principle of which the logician is in search ; 
 and no examination of the I'Siai apx<u of the various sciences 
 will give it, though we may thus obtain a ' theory of the general 
 element in science '. The art of arranging, systematizing, and 
 correctly interpreting the data of experience is distinct from an 
 endeavour to think out the nature of logical obligation; the 
 search for objective laws is distinct from the analysis of the /ex 
 legum, on which the existence of law depends. The syllogism 
 may conceivably be, as Condillac asserts, a schoolboy's pastime, 
 un amusement de college. Mill's ' smaller logic ' of ' mere con- 
 sistency ' has a restricted province compared with the wide field 
 of that larger inquiry which embraces all the general conditions 
 for the ascertainment of truth. Its precepts may possibly have 
 no other practical utility than as a handrail to keep men from 
 tumbling into argumentative pitfalls. But that is only to say 
 that the law of Reason is simple and one, while the facts of the 
 universe are a limitless ocean. Truth is most nobly sought not 
 
 * ' Logic,' say the Port Royalists, ' exists for the very purpose of being 
 an instrument to the other sciences. . . . It is the art of directing the 
 reason aright in obtaining the knowledge of things for the instruction 
 both of ourselves and others.' Descartes regards it as the practical 
 regulation of thought's procedure — 'methodus recte utendi ratione et 
 veritatem in scientiis investigandi.' Reid describes Syllogism as 'a 
 mechanical mode of reasoning, by which in all cases truth and falsehood 
 may be accurately distinguished '. This is Abailard's ' veritatis seu 
 falsitatis discretio'. Mill defines Logic as 'the science which treats of 
 the operations of the human understanding in the pursuit of truth'. 
 'Methodology,' writes Sigwart, 'should be regarded as the special, final 
 and chief aim of our science.' Yet he says a few pages earlier that ' Logic 
 proposes to set forth those criteria of true thought which are due to the 
 demand for necessity and universal validity '- 
 
 * History of Philosophy, ii. 731, 732. 
 
30 The Justification of any Thought 
 
 for its utility but for itself. Nor can it be to the advantage of 
 scientific thought that, in deference to a spurious utilitarianism 
 or to the claims of the transcendental, the logician should be 
 persuaded by scorn, menace or cajolery to cease to be ' merely 
 formal '. 
 
 § 58. Logic is, in one sense, an exact science, more abstract, 
 as Spencer remarks, even than mathematics, in that it deals 
 with the qualitative relations of thoughts rather than with the 
 quantitative relations between things ; so that it ought not to be 
 possible to say of its study — 
 
 I too in youth did eagerly frequent 
 
 Doctor and saint, and heard great argument 
 
 About it and about; but evermore 
 
 Came out by the same door wherein I went. 
 
 No new discovery can add to or modify it, and its conclusions, 
 as distinguished from its applications, are fixed and certain. 
 Nevertheless, as it is brought into living relation with the actual 
 variations of thought and language, the work of Logic is never 
 done — perhaps is hardly yet begun — and in that sense it is 
 a science capable of advance,' with countless knots to untie and 
 difficulties to disentangle. 
 
 ' I cannot, however, adopt Mr. Sidgwick's remark, that Logic, ever 
 correcting laxities of rule or formula and earlier attempts to hide real 
 difficulties under vague phrases, ' must always be to some extent at war 
 with its own earlier stages ' (Use of Words in Reasoning, p. 51). 
 
CHAPTER III 
 
 THE ONE SOUGHT IN THE MANY 
 
 §59. He was the first logician who reflected first upon the 
 rational connexion of his own and other men's thoughts, asking 
 the meaning of such illative or adversative expressions as For, 
 But, Because, Although, Therefore, Accordingly, Nevertheless. 
 Language without marks of rational sequence would be little 
 more than pantomime. Sooner or later, reasoning beings were 
 sure to turn thought in upon its own connexions, to seek to 
 read the title-deeds of inference, to ask. What right have I to 
 conclude thus and thus? For what reason do I reason in 
 this way? 
 
 § 60. Mental science is unique in regarding the mind's opera- 
 tions from the inside, which is as though a clock were to explain 
 and criticize its working. Other sciences, even the most abstract, 
 as mathematics, are not investigated by the help of their own 
 processes. Aquinas defines Logic, on the other hand, as 
 Reason reasoning about reasoning, scrutinizing her own laws, 
 seeking a rationale of her own activity. 'Ratio de suo actu 
 ratiocinari potest, et haec est ars logica.' It would be more 
 correct to say that Logic is the analysing of the reasoning 
 process by the Understanding, the examination of opOo's Adyos 
 by vovs. It is Thought thinking about the rational necessities 
 by which it is governed. That which, in every branch of 
 learning, finds the One in the Many, and abstracts the per- 
 manent, necessary and universal form from the contingent and 
 variable matter, is not the Reason (in the sense, defended below, 
 of the ratiocinating activity), but the Intelligence, apprehending 
 ultimate principles and grouping detailed intuitional facts under 
 a unity of idea. The Intelligence, in the r6le of logician, has 
 first to establish the norm or abstract type of Reason in itself 
 absolutely; secondly to analyse the contingent form or mould 
 of human Thought, examining the diverse modes of expression 
 in which the thoughts of minds constituted as ours are can be 
 
32 The One Sought in the Many 
 
 cast ; and thirdly to trace through this variety the laws according 
 to which Thought's connexions are governed and directed by 
 Reason. 
 
 § 6i. Introspective analysis, the reflexion by the Ego upon its 
 own rational energies, was not Philosophy's eldest-born. The 
 first pre-occupation of Aryan man's awakened thoughtfulness 
 was physico-theological.^ He sought some theory of the universe 
 closing him in on every side. Plato says that philosophy began 
 in an awed curiosity.' Is there a One in the Many? Had life 
 a single origin ? Is the world a chance clashing of brute and 
 blind forces ? Is it at the mercy of the capricious partialities 
 of arbitrary and jealous deities, or is it controlled by some 
 harmonizing unity, according to measure and number and 
 weight ? 
 
 § 62. The Ionian thinkers answered this question in a naive 
 spirit of mystical materialism. They were unable to form a 
 clear idea of the non-material; yet the primary Cause and 
 Substance — water, air, fire — , whose modifications are the mani- 
 fold of experience, was not conceived as wholly mechanical. 
 As contrasted with the shifting plurality and seemingness of 
 mere phenomena, the sovereign Law of unity tended to be 
 thought as super-essential and self-existent. Yet for reality and 
 truth the verity of the visible Many, disparaged by the Eleatics, 
 is as necessary as the verity of the invisible One, which Hera- 
 cleitus and the primitive nominalists denied. The Pythagoreans 
 did something to reconcile multiplicity and unity, sense and 
 reason, by means of Number, which pervades all things that 
 appear. Empedocles, seeing clearly that a moving rather than 
 a material First Cause must be looked for, accounted for the 
 existing world, with all its pain and wrong, as brought about by 
 the conflict of Love and Strife. Anaxagoras, rising above such 
 semi-mythological explanations, ascribed the evolution' of the 
 universe to Intelligence, ordering all things by combination and 
 division. The world is a Koo-/ios. The human is akin to the 
 
 ' Not that races in childhood's stage, any more than children them- 
 selves, have concrete minds. On the contrary their turn of thought, for 
 want of experience, and want of disillusionment, is legal and abstract. 
 But they do not make the operations of their own minds the object of 
 self-conscious thought; and, even if they did, they are unable to give 
 technical names to their abstractions. 
 
 "^ Theaet. 155 D. Cf. Ar. Met. i. 2, § 8. 
 
Law in all Things 33 
 
 eternal Reason, and mind is not a mere vital spark liable to be 
 blown out by a puff. 
 
 § 63. In presence of the cosmic immensities, primitive minds 
 asked, 'What is Man?' He was not yet thought of as 'noble 
 in reason, infinite in faculty, his doing and moving express and 
 admirable, in action like an angel, in apprehension like a god '. 
 He must leave, therefore, to the supernal powers the blissful 
 cognizance of the inward law of the universe — ' Canst thou by 
 searching find out God?' — and, learning his limitations, seek 
 to 'know himself. Socrates gave the first great impulsion to 
 mental and moral science. The contrast between Mind and 
 Matter had been originally a theory to account for the distinction 
 of subject and object. But later the mind was turned in upon 
 itself. Was there there also a one and a many, in the microcosm 
 of the soul as well as in the external world? What is the 
 relation of sense perceptions to general notions, of particulars 
 to universajs ? And especially in the sphere of conduct. Has 
 that its underlying laws and unities? Early man is governed 
 in his ideas of right behaviour by custom and tradition, and by 
 the desire to please more or less capricious divinities. Justice 
 is administered in accordance with case-law or the gnomic 
 wisdom of sages. Among the Greeks law (vd/ios), varying from 
 state to state, and, in democracies, from year to year, was apt 
 to seem a mere convention — what we have made we can unmake. 
 Thucydides tells us, moreover, that the accepted standards of 
 right and wrong were thrown into confusion during the Pelo- 
 ponnesian War, and that the Pest of 430 b.c. was followed by 
 great corruption of morals. But such changes always attend 
 upon multiplication of the arts and appliances of life and upon 
 speculative activity, causing moralists to sigh for the simpHcity 
 of a golden age. A hedonistic scepticism makes individual man 
 the measure of all things. Each one's perceptions hold good 
 for himself only, and all opinions are alike true. Why should 
 not the worse be made to appear the better reason when among 
 reasons there is no such thing, really, as badness or goodness, 
 and things are what we agree they are ? The extreme 
 subjectivity of Protagoras subverts morality. According to 
 him all opinions are true, as, according to Gorgias, all are false. 
 It comes to the same thing.^ 
 
 ^ We are told of Numa Pompilius that he endeavoured to bind his 
 
 D 
 
34 The One Sought in the Many 
 
 § 64. If virtuous behaviour had only isolated ends and partial 
 utilities to serve, with no universal Good behind, in whose 
 nature all several goods participate ; if the passions, the impulses 
 of the senses, were haphazard and casual, uncontrollable by any 
 central principle of Reason ; if right had no measure but might, 
 the interest of the stronger, the whim of a man-made deity, or 
 a 'calculus of expediency : then, it soon became obvious, human 
 society and civilization must quickly fall to pieces. The task ot 
 conservative thinkers was to show that morality does not live 
 from hand to mouth, but rests upon general principles of right 
 and wrong, appUcable universally. It is not a fluctuating sea ot 
 confused opinions and incoherent, blind desires. Heaven is 
 to be honoured ; but right-doing is not a matter simply of rewards 
 and punishments, or of an exchange of good offices between 
 gods and men.^ 
 
 § 65. The assertion of the reign of law in natural phenomena, 
 followed by the exhibition of a universal element in conduct, 
 involved the conceptual nature of Thought, and so pointed to the 
 logical analysis of inference, which requires to be mediated by 
 abstract or common notions. Without middle terms, knowledge 
 is not scientific, but only a guess. And if it is to rest on any 
 constant basis, the government of the particular by the universal 
 must be guaranteed. Whatever is true of the general must be 
 
 Romans together in social and commercial intercourse by establishing 
 the worship of Good Faith. But it was open to any one to ask why Good 
 Faith should be worshipped. With something of the same petifio 
 prindpii Shaftesbury bases the duty of honesty on an implied contract. 
 I am bound to keep my word because I have given my word to 
 keep it. 
 
 ' To systematize conduct and place it on a philosophic and abstract 
 footing was the especial Aryan contribution to the science of life. The 
 Semitic genius, always ethical and religious, concerned itself with Per- 
 sonality and Will, which endeavours to realize itself in individual actions. 
 For to Will the actual and concrete is not mere seeming, but is significant 
 and of high value. The entrance of the Eternal into history, into spatial 
 and temporal limitation, gives a permanent importance to the details of 
 behaviour and observance, making the terrene here and now the symbol 
 and pledge, the sacramental vehicle and veil, of what is celestial. The 
 logical Hellenic and Indian mind, on the other hand, found its interest in 
 Thought rather than in Conscience, seeking a basis for morals in general 
 ethical principles rather than in personal union with, and devotion 
 towards, God. 
 
General Conceptions 35 
 
 true of the individuals which are subsumed under it, that is, 
 to which the general or common name is applicable. 
 
 § 66; The process of concluding from one particular to another 
 through a general conception would be likely next to attract 
 attention for its own sake. Yet Logic as a science was not born 
 of pure reflexion or intellectual curiosity, but rather of the 
 practical necessities of arguing. Greek philosophy was naturally 
 disputatious, the thrust and riposte* of open-air discussion. It 
 was nursed in the schools, in lecture or debating hall, in agora, 
 garden, grove, walk and portico, rather than in cell or study 
 or on the lonely hill-side. The Greeks, who had few books, 
 communicated opinion by word of mouth. In the game of 
 intellectual athletics, where victory was sought even more than 
 truth, the philosopher never forgot his antagonist. He was 
 either questioner or respondent, and was in little danger of not 
 knowing what was to be said on the other side of any question. 
 He was, moreover, posed and troubled by tricks and subtilties 
 of language which a reasoner less bound to reduce an opponent 
 to silence — subiugare assensum — would break through like 
 gossamer. 
 
 § 67. Of course, ro SiaXeye<rOai, dialectic — a word used, however, 
 in several senses — , Plato's to StSovat koI Sixeo-Oai Xoyov, does not 
 require two persons. But the discussions which a man holds with 
 himself in the forum of his own mind would hardly have awoke 
 inquiry into the formal validity of the reasoning employed. They 
 are seldom put into words ; and, besides, no one has an interest 
 in accusing himself of sophistry. On the other hand, the necessi- 
 ties of Greek life called for mastery over argument and con- 
 futation. Men had to elaborate the art of persuasion and 
 counter-persuasion, to search the weak spots in an opponent's 
 harness, to secure the weak places in their own. It would be 
 a bracing discipline for modern thinkers to have to defend their 
 theses publicly, scholastic fashion, in mood and figure, against 
 quick-witted disputants, or to state every position formally, as 
 St. Thomas does in the Summa, with a Sed contra after it,, 
 followed by a Respondeo} 
 
 * At the Savoy Conference in 1661, the disputation was one day con- 
 ducted fiyllogistically, the Church side positing the universal negative, 
 that' nothing in the Prayer Book is contrary to God's Word, and the 
 Puritans instancing various particulars in which such contrariety existed, 
 
 D 2 
 
36 The One Sought in the Many 
 
 § 68. It so came about that the dialectical machinery whereby 
 arguments were established called for analysis. But first, why 
 should a disputant be held, against his will, to an admission 
 made by him ? By evasive quibbling and cavillation it seemed 
 that any one might slip out of anything. What was the force, 
 an Eristic might ask, of the reductio ad absurdum, and of Socrates' 
 favourite method of leading an opponent on to unpalatable con- 
 sequences of his original contention ? If to hold an opinion 
 is to be tied to hold all that that opinion involves, where is 
 the unifying law, or principle of rationality, which thus necessi- 
 tates inference? It had to be shown that the manifold of 
 presented facts admits of abstraction ; that general notions are 
 possible ; and, on the other hand, that rules hold good of cases. 
 
 § 69. Thus from the subordination of concepts we obtain 
 Syllogism, read backwards and forwards — Induction and Deduc- 
 tion. Aristotle observes that Socrates introduced the construction 
 of definitions into philosophy;^ for true knowledge is of universals, 
 and to know a thing is to have discovered its essential constitu- 
 tion, the true way to conceive it, and not merely some quality 
 with which the observer happens to be impressed. Plato, 
 
 Aubrey writes of the generation before — *Dr. Chillingworth did walk 
 much in the College [Trinity] grove, and there contemplate, and meet 
 with some cod's head or other, and dispute with him and bafiSe him. He 
 would alwayes be disputing; so would my tutor. I think it was an 
 epidemick evill of that time, which I thinke now is growne out of fashion, 
 as unmannerly and boyish ' [Brief Lives). It was possible in that age for 
 disputants actually to exchange sides in all conviction ; as John and 
 William Rainolds converted one another. One brother had been a 
 Papist, the other a Presbyterian. 
 
 ^ Definition, bringing order out of the chaos of unrelated impressions, 
 is especially needed in ethical and political discussion. ' It is true,' says 
 Mr. A.W. Benn {The Greek Philosophers, i. 143), ' that definitions are also 
 employed in the mathematical and physical sciences, but there they are 
 accompanied by illustrations borrowed from sensible experience, and 
 would be unintelligible without them. Hence it has been possible for 
 those branches of knowledge to make enormous progress, while the 
 elementary notions on which they rest have not yet been satisfactorily 
 analysed. The case is entirely altered when mental dispositions have to 
 be taken into account. Here abstract terms play much the same part as 
 sensible intuitions elsewhere in steadying our conceptions ; but ... the 
 experiences from which those conceptions are derived are exceedingly 
 complex, and exceedingly liable to disturbance from unforeseen circum- 
 stances.' 
 
Logic began as an Art 37 
 
 dissatisfied with the Socratic method of sifting vulgar opinions, 
 obtained his lower generalizations deductively from the most 
 general notions. 
 
 § 70. But it remained for Aristotle himself to think out the 
 theory of deductive Inference and to build up, from base to 
 battlement, a complete and rounded system of Ratiocination. 
 The Platonic Socrates had given a stimulus and impulse to 
 logical speculation. But his cross-examining Elenchus savoured 
 too much of the Athenian law-courts to give birth to an abstract 
 rationale of reasoning. His erotetic method^ was not that of 
 a student, nor even of. a lecturer announcing his conclusions 
 from pulpit or platform. The late Professor Jowett is said to 
 have remarked that Logic is not a science nor an art, but a 
 dodge ; and there was a good deal of artfulness in the Socratic 
 disputation ; but it was that of the family physician entrapping 
 Jacky into swallowing a bolus. Logic as a science required 
 to be excogitated more in vacuo and with less didactic aim. 
 Popular institutions are not favourable to pure thought. But, 
 with the decline of political and forensic activity, abstract 
 speculation found space and leisure to expand. Aristotle 
 established the theory of reasoning upon an inexpugnable and 
 eternal basis, though neither he nor his later exponents kept 
 Logic entirely clear of intrusive metaphysics and natural 
 philosophy. 
 
 § 71. In the same way that there is a science of Being as 
 Being, ^ abstractedly from this, that and the other thing, viz. 
 
 ^ The Socratic method of extracting from an interlocutor some opinion 
 the drift of which was not at once obvious, and then of working from 
 point to point until the view elicited was seen to evolve in principle some 
 unexpected consequence or contradiction between theory and practice, is 
 much the method which Newman describes himself in the second chapter 
 of the Apologia as having adopted in the early days of the Oxford Move- 
 ment. ' I walked with men step by step as far as they would go. ... I 
 tried to make them preach the truth without knowing it. ... I was not 
 distressed at the wonder or anger of dull or self-conceited men at proposi- 
 tions which they did not understand. ... I was not unwilling to draw an 
 opponent on, step by step, by virtue of his own opinions, to the brink of 
 some intellectual absurdity, and to leave him to get back as he could. I 
 was not unwilling to play with a man who asked me impertinent ques- 
 tions. . . . Also I used irony in conversation, when matter-of-fact men 
 would not see what I meant.' 
 
 ' The phrase to hv 5 Sv, however, does not mean t6 ov x<»pis rSai ovrav, 
 
38 The One Sought in the Many 
 
 Ontology ; of Number as Number, abstractedly from the nature 
 of the objects numbered, viz. Arithmetic ; of abstract Geometrical 
 Figure ; of abstract Grammatical Syntax ; and so forth ; so 
 there must be an important place in philosophy for a rationale 
 of Reason as Reason, abstractedly from the content of the 
 terms. This should be called, perhaps, Logology. The Post- 
 Aristotelians called it \oyLK-i) {ljria-Trifji,i}, T£)(yi], or ■TrpayfiMTeLo). In 
 Aristotle himself the adverb XoyiKZs is contrasted with ^vo-ikS)?, 
 in the sense of ' dialectically '. The adjective XoyiKov likewise. 
 The Father of Logic nowhere calls the science directly by that 
 name. 
 
 § 72. The study of the laws, or law, of Reasoning is not 
 contrasted with physical inquiry as the science of the phenomena 
 of Mind contrasted with the science of the phenomena of Matter. 
 We have nothing to do in Logic with phenomena. If pure 
 thinking, apart from experience, could teach us a concrete fact, 
 this mental or spiritual addition to our stock of knowledge 
 would be, in the view of the logician, as extra-logical as infor- 
 mation about a phenomenon which can be handled, smelled 
 and tasted. And, certain conclusions of psychology once 
 given us as data, chiefly as regards the conceptual structure of 
 thought, we have no more concern with psychology than geology. 
 
 § 73. Reason, no doubt, is apprehended by the mind, as light 
 by the eye, and becomes reasoning by passing through mental 
 moulds. But the validity of any reasoning is tested by an 
 objective standard of correctness, and is dissected as a formal 
 product, not in relation to the individual intelligence from which 
 it issued, except that the intended meaning of the words must 
 be supposed ascertained. The natural laws of Knowledge are 
 determined by the mechanism of our faculties and psychic con- 
 stitution. The normal and regulative laws are prescribed from 
 without, by an absolute principle of Reason. Psychology shows 
 in what way rational beings, constituted to correspond con- 
 sciously with Reason, differ from non-rational. 
 
 § 74. Yet the law of subject and the law of object are not the 
 
 same thing. An argument is m itself good or bad, right or 
 
 wrong, correct or fallacious. Such expressions imply an ideal 
 
 law or pattern. Our reason is not a special paramount faculty, 
 
 nor yet to 6j/ a.(^ai.pov\i.ivav tS>v oWaj/, but rather to Sv (ou;^ as vnapxov 
 dXX') 3 6V. 
 
Reason as Abstract 39 
 
 but is simply our energizing as rational creatures.' Our thinking, 
 as a cerebral activity, is compelled, while the objective nexus of 
 thought is necessitated, by the reason of the thing. We recognize 
 a universal rightness in the matter, an ought as well as a must. 
 Otherwise there is no truth. What this objective standard is 
 we now proceed to inquire. 
 
 ^ Milton, however, makes Reason the sovereign faculty : — 
 
 In the soul 
 Are many lesser faculties that serve 
 Reason as chief. {P. L. book v.) 
 
CHAPTER IV 
 IMMUTABILITY OF RATIONAL LAW 
 
 § 75. Is Reason an immutable standard and law ? 
 
 Logical necessity, the law of all possible rational relations, 
 is prior to every other form of intellectual necessity, prior to 
 the Kantian Categories of the Sensibility and the Understand- 
 ing, prior to the basal axioms of mathematics, prior to the 
 metaphysical conceptions of Cause and Substance. It is the 
 ultimate law of the thinking subject ; but the notion of it is 
 necessary in itself as well as necessarily formed by our minds. 
 
 § 76. Right reason is not even the way in which the Divine 
 Mind merely as a fact reasons. For the Divine Perfection is 
 not accidentally or arbitrarily thus and thus ; but, being its 
 own law and having no standard outside and before itself, 
 nevertheless could not be otherwise than it is. If we ask 
 whence the necessity of such self-determination arises, we 
 find ourselves at the limit of human speculation.^ 
 
 § 77. Mill, contesting Hamilton's assertion that 'the laws of 
 Logic constrain us, by their own authority, to regard them as 
 the universal laws not only of human thought but of universal 
 reason V doubts whether they are even an original part of our 
 mental constitution, of the native structure of the mind. He 
 considers that we may have adopted them as part of our mental 
 furniture by always perceiving them to be true of observed 
 phenomena, so that the opposite has now come to be incon- 
 
 ' Dean Jackson (On the Creed) remarks upon the words 'God 
 Almighty' that 'the possibility of contradicting or opposing Himself 
 must by the eternal Law be excluded from the object of Omnipotence '. 
 Bishop Butler observes that the will of the Almighty 'is as certainly 
 determined by the principles [of right and wrong] as His judgement is 
 necessarily determined by speculative truth' {Analogy, Pt. H, c. 8). 
 Shaftesbury, however, argues that to say God is just and good is to imply 
 that there is such a thing as justice or goodness independently, according 
 to which God is pronounced by us to be just or good. 
 
 ''■ Lectures on Logic, ii. 65. 
 
The Empirical School 41 
 
 ceivable.* He quotes Spencer: — 'The law of the Excluded 
 Middle is simply a generalization of the universal experience 
 that some mental states are directly destructive of other states."* 
 To suppose that a law of thought is not necessarily a law of 
 notimenal existence is no invalidation of the thinking process. 
 According to Mill's doctrine, then, we only know that black 
 is not not-black as we know that black is not green, or that 
 unripe apples are unwholesome, viz. by having found it out. 
 
 § 78. Regarding the law of Reason as merely a generalization 
 from the way in which men do as a fact reason,' a summary of 
 observed rules or uniformities of practice, an induction from 
 a vast number of examples of valid arguments, — but how are 
 they known to be 'valid'? — Mill looks on ratiocination as one 
 of the activities of the Understanding *, with all of which Logic 
 is concerned. With him, as with the Port-Royalists, Logic is 
 'I'Art de Penser', and a department of Psychology. The 
 impossibility, therefore, of supposing logical axioms to be untrue 
 is but an acquired mental cramp, or, at most, a native and 
 inherited constitutional infirmity. Such axioms are true because 
 they are universal, not universal because they are true. 
 
 § 79. Mill, in fact, recognizes no essential rightness in Reason 
 as Reason, no absolute conditions of valid inference. Yet when 
 he contends that 'in no case can thinking be valid unless the 
 concepts, judgements, and conclusions resulting from it are 
 conformable to fact',' he cannot intend to deny that valid 
 conclusions may be drawn from untrue premisses. We may 
 
 ^ On Hamilton, p. 491. 
 
 ^ See also Mill's Logic, i. 321 : — ' The Principium Contradictionis I 
 consider to be, like other axioms, one of our first and most familiar 
 generalizations from experience '. No. Such an axiom may be con- 
 sciously realized with experience, but it is in truth a pre-requisite to every 
 mental act. 
 
 ' Mill seems to regard a conclusion as following from the combination 
 of the properties of two propositions in the same phenomenal way that an 
 explosion follows upon the union of a match and powder. ' Follows ', in 
 fact, merely means ' results.' ' Res constringitur, non assensus.' 
 
 * According to Hobbes nothing is required to make reasoning possible 
 but senses and association. Reasoning is only an assemblage of names 
 connected by the word est. We reason not about the nature of things 
 but about their appellations, which are purely arbitrary, and are ex- 
 changed like counters. 
 
 " On Hamilton, p, 471. 
 
42 Immutability of Rational Law 
 
 reason connectedly from the most extravagant propositions — 
 'Si j'etais roy,' or 'If all the trees were bread and cheese 
 and all the sea were ink.' ' If Sigwart is right that Logic is 
 ' a technical science of Thought directing us how to arrive at 
 certain and universally valid propositions', logical thought 
 cannot be looked for from a person who begins : ' If I were 
 you, I should do so and so.' One person cannot be another. 
 
 § 80. Though the conclusions of logical arguments can only 
 be conditionally true, yet we claim absolute certainty for the 
 bases of Logic itself In everything else ' nous cherchons par- 
 tout I'absolu et ne trouvons que le relatif '. But the logician's 
 starting-point is the one metaphysical Absolute, not this truth or 
 that, but the reality of Truth itself ^ This is the primary and 
 ultimate notion of Being and of Knowing. Logic can only 
 prove its own principles by means of those principles ; indeed, 
 they can only be questioned by being assumed true. Reason 
 can neither be established nor subverted save by an act of 
 reason. Even if it could be shown to be certainly false, that 
 would be equivalent to showing it to be possibly true ; for its 
 falsity could only exclude its truth on the supposition that 
 contradictories are incompatible, which is the very thing that 
 was denied. To disprove reason by reasoning is to stultify 
 oneself To expose unreason by reasoning is to beg the ques- 
 tion. Nothing, some one has said, which is worth proving can 
 be proven — certainly not the process of proof itself 
 
 § 81. If inferences are not borne out by facts we are puzzled.' 
 But while we may suspect the facts, or our premisses, or else 
 look for some flaw in the reasoning, we never for a moment 
 think that a correct deduction, however complicated and pro- 
 
 ^ Or those great subtilties and high suppositions which Latimer 
 ridicules as discussed in pulpits ; ' as whether, if Adam had not sinned, 
 wee should have had stockfish out of Iseland ; and how many larkes for a 
 peny if every starre in the element were a flickering hobby.' 
 
 ^ That reality I cognize with the same immediateness of consciousness 
 with which I cognize my own existence ; indeed the two cognitions are 
 really the same. Now to speak of the consciousness of my own mind by 
 my mind as relative to my mind splits impossibly into subject and 
 object the primal, original fact of my being. To make a man's self non- 
 Ego to himself, like a kitten chasing its own tail, is meaningless. 
 
 ^ Tai ^ej/ aKrjdeL iravra avvahn ra VTrdpx^ovTayjrw 6e ^euSet Taxy di.a<p(ov€i 
 rakqBes (Ar. E. N. i. 8, § i). Parmenides speaks of the unchangeable 
 heart of truth— dXij^eiar fvireiBkos drpe/ces r/Top. 
 
Logic has an Absolute Basis 43 
 
 tracted, from true premisses can be at variance with reality. 
 Thought is about things, that is to say, about their relations; 
 and if the thinking is right the things are as they are thought.' 
 Having determined by pure reason that the square of the 
 hypotenuse equals in area the combined squares of the sides, 
 I am certain that I shall find it so also by actual measurement. 
 The multiplication table holds good, when tested, whatever be 
 the objects multiplied, and the answer to a schoolboy's sum is 
 not only to be found at the end of the book but can be verified 
 in marbles or cherry-stones. Such verification confirms us in 
 the idea that we have multiplied correctly, but does not in the 
 least strengthen our belief in the laws of arithmetic. Truth, 
 says Pascal, consists not only in the conformity of ideas with 
 facts, but also in the conformity of facts with ideas — i. e. with 
 reasonings. 
 
 § 82. There is no mystery, then, in the correspondence 
 between a rational conclusion from assured data and the realities , 
 of experience. This is no pre-established harmony between 
 Thought and Things, between Mind and Matter; nor is it a 
 psychological surprise. If an abstract law does not hold 
 good in concrete instances — assuming that they are instances 
 (no actual circle, for instance, is a true circle) and that there 
 is no counteracting law — it is merely flatus vocis. It is to 
 understate the result of supposing non-correspondence between 
 rational and actual to say that it makes our thought an illusion.^ 
 
 ' Bain, however, says : — ' That we should abide by a declaration once 
 made is indispensable to all understanding between man and man. The 
 law of necessity, in this sense, is not a law of things but an unavoidable 
 accompaniment of the use of speech ' {Mental and Moral Science, c. vi, 
 § 7). Elsewhere his standpoint is even more crudely empirical. — ' The 
 impossibility of carrying on intercourse by language on any other footing 
 compels us to be consistent in our statements. . . . We are not always 
 so. If we could get on as well by maintaining an opinion in one form of 
 words while denying it in another, there appears to be nothing in our 
 mental constitution that would secure us against contradicting ourselves ' 
 {Logic, Pt. I, Introd. § 21). The question, however, is. Why cannot two 
 conflicting statements both be true ? If the only reply is that facts are 
 found by experience to be always consistent, we naturally ask whether 
 this is an accident or due to some necessity. Might it be otherwise in 
 Mars ? 
 
 " Hamilton, for instance, says : — ' Unless existence and non-existence be 
 opposed objectively in the same manner as affirmation and negation are 
 opposed subjectively, all our thought is an illusion.' But the lesser 
 
44 Immutability of Rational Law 
 
 To affirm a statement to be ' true ' but the facts to be otherwise 
 would be to say and unsay simultaneously, involving mental 
 self-destruction and the overthrow of the very idea of truth, and 
 so of existence. Language would then be a mere making of 
 mows. Mill asks : — ' If the reality of thought can be subverted, 
 is there any peculiar enormity in doing it by means of thought 
 itself? ' ' Substitute ' reason ' for ' thought ' and the question 
 surely needs no answer. 
 
 § 83. For the mind's apprehension of the Law of Rationality 
 goes deeper even than the irresistible assurance (ttio-tis) which 
 is the prime starting-point of demonstration and the ultimate 
 criterion of knowledge. It is the sine qua non of the mind's 
 existence ; and the idiot or bedlam, however the ' sweet bells ' be 
 jangled and out of tune in his understanding, is no more able to 
 violate this pre-supposition of all being than is the sage.^ The 
 axioms of Geometry and of Arithmetic might be supposed — 
 though not conceived — as non-existent apart from Space and Time, 
 or for intelligences different from our own. The entire basis of 
 discourse would not be overthrown by such a supposition. But 
 that the principle of Truth's self-coherence should not be valid 
 eternally, everywhere and universally implies the suicide of 
 Thought itself. We are confronted with no mere contingent 
 limitation of the thinking subject. Not all notions which are 
 necessarily conceived are conceived as necessary. It is not 
 only, ' I must think it to be so ', but, ' I must think that it must 
 be so ', and to think otherwise is not to think at all. Were it 
 possible, it would involve 'the sameness of all facts and all 
 assertions and the meaninglessness of all alike, as well as the 
 
 question of correspondence between our ideas of the external world and 
 the noumenal realities is not at present before us. It is only by faith that 
 we believe that 'Ideas are God's thoughts' (Wyclif), that 'all images 
 formed by the mind correspond to patterns present to the Creator's 
 mind' (Clarke, Logic, p. no). Belief, however, that there is such a thing 
 as Truth is more ultimate even than faith. 
 
 ■^ On Hamilton, p. 493. 
 
 ^ Horace Walpole, describing (April 19, 1761) the trial of Lord 
 Ferrers before his peers on a capital charge, observes : — ' He behaved 
 rationally and coolly ; though it was a strange contradiction to see a man 
 trying, by his own senses, to prove himself out of his senses.' But Lord 
 Ferrers was not trying to prove that proof is no proof. It is often said 
 that if most men were mad they would have a right to call the rest of the 
 world mad. Not if madness were an incapacity for ratiocination. 
 
Reason and Reasoning 45 
 
 indifference of all conduct '} And the moment we built any 
 judgement upon the supposition of the untruth of Reason, we 
 should be asserting its truth again. Scepticism, to be consistent, 
 should be speechless, neither affirming anything nor denying 
 anything ; for all affirmation and denial implies the existence ot 
 truth. And yet how can we require one who says there is 
 no law of consistency to be consistent ? But this way madness 
 lies. The brain reels. ' We assert nothing,' said the Pyr- 
 rhonists ; ' no, not even that we assert nothing.' That is, they 
 asserted that they did not assert that they asserted nothing.'' 
 
 So little do we know what we're about in 
 This world, I doubt if doubt itself be doubting. 
 
 § 84. Something should be here said about the distinction 
 assumed above between Reason and Thought, by which latter 
 word I mean the intellective comparing and judging activity 
 of the mind. ' The activity in which all intentional Thought 
 fulfils its purpose is Judgement' (Sigwart, Logic, ed. Dendy, 
 i. 16). According to Sir Toby Belch, ' Judgement and 
 Reason have been grand-jurymen since before Noah was a 
 sailor.' And though we cannot judge without an element of 
 inference — so that the judgement, 'It is raining,' is equally 
 an inference whether it be a drop felt on my cheek, or the 
 seeing passers-by put their umbrellas up, which makes me say 
 so — yet the recognitive act of bringing a presentation of conscious- 
 ness under this or that rule or general notion is, taken as a 
 complete product, an act of the judgement rather than of the 
 reason. There are other general propositions which might have 
 been framed about open umbrellas. But my understanding 
 selected as important the general proposition that they show 
 that rain is falling, and united to that proposition the conscious- 
 ness that I now saw them open. Reason then compelled 
 inference, and the judgement, the ideational activity, was 
 complete — ' It is raining.' 
 
 § 85. Much wider significations may be assigned to the word 
 Thought, which has been used to include even Intuition. 
 According to Lewes, 'the current English use expresses all 
 operations of the Thinking Principle, and is tantamount to the 
 
 ^ Wallace, Outlines of Aristotle' s Philosophy, p. 63. 
 ^ ' Etiam qui negat veritatem esse concedit veritatem esse ; si enim 
 Veritas non est, verum est veritatem non esse ' (S. Thorn. Aq. Summa). 
 
46 Immutability of Rational Law 
 
 common intellectual ground of Sensibility, Judgement and 
 Reason.' 1 'A thing which thinks,' says Descartes, 'is a thing 
 which doubts, understands, conceives, affirms, desires, wills, and 
 does not will, which imagines also and feels. All the operations 
 of the will, of the imagination and of the senses, are thoughts.' "^ 
 According to others, Thought excludes emotion, and does not 
 by itself excite the will to action, but includes memory and 
 imagination.' Hamilton regards it as comprising all our cog- 
 nitive faculties,* from simple apprehension to our grasp of the 
 widest generalizations. In a narrower sense Thinking, he says, 
 is limited to the mind's discursive energies, but in a wider 
 meaning it is coextensive with consciousness." ' Not a single 
 reason has been alleged to induce us to waver in our belief 
 that the laws of thought, and not the laws of reasoning, con- 
 stitute the adequate object of the science' of Logic' 
 
 § 86. The Kantian distinction ' between Thought (or Under- 
 standing) and Reason was much insisted on by Coleridge.' 
 For him Reason is the organ of spiritual apprehension, a power 
 of intuitive insight into fundamental truth — so that 'animalis 
 homo non percipit.' 
 
 § 87. Whether this distinction be a right one or not, it is not 
 the distinction between Reason and Thought which is hence 
 intended. I do not understand by Reason the intuition 
 generally of axiomatic first-principles, such as those of mathe- 
 matics, or of primal entities and eternal verities, such as Goodness 
 
 ^ Hist, of Philos. ii. 505. ^ Medit. ii. 11. 
 
 ' hiavoia airri ov8ev Kivn (At. EiA.), * Discussions, App. I. 
 
 ° Reid's Works, p. 222 n. 
 
 'See Hamilton's Discussions, pp. 1 3 1-4. 
 
 ' Kant, dividing Intelligence into Sensibility, Understanding and 
 Reason, and regarding Understanding as the faculty of judging, which 
 again is identified with thinking, makes Understanding the province of 
 Logic and Reason the province of Dialectic. It is Reason which reduces 
 the variety of judgements to their final unity, according to the three forms 
 of reasoning, the categorical, hypothetical and disjunctive. It is the 
 general faculty which contains all the faculties of cognition. Yet Kant 
 uses Reason to mean also the mind's ratiocinative power. 
 
 * ' Our Shakespeare, in agreement both with truth and the philosophy 
 of his age, names the Understanding " discourse of reason " as an instru- 
 mental faculty belonging to Reason ; and Milton opposes the discursive 
 to the intuitive, as the lower to the higher — 
 
 Differing but in degree, in kind the same.' 
 
 (Coleridge, Church and State, App. B.) 
 
Reason and Thought 47 
 
 and Beauty, but the necessary law, and our responsive apprehen- 
 sion of it, that the connexions of Truth must be self-consistent. 
 If this exclusive meaning placed upon the word Reason be 
 traversed, at any rate it is one important meaning of the word. 
 And what is here urged is that Reason (Xoyos) and Thought 
 (Siavoia)— taking the former to mean the ratiocinative imperative, 
 and the latter the judicial, cognitive or cogitative activity — are 
 two entirely different things. Logic is neither Noetic nor 
 Dianoetic. And though the forming of correct notions, that 
 is of right thoughts about things, may be much more important 
 than the drawing of valid conclusions from antecedent data, it is 
 not the province of Logic. 
 
 § 88. Thought is of various kinds, but Reason is one. Again, 
 if we think wrongly we are not called illogical but mistaken. " 
 Erroneous thinking is that which does not correspond with 
 actuality — idea non convenit cum ideato — , but the thought is 
 not destroyed by being erroneous. Erroneous reasoning, on 
 the other hand, cannot be exhibited as reasoning at all. It 
 has no correspondence with itself) and simply falls into nothing- 
 ness. Again, Reason governs Thought, the bands and links 
 of which are dirigible by, and subject to, the principle of Rational 
 Necessitation. By 'laws of Thought' we mean either the 
 constitution (which might perhaps have been different) of the 
 thinking faculty, or else the regulation which the connexions 
 of our thought receive from Reason. 
 
 § 89. The law of Reason, on the other hand, is an absolute 
 standard imposed by Reason. So that all operations of Thought 
 have a double limitation — r,Thought's own constitution and the 
 obligation to obey Reason's behests. We are said to ' see 
 reason', to be 'taught reason', to 'have reason'— the French 
 expressions 'avoir raison' and 'avoir de la raison' distinguish 
 the objective law and the answering power of the mind — , to 
 be reasonable (cTrnrei^eis Aoym) and unreasonable. Like the word 
 'rational', 'reasonable' formerly had the double sense of 
 according with reason (e. g., ' a reasonable price '), or of exer- 
 cising reason (e.g., 'a reasonable soul,' 'our reasonable 
 service '). 
 
 § go. Though the law of Reason be not always consciously 
 apprehended, it is from moment to moment obeyed by all ' God's 
 order or society of rational beings '. Coleridge remarks that 
 
48 Immutability of Rational Law 
 
 we do not possess Reason but partake of it. Reason, therefore, 
 ' cannot rightly be called a faculty, much less a personal property, 
 of any human mind '. We have it Kara iLiBt^w, not Kara oicriW. 
 In the same way Conscience is not a separate faculty, but the 
 supreme principle of moral unity in a man's nature. In the 
 Platonist and the Christian view, 'godlike Reason' is both 
 the light and the inward eye.' It is subject and object in 
 one, Xo'yos and 6 Xdyos, and within it is the sphere of Logic. 
 
 § 91. Why then, it may be asked, does not rational argument 
 always carry conviction, and how is it that men reason wrongly ? 
 Why so often is the truth on one side and the votes on the 
 other? Is the law of Reason a precept laid upon free intelli- 
 gences, to accept or reject? Why is it not enough to supply 
 an opponent with reasons, without supplying understanding 
 
 also? 
 
 § 92. I believe it will be found, on examination, that what 
 is called false reasoning is always at bottom misapprehension. 
 Either there is an inability to grasp the significance and bearing 
 of the materials supplied to the reason, or the reasoning is 
 formulated in an obscure or unfamiliar shape. A man does 
 not 'see his way through the argument'; he has to puzzle 
 out the links, the thread, the connecting points. If he thought 
 clearly he would reason rightly. I agree with Mr. Alfred 
 Sidgwick that 'syllogistic fallacy, so far as it occurs at all, 
 occurs through misinterpretation of sentences. Whenever an 
 
 ' Coleridge speaks of Reason as a ray of the Divinity in man, the 
 presence of the Holy Ghost to the finite understanding. 'We see,' writes 
 Hamilton, ' by a light which is not ours, and reason is a revelation of 
 God in man ' (Discussions, p. 8). He quotes Cousin, who says : — ' Reason 
 is impersonal in its nature ; it is not we who make it. It is so far from 
 being individual that its characteristics are the opposite of individuality, 
 viz. universality and necessity. . . . Reason is a revelation which 
 enlightens every man on his coming into the world. Reason is the 
 necessary mediator between God and man, the \6yos of Pythagoras and 
 Plato, the Word made flesh ' {Expos, of Eclecticism, p. 69). The Stoic 
 conception of the Xdyoi cVSidfleror (God's thought) and Xoyor 7rpo(j>opiK6s 
 (its revelation in the created world), after becoming with Philo God's 
 Firstborn and Counsellor, was raised to an entirely new plane by 
 Christian theology. The correspondence between the ' spirit of man ' 
 and the ' Spirit of God ' is perfected by the Incarnation of the imndoTaTos 
 AOros, who is no emanation of Deity but the second Person of 
 Trinal Godhead, in whose archetypal image humanity was originally 
 created. 
 
Can we Reason Wrongly? 49 
 
 invalid syllogism is accepted as valid, some two sentences have 
 been wrongly interpreted as equivalent to each other. In no 
 other way, surely, can we be deceived as to whether a given 
 conclusion is implied in given premisses'.^ And again — 
 ' Mistakes in reasoning are nothing but mistakes in the facts 
 from which the reasoning proceeds.'^ Presented with some 
 intricate question of genealogical relationships, I may arrive 
 at an absurd conclusion ; it is not, however, my inferential 
 power which is at fault, but the slowness of my comprehension.' 
 § 93. It is objected that a man must at any rate understand 
 his own thoughts — how comes it, then, that he can reason 
 badly by himself? But each person has really more difficulty 
 about his own thoughts than he has about those of other 
 people. For the latter are presented to him one by one, 
 formulated in language, and with some attempt at logical 
 connexion. But his own ideas throng into the cramped field 
 of the supra-liminal consciousness (to use Myers' well-known 
 phrase), for the most part confused, shapeless, and mingled 
 with a crowd of unreflective activities. At each moment that he 
 would reason, these half-digested thoughts, scarcely-remembered 
 impressions, tangled and disordered feelings, thrust themselves 
 upon his mind. He must use them in the rough. Hamilton 
 quotes the saying of Descartes : — ' Nihil nos unquam falsum pro 
 vero admissuros, si tantum iis assensum praebeamus quae clare 
 et distincte percipimus '.* This implies, no doubt, that false 
 thinking, and not only false reasoning, ought to be impossible. 
 'What is actually thought cannot but be correctly thought 
 Error first commences when thinking is remitted.' ° In other 
 words, mistakes proceed from the will, which is the parent of 
 laziness, from prejudice, confusion, arbitrary assumption, and 
 that inattention to the limitations of our faculties which converts 
 nescience and suspended judgement into ignorance and error .° 
 
 ^ The Process of Argument, p. 65. 
 
 ''■ Use of Words, p. 362. 
 
 ' '"Can you do Addition?" the White Queen asked. "What's one and 
 one and one and one and one and one and one and one and one and 
 one?" "I don't know," said Alice, "I lost count." "She can't do 
 Addition," the Red Queen interrupted ' (Carroll). 
 
 < Cartesii Princ. Phil. i. 43. 
 
 ° Twesten, Logik, § 308, quoted by Hamilton. 
 
 * ' Attention is an act of volition, and attention furnishes to the Under- 
 
 £ 
 
50 Immutability of Rational Law 
 
 § 94. The will corrupts the understanding. But — 
 Neque decipitur Ratio nee decipit unquam. 
 What, then, about madness ? Is this really ' loss of reason ' or 
 only ' weak understanding ' and disordered imagination ? The 
 lunatic who believes himself to be Julius Caesar or an elephant 
 argues quite rationally on that supposition. Hamlet, in brainish 
 apprehension of a rat behind the arras, consistently kills Polonius, 
 and weeps to find what he has done. Ophelia, ' divided from 
 herself and her fair judgement, Without the which we are pictures, 
 or mere beasts,' very logically drowns herself. It is the intelli- 
 gence which is unhinged. Within the world of his own in which 
 the madman lives, the connexions of thought obey the rules of 
 reasoning. 
 
 § 95. It is the understanding by which the simple spatial and 
 numerical notions are grasped. To put two and two together 
 is an intellectual rather than a ratiocinative accomplishment. 
 Galton tells us that the Damaras cannot count at all. ' If two 
 sticks of tobacco be the price of one sheep, it would sorely 
 puzzle a Damara to take two sheep and give him four sticks.' 
 A learned pig were more arithmetical. Yet one of these 
 inefficient cypherers on the trail of an enemy or wild creature 
 would doubtless perform most intricate feats of inductive and 
 deductive inference. In matters which a savage thoroughly 
 understands, his reasoning process is swift. Zerah Colborn, 
 having instantaneously found the square-root to thirty-three 
 places of a number consisting of fifty-three figures, dictated it 
 from memory twenty days after. But his purely ratiocinative 
 power was no greater than that of Galton's Damaras. 
 
 § 96. ' It is not the abstract principles of correct reasoning ', 
 observes Sidgwick, 'which are unfamiliar to the average man 
 (except in their technical expression), but the limits of the safe 
 application of those principles when the concrete subject-matter 
 is taken into account '} Children are usually very logical ; where 
 
 standing the elements of its decisions. The will determines whether we 
 shall carry on our investigations or break them off, content with the first 
 apparent probability, and whether we shall apply our observations to all, 
 or only partially to certain, momenta of determination' (Hamilton, 
 Lectures on Logic, ii. ^^). Probably, since we are partly conscious of the 
 part played by the will in our judgements, we form nearly all of them 
 with certain mental reserves. 
 * Use of Words, p. 83. Because our mistakes lie in our facts rather 
 
Error arises from Vague Conception 51 
 
 they go wrong is from want of experience. They look with a 
 certain awe for a correspondence between language and realities. 
 Words are to them not the counters which Hobbes says they 
 are to the wise, but gold pieces having an intrinsic value, and 
 not simply that which he who puts them into currency chooses 
 to stamp on them. 
 
 § 97. All important error, Sidgwick says, arises from ambiguity 
 of the middle term. When an arguer proves his point with 
 triumphant but suspicious ease and simplicity, it will usually 
 be found that the middle term has been slurred and half-skipped. 
 Hobbes proves that no law can be unjust, since right and wrong 
 are derived from law — ^which assumes that iustum quia iussunt 
 est, not tussum quia iustum. If forced by logic to state its 
 reasoning in full, the mind will often shrink from avowing what 
 was consciously or unconsciously implied in it. Frequently it 
 rests upon some slovenly conception — like that of the parents 
 who proposed to bring up their boy to the butcher's trade 
 because he was so fond of animals — or some more or less 
 disingenuous appeal to prejudice. So it is in the 'pathetic 
 fallacy '. Epithets used in controversy (e.g., narrow, broad, 
 intolerant, patriotic, firm, ruthless) prove nothing apart from 
 circumstances. A jest, however, is usually spoiled by insistence 
 on complete formulation. * My dear sir,' exclaimed Pugin to 
 a clergyman in a Roman church who was praying that England 
 might be converted in a vesture of offensively modern pattern, 
 'what can be the use of praying for the conversion of England 
 in that cope ? ' So far as the great ecclesiologist's distress was 
 serious, his unexpressed major premiss was that good taste and 
 good religion go hand in hand. The following we should class 
 under the head of ignoratio elenchi. Erasmus, having in a tract 
 Ciceronianus satirized the Ciceronians, who would employ no 
 
 than in our reasoning, Sidgwick suggests very inconclusively that 'the 
 common distinction between reasoning and judgment ' is wrong. ' There 
 is no unreasoned judgment, and no reasoning process apart from its 
 subject-matter' ( Use of Words, p. 362). But, because there is a reasoning 
 element in all judgement, it does not follow that reasoning and judgement 
 are the same thing. What Sidgwick means, no doubt, is that error 
 resides in the other element in judgement, the non-ratiocinative, which is 
 rather comparison than judgement itself. The starting-point of com- 
 parison is, in the ultimate psychological analysis, perceptive rather than 
 intellective. 
 
 E 3 
 
52 Immutability of Rational Law 
 
 expression not to be found in Tully (using Pontifex maximus 
 for the pope, Dii immortales for God, and the like), Scaliger 
 ferociously attacked Erasmus' public and private character. 
 Milton himself, in his prose works, is a past master in this 
 controversial method. But the underlying assumption is that 
 intellectual and moral qualities are so intimately related that 
 a scoundrel is certain to be a sophist, and to have vicious 
 literary judgement as well.^ 
 
 § 98. An enormous number of arguments have, as expressed, 
 an undistributed middle term, that is to say, no apparent 
 universal element, and this is a fallacy in the reasoning itself 
 But I think there is always in such a case an assumption that 
 the subject and predicate of the major premiss are 'convertible'. 
 All A's {and A's only) are B ; Cis B; therefore C is A. The 
 following example of fallacy is given in the Port Royal LogicP- 
 A German poet, reproached by Mirandola with having introduced 
 into a poem describing the wars of Christians against Christians 
 all the divinities of paganism, mixing up Apollo, Diana and 
 Mercury with the Pope, the Electors and the Emperor, main- 
 tained that without this it would not have been a poem, seeing 
 that the poems of Homer, Hesiod and Virgil are full of the 
 names and fables of these gods. Obviously the German meant 
 that mythological colouring is a predominant characteristic of 
 great ancient poetry, and that all poetry is bound to resemble 
 the great models in their leading features. The contention is 
 weak, but the reasoning, thus understood, is correct. The same 
 may be said — to pass from grave to farcical — of the illustrations 
 of the advantages of water-drinking given in the report of the 
 Brick Lane committee in the Posthumous Papers of the Pickwick 
 Club? That gin and water should undermine a wooden-leg's 
 constitution is a post hoc ergo propter hoc inference which depends 
 on an audaciously convertible major premiss, the general identifica- 
 tion of wooden-legged gin drinkers with the possessors of split 
 
 ' It is perhaps pursuing the point rather too seriously to quote Vinet :— 
 ' There is a strict relation between the rectitude of the moral sense and 
 the correctness of the mind. . . . Let us remember how rare it is that 
 intellectual speculations are completely exempt from moral influence, how 
 imperfectly recognized is the bearing of Will upon Opinion' (Meta- 
 physics). 
 
 » Ft. Ill, c. XX. » Chap, xxxiii. 
 
Fallacies 53 
 
 wooden legs — the circumstance that the split wooden legs 
 had been second-hand ones being deliberately put out of 
 view. 
 
 § 99. A large number of fallacies arise from the point to be 
 proved not being kept steadily before the mind. For example, 
 boiling oil used to be counted a specific against poisoning by 
 lead bullets ; but after a certain battle, Berthon tells us,' it was 
 found that the chief surgeon had forgotten to order a supply. 
 He was court-martialled and about to be broken, 'when some 
 one had the sense to propose that they should suspend judge- 
 ment till the results of the omission were ascertained. After 
 about a week it was found that all the wounded men were alive 
 and doing well.' But the question was whether the surgeon had 
 neglected his duty ; and the court was ' illogical ' in acquitting 
 him. The elenchus is here lost sight of. 
 
 § 100. Begging the question is sometimes a defiant assumption 
 — ' It is right for me to persecute you, because I am in the right, 
 but wrong for you to persecute me, because you are in the 
 wrong'. More usually it is due to confused thinking.^ But 
 confusion of thought has countless shapes. In 1886, the festival 
 of Corpus Domini falling on St. John's Day, there was an 
 apprehension among the Piedmontese peasantry that the end of 
 the world was at hand, and many made their wills in consequence. 
 They had a vague notion of impending death. Yet possibly 
 they may have had a feeling that Christians ought to go to their 
 last account with their affairs in order, their debts provided for, 
 and a just disposition made of their goods — whether any one 
 would be left to benefit by it or not. Mill remarks that ' men 
 may easily persuade themselves that they are able to reason 
 though they are not, because the faculty which they want is that 
 by which alone they could detect the want of it'.' He infers 
 
 ' A Retrospect of Eight Decades. 
 
 ' It is the conceit, not the irrationality, which takes us aback in the 
 Paisley man's surmise that Shakespeare may very well have been born 
 in that town, 'for his abeelities would justify the inference'. Petitio 
 principii is, in fact, rather a moral than a logical fault. For if not a 
 surreptitious, it has usually an insolent, vulgar, or foolish basis. The 
 Northern Farmer shows that the poor in the lump are bad, for — ' Tisn 
 them as 'as munny as breaks into 'ouses an' steals, Them as 'as coats to 
 their backs an' taakes their regular meals.' 
 
 ' Essay on Whately's Elements, 1828. 
 
54 Immutability of Rational Law 
 
 that fallacies must be exposed not by common sense but by 
 logical analysis. Logical analysis, certainly, by securing an 
 argument being exhibited in its completeness, will enable us 
 to lay our finger on the weak place in it, and give opportunity 
 for mending it. But what the testators of Piedmont lacked was 
 not logic but clearness of ideas. 
 
 § loi. In almost every dispute there is some petitio principii to 
 be hunted down. The opponent assumes that we will grant his 
 premisses when probably we ought only to do so with qualifica- 
 tions. Or he extorts a concession in one sense and proceeds to 
 make use of it in another. To our mystification or indignation, 
 we find that an admission has landed us in an intolerable conse- 
 quence. A Cambridge professor who was asked in a mathe- 
 matical discussion, ' I suppose you admit that the whole is 
 greater than its part,' is quoted by De Morgan as answering, — 
 ' Not I, until I see what use you are going to make of it.' If I 
 am asked to allow that an indicator which is right twice a day is 
 more useful than one which is never right at all, I shall probably 
 cheerfully assent, until I find that I have granted that a watch 
 which does not go at all is more useful than one which is always 
 a minute fast. Take this syllogism : — ' Whoever says that a 
 philosopher is an animal speaks truly. Whoever says that 
 a philosopher is a goose says that he is an animal. Accordingly, 
 whoever says that a philosopher is a goose speaks truly.' This 
 looks a good syllogism. But reasoning is about thoughts, not 
 about verbal expressions. And we notice that the first ' speaks 
 truly' does not refer necessarily to everything which the person 
 may be saying about the philosopher, but only to the predicating 
 animality of him. To call a philosopher a goose, however, is 
 indeed to attribute an animal nature to him incidentally, but 
 an animal nature of a certain kind. It is to say he is an animal 
 and something more. The statement is true, then, in one part, 
 but not necessarily in the other. 
 
 § I02. De Morgan points out that the scholastic logicians were 
 so practised in reasoning, and so unaccustomed to a formal 
 fallacy being adhered to one moment after being pointed out, 
 that they treat almost entirely of material fallacies; whereas 
 with us inaccurate reasoning is very common, and its exposure 
 is regarded as a pedantic quibble. But this only means that we 
 are impatient of form and theory, and resent having to recast 
 
Fallacies 55 
 
 an argument so that it shall conform to logical rules.* The 
 slipshod reasoning which makes the wise despair of an age 
 of cheap discussion springs from undisciplined judgement and 
 hazy conception rather than actual paralogism. Confused 
 materials are supplied to the mind to syllogize. Fallacies, in 
 fact, are really psychological rather than logical. Logic forces 
 them into the light, but does not show why we make them. If 
 we are to think aright, the all-important thing is the bringing 
 things under the right notions. The ratiocinative energy can 
 be left to take care of itself, if only it is supplied with notions 
 at once clear and distinct — made clear by definition and distinct 
 by division. 
 
 § 103. 'We are wrong,' says Vinet, 'in speaking of reason 
 misled, reason corrupted. In itself it is never corrupted. It is 
 the elements on which reason operates that are corrupt. And 
 just as reason alone cannot pervert, so neither can it redress 
 alone.' 
 
 § 104. The classification of fallacies is treated so fully in the 
 ordinary books that it need not be handled here." Mansel 
 adopts a threefold division — Fallacies in the Thought, Fallacies 
 in the Matter,, and Fallacies in the Language — Aristotle's irapa.- 
 XayuTfiuoi iv Tg Xi^ei. 
 
 'Strictly speaking,' he says, 'Formal Fallacies alone come 
 under the cognizance of the Logica docens, or logic properly 
 so called, as being apparent but not real thoughts, or at least 
 not the kind of thoughts which they profess to be. Material 
 Fallacies, where the thought is legitimate but the relation to 
 things inaccurate, belong properly to the province of the Logica 
 utens, and can only be adequately guarded against by that branch 
 of knowledge which takes cognizance of the things. A minute 
 division of Material Fallacies may thus be carried on to an 
 indefinite extent. . . . Fallacies of Language, it is obvious, will 
 become more numerous as the process of thought becomes more 
 complicated. . . . Any defect in this indispensable instrument of 
 thought is communicated to the operations which it performs.' 
 
 § 105. If, however, our contention is right that it is always 
 our understanding and not our reason which is deceived, formal 
 fallacies are at bottom fallacies either of matter or of language. 
 
 * Unlike the Oxford man of the old Aldrich days who came away from 
 a sermon indignantly exclaiming, ' The rascal made a fallacy in Baroso ! ' 
 
 ''■ e.g. in Mansel's Aldrich, App. M, and his Prolegomena Logica, 
 chaps, iv and v. 
 
56 Immutability of Rational Law 
 
 No one with a perfect comprehension of the terms he is using 
 and of their propositional relations would ever syllogize wrongly. 
 
 § 106. A further question should be glanced at before this 
 chapter closes. Is it possible to be ' too logical ' ? Not unless 
 it is possible to be too rational. If a man is unreasonable he is 
 not really rational. Carlyle assures us that 'not the least 
 admirable quality of Bull is, after all, that of being insensible to 
 logic '. Less complimentarily it has been said, ' L'esprit anglais 
 est tres inconsequent.' The Englishman usually thinks that he 
 can carry a principle just so far as is convenient, and no further. 
 Macaulay speaks of the promoters of a bill in Parliament caring 
 little about the major premiss contradicting the conclusion if the 
 major won two hundred votes and the conclusion a hundred 
 and fifty more. On the other hand De Tocqueville said of his 
 countrymen : — ' We are too logical, and cannot endure any 
 institution in which a blemish may be found.' French thought 
 is rectangular and somewhat unimaginative. 
 
 § 107. If our premisses are exactly and certainly true, we 
 cannot too logically act upon them. To do otherwise is to 
 be irrational. It has been remarked that when we are right 
 we are always more right than we believe ; if we hold a truth 
 we never believe it enough, never trust it sufficiently. What 
 is faith but the deductive loyalty to convictions of unseen 
 things which refuses to be turned out of the way by the things 
 of sight, and is verified by obedience? On the other hand, 
 terms used in religion ought always to be filled with content, 
 not used as tokens but realized in heart and understanding. 
 Otherwise preciseness of thought may lead to an 'horribile 
 decretum, fateor '} St. Paul's logic is ever spiritual and human, 
 not algebraic, wooden, and 'hard-church'. Still, it is right to 
 apply principles steadfastly. It was said of Hurrell Froude: 
 
 ' See Calvin's Institutes, lib. iii, c. 23, § 7, on the doctrine of irrespec- 
 tive reprobation. But, though the impossibility of expressing Divine 
 mysteries adequately and without one-sidedness makes an over-dogmatic 
 temper dangerous— ' non in dialectica,' says St. Ambrose, 'complacuit 
 Deo salvum facere populum suum,'— yet, if truth has been revealed to 
 human intelligences at all, it must be capable, under Divine guidance, 
 of deductive elucidation. There is a softness about the blurred and hazy 
 outlines of English beliefs, as of English scenery. But much of the cheap 
 contempt of popular writers for scientific divinity is nothing but a prefer- 
 ence for illucidity and down-at-heel slatternliness of thought. 
 
 i^^^sJi 
 
' Too logical ■" 57 
 
 'He is not afraid of inferences.' The weakness of the English 
 mind, which is seldom extremist and intransigeant, is usually a 
 shrinking from all methodical and definite thought. George Eliot 
 avers that this trimming extends even to the exact sciences, 
 and that an Englishman, confronted with the proposition that 
 the radii of a perfect circle are equal, struggles to avoid assenting 
 to more than that they have, under favourable circumstances, 
 a tendency to be equal. He would sooner make an answer 
 in arithmetic highly probable than prove it. 
 
 § io8. Nevertheless, how few ordinary rules are true unre- 
 servedly. And, again, how soon a formula gets separated from 
 the idea which it never, perhaps, perfectly expressed. For 
 language — to adopt Bosanquet's phrase — fits thought like a loose 
 glove. The glove may slip off and keep the shape of a human 
 hand, yet lie empty. Vinet apologizes for a forcible image. He 
 says : — 
 
 ' Unless we constantly hold fast the idea, we lose it on our 
 way, and perhaps at the beginning of the way, much as a 
 postillion riding his horse, and turning his back to the carriage, 
 may chance to leave it on the road, and arrive at the journey's 
 end with nothing behind him. This cannot happen in an 
 algebraical calculation, where the separation of the sign and the 
 thing signified never takes place. In reasoning upon moral 
 matters, it is a condition of safety to keep incessantly testing 
 the substance of ideas. Dialectics end by reconciling the mind 
 to enormities. It becomes callous, as does the hand that has 
 too long grasped a hard tool. There are truths and errors to 
 which we soon cease to be sensitive.' 
 
 § 109. Vinet, however, goes on to say : — 
 
 ' I have never understood that species of disdain which is 
 nowadays affected for theory, which is continually contrasted 
 with practice. Theory is nothing else than truth itself Theory 
 is inflexible as truth ; it survives all the usurpations of violence 
 and all the sophisms of injustice, and in the midst of disorders 
 presents itself majestically as the indelible type of all that ought 
 to be.' 
 
 He objects to a remark made by Catherine the Great to 
 a theorist : — ' You work on paper, which endures everything ; 
 and we unfortunate monarchs have to work with human flesh 
 and blood.' No, Vinet urges. ' We must, no doubt, take man 
 as we find him ; but we must not leave him there. This expres- 
 sion of Catherine's, taken absolutely, is a protestation against 
 
58 Immutability of Rational Law 
 
 principles, against the invisible, against the ideal, against God. 
 Let us take account of facts ; but let facts also take account of 
 principles.' ^ 
 
 § no. Again, that there is a logic of the heart does not prove 
 that the heart's reasons — 'le coeur,' says Pascal, 'a ses raisons, 
 que la raison ne connoit pas* — have not at bottom a rational 
 character, admitting of formal explication. It may not be easy 
 to reduce the lightning-hke conclusions of the emotions and 
 passions to syllogistic form. A woman's mind is called illogical 
 because it is intuitional. She sees things in a flash. Compared 
 with man, 
 
 Her subtile wit 
 At that which he hunts down with pain 
 Flies straight and does exactly hit.'' 
 
 And if challenged for her reason she very likely gives an 
 absurdly wrong one. She knows her boy will get a First Class 
 because he has such a noble disposition. Seek to convert her 
 to Rome with all the folios of Bellarmine, or to Geneva vnith 
 Calvin's whole armoury of texts, she will reply, ' Oh, but you 
 should hear dear Mr. Cope preach.' Still the reasoning is 
 there, and the illogicality is often on the surface. The nut is 
 not really got at without cracking the shell, nor even feminine 
 conclusions reached without grounds. After all, ' I think it so 
 because I think it so ' is the ultimate reason for all belief. 
 
 § III. Lastly, we do not expect in imaginative literature that 
 statements shall bear the weight of every inference which might 
 formally be based on them. The poet leaps broad chasms of 
 the unexpressed. He reasons by imagery. He does not 
 trouble to express facts with pedantic preciseness. When 
 Tennyson writes — 
 
 Every moment dies a man. 
 Every moment one is torn — 
 
 we do not suppose him to wish us to infer that the population 
 remains stationary, any more than we suppose Macaulay to give 
 the Huguenot horsemen at Ivry one spur apiece in the lines— 
 
 A thousand spurs are striking deep, a thousand spears in 
 rest, 
 
 A thousand knights are pressing close behind the snow- 
 white crest. 
 
 ' Metaphysics. 2 Patmore. 
 
'Too logical^ 59 
 
 On the other hand, Renan says of Claude Bernard's prose 
 style that it ' repose sur la logique, base unique, base ^ternelle, 
 du bon style '. 
 
 Note. 
 
 Of the Doctor Illuminatus, Raymond Lull (1236-1315), 'the 
 most eccentric product of the scholastic age,' it is said : — 
 
 ' His great aim was to identify philosophy and religion. He 
 undertook to demonstrate the highest mysteries of faith and to 
 spiritualize the plainest forms of science. ... He often treats 
 the exalted verities of religion with cold formality, but kindles into 
 rapt enthusiasm at the contemplation of logical forms. In the 
 missionary enterprises to which so much of his life was devoted 
 he laid little stress on the ordinary signs of apostleship, on the 
 living voice uttering living truth under the consuming fervour of 
 higher inspiration and with the witness of marvellous signs ; 
 but in place of these propounded his Art of Mechanical Syllo- 
 gistic, which he successfully forced on the attention of kings, 
 popes, cardinals, and councils, as the true theological machine 
 for the conviction of the infidel and the conversion of the 
 world. In this his great art {Ars magna Lulliana) his aim was 
 to reduce all the operations of thought to a mechanical sim- 
 plicity, or rather to enable any one to investigate all relations 
 and discourse of all truths, without the trouble of thinking at all. 
 It is an attempt to determine a priori not only all the possible 
 forms, but almost all the possible matter, of thought. He 
 endeavoured to do this by means of circles ... so that, by 
 allowing the first circle to remain stationary and the others to 
 revolve, all the attributes and relations which belonged to a 
 subject should in turn be assigned to it. This mechanical 
 scheme has a certain grandeur of purpose. Leibnitz, in his 
 treatise De Arte Combinatoria, has treated it with seriousness 
 and, to some extent, with approval' (T. Spencer Baynes' 
 translation of the Port Royal Logic, xiv). 
 
 Lull, however, has been styled 'the greatest of mediaeval 
 missionaries '. His practical labours were enormous, and closed 
 in martyrdom. Moreover, using a method the antithesis of the 
 Baconian, he drew scientific attention to the possibilities of the 
 magnetic needle and to the idea of a sea-route round Africa, 
 
CHAPTER V 
 REASON REGULATES THOUGHT 
 
 § 112. Having distinguished Reason and Thought, and seen 
 that the former imposes absolute and irresistible behests upon 
 the latter, we now go on to consider the law, or laws, given by 
 Reason to Thought generally, and next the rules governing the 
 connexions of Thought constituted as ours is. 
 
 § 113. Thought, for us, is a 'knowledge of things under con- 
 ceptions ', a knowledge of one thing or notion ' through another '. 
 It is discursive, a running to and fro, between fact of consciousness 
 and idea, a comparison, a recognition of similarity and difference. 
 We come to know each thing by something which we know better. 
 
 § 114, The Divine Thought, on the other hand, is intuitive 
 and immediate. All things are naked and open unto it. We 
 conceive, judge, syllogize. But to an Intelligence free from 
 limitations all knowledge is spread out, not cognized but con- 
 templated. Nor can it be supposed that the mind of Deity draws 
 consequential inferences, or proceeds from known to unknown. 
 For though we say that a conclusion follows — ' as the night the 
 day ' — yet regarded objectively in itself the conclusion comes into 
 existence simultaneously with the conjunction of the premisses. 
 
 § 115. Yet, even though the Thought of a perfect Mind be an 
 open vision of truth, it obeys the imperative of Reason, which is 
 violable neither by the instinct of the brute nor by the NoSs 
 Eao-tXcvs itself. Logical law not only does not admit of modifica- 
 tion in the way that physical laws blend with and modify one 
 another. It also transcends even mathematical necessity. For 
 example, the distance of a star may be determined partly by 
 spectrum analysis and partly by stellar parallax. The former 
 rests on natural laws of chemistry which we find hold good billions 
 of miles from our earth. But the measurement of distance by the 
 geometrical properties of lines and angles — given, of course, true 
 measurements and eliminating physical questions as to the refrac- 
 tion of light, optical deception, and so forth— rests on a postulate 
 
Law of Rationality 6i 
 
 wholly different from the idea of physical uniformity.' Given our 
 spatial conceptions, the theorems of Euclid have an absolutely 
 universal validity. The laws of space govern all human measure- 
 ment. We not only ' fail to see ' how parallels can meet, but we 
 are obliged to think they cannot.'' I am assuming that not meet- 
 ing is no part of the definition of parallel lines. It is an old 
 question whether mathematical axioms are analytic or synthetic. 
 
 § ii6. The Law of Rationality is of a' still more universal 
 reach than the Laws of Mathematics. It transcends Space and 
 Time. It cannot be thought as operating less in the spiritual 
 than in the sublunary sphere. It is ultimate and sovereign, and 
 governs all thinking whatsoever and wheresoever. 
 
 § 117. There must be an ultimate postulate both of the Matter 
 and the Form of Reasoning. We are concerned here only with 
 the latter. The Law governing the formal relations of thought is 
 twofold. On the negative or prohibitive side it is the Law of 
 Consistency. On the positive and obligatory side it may be 
 called the Law of Persistency. The former disallows the con- 
 junction of formally inconsistent attributes or the co-statement of 
 two conflicting propositions. The latter justifies and compels 
 the thinking of whatever is formally implied in a conception or 
 judgement, or connexion of judgements. The former is expressed 
 in the double Principle of Contradiction and Excluded Middle ; 
 the latter in the Principle of Identity. These are the metaphysical 
 bases of logic. They are not merely the ' negative conditions of 
 the thinkable'.' 
 
 At bottom, the three Principles are one and the same, and if 
 one could be supposed violable the other two could not stand.* 
 
 ' ' The measure of a man, that is of an angel ' (Apoc. xxi. 17). But we 
 might be constituted to apprehend a world of four dimensions. See 
 G. Howard Hinton, The Fourth Dimension ; Swan Sonnenschein, 1904. 
 A history of the doubts raised respecting Euclid's assumptions about 
 Space to the end of the eighteenth century will be found in Stackel and 
 Engel's Theorie derParallellinienvon Euclid bis auf Gauss, Leipzig, 1895. 
 
 " Dr. Bosanquet says : — ' You cannot prove that parallels never meet. 
 In order to do so, you would have, like the Irishman, to " be there when 
 it did not happen " ' (Lo^c, i. 339). But this is to make mathematical 
 necessity a mere empirical summary of observations. 
 
 ' Hamilton {Lectures on Logic, i. 106). 
 
 * Hamilton says :— ' The laws of Identity and Contradiction infer each 
 the other, but only through the principle of Excluded Middle ; and the 
 principle of Excluded Middle only exists through the supposition of the 
 
62 Reason regulates Thought 
 
 The Law or Axiom of Consistency. 
 
 § ii8. The Principles of Contradiction and Excluded Middle 
 are the same principle regarded from opposite sides. Together 
 they constitute the law concerning Contradictories. ^ The one 
 denies that, if a statement be true, it can at the same time and in 
 the same sense be untrue, or that if a statement be untrue it can 
 simultaneously be true. The other asserts that a statement must 
 either be true or be untrue. That is to say— since this is the 
 meaning of 'either . . . or'— if it is not the one it must be the 
 other. In other words, if a statement is not true it must be 
 untrue, and if not untrue it must be true. 
 
 § 119. The Principle of Contradiction— which Hamilton pre- 
 fers to call the Principle of Non-Contradiction, principium 
 non-repugnantiae — declares that if a statement be true the contra- 
 dictory of it must be false. The Principle of Excluded Middle 
 declares that if a statement be false the contradictory of it must 
 be true. In other words, of two mutually contradictory proposi- 
 tions both cannot be true, but one must be. Of the two one is 
 true, and only one. 
 
 As the self-evidence of both these Principles has been called 
 in question, something more must be said about them. 
 
 The Principle of Contradiction, 
 
 § 120. When we say that a proposition cannot be both true and 
 false — non est simul qffirmare et negare — we are asserting some- 
 thing about the nature of Existence. We are not stating simply 
 a mental limitation — as that two attributions cannot be combined 
 in one act of consciousness, or that no object can be thought 
 under qualities known to be incompatible. But we are making 
 an ultimate assertion about the truth of things in themselves. 
 We are laying down, in fact, what we mean by truth. And we 
 say that we are logically precluded from making two contradic- 
 tory predications about a subject because, metaphysically, an 
 object cannot possess a quality and also not possess it. For 
 a thing to be itself, a characteristic which it now has cannot also 
 now be absent from it. The point must not be confused by the 
 introduction of questions about personal continuity ; as whether 
 
 two others.' These two cannot move without the third; and without 
 them the third cannot be conceived as existent (Lectures on Logic, ij. 
 244). Mr. Stock holds that each law is independent {Logic, pp. 6, 7). 
 
Principle of Contradiction 63 
 
 Socrates seated is identical with Socrates standing ; or whether 
 Ludovicus Rex is ' himself as Ludovicus without the Rex ; or 
 whether St. Hubert's hunting-knife was the same knife after 
 being several times re-bladed and new-handled. 
 
 It is difficult to state a truism without making it a mere tauto- 
 logy. But even tautology is in form assertive; whereas the 
 possibility of assertion, implying the existence of truth, is what 
 is really impugned when the Principle of Contradiction is 
 impugned. 
 
 § 121. The Empirical School, as we have noticed, see in this 
 Principle merely a statement on our part that by long familiarity 
 with the contingent circumstances of truths not conflicting we 
 have come to be incapable of conceiving such confliction.^ Grote 
 writes : — ' You can only prove the Maxim of Contradiction by 
 uncontradicted appeals to particular facts of sense ; and if your 
 opponent will not admit these facts of sense you cannot prove it 
 at all.' " Dr. Bradley, after pointing out that there is no logical 
 principle which will tell us what qualities are really disparate, 
 goes on : — 
 
 ' In logic we are not called upon to discuss the principle but 
 to rest upon the fact. Certain elements we find are incompatible 
 and, where they are so, we must treat them as such. It can 
 hardly be maintained that there are no disparates except those 
 qualities which at the same time imply each other. And the Law 
 of Contradiction does not say any more than that, when such 
 sheer incompatibles are found, we must not conjoin them. Its 
 claims, if we consider them, are so absurdly feeble, it is itself so 
 weak and perfectly inoffensive, that it cannot quarrel, for it has 
 not a tooth wherewith to bite any one.' 
 
 ' Even Ueberweg is found doubting whether the Principle of Con- 
 sistency is fundamental, underived and unchallengeable. He looks for 
 the ultimate rational principle in the correspondence of the content of 
 perception and thought with existence {System of Logic, § 'j']). But in 
 what sense is the perception of that correspondence ' rational ' ? Locke 
 {Human Understanding, iv. 7, 9) says : — ' A child certainly knows that 
 a stranger is not its mother, that its sucking bottle is not the rod, long 
 before he knows that it is impossible for the same thing to be and not to 
 be.' Before he realizes it consciously, no doubt. But the child could not 
 apprehend mother, bottle or rod as constants if at the back of all its 
 knowledge there were not the idea of truth. And truth means that a 
 thing cannot both be and not be. 
 
 * On Taine's De F Intelligence. Minor Works, p, 359. 
 
64 Reason regulates Thought 
 
 And, in the same comico-metaphysical vein, just before : — 
 
 ' This axiom is not like the principle of Identity. It is a very 
 old and most harmless veteran ; and for myself I should never 
 have the heart to attack it, unless with a view to astonish common 
 sense and petrify my enemies.' ' 
 
 So that to say that a button cannot be both off and on is on the 
 same level as the proposition that it cannot both be made of horn 
 and be worth twenty thousand pounds ; and to say that a build- 
 ing is at once empty and not empty is on the same level as the 
 proposition that it is at once fireproof and built of pine and 
 thatch. 
 
 § 122. There are some native incapacities of conception which 
 are part and parcel of the mind's structure and yet are seen at 
 once to involve no limitation of reality. We can conceive 
 nothing of which, or of the elements of which, we have had no 
 outer or inner experience ; for example, infinity. A man born 
 deaf cannot conceive harmony of sound. A street hooligan 
 cannot conceive the pleasure which the connoisseur gets from 
 a delicate piece of Sevres or a fine proof engraving. The 
 happiness of an unselfish life is a sealed book to the selfish, and 
 there are many things in religion which are too high for our 
 conceiving, but which nevertheless we believe true. 
 
 § 123. On the other hand we assert with Aristotle and with 
 
 mankind that to avTO a/ia iirapx^eiv TE Koi fjLYi xnroipxeiv aSvvwrov T<5 
 clvtZ Kol Kara to aiiTO, and that this is 7racrS)V tS>v apxSiv /3e/3aioTa.T7i,'' 
 
 the indispensable condition of thought and of truth, guaranteed 
 both by the impossibility of making or believing any assertion 
 whatever unless it be conceded, and by the primary instinct of 
 mental self-preservation. It is a choice between this and an 
 Heraclitean flux of all things. 
 
 § 124. Hegel, however, confines the Principle to the sphere 
 of phenomena. All contradictories are reconciled in the sphere 
 of the Absolute by a higher unity, as partial aspects of a more 
 comprehensive truth. Motion and change — each thing passing 
 into something else — imply contradiction at every instant, a 
 union of being and not-being in the same object at the same 
 moment. But not only does nothing come into being without its 
 opposite in thought : all assertion in itself necessarily involves 
 a correlated contradiction, and every say is a gainsay. Silence 
 ' ^'>^i'^> PP- 136-41- " Meiaph. i. 3, 1005!', 20. 
 
Principle of Contradiction 65 
 
 implies sound, order implies confusion, compulsion implies 
 freedom. Thus identity and difference are mutually creative. 
 The clearness of a notion is obtained by differentiation and the 
 recognition of limitation. Omnis determinatio est negatio. 
 Limitation is essential to consciousness. We cannot know A 
 without being aware of non-^. The identity (co-existence?) of 
 contradictories is the very condition of being and of knowledge. 
 
 § 125. Pure being and pure not-being are, in this theory, 
 identical because they are species of a common genus, the 
 Unconditioned, and so have a common nature. In union they 
 constitute the conditioned existence around us. The Absolute 
 (i. e. God) is the abstraction from, and prius of, every discrimen 
 and particularity — the whole sum of possible logical conscious- 
 ness. The Hegelian Logic expounds Him in His essential 
 self-Existence before being differentiated into this, that and the 
 other concrete creation. Being, passing through not-Being, 
 is determined as quality of things. There is a perpetual 
 Becoming or development, a transition from the notional to the 
 actual, an unresting river of thought. Not-being is necessarily 
 thought simultaneously with being, and, since the process of 
 thinking is the process of creating, necessarily co-exists with it. 
 
 § 126. There appears to be in this doctrine a fundamental 
 confusion between not-being and being not (observe the absence 
 of the hyphen), between ' aoristic ' negation, or mere otherness, 
 and contradiction.^ An object cannot have an attribute and not 
 have it. But it can have an attribute and also have a number 
 
 ' Prof. Caird points out (' On the Evolution of the Idea') that in Plato's 
 Sophistes to \u) ov is not the negation, but only the other, of ov. If the 
 Real is real, It, or He, cannot be modified as true and also as false. God 
 cannot be the perfect indifference of contraries if He is the Truth, the 
 Amen, the Yea — not a higher unity of Yea and Nay (2 Cor. i. 17-20), 
 ' He abideth faithful ; He cannot deny Himself.' The ' catholicity ' of 17 
 akififla is a synthesis not of contradictions but of contrasts. Every state- 
 ment about Reality is a limitation, and to transcend limit is to pass into 
 the sphere not of the Absolute but of the Meaningless— why should it 
 not be equally entitled to a capital letter ? To be blind to the comple- 
 mentary aspects of the depositum fidei is the partiality of alpea-is. But 
 one-sidedness is preferable to a boneless and pantheistic mysticism. The 
 oecumenical Confessions, by affirming the doubleness and completeness 
 of truths (e.g. 'licet Deus sit et Homo, non duo tamen sed unus est 
 Christus '), shut out the narrowing explanations advanced by particularism 
 on the one side or the other. 
 
66 Reason regulates Thought 
 
 of other attributes which are not that attribute. Length is not 
 breadth ; yet a table may be both long and broad. To be rich is 
 not to be thirty years old ; yet a man may be both. In relation 
 to every attribute all other attributes are not it, are other than it. 
 ' Not J[-ness ' (by which is meant ' a quality which is not that 
 oiA' rather than 'the quality of not being A') embraces the 
 potentially infinite number of qualities which are not identical 
 with A-n&ss. Now, if an object had only the one quality, ^-ness, 
 it could not be distinctly known, for all knowledge is by distinc- 
 tion. To say that it is A, then, is to imply that it is something 
 else, B, C, D, &c., as well— J5-ness, C-ness, Z»-ness, &c., not 
 being ^-ness. In this sense 'being' involves the existence of 
 'not-being ' in the same subject. Though B-ness is not .<4-ness, 
 though age is not wealth, yet a thing may be both B and A : 
 a merchant, e. g. may be both aged and wealthy.' 
 
 § 127. On the other hand contradictory ' being not ' has only 
 a notional correlation with ' being ', and cannot co-exist with it in 
 predication. A man may be of noble birth and bankrupt, but not 
 of noble and of ignoble birth. He may be prejudiced and 
 athletic, but not prejudiced and unprejudiced. It is not even 
 certain that a positive impression always calls up an opposed idea. 
 If the whole universe were a uniform blue, we should distinguish 
 the colour of things from their shape and other qualities ; but 
 we could not, I think, frame the conception of not-blue extension. 
 We can imagine blest spirits beholding with awe and joy the 
 Creator's goodness and beauty, yet shielded from the knowledge 
 of the existence of sin or ugliness. 
 
 §128. But even if the notional co-existence of opposites be with- 
 out exception — as ' wise king ' implies the possibility of ' unwise 
 king', 'full jug' of a jug which is not full — yet truth belongs to 
 judgements, not to notions. In the Idea opposites lie side by side 
 
 ' The Hegelian Absolute is really pure Abstraction, void of all reality, 
 and also of all power or tendency to be determined in one way more than 
 in another— otherwise the Unconditioned is subject to conditions. Pure 
 and impure both are, and neither is the other. Each, if it is, also is not. 
 The self-movement of the Deity realizes the Idea impartially in both. 
 But this is to make not righteousness and peace kiss each other, but 
 righteousness and unrighteousness, peace and wrath. 'Not-good' is not 
 not-Being determined as goodness, but Being determined as not-goodness. 
 Everything is thought as really yes or really no ; and non-Reality, not- 
 Being, is not a conception at all. 
 
Principle of Contradiction 67 
 
 as opposed ; but they do not interfere with one another, and so 
 need no ' reconciliation in a higher synthesis '. Strife implies 
 simultaneous affirmation and denial. ' Being is the other side 
 of thought' only if by thinking we mean judging. Judgement, 
 unlike conception, involves assertion. Now this 'I assert' 
 is the one thing which cannot possibly be made ideal, but is 
 always actual. 'Nothing,' says Dr. Bradley, 'excludes any 
 other, so long as they are able to remain side by side ; incom- 
 patibility begins when they occupy the same area." But 
 contradictory statements do occupy the same area. Conflicting 
 assertions of actuality cannot be combined in judgement. 
 
 § 129. Though the notion XY, then, involves the notion not- 
 XY, the assertion ' Y is X' only requires the distinguishing 
 .^^-ness from qualities which are other than it. In other words, 
 the counter-relativity of ideas as actual does not involve as true 
 the counter-relativity of statements about reality. Indeed if 
 every ideal combination has in the noiimenal sphere a reality to 
 correspond to it, the Hegelian system must, on its own showing, 
 be in that sphere both true and false, since its falsity is as much 
 a thought as its truth. Again, since the idea of the non- 
 existence of God Himself is as much in tntelledu as the idea of 
 His existence, it must be noOmenally as true. The confining 
 the validity of the law of rationality to finite understandings, 
 dealing with finite objects, results, in fact, not so much in what 
 Mansel calls ' a gigantic scheme of intellectual pantheism ' as in 
 an incoherent scepticism. Religion especially is undermined 
 by the resolution of historical fact into mere beauty of idea. 
 Modern monism regards everything as' good and true from 
 a certain standpoint. Certainly, seeming oppositions of thought 
 might find reconciliation in a wider grasp of the body and 
 system of truth. But if two views really conflict, one must give 
 way. Again, error may bring out truth, just as light would not 
 be visible apart from darkness. But error and truth cannot, 'in 
 the great chime and symphony of nature,' be the same thing. 
 The denial of any attribution implies, no doubt, the existence 
 'Of the attribute in thought — and in this sense we can say with 
 Spinoza, 'omnis negatio est determinatio ' — ; but it excludes 
 existence, as attributed to that particular subject, in reality. 
 The eternal distinction between the True and the False is not 
 
 * Principles of Logic, p. 136. 
 F 2 
 
68 Reason regulates Thought 
 
 dualistic ; for Truth has no meaning apart from the possibility 
 of falsity. 'Not-being,' it is asserted, 'exists because it is a 
 thought.' Is it, however, a thought, that is to say, a thought 
 about reality? Thought which is to agree with reality must 
 agree with itself 
 
 § 130. If we are satisfied that two truths can never clash, and 
 that the true and the untrue cannot be blended in one, we shall 
 find practical safety, whenever a perplexing problem refuses to 
 be untied, if we get back to something of which we feel perfectly 
 convinced, and follow deductively the clue which it gives us. 
 What is the logical course to take ? We need not fear that 
 what seem to be rival claims of right and truth will really be 
 found incompatible. If two principles or claims do undoubtedly 
 conflict, without any possibility of reconciliation, we may be 
 certain that one or the other is wrong. 
 
 § 131. While the formal compatibility of two conceptions does 
 not indicate that they are actually and empirically compatible 
 as judgements, the formal incompatibility of two conceptions at 
 once disproves their compatibility in fact. 
 
 § 132. In answer to more popular objections to the Principle 
 of Contradiction, it is of course true that predicates are often 
 employed in a relative sense ; the same person is both father and 
 son, both superior and subordinate. A battle or bet which is 
 won is also lost. Weather which is bad for the corn may be 
 good for the roots, and a pouring day is a fine day for the 
 ducks — il fait beau temps pour les canards. In another sense 
 Macbeth says, 'So fair and foul a day I have not seen.' 
 ' Antiquitas saeculi ' is ' inventus mundi '. At a level crossing, 
 gates open for trains are ipso facto closed for vehicles. Again, 
 words like tall, loud, better, and the like, are comparative 
 only. The robin in Rogers' poem sees a ' schoolboy's giant 
 form '. 
 
 § 133. Contradictory attributes, moreover, are predicable of the 
 same subject at different times. Philip, drunk last night, is sober 
 this morning. Tertullian said he had known ' pastores in pace 
 leones, in praelio cervos'. It is possible to 'make a heaven 
 of hell, a hell of heaven '. 
 
 She sinks on the meadow in one morning-tide 
 A wife and a widow, a maid and a bride. 
 Or they are rhetorically conjoined, St. Hilary has the bold 
 
Principle of Contradiction 69 
 
 phrase, 'irreligious solicitude for God.' Hooker speaks of 
 devout blasphemies, Bunyan of bold-faced shame, Laud (ironi- 
 cally) of ail innovation of above thirteen hundred years old, 
 Gibbon of organized anarchy, Drummond of Hawthornden of 
 the dolorous felicity of life. Life in Holy Dying is called a sickly 
 health. Elia calls his life with his sister double singleness. 
 Horace speaks oiinsaniens sapientia. Milton accuses St. Peter 
 of being arrogant and stiff-necked in his humility. Knox has 
 been called a presbyterian pontiff, and Mill 'the saint of ration- 
 alism '. There may be even verbal confliction, as in phrases like 
 'joyless joys' (Faber), TrdXe/^ios aTrdXc/xos, ' Beauty is most adorned 
 when unadorned.' A subject may be qualified in opposing ways 
 according to the point of view ; as in St. Augustine's apostrophe, 
 ' O Pulchritudo, tam antiqua et tam nova ! ' Man, in the Sphinx's 
 riddle, is four-footed, two-footed, and also three-footed. A sopho- 
 more, or learned blockhead, is wise in one sense and unwise in 
 another. ' Fairest Cordelia, thou 'rt most rich, being poor.' The 
 bitter-sweet apple — but aigre-doux in French means sourish — 
 combines two unlike flavours. The Quietists spoke of an 
 actively-passive state of the soul. (See §§ 48, 235 seq.) 
 
 § 134. It is obvious, however, that in such cases a quality is 
 not simultaneously afSrmed and denied of the same subject in 
 the same relation and in the same sense. If ever it be really 
 so, the intention of the words is nonsensical ; like the tragical 
 mirth enacted before Duke Theseus; or Mistress Ford's 'an 
 eternal moment or so '. Slender says : ' All his successors gone 
 before him have written armigero, and all his ancestors that come 
 after him may.' And Launce declares : ' My grand-dam, having 
 no eyes, wept herself blind at my parting.' More tragically, 
 Constance in King John, 'Thou odoriferous stench, sound 
 rottenness.' The Londoner's explanation to a surprised com- 
 panion on an August bank-holiday — ' You see, blackberries are 
 always red when they are green ' — was ridiculous only on the 
 surface. For other illustrations see Appendix K. 
 
 § 135. The Principle of Contradiction is usually expressed 
 symbolically with a singular subject : ' X cannot be, and not be, 
 Y: More fully, 'No YX (i. e. no X which is Y) is non-F (a 
 non-yZ), and no non-YX (i, e. no X which is not Y) is Y (a 
 
 Yxy 
 
 The Principle of Excluded Middle is stated symbolically thus : — 
 
70 Reason regulates Thought 
 
 'Neither is For is not Y.' ' Every non-YZ is not F; and every 
 not-non-y^is Y.' 
 
 § 136. But the Principles also apply to opposed quantified pro- 
 positions, where the opposition lies between the respective 
 quantifications, which may be regarded as the real predicates. 
 Thus : — 
 
 A. Universal Affirmative. All X's are Y. 
 E. Universal Negative. No X is Y. 
 I. Particular Affirmative. Some X's are Y. 
 O. Particular Negative. Some X's are not Y. 
 
 A is contradicted by O and O by A. E is contradicted by / 
 and / by E. If a proposition be true its contradictory is ex- 
 cluded, and if untrue its contradictory must be accepted. 
 
 A and E are Contraries and incompatible. But if the one be 
 untrue it does not follow that the other is true. A middle between 
 contraries is not excluded. / and O, often called Sub-contraries, 
 may or may not be true (they cannot be untrue) simultaneously. 
 
 § 137. A strict dichotomizing, then, yields us only three kinds 
 of objective possibility as regards the attribution of Yto X. The 
 first dichotomy tells us that either all X's are Y (i) or not all 
 X's are Y. The second dichotomy divides ' Not all X's are Y* 
 into ' No X is Y' (2) and Some, but only some, X's are Y {3). 
 These are the three kinds of objective possibility about the rela- 
 tion of Yto X. For a verbal fourth possibility, ' Some, but only 
 some, X's are not Y,' is really identical with (3). 
 
 § 138. But, regarded as subjective judgements, there is a four- 
 fold division. For, if I judge that some X's are Y^ I do not 
 exclude the possibility of all X's being Y; and, if I judge that 
 not all X's are Y, I am not necessarily denying that no X's are Y. 
 Tts is logically consistent with vras, and ov iras with ovSets. Accord- 
 ingly ' Some, but only some, X's are Y' is a double judgement, 
 though it is only a single possibility. And the word 'dicho- 
 tomy' is properly used for a logical division of judgements 
 rather than a material division of possibilities. 
 
 § 139. As applied to quantified propositions the Principle of 
 Contradiction says that, if it is true that all X's are Y, it is untrue 
 that some (any) .X''s are not Y; and vice versa. Also that, if it 
 is true that no X is Y, it is untrue that some (any) X's are Y; 
 and vice versa. 
 
Principle of Contradiction 71 
 
 § 140. Excluded Middle has exactly the same formulae, sub- 
 stituting ' untrue ' for ' true ', and ' true ' for ' untrue '. 
 
 § 141. If 'AH ^'s are Y' is meant to be contradicted by 'AH ^'s 
 are not Y' , a. heavy stress must be laid upon all. E.g. 'All is 
 not lost ' ; ' All are not of that opinion ' ; ' Toutes les Veritas ne 
 sont pas bonnes a dire ' ; which are / propositions. But, ' All 
 they that trust in Him shall not be destitute,' ' non est impos- 
 sibile apud Te omne verbum ' are E propositions. 
 
 § 142. Again, to contradict ' Some men are sinless ' by ' Some 
 men are not sinless' is awkward and ambiguous. For con- 
 tradiction, not would require to be emphasized. A stress upon 
 'some' would appear to give an A proposition strengthening 
 the original one ; ' Not some are sinless, but all.' Some cannot 
 ordinarily in English be contradicted by not some, as all can be 
 by not all, but only by not any. In Greek, however, enclitic tis is 
 contradicted by ourts. oiJTives is a rare plural form. Latin has 
 the phrases nullus {ne ullus), nemo (ne homo), nonnullus, non 
 nemo. 
 
 § 143. We are here somewhat anticipating the application of 
 the metaphysical Law of Consistency to the structure of human 
 thought. But it is necessary to examine an objection to the 
 Principle of Contradiction which Bosanquet advances. ' Apart,' 
 he says, ' from the distinction of quantity, the difference between 
 the logical contrary and the logical contradictory disappears.' ' 
 ' The tax-collector is gone.' No, he is not gone (i. e. he is here). 
 Bosanquet calls it 'an inconvenient accident that the Law of 
 Contradiction applies to Contraries only, while logical Contra- 
 dictories come under Excluded Middle'." But why adopt an 
 unquantified formula ? What is denied when a quantified pro- 
 position is contradicted is the number of objects of which the 
 predication is asserted. Contradictory, here, cannot coincide 
 with contrary. ' Not all ' cannot be intended to mean ' none ', 
 nor nonnulli to mean omnes. On the other hand, when a judge- 
 ment with a singular subject is denied, the negation qualifies, 
 no doubt, the entire predication, so that to contradict ' The sauce- 
 pan is dead ' need not imply that the saucepan is alive ; and yet 
 usually the negation is considered as attached to the predicate 
 itself. ' This cheese is palatable.' No, it is not (= un-) palatable. 
 
 ^ Logic, i. 311. ^ Ibid. ii. 210. 
 
72 Reason regulates Thought 
 
 'James went.' No, he stayed. ' He sleeps.' No, he is awake. 
 'The letters of the alphabet are of European origin.' No, they 
 are of non-European origin. (But they might have come from 
 heaven.) 'The Scriptures are inspired.' No, they are uninspired. 
 Snakes inhabit Iceland. That is a mistake. They do not 
 inhabit Iceland. 
 
 § 144. Yet even in such propositions there is not necessarily 
 a coincidence between contrary and contradictory.^ To deny 
 that the water is hot is not to say that it is cold. To deny that 
 knowledge is power is not to say that it is weakness. To say 
 that logicians are not unanimous does not imply that they are 
 entirely at sixes and sevens. An egg which is not good may be 
 good in parts. The contradiction of 'John is a harmonious 
 blacksmith ' may certainly convey the idea that he is an unhar- 
 monious blacksmith. But logically it need not imply that he is 
 a blacksmith at all. He may be a dentist, or an infant, or play 
 in a German band. If it is untrue that Wellington was victorious 
 at Cannae, it does not follow that he was beaten there. 
 
 § 145. A singular judgement about a past event usually admits 
 of no degrees of predication. The countess rose from her chair. 
 The countess did not rise from her chair— that is, she sat still. 
 But in the present tense a singular or collective judgement has 
 usually some abstract character — 'The devil,' says Latimer, 'is 
 never out of his diocese ' — and may be regarded as quantified. 
 If it is asserted — ' Enough is not as good as a feast,' or 'Japan 
 
 1 Chrysippus' well-known catch, called Mentiens (for which see 
 Mansel's Aldrich, App. § 6), about the Cretans being always liars, derives 
 half its force from the confusion of contrary and contradictory. Epi- 
 menides, who said this, is a Cretan, and is himself therefore a liar. If 
 what he says, then, is true, it is untrue ; and accordingly Cretans are not 
 always liars. It is only by stating this contradictory as a contrary, 
 ' are always veracious,' that the rest of the dilemma has any point. If 
 the Cretans are always veracious, Epimenides, being a Cretan, speaks 
 truly, and Cretans are always liars, and in that case, Epimenides is a liar. 
 And so on, ad infinitum. The simplest but ' most insoluble ' form of the 
 puzzle is this; «I say truly that what I am now saying is untrue.' ' Si te 
 mentiri dicis, idque verum dicis, mentiris an verum dicis ? ' (Cic. Acad. 
 Pr. § 95 ; cf. Aul. Gell. N. A. xviii. 2, § 10.) But where, now, does 
 Excluded Middle come in? The answer is that the statement is not 
 merely formally self-contradictory, but formally impossible, except as 
 a collocation of words. ' My present words are untrue ' simply sublates 
 predication. It can neither be affirmed nor denied ; for there is nothing to 
 affirm or deny. 
 
Principle of Contradiction 73 
 
 is not the England of the East,' or ' Westward the course of 
 Empire does not take its way,' or 'Silence does not give consent,' 
 what is meant to be contradicted is the too general and unquali- 
 fied character of the statement denied. The proposition, ' If it 
 is about to rain the glass falls,' is contradicted by ' Not always,' 
 ' not necessarily.' The logical contrary would be, ' It never 
 falls.' Material contrariety would be the assertion that under 
 such circumstances the glass rises. Observe that the English 
 verdict 'not guilty' means, not proved to be guilty; but the same 
 verdict in Scotland signifies, proved to be not guilty, the Scots 
 having a third verdict, ' not proven.' 
 
 § 146. Logic can take no cognizance of material contrariety — 
 black and white, up and down, thick and thin, rich and poor, and 
 the like — unless the contrariety is given formally. It is true 
 that under the Law of Relativity we cannot be conscious of any- 
 thing except by a mental transition. We get the idea of heat by 
 passing out of cold, of light by transition from darkness, of light- 
 ness or softness by first (even if without conscious attention to the 
 experience) experiencing weight or hardness. But the distinction 
 between positive and negative states is psychological rather than 
 logical. 
 
 § 147. It should be observed that while the universal negative 
 ' No men are happy ' is upset by a single instance, ' Caius is 
 happy,' and the latter proposition is upset by the former, this 
 eversion requires formally the additional statement, ' Caius is a 
 man.' Obviously the contradictory of ' Caius is happy ' is not, 
 ' No men are happy,' but ' Caius is not happy '. And this again 
 need not mean that he is unhappy. 
 
 § 148. There must always be some ambiguity about unquanti- 
 fied propositions. ' I ought to go ' and ' I ought not to go ' are 
 in truth contraries. The former is really contradicted by ' I am 
 not bound to go', and the latter by 'I am not bound not to go'. 
 These are the four types. A, E, I, arid O. 
 
 § 149. Talleyrand, being asked if the report of George Ill's 
 death were true, replied :— ' Some say so. Others deny it. For 
 myself, I believe neither. But this is, of course, in confidence.' 
 
 Which brings us to the consideration of the Principle of 
 Excluded Middle. 
 
74 Reason regulates Thought 
 
 The Principle of Excluded Middle, or Third. 
 
 § 150. This is the Law of disjunctive reciprocity.^ It says 
 that two contradictory propositions cannot both be denied, 
 as the Principle of Contradiction says that they cannot both be 
 affirmed. 
 
 § 151. What has been said above about confusion between 
 contradictory and contrary opposition will guard us from the 
 crudity of charting everything and everybody ' in coarse blacks 
 and whites ', going about the world, as it were, with a piece of 
 chalk in one hand and a piece of coal in the other.'* An argu- 
 ment is often directed against disciplinary rules that they do harm 
 to the bad and are not needed by the good. But of the persons 
 affected by such regulations the great majority can neither be 
 called good nor bad, and it is these for whose benefit rules are 
 made. 
 
 § 152. There may in practice be no choice save in one extreme 
 or the other. 'Aut amat aut odit mulier ; nil tertium.' A man 
 sometimes stands betwixt the devil and the deep sea. But of 
 contraries both may be untrue without denial of the existence of 
 the subject or of the 'universe of discourse ' (see § 158) — which 
 is denied when contradictories are both apparently stated as 
 untrue. ' Nee possum vivere tecum, nee sine te ' implies that I 
 cannot live at all. Caesar says of the Gauls: — 'neque tyrannum 
 nee libertatem pati possunt.' That is, they cannot put up with 
 
 ^ Jevons calls it the Law of Duality, and states it mathematically in the 
 form, A = A(B + 6). Dichotomizing further, we get, 
 
 A =A{B + b) {C+c) =ABC + ABc + AbC+Abc. And so on. 
 
 '^ Newman, not without reason, ridiculed the ' moderate man ' who can 
 ' set down half a dozen general propositions which escape from destroying 
 one another only by being diluted into truisms. . . . This is your safe man 
 and the hope of the Church,' guiding it between the Scylla and Charybdis 
 of aye and no. Still, there_ is a proportion (avdXoyia) of the faith. The 
 successive Church Councils have been likened to a smith hammering first 
 on one side, then on the other, of the hot iron, not so as to produce a 
 negative and neutral result, but so as to shape a well-balanced sword of 
 the Spirit. In life and practice 'he that is not with Me is against Me'. 
 But in speculative thought there is a danger lest one too emphatic doctrine 
 should exclude others, no less vital. For scientific fullness Christianity 
 needs, not a mere ' live and let live ' of unrelated and fragmentary ' views ', 
 but a unifying and subordinating of partial and sectional aspects of truth 
 in the Fides Catholica. 
 
Excluded Middle 75 
 
 any form of government whatsoever. So Wellington declared 
 that his army was a rabble which could bear neither success nor 
 failure. 
 
 § 153. Bosanquet writes: — 'According to the traditional rule 
 a statement may be so denied that both judgement and denial are 
 false.' ' This is inexact. A judgement and its contrary may both 
 be false ; but a contrary is denial and much more. Now it is the 
 ' much more ' which is untrue, not the denial. 
 
 § 154. This principium exclusi medii, aut tertii, inter contradi- 
 dona, which Bain considers to be ' too much honoured by the 
 dignity of a primary law of thought ', has been exhibited above as 
 only the other side of the principium contradictionis. Yet it is 
 much more obvious that a given predicate cannot be botli affirmed 
 and denied of a subject than that it must be either affirmed or 
 denied. Is it the case that every possible judgement must be 
 either true or false ? Aristotle says explicitly : — /jLera^v di/Ttc/xio-eaJs 
 evSi^erai etvai ovOiv, aX\ avdyKi) -q fjidvai rj wiroffidvai tv Ka& evos briovv.^ 
 
 § 155. No subject stands out of relation to any predicate, but 
 must stand in one of two mutually destructive relations to it. 
 Everything must be affirmed or denied of everything.' ' Every 
 real,' says Bradley, ' has a character which determines it with 
 reference to every possible predicate.' * 
 
 § 156. Mill, however, with many other writers, maintains that 
 this Principle is only true with a large qualification. We can 
 only say that every assertion must be true or untrue where ' the 
 predicate is one which can in any intelligible sense be attributed 
 to the subject . . . ^' Abracadabra is a second intention " is neither 
 true nor false. Between the true and the false there is a third 
 possibility, the Unmeaning.' ^ Bosanquet also seems to hanker 
 after the forbidden mingling of formal and material, and to argue 
 that two contradictories may both be false, if non-significant. 
 But this is really the question already discussed of the coinci- 
 dence of contradictory and contrary. A friend is either faithful 
 or unfaithful; but an attitude or a stick of chocolate need not be. 
 
 ' Logic, i. 209. 
 
 ^ Met. iii. 7 ; of. An. Post. i. 11. 
 
 ' ' Oportet de omni re aut afiSrmare aut negate ' (Goclenius). 
 * Principles of Logic, p. 143. 
 
 ° Logic, i. 321. Mill cannot mean ' is a noun of the second intention ' 
 (supfositio maierialis), which would not be a meaningless proposition. 
 
76 Reason regulates Thought 
 
 A line which obeys a regular law if it is not straight is curved ; 
 but this is not true of digestion or philanthropy. Two straight 
 lines either meet or are parallel, but not two lumps of sugar.^ 
 All, however, that our Principle says is that if it is not true that 
 digestion is a straight line, &c., it is untrue, and if it is not untrue 
 it is true. 
 
 § 157. Veitch, in the same way, contends that much miscon- 
 ception has arisen regarding the law of Excluded Middle, from 
 supposing that it warrants ' a universal comparison of any 
 possible subject-notion with any possible predicate-notion, and 
 that the predicate must either inhere or not inhere in the 
 subject.' ' This,' he says, ' is irrelevant and puerile. In accor- 
 dance with the essential nature of logical law it supposes a 
 definite subject with its definite sphere of at least possible 
 predication.' He defends Hamilton from the charge of 
 advancing this puerility, and meets Hegel's objection to the 
 Principle that it does not distinguish between partial and total 
 negation, requiring us to say, e. g., that Spirit is either green or 
 not green, by the remark that 'the Law does not prescribe 
 playing with predicates, but assumes that people are reasonable 
 beings and in earnest in their inquiry 'J^ 
 
 § 158. La raison est pour les raisonnables. But what has the 
 logician to do with play or earnest, or with anything but the 
 actual value of a proposition as a proposition ? And what can 
 he know about ' definite spheres of possible predication ' ? He 
 is something else than a logician if he goes outside the formal 
 connexions of the data supplied to him. No doubt, if it is 
 understood that a particular system of things — what De Morgan, 
 Boole, Bain * and others call a universe of discourse — is being 
 
 ^ ' The postulate in question is an absolute affirmative between two or 
 more positive and significant members' (Bosanquet, Logic, ii. 21 1). 
 Again : — ' How can a universal prescribe a relation between itself and 
 a content which falls wholly outside it and is absolutely disparate and 
 alien to its nature ? Where there is absolutely no connexion, it is impos- 
 sible for denial to be intelligible' (Ibid. ii. no). But he rightly rejects 
 the ' negatively infinite ' judgement, as though not-hotness, the quality of 
 not being hot, apart front any question of temperature, were in itself a 
 predicable attribute (predicable, e. g. of monthly wages or the peerage 
 or troy weight). ' Significant negation is intelligible within, and with 
 reference to, a system judged to be actual ' (i. 306). 
 
 ^ Institutes of Logic, pp. 124, 125. 
 
 ' Logic, Pt. I, p. 195. 
 
Excluded Middle 77 
 
 spoken of, in that case a negative term acquires a positive 
 significance.^ Thus, if nationality be in question, non-English 
 must mean foreign. A driver who is said not to be sober must 
 be to some extent tipsy. A day which is not bright must be 
 more or less dark. A paint which is not of one colour must be 
 of another. A story which is not credible is incredible. A feat 
 which is not possible is impossible. A watch which was once 
 started and is not going must have stopped. A door which is 
 not open at all must be shut. Bain, however, speaks as though 
 such implication were independent of the particular area of 
 discussion, and asserts that ' the negative of a real quality is as 
 much real as the positive,' — instancing north and south, hot, 
 cold and tepid. Handwriting cannot be said to be either hot, 
 cold or tepid. Therefore the Principle of Excluded Middle is 
 at fault. Bain is clearly wrong. Most statements have an 
 understood, or given sphere. If promotion cometh neither 
 from the east, nor from the west, nor yet from the south, it 
 must (as the eighteenth-century placeman suggested) come from 
 the (sc. Lord) North. ' If it comes from anywhere,' subaudito. 
 Against the Puritan contention that no practice of a Church 
 in error ought to be followed, and that Greeks and Latins 
 were both in error, Hooker pointed out that in the Eucharist 
 the Greeks use leavened, and the Latins unleavened, bread. 
 Now bread must be either leavened or unleavened. Had the 
 Puritans rejected the 'breaking of bread'. Hooker's argument 
 would have been pointless. 
 
 § 159. After all, we can never tell what propositions, as lacking 
 a universe of discourse, are meaningless. ' The Torrid Zone is 
 not a fellow of a college ' sounds nonsensical enough. Yet 
 Caligula's horse nearly became consul, and some pocket- 
 boroughs, it has been said, would have returned their owner's 
 riding-whip to Parliament, if so bidden. 'Tithonus is not 
 mortal.' Is he then immortal ? But Tithonus may be a hill or 
 a diamond. And the practical identification, where the universe 
 
 ^ We cannot, however, say that a non-voluntary action is involuntary if 
 we accept Aristotle's distinction between ohx «<»»' and aKav {Eth. N. iii. i, 
 § 13, and mob 1 8). Similarly a non-rational act is not necessarily irra- 
 tional, nor a non-moral act immoral. Is peace merely not-war? But 
 Spinoza says : — ' Peace is not the mere absence of war, but a virtue which 
 springs ab animi fortitudine ' ( Tract. Pol. v. 4). 
 
78 Reason regulates Thought 
 
 of discourse exists, between contradictory and contrary, is always 
 liable to some error. A town in this island which is not in 
 England might be confidently affirmed to be in Scotland if one 
 knew nothing about Berwick-upon-Tweed. 
 
 § i6o. There can be no possible exception taken to the 
 Principle of Excluded Middle if it be observed that it can be 
 worded so as to be actually tautological. ' Either ... or' signi- 
 fies, ' if not the one, then the other.' We thus lay down that if 
 a proposition be not true (even though it be just not true) it is 
 untrue, and if it be not untrue it is true. Or, if the words ' true ', 
 'untrue', 'false' are thought to suggest that the proposition has 
 an intelligible meaning, it might be better to say,.' If it is not the 
 case that Abracadabra is a second intention, it is not the case.' 
 Or, ' If a five-act tragedy is not otherwise than tedious, it is 
 tedious.' Or, ' If yellowness be not predicable of patriotism, it 
 must not be predicated of it.' 
 
 § i6i. The force of the Principle is, however, clearer when 
 quantified propositions are opposed. If it is not true that 
 all X's are Y, it must be true that at least some X's are not 
 Y ; and vice versa. And if is not true that no X's are Y, 
 it must be true that at least some X's are Y; and vice 
 versa. 
 
 § 162. The Principle of Contradiction is confronted with a 
 metaphysical problem, that of Change or Becoming, which, it is 
 contended, involves a union of being and not-being in the same 
 object at the same moment. 'At the same moment,' however, 
 begs the question. It is, no doubt, difficult to analyse the idea 
 of becoming, but that is because it is difficult to analyse the idea 
 of the efflux of time. When now can be shown to be simul- 
 taneous with/ws^ now, we shall be ready to agree that quod nunc 
 est is identical with quodfuit modo. 
 
 § 163. Excluded Middle also has a metaphysical difficulty to 
 meet, in the case of propositions such as those relating to 
 Space, Time, or Free Will, which we can neither conceive to be 
 true nor yet untrue. Space is bounded. Space is unbounded. 
 Time had a beginning. Time had no beginning. The will is 
 free. The will is not free. But conceivability is not a test of 
 possibility ; and in these matters the mind is so wholly out of 
 its depth that we are not called upon to say which of the two 
 contradictories, both inconceivable, is true and which false. But 
 
Excluded Middle 79 
 
 one or the other must be false.^ Here again the Reason is not 
 the Understanding. 
 
 § 164. The ' Fallacy of Many Questions' would not embarrass 
 any one if it were remembered that in every proposition there 
 can be only one logical predication, and that it is this, and 
 nothing else in the proposition, which has to be admitted or 
 denied.^ In the time-honoured example, 'Have you ceased 
 beating your father ? ' ceased is the real predicate, and he who 
 has not begun can truly say that he has not left off. Any 
 sophistical inference drawn from my 'No' would be at once 
 disallowed by a dialectical referee. Asked, ' Does this diamond 
 sparkle ? ' I may answer ' Yes ', without being taken to admit 
 that the object pointed to is a diamond. ' This diamond ' means 
 'this thing which I, or you, call a diamond'. Indeed, all 
 demonstrative pronouns, and the definite article too, are 
 question-begging. ' Our able chairman remarked ' — ' This 
 eligible mansion is to let' — 'The turtle soup is ready' — here 
 able, eligible and turtle are negligible assumptions. The same 
 is the case with merely epithetical additions — 'Good Queen 
 Bess,' 'perfide Albion,' 'rural Hampstead,' 'glorious liberty.' 
 
 § 165. ' Other ' is with us a question-begging word — ' he and 
 other criminals.' 'He and the other criminals' begs two 
 questions. But the Greeks spoke of ' horses and other cows '. 
 Again, if asked, ' Is your objection merely one of sentiment ? ' 
 I may reply ' Yes ' or ' No ' without admitting the innuendo 
 conveyed by 'merely'. 'Only', said in a particular tone, 
 suggests a like disparagement. Interrogations beginning Why? 
 assume the fact for which an explanation is demanded. ' Why,' 
 a Scotsman was asked, ' do your countrymen always reply to a 
 question by asking one ? ' ' Do they ? ' he returned. Other 
 interrogative particles likewise. ' Where is the stolen money ? ' 
 ' Which overcoat shall you wear ? ' ' When did he die ? ' 
 
 * It should be remembered that to deny commencement to Time or 
 a limit to Space is not necessarily to affirm the eternal pre-continuance of 
 the one or the infinite extension of the other. In the Kantian view Time 
 and Space are subjective. 
 
 ^ It may happen that the negations of a protesting attitude of thought 
 will be true as denials, and yet the system in which a breach has been 
 thus effected be nearer to the truth than the negative and merely pro- 
 testant scheme which sets up a rival claim to it. 
 
8o Reason regulates Thought 
 
 ' How long were you away ? ' 'Whither will you run?' Dis- 
 junctive questions, again, seem to imply that one of the alter- 
 natives must be true, as, ' Did you get tipsy on port or on 
 claret?' The predication Hes in every sentence where the 
 stress falls— so that false stress is the converse fallacy to the 
 fallacia plurium interrogationum — , and in such a disjunction 
 there is a double stress, e. g. ' Which did sin, this man or his 
 parents, that he was born blind ? ' 
 
 § i66. The conjunction ' and ' often lays a trap. ' Is she 
 young and thoughtless ? ' ' Will you be charitable and lend me 
 another twenty pounds ? ' But the same fallacy of assumption 
 takes many interrogative shapes. 'Are you so base as to ask 
 me to repay that small loan ? ' 'Do you wish me to act as 
 wrongly as you did ? ' ' Am I to fall in with such a whim ? ' 
 And so forth.' 
 
 § 167. The doctrine that every question admits of a categorical 
 answer, and that every proposition can, and must, be rationally 
 affirmed or denied, will be found, when Modal Propositions are 
 discussed, to preclude any modification of the so-called Copula. 
 
 § 168. From the axioms of Excluded Middle and Contra- 
 diction proceed respectively the force of the Dilemma and its 
 danger to its propounder. If an opponent is bound to accept 
 one of two alternatives, the consequences of which are alike dis- 
 agreeable to him, he may retort that, as mutually contradictory, 
 they cannot both be true, and that the horn of the dilemma on 
 which he is not transfixed pierces the proponent of it, who has 
 thrown away the advantageous consequence to be inferred from 
 the one alternative or the other. \i A is B, C is D ; and HA 
 is not B, C is D. Therefore either way C is D. Yes, he 
 rejoins, but you cannot have it both ways. One line of argu- 
 ment or the other is closed to you. A fuller form of the 
 Dilemma is this : l[ A is B, C is D ; and if ^ is not B, E is F, 
 both consequences being distasteful to me. But I retort : A 
 cannot both be and not be B. If the former is false, C is not 
 
 ' The difficulty of asking any question which does not either involve 
 a disputable assumption, or else another interrogatory inside the first, is 
 shown by the confused issues which almost invariably arise out of a demo- 
 cratic referendum, even when, as in Switzerland, most carefully drawn. 
 The result of a recent educational referendum in Australia was claimed by 
 both sides as a victory. 
 
Excluded Middle 8i 
 
 (shown to be) D, and if the latter, E is not (shown to be) F. 
 Such a rebutter is, as the words in brackets indicate, weak 
 formally, but in practice may be very damaging. In the famous 
 fresco in the Spanish Chapel in the cloister of Santa Maria 
 Novella at Florence ' Logic ' holds a scorpion with a double 
 sting, signifying dilemmatic argument. 
 
 § 169. The complaint, 'li A is B, you say that C is D; and 
 if A is not B, you still say that C is D' is formally illogical, for 
 an effect may have several causes. But when there is a close 
 connexion between consequent and antecedent, there may be 
 force in it. The following are all in the same form, but not 
 equally forcible as objections : — 
 
 (1) If I die you say the sun will rise to-morrow, and if I do 
 not die you still say it will rise. 
 
 (2) If I confess I am to be punished, and if I do not confess 
 I am to be punished. 
 
 (3) Mihi, errato, nulla venia, recte facto, exigua laus (Cic. de 
 Leg. Agr, ii. 2). 
 
 In the following, again, the paradox depends on the 
 material connexion between learning the truth and distress 
 of mind. Cicero says: — 'O miserum te si intellegis, miserio- 
 rem si non intellegis.' One would have expected that only by 
 hearing the truth would pain arise ; in other words, that in this 
 case consequent and antecedent might be presumed convertible.' 
 § 170. Horace's line, ' Sume, catelle ; negat. Si non des, 
 optet,' is of the form — ' If A isB,C is not D; and if ^ is not B, 
 C is D.' At first sight there is nothing to criticize in the alter- 
 native consequences. ' If rain falls, I do not leave my umbrella 
 at home ; if it does not fall, I do.' But the umbrella is taken at 
 one time and left behind at another. Whereas in, ' Say, Take 
 it ; he won't. Do not offer it, and he will long for it,' the point 
 is that at (practically) the same moment he pretends to want and 
 not to want it. For further discussion of Dilemmatic Reasoning, 
 see below, §§ 966 seq. 
 
 ' So in I Henry IV, i. 2 :— 
 
 Poins. Jack, how agrees the devil and thee about thy soul that thou 
 Boldest him on Good Friday last for a cup of Madeira and a cold capon's leg ? 
 
 Prince. Sir John stands to his word ; the devil shall have his bargain. 
 For he was never yet a breaker of proverbs ; he will give the devil his due. 
 
 Poins. Then art thou damned for keeping thy word with the devil. 
 
 Prince. Else had he been damned for cozening the devil. 
 
 G 
 
CHAPTER VI 
 THE AXIOM OF PERSISTENCY 
 
 § 171. The two-sided Axiom of Consistency, or Doctrine of 
 Contradictories, as above set forth, is negative and regulative. 
 It prohibits the uniting of formally incompatible attributes, either 
 ideally in the Concept or assertively in the Judgement. On the 
 side of Excluded Middle it takes, it is true, an affirmative form, 
 compelling us to judge, if a thing is not somewhat, that it is its 
 contradictory. 
 
 § 172. But this would not, in itself, have given us Inference 
 through a Middle Term. No doubt, if a conclusion which is 
 inconsistent with its premisses is attempted to be drawn, or a 
 conclusion which ought to be drawn from given premisses is 
 denied, the Axiom of Consistency can disprove the one and 
 prove the other by a reductio ad absurdum. That any or all of 
 the S portion of the M'& should not be P when every M is P 
 is impossible. But to argue thus the constructive principle of 
 the syllogism has to be assumed. Syllogistic law has been 
 established by employing the syllogistic process. 
 
 § 173- Again, it may seem that, a wrong conclusion being shown 
 to contradict the premisses, its contradictory, the right conclu- 
 sion, is then reconstitutively established by the Principle of 
 Excluded Middle. But this is not so when the disallowed con- 
 clusion more than contradicts the premisses. Thus, Every X is 
 y, every F is Z ; therefore no X is Z. We cannot by showing 
 this to be a wrong conclusion get the right one, Every X is Z. 
 Further, the Law of Consistency is powerless to expose a mere 
 non-sequitur. ^ is Y, F is Z; therefore Q is R. ' No wonder,' 
 said the traveller, 'this place is called Stony Stratford. I was 
 never so bitten by fleas in my life.' Or, X is Y, Z is Y, there- 
 fore Z is X. Or, Jf is V; Z is not X, therefore Z is not 'Y. 
 Here are three conclusions from the fact that fishes live in the 
 water, (i) false, (2) and (3) true, but all non-sequiturs :— 
 
 (i) Whales live in the water. Therefore whales are fishes. 
 
Identity 83 
 
 (2) Herrings live in the water. Therefore herrings are fishes. 
 
 (3) Cats are not fishes. Therefore cats do not live in the 
 water. 
 
 § 174. We seem, therefore, to need a complementary Axiom, 
 not merely a conditioning of thought by the exclusion of incon- 
 sistency, but a positive, constitutive, directive, and actively com- 
 pulsive Principle of rational consequence. 
 
 § 175. The Principle of Identity has been generally regarded 
 as only another way of stating the Principle of Contradiction. 
 If a statement is true it is true, and if it is true it is not untrue. 
 As a judgement which is contradictory must be denied, so a 
 judgement which is identical must be affirmed. Accordingly 
 the Principle of Identity — though Mill calls it 'our ancient 
 friend ' — was ignored by all philosophers till Andreas, who died 
 in 1320. 
 
 § 176. Identity, however, is no mere repetition of the subject in 
 the predicate. It asserts the perdurance of the one in the many, of 
 form in matter, of the abstract in the concrete, of the rule through- 
 out its applications, and of the principle in every manifestation 
 of it. I venture to call this complementary axiom the Axiom of 
 Persistency, 
 
 § 177. Hamilton's statement of the Principle of Identity as 'A 
 is A' or 'A = A' ('everything is equal to itself) ^ has been not 
 unfairly termed a lifeless branch, an unfruitful truism based on 
 a false theory of conception.'' If ' everything is itself* means 
 that a thing is identical with its own nature or attributes, judge- 
 ment becomesamere equivalence, if it is even that. 'The Concept,' 
 Hamilton explains, 'is equal to all its characters.' Z=^{a + b+c}. 
 But conceptual reasoning is not, 'A=A,A=A, therefore A = 
 A.' Nor is it even 'A=B=C, therefore A = C'. But it is, ' A 
 is a B, every .S is a C; therefore A is a C — though this is not 
 the only way of expressing the formula. And, as against the 
 Hamiltonian view of predication, it will be contended here that, 
 
 ^ Lectures on Logic, i. 80. 
 
 * ' All judgements to be absolute,' says Lewes, ' must be identical ' 
 {Hist, of Phil. ii. 463). But he uses ' identical ' or ' equivalent ' for 
 primary judgements of sensations and for necessities of thought (see i. 
 p. Ixii). On the other hand he writes : — ' No propositions are true unless 
 identical ' (ii. 541) — that is, I suppose, unless reducible ultimately to an 
 immediate perception and an axiomatic principle, or the former alone. 
 But a mere consciousness of sensation is not yet a judgement. 
 
 G 2 
 
84 The Axiom of Persistency 
 
 except where the major premiss is an analytical judgement, the 
 content or meaning of a Concept, its equivalence to the sum of 
 its essential and constitutive characters, does not enter into 
 reasoning. If I say, 'This plate is valuable (or breakable) because 
 it is a piece of old Nankeen,' or ' This child must pay full fare 
 because he is over twelve *, I am not arguing from the meaning 
 of concepts but from circumstances which I or others happen to 
 know about things. 
 
 § 178. The 'omne subiectum est praedicatum sui' of Aquinas, 
 or the saying, ' Nothing can be predicated except of itself,' attri- 
 buted first to Euclid of Megara, does not express the import of 
 the proposition. Unless we can find more in the predicate than 
 in the subject, ' Abracadabra is Abracadabra ' is not a judgement, 
 and really asserts nothing. Even the claim to be allowed to 
 repeat the same thing in a different form of words, though Mill 
 declares that the Principle of Identity is thus made to ' mean 
 much more than it ever meant before '^ cannot rank as a logical 
 postulate, since it must first be stated that the two sets of words 
 are equivalent, and this knowledge is given materially, not 
 formally. 
 
 § 179. Assertion is an ideal synthesis, a real amplification of 
 the subject by the predicate ; and identity which excludes differ- 
 ence is tautology without a meaning." Such a theory of Thought, 
 resting on atomism, on a metaphysical egalitarianism, destroys 
 Thought. Seeing this, Bosanquet states the Principle in the 
 form, not A=A, but A is AB. A tailor is a tailor kind of 
 man. I prefer the formula, BA '\?, A. A does not cease to be 
 A when conditioned by, and manifested as, B. A journeymah 
 tailor is a tailor. A suffragan bishop does not the less exercise 
 the episcopal office because he is a suffragan. A Cambridge 
 undergraduate has not yet taken his degree, because no under- 
 graduate has. A does not cease to be what it is, to have its 
 proper attributes, when it is this, that or the other kind, or 
 example, oi A. Thus we get the Syllogism. \i A is (a + 6-f c), 
 BA is(a-f 6-l-c). Ofthe jB sort of^'s we must predicate whatever 
 we predicate of A generally. If ill weeds grow apace, it does 
 not matter what variety they are of— nettles, docks, buttercups. 
 They all grow apace. 
 
 ' On Hamilton, p. 481. 
 
 * See Bradley, p. 131, and Bosanquet, i. 357 and ii. 207. 
 
Identity 85 
 
 § 180. Bosanquet observes : — 'We can only assign a meaning to 
 the law 'M is ^ " if we take the repeated ^not to be a specifica- 
 tion of the identical content, but an abstract symbol of its identity. 
 The law will then mean that in spite of the differences expressed 
 in a judgement, the content of judgement is a real identity, that 
 is to say, has a pervading unity. It says that there is such 
 a thing as identity in difference, or, in other words, there is such 
 a thing as genuine afBrmation. . . . The Law of Contradiction 
 simply confirms and reiterates that assumption of the unity of 
 reality which the Law of Identity involved. You cannot play 
 fast and loose with Reality. What is true at all is true through- 
 out Reality.' ' 
 
 § 181. The element of continuity which persists through differ- 
 ences supplies that stability of ideal content which guarantees 
 the connexions of thought and enables us to reason about things. 
 Difference is essential to a real judgement — even if it be an identi- 
 fication " or definition. Though thought of in various connexions 
 and at various times, that of which we think is throughout what it 
 is ; for reality or truth, correlated as it is to the unvarying self-con- 
 sciousness of the judging Ego, is out of relation to spatial and 
 temporal conditions. 
 
 § 182. No doubt, inference through identification of singulars 
 or of aggregates is the same logical process as inference through 
 a concept or universal. ' The person buried to-day was the Lord 
 Chancellor. Lord X is the Chancellor. Then it was he who 
 was buried.' Syllogisms in the Third Figure (see below) with 
 a singular middle term are common. ' This glass is broken. 
 This glass cost five shillings. Then something costing five 
 
 shillings is broken.' 'Mr. is dead. Mr. was a good man. 
 
 A good man, then, is dead.' But even in an algebraic equation 
 there is an ampliation of judgement ; and '(a + 6)' = (a-\-b){a->fb) 
 = a'^+2ab + b'^; therefore {a +bf = a^ + zab + 6^' is an infer- 
 ence which is really mediated through a universal element. 
 
 § 183. Verbally identical propositions, such as 'Les affaires 
 . sont les affaires,' or Caesar's, ' Death will come when it will come,' 
 have been^shown above to be, if serious, real judgements, con- 
 taining an extension of idea. If they are not, they are merely 
 
 ' Logic, ii. 208, 210. 
 
 * 'What's yonder floats on the rueful, rueful flude? 
 
 What 's yonder floats ? O dule and sorrow ! 
 'Tis he, the comely swain I slew 
 
 Upon the duleful Braes of Yarrow ! ' 
 
86 The Axiom of Persistency 
 
 nonsensical and on a par with those of the Clown in Twelfth 
 Night : — ' As the old hermit of Prague, that never saw pen and 
 ink, very wittily said to a niece of King Gorboduc, That that is, 
 is ; so I, being Master parson, am Master parson. For what is 
 that but that, and is but «s ? " 
 
 § 184. Identity implies abstraction. The pure Concrete, the 
 unrelated sensation, cannot be conceived, known or named. 
 Even the rdSe tl persists through differences. ' Whatever exists 
 in time at all has some permanence, and whatever has perman- 
 ence at all has existence in time. And since time is infinitely 
 divisible, what exists in time is necessarily an identity in diversity, 
 namely, of change (succession) in time. One cannot conceive 
 anything which does not to some extent perdure, and thus exist 
 as a unity in diversity.' ^ 
 
 § 185. ' The term Identity cannot be applied to an idea which 
 is quite simple and occurs only once. I cannot even recognize 
 the identity of something which remains absolutely the same, 
 unless I am aware that I have thought of it at diiferent times and 
 compare the recurring ideas. . . . [Logical] identity is either com- 
 plete or not at all. It has no degrees.' ' ' Carlo barked just now.' 
 But barking is a familiar concept in my mind ; and the name 
 Carlo suggests to it a number of images and memories — the long- 
 haired creature ; the children's pet ; the prize dog ; the animal 
 that lies before the fire ; my companion in yesterday's walk. So 
 again, 'The games are done and Caesar is returning.' Every 
 subject has successive moments in the memory or in significance, 
 if not in time or space. We shall see later how difficult it is to 
 distinguish concrete from abstract propositions. No doubt, a 
 name or a presentation to consciousness conveys much more to 
 one mind than to another. To one observer a primrose by the 
 river's brim is a yellow primrose and nothing more ; to another 
 it is a chalice of sweet thoughts. But its necessary self-identity 
 as permanently supporting its own attributes, whether known 
 or unknown, is the same to both. 
 
 ^ Compare Moses' cheerful admission to Squire Thornhill that ' what- 
 ever is, is ', and invitation to make the most of it. Another of Shake- 
 speare's clovifns cloaks in various phrases mere repetition in thought, in- 
 structing his fellow that ' an act hath three branches : it is to act, to do, 
 and to perform '. 
 
 ^ E. E. Constance Jones, Elements of Logic, p. 189. 
 
 ^ Sigwart, Logic, i. 84, 85. 
 
Identity 87 
 
 § 186. Truth means that a statement once made does not 
 straightway vanish elusively [^into air, but falls under laws and 
 submits to rational treatment. Whatever is implied in an 
 assertion is equally true with the original assertion. Whatever 
 is, is. This is seen not to be a sapless ingemination if we lay 
 stress on whatever and on the second is. Whatever is A is A. 
 Any object whatsoever which is included in the class A (which 
 bears the name A, has the attribute of ^-ness) possesses all the 
 attributes attributable to A. Whatever has a quality has every 
 quality that goes with that quality. 
 
 § 187. This basis of Syllogism is sometimes stated as though 
 all propositions were analytical. It is enunciated in some such 
 form as this, that everything which shares the common name A 
 is whatever is implied in being A ; or that all the attributes 
 which a name connotes are predicable of every object which that 
 name denotes ; or that the whole extension of a name possesses 
 the whole intension of that name. The 'intension ', ' connotation ', 
 ' implication ' of a name can only signify its meaning, the content 
 of the concept when analysed. But if we infer that a spaniel is 
 liable to a tax of seven and sixpence, because it is a dog and all 
 dogs are so liable, we do not suppose that bringing seven and 
 sixpence to the Exchequer is part of the analysis of the notion 
 of dog. English letters below 4 ozs. in weight go for a penny. 
 Therefore the letter I have written will do so. But the going 
 for a penny, while it is a circumstance known to me about letters 
 of a certain weight, is assuredly not what that expression 
 connotes or means. Whatever is the intension of a predicate 
 name is directly predicated by the judgement. 'John is a baker ' 
 tells me that John bakes. But any further circumstance that is 
 known about bakers, e. g. that they are bound by law to carry 
 scales, has to be conveyed in a further judgement, and can only 
 be predicated of John by help of a syllogism. 
 
 § 188, Sigwart seems to misapprehend the bearing of Identity 
 on inference when he says : — ' It is only when an attempt is 
 made to base the Syllogism entirely upon the so-called Principle 
 of Identity-^M)A«« therefore the premisses are purely analytical 
 propositions — that the syllogistic process seems to be without 
 value." The identity which runs through a syllogistic con- 
 struction has nothing to do with any analytical character the 
 
 ' Logic, i. 362. 
 
88 The Axiom of Persistency 
 
 premisses may possess. The force of the reasoning, as reason- 
 ing, would not be in the smallest degree strengthened by their 
 being analytical or identical. On the other hand it is not clear 
 why Sigwart says it would then be ' useless '. Take the 
 following double syllogism : — 
 
 Socrates is a philosopher ; 
 
 Philosopher means one who pursues wisdom for her own sake; 
 
 Pursuing anything for its own sake implies disinterestedness : 
 
 Therefore Socrates is disinterested. 
 The reasoning here is just as useful as if each premiss had 
 been a synthetic proposition, and we had been told that 
 philosophers marry unwisely, or do not pay their rent. 
 
 If A is B, A is all that B is,^ or means. In Aristotle's 
 
 words : — oa-a Kara. Tov KaTrjyopov/jLevov Xeyerai, iravTa /cat koto. toS 
 viroKeijxivov prjOTQiTeTaL.^ 
 
 § 189. The subject of a non-analytical proposition is primarily 
 regarded as in extension — it is the object or objects to which 
 the subject name applies that are spoken of — , the predicate as in 
 intension — it is the attributes implied by the predicate name 
 which are ascribed to the subject ; * e. g., ' Old shoes need 
 
 ^ A friendly critic writes : — ' Is it true that, if man is animal, man is all 
 that animal " is " ? Any triangle is either equilateral, isosceles, or scalene. 
 An equilateral triangle is a triangle. It follows that it is equilateral, iso- 
 sceles, or scalene.' But this is the disiunctio ambigui discussed below 
 under Disjunction. What is meant by ' any triangle ' ? The either . . . or 
 . . . or cannot mean that every actual triangle has an undetermined 
 character : no triangle can exist, actually or ideally, until its character 
 is determined. There is a subjective and problematic uncertainty in our 
 minds beforehand. But directly the minor term is given as equilateral, 
 the doubt disappears. Triangularity is objectively equilateral, isosceles, 
 or scalene. But triangularity is not the middle term. 
 
 ^ Cat. iii. I. 
 
 ' Intension (Comprehension, Connotation) is not all that a thing is, but 
 all that a name means. It is the attribute or attributes connoted by the 
 common designation ; or rather the name's relation to the attributes. 
 Strictly speaking the meaning of a name is that which marks it off and 
 differentiates it from other names, and is therefore the same thing as its 
 definition. Yet not all qualifications which are sufificient to define or 
 mark off ought to be regarded as the meaning of a name— e. g. 'A barrister 
 is a man who wears wig and gown ' ; ' A Jew is a Semitic who eats no 
 bacon.' Psychologically, intension precedes extension ; the adjective 
 (sensory perception) precedes the substantive— blue and cheerful come 
 not only before blueness or cheerfulness, but before blue or cheerful object. 
 Yet it was experience of this and that blue object which gave the sensation 
 
Identity 89 
 
 mending.' I am thinking of old shoes as a class of things and 
 the need of mending as a circumstance or quality to be 
 predicated of that class. Every significant term has necessarily 
 both aspects. ' Old shoes ' suggests certain characteristics, and 
 things that need mending form a class of objects. But the other 
 is the primary significance. (See below, §§ 644 seq.) 
 
 § 190. It follows that in the syllogism the middle term is 
 naturally regarded from the point of view of intension in the 
 minor premiss, where it is the predicate, and of extension in the 
 major premiss, where it is subject. (To avoid confusion we are 
 confining ourselves to the First Figure.) All.<4's are B, and all 
 jB's are C; therefore all .^'s are C. Because A's, as a matter of 
 fact, have all the B qualities (every quality connoted by the 
 name B), they have necessarily every quality or circumstance 
 belonging, as a matter of fact, to objects generally which have 
 the B qualities. In this case C-ness is such a quality or 
 circumstance. Therefore all A's are C. 
 
 § 191. But the predicates may be regarded from the point of 
 view of extension.' Then, all A's are part of the class B, and 
 
 of blueness. Once, however, the universal is named, every similar object 
 will be given that name ; and thus connotation precedes denotation ; for 
 the name's intension is known, but the class's possible extension is un- 
 known. The latter is conditioned by the former. See Sidgwick, Use of 
 Words, pp. 245 n., 248. 
 
 ' The simplest forms of statement are, for Extension — ' Class X (all or 
 some) is part of class Y, and class Y is part of class Z ; then class X 
 (all or some) is part o class Z.' And for Intension — 'Z-ness goes with 
 F-ness, and F-ness (always or sometimes) goes with X-ness ; then Z-ness 
 (always or sometimes) goes with A"-ness.' By A going with B it is not 
 meant to be implied that B necessarily goes with A. As, however, this 
 means that A can 'go' without B, whereas we had just said that it goes 
 with B, ' goes with ' had better, perhaps, be ' accompanies '. Less 
 ambiguously still — ' Where ^-ness is found K-ness is found, and where 
 F-ness is found .2'-ness is found; then,' &c. Or, '.^-ness carries with it 
 F-ness,' &c. 
 
 The simplest form of the Analytic Syllogism is this — ' .AT-ness implies 
 F-ness and F-ness implies Z-ness ; then ^i^-ness implies Z-ness.' Yet 
 the statement might be in extension ; e. g. 'A burglar is ipso facto a 
 criminal, and a criminal necessarily belongs to the dangerous class ; 
 therefore,' &c. 
 
 To express intensive inclusion, the ordinary Syllogism must be stated, 
 in full, thus—' The attribute connoted by the name Z is among the attri- 
 butes belonging to things which have the attribute connoted by the name 
 F; and those attributes are among the attributes belonging to things 
 which have the attribute connoted by the name X\ then,' &c. 
 
go The Axiom of Persistency 
 
 the class B (all 5's) is part of the class C. Therefore all ^'s are 
 in the C class. A part of a part is a part of the whole. This, the 
 dictum de omni et nullo, Hamilton speaks of as ' constituting the 
 one principle of all Deductive reasoning '> We shall see here- 
 after, however, that he has an illegitimate use for it, making 
 'All ^'s are B ' to mean that 5-ness is part of the notion of A. 
 
 § 193. Regarding subject and predicate as cause and effect, 
 the Rule has been stated (e. g., by Alanus of Clairvaulx) thus :— 
 Quicquid est causa causae est etiam causa causati. Water 
 quenches thirst. Whatever quenches thirst allays fever. 
 Therefore water allays fever. 
 
 § 193. To glance for a moment at the other great syllogistic 
 Figure, the Second, the subject and predicate of the conclusion 
 seem naturally to be regarded as classes. A'^ have a certain 
 characteristic, B, which C's have not. It follows that the classes 
 A and C are distinct. No ^ is a C, and no C is an ^. But the 
 mind's interest might be different. The attributes ^ -ness and 
 C-ness are never found united in the same subject. 
 
 § 194. The Principle under discussion, then, is the foundation 
 of the Syllogism, and is the reason, consequently, of that search 
 for middle terms, that endeavour to detect the abstract one in 
 the concrete many, that demand for a universal element, which 
 is called Induction. Why is 5 P? Because it is M, and M 
 is always P. 
 
 § 195. Mill asks what we learn ' by being told that whatever 
 can be affirmed of a class can be affirmed of every object con- 
 tained in the class. The class is the objects contained in it; and 
 the dictum de omni merely amounts to the identical proposition 
 that whatever is true of certain objects is true of each of those 
 objects. If all ratiocination were no more than the application 
 of this maxim to particular cases, the syllogism would indeed be, 
 what it has so often been declared to be, solemn trifling.' ^ 
 
 We no longer suppose, he urges, that a class or universal is 
 an entity per se, or anything more than a common name for the 
 individuals which compose it. But this is the baldest no- 
 minalism. Mill talks himself of applying a maxim to particular 
 cases. Was it known to be true of all the cases before becoming 
 a maxim? Salt is wholesome. Wine intoxicates. Soldiers 
 
 ' Lectures on Logic, i. 145. " Logic, i. 234. 
 
Identity gi 
 
 must obey. The two former propositions might be learned by 
 a chemical analysis. The third by considering what soldiers 
 are for. Mill cannot mean that before stating them we must have 
 made proof of every existing, or possibly existing, ounce of salt 
 or bottle of wine, or considered separately the individual duty 
 of every soldier enlisted or who might at any time throughout 
 all the ages enlist ! What can be more perverse, then, than to 
 maintain, in effect, that a generalization, law, rule, principle or 
 maxim does not need to be applied because ' the class is the 
 objects contained in it '. By a soldier hesitating about his duty 
 the general principle * It is the duty of soldiers to obey ' is 
 remembered usefully because it is a principle, and not a mere 
 recapitulation or summary of a number of individual cases of 
 duty, his own included. 'The Scripture bids us fast; the 
 Church says now! It would be indeed a feeble marking of 
 time if ' quicquid valet de omnibus valet etiam de singulis ' 
 meant that what is true of certain objects severally and 
 individually is true of each of those objects singly and one 
 by one. 
 
 § 196. To state the Principle of Identity in yet one more 
 light, it is this, that we necessarily think everything as abiding 
 as it was in its nature and circumstances until some, not change 
 but, cause of change, occur to modify it. It is not — 
 
 but- 
 
 Old Pillicock sate on a grassy hill ; 
 And if he 's not gone he sits there still. 
 
 In my faith and loyalty 
 
 I never more will falter ; 
 
 And George my lawful King shall be — 
 
 Until the times do alter. 
 
 So in the Winter's Tale — 
 
 Camilla. They that went on crutches ere he was born desire 
 yet their life to see him a man. 
 
 Archidamus. Would they else be content to die ? 
 
 Camillo. Yes, if there were no other excuse why they should 
 desire to live. 
 
 § 197. Nothing can alter, vary, or be different without a suffi- 
 cient reason. While the conditions of a thing remain what they 
 were, the thing will remain what it is. 'Truth,' observes 
 Bradley, 'does not depend upon change or chance. What is 
 
92 The Axiom of Persistency 
 
 true in one context is true in another. . . . Every judgement, if 
 it really be true, asserts some quality of that ultimate real which 
 is not altered by the flux of events.' ^ Achilles absent is Achilles 
 still. Pigmies are pigmies still, though perched on Alps. ' Simla 
 simia est, etiamsi aurea gestat insignia.' I recall a phrase in 
 the Holy Dying: 'A coffin is a coffin, though covered by a 
 pompous veil.' Rousseau taught that every human being pos- 
 sessed of reason possesses an inalienable sovereignty; but this 
 did not prevent the National Assembly from disfranchising 
 women. The logician, of course, does not deny that circum- 
 stances alter cases. All he postulates is the change of circum- 
 stance. Things are not all a casual and shifting fortuity. Truth 
 does not at once slip through our fingers. Xerxes acted on the 
 Principle of Identity when he counted his vast host by making it 
 pass through pens of ascertained size — though, to be sure, there 
 might be burly and lean nations in it. A bank cashier acts on 
 it when he pays out a required number of sovereigns by weight 
 rather than by tale. Rules have exceptions. Cowper says : — 
 ' A fool must now and then be right by chance.' But that is 
 only to say that the rule has been stated in too unqualified a way, 
 and without allowing for counteracting causes. The parallelo- 
 gram offerees in Mechanics may result in an equilibrium. Yet 
 the law of each force has had its full effect. Strychnine poisons 
 dogs ; yet on certain constitutions it acts as a tonic. In spite of 
 possible Yahoos we describe mankind as rational. We do not 
 hesitate to say that lions are savage because they have left deer 
 unmolested when seeking common shelter from some cataclysm, 
 or because in a millennial state they will couch with Iambs.'' 
 
 § 198. The comparatively simple case of intermixture of 
 physical effects may be studied in Mill's Logic, i. 518 seq. It 
 must be understood that a tendency does not mean a law which 
 sometimes operates and sometimes does not ; for all laws, so far 
 as they are laws, always operate. The word merely indicates 
 the liability to counteraction. Mathematical laws cannot be 
 counteracted. And the higher spiritual truths may be regarded 
 
 ^ Principles of Logic, pp. 133, 135. 
 
 '^ Certainly it is more difficult to understand 'exceptis excipiendis' 
 when a rule is stated in extension ; e.g. if, instead of saying, ' Man responds 
 (or men respond) to kindness,' we were to say 'AH men respond to 
 kindness '. 
 
Identity 93 
 
 as admitting no exceptions — e. g. ' Blessed are the meek.' On 
 the other hand, many statements of revelation are cast in a 
 designedly general form, without simultaneous -mention of other 
 and complementary truths. We are to compare spiritual things 
 with spiritual. 
 
 § 199. Identity, however, has nothing whatever to do with con- 
 tingent uniformities. It does not say that things will not depart 
 from their more or less fixed sequences — e. g. ' gentilhomme est 
 toujours gentilhomme ' — , but only that, apart from any reason 
 to suppose differently, a fact as given may be built upon infe- 
 rentially. The universe is not a flux. Truth exists. Reality 
 is self-consistent. Reasoning is possible. 
 
CHAPTER VII 
 SUFFICIENT REASON 
 
 § 200. The Principle of Identity, we have seen, afBrms that a 
 thing being thought generally as having certain characteristics 
 must be thought as having the same characteristics at various 
 times and in various circumstances, unless and until some cause 
 of change occurs. There is stability in things, else there is no 
 truth. 
 
 § 20I. Or, avoiding the metaphysical ideas of change and cause, 
 let us lay it down — though the thought may be a more difficult 
 one — that for every difference there must be a sufficient reason. 
 
 Thus regarded from the logical standpoint, the Principle of 
 Identity may be called a principle of Sufficient Reason. 
 
 § 202. As no phenomenon can come to exist — since coming 
 into existence implies modification of the previously existing 
 order of things — without a cause, so no statement can be made, 
 no advance can take place in our thought, without an adequate 
 ground. For by every new assertion or judgement our existing 
 knowledge is varied. A proposition must be in a sense fresh, or 
 it would not be made.' 
 
 § 203. As the metaphysical doctrine that every change must 
 have a cause has to be distinguished from the physical theory of 
 the Inertia of Matter — even if this may ultimately be resolved 
 into that — , so the impossibility of judging without a logical 
 ground must be distinguished from the psychological inability 
 of any judgement to be formed, or to find utterance, without 
 certain material conditions, such as a judging subject, the con- 
 stitution of the thinking faculty, data of experience, and some 
 occasion effectuating decision. 
 
 § 204. Objectively, no assertion can be justified apart from the 
 allegation of a ground. And, subjectively, there can be no con- 
 sciousness of validity in the synthesis between subject and 
 predicate apart from some element of universality in the factors 
 of the judgement. A judgement is always considered by him 
 
All Assertion is thought as necessary 95 
 
 who judges as necessarily formed.^ The apprehension of justi- 
 fication is essential to all our thinking. Even an actor's, or liar's, 
 words are propounded as unavoidable. ' Universality,' observes 
 Bosanquet, 'is a property of all judgement whatever. I not 
 only feel that my judgement is inevitable for me, but I never 
 think of doubting that, given the same materials, it is obligatory 
 for every other intelligent being. If some one disagrees with 
 a judgement of mine, I try to put the case before him as it is in 
 my mind ; and I am absolutely sure that, if I could do so, he would 
 be obliged to judge as I do. If it were not so, we should never 
 think of arguing.' ^ ' But,' says the same writer, ' necessity 
 involves mediation or inference. No isolated judgement, qua 
 isolated, can have necessity. Every necessary truth must, in so 
 far as it is necessary, present itself as the conclusion from an 
 antecedent.' ' In other words, every assertion is an interpreta- 
 tion. Hence the possibility of mistake.* But, while conscious 
 of fallibility, we enounce every judgement as necessarily formed. 
 The weather is bad. Badness must be predicated of the weather. 
 § 205. The rule ' infer nothing without a reason ' obviously 
 forbids a logical impossibility. But 'think nothing without 
 a reason ' is an equally jejune and superfluous counsel. It 
 should be, ' think nothing without putting the reasoning clearly 
 and plainly before your mind.' What makes us smile at a state- 
 ment is often the paradoxical character of the mediation, were it 
 explicitly enunciated ; either its absurdity, as in the old play — 
 ' I am sure they talked of me, for they laughed consumedly ' ; or 
 its audacity ; as in King Henry the Fourth — ' She 's a woman, 
 and therefore to be won ' ; or its simplicity, as when in Reade's 
 great historical romance, The Cloister and the Hearth, Gerard 
 out of gratitude offers to pen a letter for the serving-maid, 
 which she declines, saying, 'He is in the house'; or its un- 
 expected insinuation, as in the moral to the American inversion 
 
 ' ' Judgements are regarded as true only in so far as they are necessary ' 
 (Sigwart, Logic, i. 184). ' Every truth is necessary, although every pro- 
 position is not necessarily true ' (Lewes, Hist, of Phil. ii. 476). 
 
 ^ Essentials of Logic, p. 26. 
 
 ' Logic, ii. 324. 
 
 * 'AH error and strife are due in the last instance to a difference 
 between the psychological ground of certainty and the ground of truth, to 
 the possibility that momentary belief may err, and the temporary feeling 
 of certainty deceive us ' (Sigwart, Logic, i. 193). 
 
96 r Sufficient Reason 
 
 of the hare and tortoise fable — ' The race is not always to the 
 sl(yw ' ; or its bantering malice, as in Tancred — ' " Jerusalem ! 
 What on earth could they go to Jerusalem for?" said Lord 
 Carisbrooke. " I am told there is no sort of sport there." * 
 
 § 206. We are certain that; ' every why has a wherefore ', 
 whether a plain reason is forthcoming, like the footprint from 
 which Crusoe inferred human neighbourhood, or we have to say 
 with Lucetta — 
 
 I have no other but a woman's reason. 
 
 I think him so because I think him so. 
 Her judgement of Protheus rested on an intuition of taste. ' To 
 those who like that kind of thing,' said Abraham Lincoln, ' that is 
 the kind of thing they like.' Our not being able to sound the 
 depths of our thoughts does not prove that they are non-rational. 
 The reason is there, though it cannot be produced. No doubt 
 we must ultimately come to primary facts of belief, where the 
 material for judgement passes into judgement without it being 
 possible to analyse the psychological transition.^ This unanalys- 
 able starting-point of conviction ought not, I consider, to be called 
 an act of judging; at any rate the phrase 'sensory judgement' is 
 objectionable. TertuUian's reason for belief is an O altitudo! 
 ' Credo quia absurdum '. Newman says that to him there were 
 ever only two perfectly self-luminous existences — himself and 
 God. To seek a proof of one's own existence, indeed, is to try 
 to get behind consciousness. It is as though a person going 
 round in a wheel were to think that by going faster he could see 
 his own back, to airo voiiv ia-riv re kol etvai. ' CogitO, ergo sum.' 
 As St. Austin writes : — ' Omnis qui utrum sit Veritas dubitat in 
 se ipso habet verum unde non dubitet.' ^ But, though percep- 
 tion is not judgement, to assert something 'on the evidence of 
 
 ^ Fichte asks :— ' Why not rest contented with the fact that something 
 is, instead of supposing that it must have become through some source 
 outside itself ? You have been wont to think a ground of everything, but 
 forget that the ground itself is your thinking ' (qu. Lewes, If. of P. ii. 568). 
 But it is one thing to say that a ground cannot be given, and another to 
 argue that it does not exist. 
 
 " De Vera Religione. The man who prayed, ' O God, if there be a God, 
 save my soul, if I have a soul,' had nothing whatever to start from, no jroO 
 o-Tci of consciousness. Hegel says, ' If God be not, there is nothing.' If 
 / am not, I cannot say even that. To Locke the ontological certainties 
 were God, the world and the soul. 
 
Authority as a Ground 97 
 
 my senses ' is the first stage of judging. This, as Bosanquet 
 remarks, is not a refusal to give a reason for my assertion, since 
 sense-perception is not the asserted fact itself but the evidence 
 for it.^ 
 
 § 207. Nor do we refuse to justify a judgement when we rest 
 it upon authority. -To appeal to an Ipse dixit, awos €<^a, 'the 
 Master said it,' is open to no rational objection. It only throws 
 the rationale a step further back. Why do you trust the 
 authority? And the answer is no less an answer because it 
 may be an unanalysable instinct of devotion, or a vague 
 recognition of superior knowledge. Is there any statement we 
 ever make in daily life which has not in it some element of 
 deference to the knowledge, information, or character of others? 
 ' It is midnight.' ' There was a scene in the Commons last 
 night.' 'Mr. X is unmarried.' 'This is Radstock coal.' 
 ' My letter gave universal pleasure.' Which of these state- 
 ments have we verified by the direct testimony of our own 
 faculties ? No assertion is ever in practice really demonstrated, 
 carried back to ultimate intuitions, and very few minds could 
 follow the demonstration if it were. Authority intelligently 
 recognized makes the tedious task unnecessary.^ We do not 
 wrangle with our dentist as to which implement he is to use, 
 nor with a cabman as to the shortest way to Charing Cross. 
 The rationabik obsequium of which Joubert speaks — ' In poetry 
 
 " Logic, ii. 17. 
 
 ' The Right Hon. A. J. Balfour, in his Foundations of Belief, remarks 
 that alike the ultimate analysis of what we believe and the ultimate proof 
 of by what right we believe elude us. Yet we do believe ; and ' in all 
 branches of knowledge conclusions seem more certain than premisses. . . . 
 In all of them ideas so clear and so suflScient for purposes of everyday 
 thought and action become confused and but dimly intelligible when ex- 
 amined in the unsparing light of critical analysis.' He speaks of the 
 ' comparative pettiness of the r61e played by reasoning in human affairs ', 
 and finds our superiority over brutes to consist ' not so much in our 
 faculty of convincing and being convinced by the exercise of reasoning, as 
 in our capacity for influencing and being influenced through the action of 
 Authority '. He points out the falsity of the popular conception that Reason 
 ' is a kind of Ormuzd, doing constant battle against the Ahriman of tradi- 
 tion and authority ', and that ' its gradual triumph over the opposing powers 
 of darkness is what we mean by progress' (pp. 281, 283). Mr. Wilfrid 
 Ward's Essay in Problems and Persons (igo^) on Mr. Balfour's treatment 
 of the subject is well worth reading. 
 
 H 
 
gS Sufficient Reason 
 
 I should fear to go wrong if I differed from poets, in religion if 
 I differed from the saints' — applies to much commoner matters. 
 There are very few things we can attempt to think out for 
 ourselves. But in the higher kinds of self-surrender faith is 
 touched by the spirit of sacrifice and disciplined by trial. It 
 must be man's care not, out of laziness or cowardice, to bow 
 before that which he does not really respect. Never was 
 individuality more needed than in a period of individualism, in 
 which the leadership of imperial and commanding minds has 
 given place to the tyranny of a stereot3^ed and commonplace 
 mould of average opinion. ' La faiblesse,' says Mme. Roland, 
 'tremble devant I'opinion, le fou la brave, le sage la juge.' 
 
 § 208. Inasmuch as every cause is an effect, and for every 
 ground we must give a reason — everything, that is to say, has to 
 be explained by some other thing — we are carried back finally 
 in the one case to Creative Will, causa sui^ — so that 'if there 
 were not a God it would be necessary to invent one ' — and in 
 the other to the original facts of consciousness and self-evidence. 
 Otherwise, either we have an infinite regress, or else all things 
 revolve in an eternal circle. The absolute Whole is then to 
 itself both subject and predicate, its own cause and its own 
 effect. Demonstration is reduced to one term ; the world 
 becomes a single Thought. 
 
 § 209. The First Cause, causa causans et non causata, admits, 
 consequently, of no proof a priori, that is, from cause to effect.^ 
 But if we believe in it as Primal Will, it cannot be irrational to 
 think of vovs Kttt TvoM TO 81' avOpwTTov as a minor spring of action, 
 an apxfj xpafecos, and of creaturely wills — whether conceived as 
 
 ' ' That which persists, unchanging in quantity but ever changing in 
 form, under these sensible appearances which the universe presents to us, 
 transcends human knowledge and conception. It is an unknown and 
 unknowable power which we are obliged to recognize as without limit in 
 space and without beginning or end in time' (H. Spencer). Spencer 
 speaks of being painfully overpowered by ' the consciousness that, without 
 origin or cause, infinite Space has ever existed and must ever exist '. He 
 rejects Kant's doctrine of Space as ' the subjective conditions of the sensi- 
 bility, under which external intuition is possible, even as Time is the 
 formal condition of al/ phenomena whatsoever '. He maintains that all 
 the suggested origins of the universe of things are unthinkable. 
 
 ^ Benn (i. 150) quotes the baron in Thorndale: ' I believe in God until 
 your philosophers demonstrate His existence.' 
 
St'f pro Ratione Voluntas 99 
 
 finite portions of 'will-stuff' detached for each personality or 
 in some other way — as to some extent creative ; each ' a god 
 below V a cause and not an effect, able in a limited, sphere to 
 originate and therefore to revolt, yet finding itself by losing 
 itself in the perfect Will of God. The relation of motives to 
 freedom of choice is an insoluble problem^ Yet motives only 
 become motives by being taken up into the self, which is free 
 from necessity (dvay/o;) as well as from coaction (^id). 
 
 Decius. Most mighty Caesar, let me know some cause; 
 
 Lest I be laugh'd at when I tell them so. 
 Caesar. The cause is in my will. I will not come. 
 
 It is noticeable that, when we speak of being ' determined ' to 
 do this or that, we use determinist phraseology, as though we 
 were pulled and pushed about by our wants and environment. 
 Yet no word seems so strongly to convey the idea of complete 
 freedom of the will to react on circumstances as the word 
 ' determination '. 
 
 Thou art thou> 
 With power on thine own act and on the world. 
 
 If freewill is a delusion,^ it is, of course, as irrational to 
 praise the victorious in the agony of self-conquest as to 
 commend a turnip for growing.' We should talk rather of 
 golden events than of golden deeds. 
 
 § 210. A proposition, then, is not irrational and groundless 
 because the ground assigned is the fiat of volition — sit pro 
 ratione voluntas — any more than it is ungrounded because the 
 
 ' Not, however, in Virgil's sense of — 
 
 Sua cuique deus fit dira cupido. 
 ^ Shakespeare repudiates the Calvinistic or Mahometan view of the 
 ' Divine decrees : — 
 
 K. Rich. All unavoided is the doom of destiny. 
 Q. Eliz, True, when avoided grace makes destiny. 
 
 King Richard the Third, iv. 4. 
 Whitefield himself allowed that an ounce of grace would go as far with 
 some as a pound with others. In theological language grace is both/re- 
 veniens and co-ofierans, the latter word implying the will's liberty of choice. 
 ' Praise, of course, may be a stimulus to well-doing, and so finds a 
 place in Determinist systems. But inward commendation is what is here 
 meant. 
 
 H 2 
 
loo Sufficient Reason 
 
 ground is a primary intuition, of which no further account can 
 be given. 
 
 § 211. ' Why? ' asks the reason for a thing being what it is 
 said to be, and this reason may be either the cause of a 
 phenomenon or the ground of a statement, (i) How do you 
 account for S being P [ratio essendi)? How (unde) does it come 
 to be so ? Or (2) How do you know that S is P (ratio cogno- 
 scendi) ? Why {cur) do you say it is so ? This man is deaf 
 Why ? Because he had a fall, which makes him deaf. Because 
 he takes no notice, which shows him to be deaf 
 
 § 212. Either of the answers itself requires an explanation. 
 In the explanation of cause and effect we arrive ultimately at the 
 fact of the constitution of the universe, beyond which lies the 
 will of the Creator. In assigning the ground of a statement we 
 are pushed back and back to the native necessities of thought. 
 But while we are not bound to know anything about the cause 
 of S being P, the ground for our asserting 5 to be P must, 
 whether consciously realized or not, have been in our mind. 
 Even if we repeated it at second hand, we had a reason for 
 trusting our informant. No one thinks a thing without thinking 
 he has a reason for thinking it ; though to demand that he 
 shall give a reason for thinking he has a reason cannot be 
 repeated ad infinitum. The final reason, for instance, for all 
 conduct is our conception of the Summum Bonum. 
 
 § 213. Not only does the justification of a statement by its 
 ground require two premisses, tut the explanation of a 
 phenomenon by its cause requires two antecedent statements. 
 This wax is melted, because it has been near fire, and fire melts 
 wax. Either statement again has to be explained by two other 
 statements, the one a fact, the other a law. (i) How did the 
 wax come to be near fire ? I put it in the fender, and whatever 
 is in the fender is near fire. (2) Why does fire melt wax? 
 Because of the material constitution of wax on the one hand 
 and a general law of liquefaction by heat on the other. And so 
 on. Similarly, the ground for every assertion is itself grounded 
 on two assertions, the one, the major premiss, stating a general 
 principle, the other, the minor premiss or subsumption, stating 
 what is, relatively, a presentation of consciousness. And either 
 premiss branches out again regressively in two directions, 
 leading back, on the one side to primary perceptions, on the 
 
Double Meaning of ' Why?' loi 
 
 other to axiomatic laws. The plasticity and fertile energy 
 of nature corresponds to the ramifying complexity of demon- 
 stration. 
 
 § 214. It is of importance to notice that the explanation of 
 a phenomenon is a rational process, and gives the reason why 
 the phenomenon might be expected to be as alleged. The reason 
 your dog loves you is that you treat him kindly, and dogs 
 always love those who treat them kindly. What we have here 
 is an inference, that the dog may therefore be expected to love 
 his master. X is unbusinesslike, because he is a poet and 
 poets are unbusinesslike. In assigning a cause we s^xe justifying 
 an expectation. The middle term, which gives the cause of 
 the fact, is the ground of the judgement. The observed fact 
 is explained by the theory, the conclusion and the fact 
 corresponding. 
 
 § 215. The causa essendi, then, must be & ratio eognoscendi,^ 
 though, as we shall see, the converse is not always true. The 
 material process in rerum materia, being apprehended by us, 
 gives rise to the logical process in our mind. But the conclusion 
 (which^//oze;s, not results) has always an ideal, abstract, neces- 
 sary, and rational character. Sir Galahad's strength is as the 
 strength often because his heart is pure. And knowing his 
 heart to be pure we may be sure (conclusion) that (as a result) 
 his strength is as the strength of ten. It is slippery because it 
 has frozen. It has frozen, therefore I conclude that it is 
 slippery. All statesmen who speak truth are unpopular. This 
 statesman speaks truth. You may be sure, then, that he is 
 unpopular. 
 
 § 216. This is deductive inference, from cause to effect. But 
 we also argue inductively from effect to cause. The knight's 
 heart, we are certain, is pure because his strength is as the 
 strength often. It must have frozen because it is slippery. That 
 
 ' Why has no one recently entered the cave ? Because a spider has 
 built her web across the mouth of it (cognoscendi). Because a lion has 
 made his lair in the entrance {^essendi and cognoscendi). The lion could 
 keep a man out. The spider could not. Again, debate of battle could 
 not make a knight's lady to be fairer than others ; though, given the pre- 
 miss that right and truth in such an arbitrament always prevail, it could 
 frove her to be so. On the other hand, in the doctrine of grace, the 
 means whereby we receive the same is a pledge to assure us thereof. 
 
I02 Sufficient Reason 
 
 the politician speaks truth is shown by his being unpopular. The 
 ratio cognoscendi here is not the ratio essendi, but an a posteriori 
 sign or indication. ' Rain has fallen because the brook is 
 swoln ' is not the same kind of proposition as ' Rain will fall 
 because the clouds are low ', FalstafF combines both — ' The tree 
 may be known by the fruit, as the fruit by the tree.' Compare 
 the force of the two ' bys ' in the following : — 
 
 (i) Brave duke Schomberg was no more 
 By venturing over the water. 
 
 The Boyne Water. 
 
 (2) By the pricking of my thumbs, 
 Something wicked this way comes. 
 
 Macbeth. 
 
 § 217. It might be said of some place that it must be healthy 
 because it has so few deaths, or so few doctors, or so few fogs 
 and east winds. The first reason is a sign, the last is a cause. 
 The second, intended as a sign, might be jocosely taken as 
 a cause. In the report of a Dublin benevolent society it was 
 remarked that, 'notwithstanding the large amount paid for 
 medicine and medical attendance, very few deaths occurred 
 during the year.' 
 
 § 218. If the major premiss of an a posteriori dsgaraent directly 
 asserts F to be an invariable sign of the presence or existence 
 oi X, the reasoning is unchallengeable. Since 'by Tre, Pol and 
 Pen you may know the Cornish men ', I can infer at once that 
 the house of Pendennis is from the Duchy. ' Blue-eyed white 
 cats are always deaf cannot mean that blue eyes and white fur 
 cause cat -deafness, but only that they are an indication of its 
 presence. I am sure then that this blue-eyed white cat is deaf. 
 Contrast ' Cooks are always bad-tempered '. Contrast also 
 ' There is no smoke without fire ' with ' There is no fire without 
 danger'. ' Creaking shoes have not been paid for,' 'Those who 
 shun quarrels are wise,' ' Still waters run deep,' and many by- 
 words about the weather, are examples of sign propositions. 
 There is often nothing to distinguish them from causal proposi- 
 tions or propositions about the inherence of a quality in a 
 subject — e. g. 'Whoever speaks thus is foolish' from ' Whoever 
 speaks thus is punishable '. But, just as causal propositions are 
 sometimes stated as such — e.g. 'A green Yule makes a fat 
 
Cause and Sign 103 
 
 churchyard ', so others are stated as symptomatic — e. g. * The 
 habit proclaims the man ' ; ' A fool is known by his laughter ' ; 
 ' Eyebrows which meet indicate bad temper ' ; ' A mole is a sign 
 of riches ' ; ' Not to know me argues yourselves unknown.' Old 
 men are bald, scant of breath, and the like, and FalstafF is 
 ' written down old with all the characters of age '. 
 
 § 219. A sign is not always distinguishable from formal cause. 
 E. g., a ripe strawberry is red, juicy, sweet, and fragrant Being 
 a true gentleman makes a man (ratio essendi) courteous to all, 
 self-respecting, &c. ; and we say he is a true gentleman because 
 he is courteous, &c. [ratio cognoscendi). But such constituent 
 characters are together the formal cause of true gentlemanliness. 
 A tinker mends pots, and we know him to be a tinker thereby, 
 mending pots being both sign and formal cause. In the line 
 ' Non volucres pennae faciunt, nee cuspis Achillem ' faciunt 
 means 'constitute formally'. 
 
 § 220. It is only when, as in a definition or the predication of 
 a property, the predicate of a proposition is convertible with the 
 subject, that inductive inference from a sign, that is, from effect 
 to cause, is secure. In other cases it is liable to be upset by 
 plurality of causes. ' Why do you say it has rained ? ' 
 ' Because the pavement is wet.' But a watering-cart may have 
 passed. Courtesy may be a mask, like Absalom's or Bolingbroke's 
 in Richard the Second. Similarly, when we are explaining a fact 
 rather than justifying an assertion — e.g. 'Your dog loves 
 you because you treat him kindly' — we can suggest a cause 
 for the phenomenon, but not say certainly that this is the 
 cause. 
 
 § 221. A cause is a reason for a thing being what it is, and 
 a reason is a cause of a thing being known to be what it is.' 
 The presence of a cause makes the effect to be expected, and 
 the presence of an effect makes the cause to be suspected. A 
 
 ' Dr. Bradley asks the question — Is the Cause, as we know it, always 
 a Because ? Does every because appear as a cause ? He denies that the 
 process of our logical movement is bound ideally to counterfeit the course 
 of phenomena, and to present us with the actual changes of events (Prin- 
 ciples of Logic, pp. 486, 529). The chapter is worth study ; but the de- 
 railing of logical trains of thought by the nomad Chunchuses of philosophy 
 is truly mischievous. If Dr. Bradley's general argument is right, there 
 is no such thing as science. 
 
I04 Sufficient Reason 
 
 cause is a sign justifying an expectation, and a sign is a cause 
 producing an assertion. When we can justify a judgement both 
 a priori and a posteriori, by the yv(opiiJ,u>Tepov <j>v(r€i and also the 
 ■ycw/aiyuwrepov rjiuv, by the coincidence of crviJi,Trepa(rim (conclusion) 
 and oTi (observed fact), the judgement is on the way to be 
 demonstrated/ 
 
 § 222. Although in General Propositions the cause or ground 
 for an assertion is commonly indicated in the subject of the 
 sentence — ' Judges should be uncorrupt ' ; ' Vaccinated persons 
 escape small-pox'; 'The hireling fleeth because he is an hireling' 
 • — it is never confined to the subject.^ 'The King is above party' 
 — the King being who he is and party being what it is. We 
 learn that honesty is the best policy by considering what we 
 know about honesty and also about good policy. No man (i. e. 
 no hero) is a hero to his valet-de-chambre, because the one is a 
 hero and the other is a valet. In Negative Judgements, which 
 are converted simply (No A is 5= No B is A), the ground may 
 be considered as lying evenly between subject and predicate. 
 Of Particular and Concrete-universal Judgements, the ground 
 must be sought outside the sentence. — 'Some Indians are fair- 
 skinned.' 'All the men of my year took honours.' But this is 
 so also in the case of general propositions when the cause of an 
 observed uniformity is not known (e. g. ' Blue-eyed cats are 
 deaf), or not suggested (e. g. ' West country ballads are the 
 finest '). In Analytical Judgements the ground resides explicitly 
 in the subject, as ' Development must be in accordance with 
 type' (or it is not development). In 'Synthetic Judgements 
 a priori', the reason must be sought not in the definition but in 
 ' the necessity of the thing ' ; e. g. 'A triangle has its angles 
 together equal to two right angles '. 
 
 § 223. The sufficiency of a reason cannot be investigated by 
 logic. We are constantly, however, protesting against insufficient 
 reasons. 'Because thou art virtuous shall there be no more 
 
 ' Demonstration should be j>er causam proximam et immediatam et 
 prinuim. But Aristotle uses a/ico-os and irparos to signify either the first 
 cause in a series of events, or the cause which lies nearest to the ultimate 
 effect, or phenomenon under consideration. See Trendelenberg, § 16. 
 
 ^ ' The ground in thought often belongs to the effect in time, but may be 
 any element whatever related to the real ground, whether cause, effect, or 
 abstract principle ' (Bosanquet, Logic, i. 267). 
 
A Defensive Principle 105 
 
 cakes and ale?' Such insufficiency is often intentional and 
 humorous. ' A propos de bottes, o\x est ma tabatiere ? ' The 
 imprudent marriage with the barber in the Great Panjandrum 
 will possibly occur to the reader. The following may be quoted 
 from the Vicar of Wakefield : — ' My wife protested she could see 
 no reason why the two Miss Winklers should marry great fortunes 
 and her children get none. As this last argument was directed 
 to me, I protested that I could see no reason for it neither ; nor 
 why Mr. Simpkins got the ten thousand prize in the lottery, 
 and we sate down with a blank.' 
 
 § 224. But, though Logic cannot investigate the sufficiency of 
 a reason, it is bound to examine the sufficiency of reasoning. 
 As the Axiom of Consistency, then, forbids a conclusion which 
 contradicts the true one (the Axiom of Persistency having com- 
 pelled the drawing of the true conclusion), so the Principle ot 
 Sufficient Reason (or Reasoning) prohibits irrelevance and 
 inconsequence. It is not a positive criterion of truth, but is 
 defensive and protective, standing at the entrance of knowledge 
 to keep out judgements which cannot justify themselves ration- 
 ally, i. e. which are not the conclusions of a valid syllogism.^ 
 
 § 225. In elucidating the Law of Rationality, the structure of 
 Thought, whose connexions are governed by that Law, has 
 been inevitably, to some extent, assumed. We have now to 
 examine the Form of Thought, the mould in which human 
 intelligences are constituted to think, more closely. If thought 
 were only an identification, or an equation of quantities, 
 A = B = C, Logic would be a simple thing. But the con- 
 struction of our thought is conceptual. Its connexions are, so 
 to speak, qualitative. Instead of counting facts, we have to 
 bring each fact under a principle. Instead of bundles of 
 unrelated impressions, we have to do with cases subsumed 
 under abstract notions, with the one in the many. 
 
 But first it will be necessary to consider whether the usual 
 doctrine that there are three Forms of Thought is correct. 
 
 ^ Mansel says that SufiScient Reason is ' no law of thought, but only 
 the statement that every act of thought must be governed by some law or 
 other' (jProleg. Logica, p. 198). But why must? It is a law that every 
 act of thought shall be governed by a law. This is more than a mere 
 observed fact. 
 
io6 Sufficient Reason 
 
 NOTE 
 Narrative Judgements 
 
 In logical treatises the examples are nearly always in the 
 present tense, historic and narrative assertion being almost 
 wholly ignored. For what is universal and general is not very 
 naturally predicated from the standpoint of the past or of the 
 future, and there must be a universal element in all reasoning. 
 And yet by far the largest number of our assertions are state- 
 ments that something has happened, and that the causes and 
 consequences were this or that. 
 
 It is only in reflective and philosophic prose that the 
 principles and laws underlying the succession of events are 
 dwelt on. Usually a narrator states only concrete happenings, 
 not abstract rules. He concerns himself with effects, not with 
 inferences. All connected narrative — even Homeric adventure- 
 tale or the most artless ' once upon a time ' — implies, it is true, 
 at every step some law or generalization to explain how an 
 event came about. But the implied law is usually too obvious 
 to need stating. Only the facts, then, are given. 'The 
 frightened cow tugged at the rope, and this, being rotten, 
 snapped ; whereupon Daisy, finding herself free, jumped the 
 hedge ; but, catching her foot, fell, and in this way broke a leg. 
 In consequence, she had to be destroyed. The children wept, 
 as she was a great favourite, owing to her gentleness. I showed 
 them, however, a picture-book, which dried their tears.' The 
 implied generalizations are such as 'creatures which are 
 frightened try to get loose ' ; ' ropes which, being rotten, are 
 tugged at snap'; and so forth. The ratio essendt is constantly 
 suggested only. ' The rain had fallen, the poet arose.' ' You 
 have said your lesson well ; you shall have a penny.' 
 
 A universal can, no doubt, be stated from the standpoint of 
 past time. ' Ever upon the topmost roof the banner of England 
 blew.' ' Quicquid conabar dicere carmen erat.' ' In Adam all 
 died.' It is not more easy to say ' An Amurath to Amurath 
 succeeds ' than ' Aylmer followed Aylmer at the Hall, and 
 Averill Averill at the Rectory.' But narrative universals 
 are usually concrete. ' They all slumbered and slept.' 
 ' Everything was lost.' 
 
 Mr. Sidgwick gives the name ' abstract-concrete ' to concrete 
 propositions which directly assert causation^. ' X caused Y' 
 If so, ' Fwas an effect of X' must also be so called. 'Just for 
 a handful of silver he left us,' or ' The hot sun is melting the 
 wax,' may be read either way. The concrete meaning, Sidgwick 
 
 ^ Fallacies, p. 77. 
 
Narrative Judgements 107 
 
 observes, is primary, and the abstract meaning is implied rather 
 than asserted. In other words, when we find inductively that 
 one thing, X, caused another, Y, though this is a concrete 
 statement the Law of CausaHty entitles us to generalize it in 
 the abstract form, ' X causes Y! The same with the inherence 
 of a quality. ' This wax, because it is wax, is sticky.' Then 
 wax is sticky. 
 
CHAPTER VIII 
 WHATEVER IS RATIONAL IS SYLLOGISTIC 
 
 § 226. Thought has both form and matter. The matter is 
 the things thought about, the content of the terms. The form 
 is the conceived or judged relations of the terms. The matter 
 of Thought is supphed to it. The form is produced by the 
 activity of Thought itself, exercised upon the objects. 
 
 § 327. The relations between objects which are governed by 
 rational law are not material relations — e. g. gold is heavier than 
 silver; nor those which are subjectively related to the thinker's 
 own mind ; but only objective relations in thought. Modal 
 elements, accordingly, must in Logic be viewed as part of the 
 content of thought, not as part of its form. Mansel, following 
 Kant, observes that psychologically modality belongs to the 
 form of the judgement. But, he adds, 
 
 ' the forms cognizable by Psychology must not be confounded 
 with the forms cognizable by Logic. The latter science is not 
 concerned, as is sometimes maintained, with the Forms of 
 Thought in general, but only with the forms of thought as 
 related to pure or formal thinking ... In cases where a modal 
 conclusion is drawn from modal premises, it is only the form 
 of the conclusion, as a judgement, that differs from that of the 
 pure syllogism. Its relation to the premises as a conclusion 
 from them, consequently the entire form of the reasoning, is the 
 same in both.' ^ 
 
 For example, ' The men of that regiment are, perhaps, coming 
 home. My son is in that regiment. Therefore he is, perhaps, 
 coming home.' The conclusion, as a proposition, is modal. 
 But, as a conclusion, it is drawn necessarily from the premisses. 
 For every conclusion is necessary. 
 
 The subject of Modality will be further considered below 
 (§§ 605 seq.) under Judgement. 
 
 § 228. If — which is the view taken in this book — thinking is 
 the same thing as judging, the Form of Thought is identical 
 ' Proleg. Logica, p. 233. 
 
How many Forms of Thought? 109 
 
 with the Form of Judgement. But, because Judgement is con- 
 ceptual, the thinking of objects under concepts, it will be found 
 necessary also to analyse Conception. 
 
 § 229. Should, however, the right of Conception to be 
 regarded as a separate Form of Thought be maintained, the 
 Form of Thought is then twofold. Logical treatises, on the 
 other hand, almost invariably speak of Three Forms of Thought 
 — Conception, Judgement, and Ratiocination. To these corre- 
 spond the Term, the Proposition, and the Syllogism. And 
 most writers say that Logic is concerned with all three alike. 
 
 § 230. It is necessary, therefore, to point out the entirely 
 different footing on which Syllogizing stands in Logic from that 
 which is occupied by Conception and Judgement. 
 
 § 231. The Syllogism is essentially rational, whereas Con- 
 ception and Judgement are intellective and cognitive, not rational 
 per se. But Logic is only concerned with rational processes. 
 If it deals with Cognition, it is only with a view to understanding 
 how the connexions of actual Thought are subject to the Law of 
 Rationality. 
 
 § 232. Logic is not therefore concerned with Conception and 
 Judgement directly, unless concepts and judgements can be 
 shown to possess, always or sometimes, an internal rational 
 character. Every judgement, as we have seen (§ 27), is 
 rationalizable through its ground. But the statement of the 
 ground turns the judgement into a syllogism. 
 
 § 233. I have above (§§ 38 seq.) attempted to show that there is 
 no such thing in thought as immediate consequence, though a 
 language rich in synonyms like the English will show many 
 pleonasms — e. g. ' strolling vagabond '. The argument may 
 be further illustrated in this chapter. 
 
 § 234. The nearest approach, perhaps, to a seemingly immediate 
 implication in a Concept is the Hebrew idiom to express 
 emphasis, imitated in the Versions in such phrases as 'gaudens 
 gaudebo * (translated ' I will greatly rejoice ') ; * dying thou shalt 
 die' (Gen. ii. 17); yivwa-Kmv yvuxTg (Gen. xv. 13); ' circumdantes 
 circumdederunt me ' (Ps. Ixxxviii. 17) ; ' exspectans exspectavi ' 
 (Ps. xl. i); 'castigans castigavit me' (Ps. cxviii. 18); 'blessing 
 I will bless thee, and multiplying I will multiply thee ' 
 (Gen. xxii. 17) ; * with desire I have desired ' (Luke xxii. 15). 
 Akin to this idiom is the grammatical cognate accusative, not 
 
no Whatever is Rational is Syllogistic 
 
 further qualified — ' I will tell you a tale ' (not, ' a moving tale ') ; 
 ' ludere ludum ' (not, ' ludum insolentem ') ; ' somniare som- 
 nium ' ; ' iurare iusiurandum '. Again, we get phrases like 
 'the footstool of his feet' (Matt. v. 35 R.V.). 
 
 There does not, however, appear to be much more rational 
 implication in such idiomatic phrases than in the ' hear, hear ' 
 or 'divide, divide, divide' of parliamentary emphasis. The thing 
 affirmed is re-echoed, though in a diiferent grammatical form. In 
 phrases like ' cent nouvelles Nouvelles ' or 'la v6rit6 vraie ' 
 the substantive has a quasi-conventional sense. 'A kingly king,' 
 again, draws attention to the qualities a king should possess. 
 There could be an unkingly king, but not a non-royal king. 
 
 § 335. Seeming verbal confliction in the elements of a Concept 
 is much more common than verbal necessitation. Oxymoron is 
 found in all languages, but especially in the Greek poets— ^Si'os 
 HALO'S ; 8(5pov aSmpov ; vvix^rfv r awfi,^ov, irapOivav t aTrdpOevov ; 
 €Kwv aeKovn 8i 6vp.<a. Philo speaks of ^i^Xia afiifiXia. Even 
 Latin has this figure — e. g. ' concordia discors '. In King John 
 the line occurs — 'Most forsworn to keep what thou dost swear.' 
 Fuller says of Henry VIII 'that he was certain only in uncer- 
 tainty ' ; which is like ' constant only in inconstancy.' Hooker 
 speaks of 'confessing without confession that God's glory is 
 inexplicable', and of silence being our safest eloquence con- 
 cerning Him. 
 
 It is obvious, however, that in these and similar tropes there 
 is not any attempted combination in the same notion of an idea 
 and its actual contradictory, as there would be if we tried to 
 conceive a four-footed biped, compulsory volunteering, a 
 cultured boor, or twelve a.m. 
 
 § 236. Logic disallows real contradictions. A distinctly con- 
 ceived contradiction in thought is, in fact, impossible. But .the 
 admissibility of any verbal combination cannot be decided by 
 the logician until the facts are given him, which datum con- 
 stitutes a middle term. Modern chemistry declares, for 
 instance, that common salt has. been wrongly analysed and 
 that 'salt is not a salt'. Literature is full of paradoxical 
 expressions, such as the following : — 
 
 Trinal unity; dStves toC Oavarov (Acts ii. 24, birth pangs of 
 death); a noonday night (Pope); laborious idleness (cf 'strenua 
 nos exercet inertia'); elaborate simplicity; curiosa felicitas; 
 
'Contradictions in Terms' m 
 
 stale news ; gospel of gloom ; living death ; and many similar 
 expressions. Burke calls the French constitution-mongers 
 architects of ruin. Macaulay styles Harley a solemn trifler. 
 We use the phrase ' crowned republic ', but could hardly speak 
 of a monarchical republic. The rack is persuasion through 
 force, but we could not well say 'persuasive coercion*. 
 Herrick's lines are familiar : — 
 
 Be she shewing in her dresse 
 Like a civtll wildemesse, 
 That the curious may detect 
 Order in a sweet neglect. 
 
 George Eliot's Amos Barton was ' superlative in nothing unless 
 he was superlatively middling'. Charles the Second said 
 pleasantly of Godolphin that he was never in the way and 
 never out of the way. It was a whimsical saying of Bishop 
 Creighton's that none do so much harm as those who go about 
 doing good. ' Sir/ said Johnson to M^Aulay, who was ' rhap- 
 sodizing against creeds and confessions,' 'you are a bigot to 
 laxness.' 
 
 Sacred paradoxes are common in divinity. Such are the 
 words, 'He that keepeth his life shall lose it,' or St. Paul's, 
 ' As deceivers and yet true ; as unknown and yet well known ; 
 as dying and, behold, we live ; as sorrowful, yet alway rejoicing ; 
 as having nothing, and yet possessing all things.' Compare 
 'There is that scattereth and is more increased ' (Pro v. xi. 24). 
 Tertullian sublimely writes : ' Crucifixus est Dei Filius ; non 
 pudet, quia pudendum est. Et mortuus est Dei Filius ; prorsus 
 credibile est quia ineptum est. Et sepultus resurrexit ; certum 
 est quia impossibile est.' St. Paul calls the Ephesian polytheists 
 'atheous' (Eph. ii. 12). 
 
 § 237. Sometimes contrary attributes are combined in an 
 expressive compound, such as -yXuxviriKpos, Opaxrv^aXos, theandria, 
 triune, chiaroscuro, pianoforte, forcible-feeble, hysteron-proteron, 
 deadly-lively (or dead-alive), modern-antique, tragi-comedy, 
 Voltaire's Microm^gas, or the word oxjraioron itself. Shake- 
 speare speaks of ' this senior-junior, giant-dwarf, Dan Cupid ', 
 and of devilish-holy fray ('when truth kills truth'). Byron 
 speaks of a cherub-hydra. In ' Demeter and Persephone ' we 
 find 'human-godlike'. 
 § 238. Bulls of the Sir Boyle Roche type arise from the 
 
112 Whatever is Rational is Syllogistic 
 
 imaginative nimbleness which outstrips the mere verbal phrase.* 
 ' His remarks are so ambiguous that only one construction can 
 be placed upon them.' 'The best way to avoid danger is to 
 meet it plump.' ' If he had lived till to-morrow he would have 
 been dead a fortnight.' ' The Liberal party can only stick to its 
 present position by moving forward.' ' Would he were at the 
 bottom of the bottomless pit.' 'Absentee landlords! Why, 
 sir, my unhappy country swarms with them ! ' A native of that 
 country said of a pig that had not come up to his expectations, 
 ' I never thought it would.' 
 
 § 239. Besides contradictions in terms which are superficially 
 such, there are actual incompatibilities due to confusion of thought. 
 ' I said nothing against Episcopacy,' protests Mr. Tomlinson in 
 Janefs Repentance ; ' I only said I thought we should do as well 
 without bishops.' ' Every one to do as he likes, and those who 
 won't to be made to ' is the well-known definition of liberty, as 
 ' One man is as good as another, and a vast deal better too ' was 
 the definition of equality. The undergraduate defined faith as 
 belief in what we know to be untrue ; and justifiable homicide 
 was explained by some one as when a man kills himself in self- 
 defence. In this class must be placed malapropiana like ' relics 
 of the future ' or ' anticipate the past '. On the other hand, 
 ' Retrospection is best before the event ' is a perfectly intelligible, 
 though laughable, proposition. 
 
 § 240. Many incompatibilities are, of course, intentional and 
 merely ridiculous, like the schoolboy's pleasantry, 'no compulsion, 
 only you must ' ; or the inscription to the gentleman who ' of his 
 great bounty built this bridge at the expense of the county ' ; or 
 that lamentable comedy in which the sweet moon is thanked for 
 her sunny beams. There is mere ranting extravagance in love- 
 sick Romeo's string of absurdities : — 
 
 Why then, O brawling love ! O loving hate ! 
 
 O heavy lightness ! serious vanity ! 
 
 Misshapen chaos of well-seeming forms ! 
 
 Feather of lead, bright smoke, cold fire, sick health ! 
 
 Still-waking sleep, that is not what it is ! 
 
 This love feel I, that feel no love in this ! 
 
 * Sydney Smith, however, defines a bull as ' an apparent congruity 
 and real incongruity of ideas, suddenly discovered. Wit discovers real 
 relations that are not apparent. Bulls admit apparent relations that are 
 not real '. 
 
Incompatibles 113 
 
 A woman, we read in Antony and Cleopatra, should not lie but 
 in the way of honesty. 'I have no land-hunger,' said the 
 New Englander. 'I only want the ground which joins mine.' 
 Then there are conceits like ' the other end of nowhere ', ' less 
 than no time ', * an infinite deal of nothing ', or Smalgruenius' 
 • de omnibus rebus et quibusdam aliis '. 
 
 § 241. But even when the inconsistency is real and not 
 seeming, it is given materially rather than formally ; and the 
 logician is no more able to pronounce that good is never bad, 
 nor blue black, nor solitude (in Shelley's phrase) populous, nor 
 the self found by being lost, than he can pass a verdict on 
 material impossibilities such as a mare's nest, hay-fever at the 
 North Pole or skating on Phlegethon, the same fountain sending 
 forth sweet water and bitter, the blind leading the blind, a 
 Sunday in the middle of the week, or a crab hunting a hare. 
 'Demander de la laine de I'ane,' and 'in aere piscari, in mari 
 venari ', are as materially impossible as ' in silvam ligna ferre ' is 
 materially superfluous. Liician has a conceit of milking a he- 
 goat and catching the liquid in a sieve ; and some one absurdly 
 describes a tipsy man lighting his pipe at the pump. The man 
 in the south burnt, we know, his mouth by eating cold plum 
 porridge. Pure reason can no more condemn such combina- 
 tions than it can declare impossible a midnight sun or 'April- 
 autumns of the antipodes ', If its jurisdiction is allowed here, 
 where is it to stop ? Can a figure face north by south ? 
 Certainly, if it be, like Janus, bifrons. Petrarch speaks of a 
 fountain in Epirus that kindled the quenched torch. Origen's 
 phrase, ' aeterna et sempiterna Generatio ' — a fact rather than 
 an event — has its seeming self-contradictor in ess only from 
 the accidental association in our minds of begetting with 
 a temporal beginning. 'Spiritual but real' is a common 
 but quite false antithesis; and so also, since a body may be 
 TTvev^uaTiKoi/, is the opposition between 'spiritual' and 'corporeal'. 
 
 § 242. Most of the above illustrations are taken from concepts 
 rather than from judgements. The only difference is that, 
 whereas concepts couched verbally in the form A A are hardly 
 to be found, while those in the form A not-^ are not uncommon, 
 with judgements it is the opposite. ' Wise men are men,' says 
 Jeremy Taylor, ' and truth is truth.' We say, ' Right is right 
 and wrong is wrong.' Such expressions draw attention to the 
 
 I 
 
114 Whatever is Rational is Syllogistic 
 
 intensive content of the subject term. But they can have, in 
 this sense, no negative counterpart—^ is not A — but only BA 
 is not A. Shakespeare says : ' Love is not love. Which alters 
 when it alteration finds.' In paradoxical expressions like <j>^ 
 cniDTTUiv, or ySXeTTovres ov ^Xiirovcri koX aKovovm ovk aKovovcnv (St. 
 Matthew xiii. 13), the same word has a meaning in the predicate 
 varied from that which it had in the subject.; so that ^Xeirovra 
 appears in St. Mark as S^iOaXfjLovg I^ovtcs and aKouovres as 
 Sra ex""'''^^' Compare Aeschylus's KXvovre^ ovk ijkovov. This is so 
 also in riddling sayings, like the French ' Si je suis ce que je 
 suis, je ne suis pas ce que je suis ' (a man driving an ass); or 
 ' I went to India and stopped there ; I came back because I did 
 not go there ' (a watch) ; or in Gareth and Lynette — 
 
 The city is built 
 To music ; therefore never built at all ; 
 And therefore built for ever; 
 
 and the familiar ' When is a door not a door ? ' Of 
 course self-contradictions in epigrammatic form are common. 
 Such are — ' Evil, be thou my good.' ' Magna civitas magna 
 solitude' ' Quod expendi habui ; quod servavi perdidi ; quod 
 donavi habeo.' ' Fair is foul and foul is fair.' ' Nihil peccat 
 nisi quod nihil peccat.' ' The queen died every day she lived ' 
 (cf. ^So-a redvYjKe). ' Non est vivere, sed valere, vita.' 
 
 § 243. But as no idea can be seriously denied of itself s6 no 
 idea can be really predicated of itself.^ Instances to the con- 
 trary are merely whimsical or nonsensical. As in Twelfth Night— 
 ' Not to be abed after midnight is to be up betimes.' Or in 
 Antony and Cleopatra — " It is as broad as it hath breadth.' Or 
 in Love's Labour's Lost — 'To be forsworn is a great argument 
 of falsehood,' Or in Hamlet — ' How came he mad ? — Grave- 
 digger. Very strangely, they say. — How strangely? — Faith, 
 e'en with losing his wits.' The Spanish fleet in the Rehearsal 
 could not be seen because it was not yet in sight. Madam 
 Blaise never wanted a good word from those that spoke her 
 praise; like the man in the Elegy on a Mad Dog — ' The naked 
 every day he clad, when he put on his cloaths.' The following 
 from Twelfth Night is mere clowning — ' Sayest thou that house 
 
 ^ Such otioseness would be like, in action, 'preaching to the con- 
 verted,' painting the lily, gilding refined gold, 'iuxta fluvium puteum 
 fodere,' ' iugulare mortuos,' or carrying coals to Newcastle. 
 
All Reasoning involves a Middle Term 115 
 
 is dark ? Why, it hath bay windows transparent as barricadoes, 
 and the clerestories towards the south-north are as lustrous as 
 ebony. And yet complainest thou of obstruction ? ' 
 
 § 244. From what has been said in this and previous sections 
 (§§ 48, 134), it is, I think, clear that there are no concepts 
 the elements of which can be pronounced by pure reason 
 formally to necessitate or invalidate one another; and similarly 
 thatnojudgementis,assuch,/orma//vrational or irrational. Pure 
 reason can never give its verdict on a proposition until a term 
 mediating between subject and predicate has been appealed to ; 
 and the doing this constitutes ratiocination.^ Concepts can 
 only be rationalized in the same way. If words were guaranteed 
 always to preserve identically the same meaning in every con- 
 text, it would be otherwise. But then a concept like ya/xos 
 oya/M)s would be impossible, and no concept at all. 
 
 No one would then speak of a white pink, of a ten days' 
 quarantine, of a steel pen, a brass shoehorn, or a leather 
 carpet-bag. Urbanity would be a proprium of cockneys, and 
 an examinand in a black coat would cease to be a candidate. 
 Grenadiers no longer throw grenades, and the Fortnighity 
 Review since 1866 has been published once a month. Nor is 
 a carte-de-visite for us a visiting card. ' Pagan,* originally a 
 villager, came to mean (e. g. in Pliny) a civilian ; in which sense 
 St. Cyprian first applied it to non-Christians, as not vowed to the 
 Holy War. 
 
 § 245. To our conclusion that Logic is concerned with 
 Syllogizing is quite a different way from the way in which it is 
 concerned with Conceiving and Judging, it may still be demurred 
 that at any rate Judgements frequently contradict one another, 
 in which case a rational relation exists between thoughts apart 
 from any mediation. All inconsistency between words and 
 acts is really an attempt to combine incompatibles in thought. 
 ' Clodius accusat moechos.' A Spanish official, being asked to 
 help the Society for preventing cruelty to animals, suggested 
 
 ^ The concept cannot be analysed into its elements by an act of pure 
 reason, any more than an object can be resolved into its attributes ; and 
 the ' discord ' of ' hot ice ' is as much and as little perceptible to pure 
 reason as that of 'merry and tragical, tedious and brief. Hobson's 
 choice is no choice at all, and ' un seul choix ' is no choice at all. But 
 the one we learn by being told about Hol^on, and the other by explica- 
 tion of the ideas of ' seul ' and ' choix '. 
 
 I 2 
 
ii6 Whatever ts Rational is Syllogistic 
 
 raising funds by means of a bull-fight. There are iconoclast- 
 idolaters. There are prophets who bite with their teeth and 
 cry Peace (Micah iii. 5). It has been said of Shelley that he 
 made a mythology of atheism; of Rousseau, that he was an 
 apostle of nature in a periwig. The peacock bids to fly pride, 
 and there is a ' pride which licks the dust *, a pride, too, which 
 builds, as Coleridge says, a cottage with a double coach-house. 
 ' Quis tulerit Gracchos de seditione querentes ? ' In the Noyades 
 Ferrier drowned in the Loire three thousand royalists in the 
 holy name of humanity. The American Declaration of Inde- 
 pendence, asserting that 'all men are created equal' and 
 endowed with an ' unalienable right ' to ' liberty ', was issued by 
 a body consisting largely of slave-owners. In the early decades 
 of the nineteenth century doctrinaire individualism was in many 
 parts of Europe found associated with military dictatorship, 
 rights of man with coercionism. Daniel O'Connell was opposed 
 to revolutionary violence; but Lord Clarendon said that the 
 ' physical force ' followers of Young Ireland had to be protected 
 by the constabulary from the shillelaghs of the ' moral suasion ' 
 party. Some have ' fought like devils for conciliation *, and 
 some repent in purple and fine linen. ' When I tell Caesar he 
 hates flatterers, He says he does — being then most flattered.' 
 irS><s ovv SiKaiov Tovs vofiovs iS/i.as ^poTois ypaxj/avrai avroiis avo/iuw 
 otjikuTKcivfLv ; ' Inconsistencies, said the prince, cannot both be 
 true. Inconsistencies, answered Imlac, cannot both be right; 
 but, imputed to man, they may both be true.' The anarchist, if 
 assaulted, calls for the police. The absolutist invokes liberty. 
 Rabagas, in office, fires on the mob. The latitudinarian is 
 intolerant of intolerance \ and dogmatizes against dogma. 
 It has been said of Friedrich Nietzsche that he 'raised Im- 
 morality into a philosophic principle' — he called himself 'the 
 first immoralist'. But his biographer, Dr. Cams, remarks — 
 ' If there was a flaw in Nietzsche's character it was goody- 
 goodiness, and his philosophy is a protest against the principles 
 of his own nature.' 
 
 ' Intolerance being a genuine form of opinion. The argument is ad 
 hominem on both sides. 'How can you, so enthusiastic for tolerance, 
 persecute one form of belief, viz. mine ? ' ' How can you, who believe in 
 intolerance, object to my suppressing you ? ' But perhaps he does not 
 object on principle. 
 
'Immediate Opposition' 117 
 
 § 246. But, whatever the confusions of thought by which men 
 are led into inconsistencies, they never formulate their beliefs 
 in the form of direct contradiction. Falstaffs tale about the 
 footpads is so farcical because it unblushingly changes its state- 
 ments as it proceeds. The men in buckram grow from two to 
 eleven. Some were in Kendal green, and yet it was so dark 
 you could not see your hand. The inconsistencies repose side 
 by side. There is a reason for them ; but the knight will 
 not give a reason upon compulsion. When the inconsistency 
 is pointed out it may often be denied. De Maistre spoke of 
 'un revolts qui preche I'obdssance' as 'un spectacle un peu 
 ridicule'. But that depends on circumstances. It is not like 
 Pope's description of — 
 
 those who temperance advance, , 
 Cramm'd to the throat with ortolans. 
 
 Again, if I change my mind — 'Man,' says Herbert, 'is some 
 twenty several men at least each several hour ' — I am not trying 
 to combine incompatibles. Scales fall from King Clovis' eyes, 
 and then he is bidden — 'Adora quod incendisti, et incende quod 
 adorasti.' 
 
 § 247. The only form of ' immediate ' opposition between pro- 
 positions is that between symbolic A and O, E and /. The only 
 form of apparently immediate implication is that of / in A and 
 of O in E. As regards the latter, I consider that we do not get 
 from universal to particular without an appeal to the axiom 
 that what is true of all is true of some. As regards the former, 
 the impossibility of contradictories both being true is simply the 
 basal law of Reason itself, some being conceived as equivalent 
 to not none, and some not to not all. The ultimate law has 
 to be invoked in any particular case of attempted self-contra- 
 diction. 
 
 § 248. Once again, then, it has to be affirmed that Logic is 
 cohcerned with Syllogizing directly, as an essentially rational 
 process, and with Conceiving and Judging only indirectly, as 
 the Form or Forms of Thought, the structure of which must be 
 to some extent analysed that the government of Thought's 
 connexions by Reason may be understood. 
 
 Yet it might be urged that as an act of comparison Syllo- 
 gizing is a Form of Thought on a level with Conception and 
 Judgement. Hamilton, for instance, says : — 
 
ii8 Whatever is Rational is Syllogistic 
 
 'All thought is a comparison, a recognition of similarity or 
 difference, a conjunction or disjunction. ... In Conception it 
 compares, disjoins, or conjoins attributes ; in an act of Judge- 
 ment it compares, disjoins or conjoins concepts ; in Reasoning 
 it compares, disjoins, or conjoins judgements.' ' 
 
 § 249. It is clear what 'comparison of attributes' means. 
 Comparing the shape of the full moon and the shape of a 
 plate and that of a wheel, or again comparing the appearance of 
 the moon in its various phases, I get the notion of circularity. 
 As regards ' comparison of concepts ', however, we must insist 
 again and again that this is not the import of Judgement 
 generally, but only of Analytical Judgement. Comparison of 
 concepts will show me that hope which is seen is not hope, but 
 not that hope deferred maketh the heart sick. It will show me 
 that a mule is a hybrid, but not that a mule is obstinate. Judge- 
 ments which are not analytical are based on a comparison of 
 percept with concept. 
 
 § 250. What we really do in judging is to compare some attribute 
 or combination of attributes, perceived as belonging to an object, 
 with our conception of the distinguishing characteristics of some 
 class. This ship, I see by its machinery, is a steamer. Or the 
 ground of the judgement may be an attribute or circumstance 
 thought of as peculiarly characterizing a portion of a class, 
 divided extensionally. This ship, I see by its paddles, is a 
 steamer. Not all steamers have paddle-wheels; but these, as 
 belonging to a ship, are a peculiar characteristic of a sub- 
 division of the steamer class. We could not have inferred that 
 the ship was a steamer because it was built of iron, even if all 
 steamers were iron-built ; for some sailing ships are iron-built 
 also. Judgement then is not a comparison of notions, nor yet 
 of the attributes of two classes ; for bread is nutritious and beef 
 is nutritious ; yet bread is not beef; but it is the comparison of 
 some attribute of an object with a notion, by which, as a ground, 
 the object is brought under the notion. Negatively, the 
 judgement is diagnostic. This knight is not Sir Launcelot ; for 
 he wears a lady's favour, which does not agree with my notion 
 of Sir Launcelot. 
 
 § 251. We can thus scrutinize the assertion that Syllogism is 
 a 'comparison of judgements'. For when we syllogize we 
 ^ Lectures on Logic, i. 13, 14. 
 
Is Syllogism a Comparison of Judgements? 119 
 
 do not pronounce two propositions to be like or unlike. 
 What we do is to relate a concept with a concept, or 
 a percept with a concept, by means of a middle term. 
 We bring one term under another on certain ascertained 
 grounds. But such result of our comparison is a rational, not a 
 cognitive or judicial act. Syllogism is not like Squire Thorn- 
 hill and Olivia placed back to back and judged to be 'extreamly 
 of a size ', but is like the height of the sentinel at Windsor being 
 compared with the height of the soldier stationed at Hounslow 
 by the help of an intermediary, who measured himself first with 
 the one and then with the other. Reasoning, then, is not, as 
 Jevons asserts, a judgement concerning judgements, but a 
 rational conclusion based on judgements. 
 
 § 252. We can syllogize by means of symbols only. But we 
 cannot conceive without knowing what it is we are conceiving, 
 or judge without knowing what we are judging about. Few 
 concepts or judgements even suggest, on the surface, a rational 
 process. Syllogism, on the other hand, is not syllogism at all 
 except as it is seen to be reasoned. To the mere logician ' a 
 wicked baronet' and 'a wicked saint' are like concepts. 
 'Cockney sportsman,' 'cockney countryman,' and 'cockney 
 Londoner ' being submitted to him, he can only say of each, 
 ' nihil obstat ; per me licet.' But tell him that a cockney is a 
 person born within sound of Bow Bells, and that any one so born 
 is born in London, and he will at once decree the last concept 
 to be a necessary one, the second an impossible one, while the 
 first, as far as he knows, is purely contingent. There is no 
 formal objection to it. A syllogism, on the other hand, cannot 
 consist of mere compatible elements, but only of such materials 
 as enable an energy of pure reason to set itself in motion. 
 
 § 253. The only reason that can be given for ranking Syllo- 
 gism with Conception and Judgement as a third Form of Thought 
 is that it is discursive, and so dianoetic.^ We may reply that it 
 is an operation of the reason upon the connexions of thought, 
 not an exercise of the intelligence upon the properties of things. 
 But still (a critic may urge), ' putting two and two together ' is 
 the mode of human ratiocination as distinguished from the clear 
 
 ^ McCosh defines discursive thinking as ' an exercise of mind in which 
 we proceed from something given or granted to something further which 
 is founded on it' (Laws of Discursive Thought , p. 47). 
 
I20 Whatever is Rational is Syllogistic 
 
 rational insight of the Divine Mind, which has not to pass from 
 point to point, from one thing to another, neither 'becoming 
 aware ' of truths, nor ' arriving ' at them by any process, but (as 
 we must suppose) embracing condition and conditioned, ante- 
 cedent and consequent, premisses and conclusion, in a simul- 
 taneous, indivisible act of contemplation.^ At the other end of 
 the scale brutes, that 'great and sane and simple race', with 
 their marvellous instinctive powers, to some extent ' partake ot 
 reason ', but do not exercise it, do not reason things out, or only 
 dimly. Not to be bound to discursive ratiocination, then, one 
 must be ^ Oiqpiov rj 6f.6<s. 
 
 Charles Lamb in New Year's Eve amusingly deprecates trans- 
 lation to a higher sphere which shall separate him from his 
 midnight darlings, his Folios. He has an 'intolerable disinclina- 
 tion to dying '. ' A new state of being staggers me. Must know- 
 ledge come to me, if it come at all, by some awkward experiment 
 of intuition, and no longer by this familiar process of reading ? ' 
 
 § 254. Certainly syllogism may be regarded as a proposition 
 about a rational necessity in the form, 'All 5 being M when 
 M is P necessarily involves S being P'; or thus, 'Every X 
 which is Y when Y is Z is necessarily Z.' What is predicated 
 in every such sentence is necessitation. 'The conclusion "S 
 is P", under the simultaneous conditions of S being M and M 
 being P, is a thing which follows necessarily.' But such an 
 assertion of rational implication of 'predicate' in 'subject', 
 though, in a sense discursive, cannot, I submit, be regarded as a 
 judgement, either syllogistic or analytic. There is no real judicial 
 comparison between a subject and the concept ' rationally neces- 
 sary '. If this view be combated, at least the nature of the com- 
 parison is different in kind from that of a comparison between 
 chalk and white (synthetic), or between ice and frozen (analytic). 
 
 ' ' Inference, as a mental process, has duration in time ; but as intel- 
 lectual insight its parts are inward to each other, and exempt from 
 temporal succession ' (Bosanquet, Logic, ii. 5). ' To God, indeed, wisdom 
 is as a high tower of pleasure, but to us a steep hill, and we toiling ever 
 about the bottom ' (Milton, Tetrachordon). 
 
CHAPTER IX 
 CONCEPTION 
 
 § 255. Having distinguished the Form of Thought from 
 Rational Process, we can now proceed to analyse that Form, so 
 far as is necessary for logical purposes. It is not necessary to 
 wait till every psychological problem has been settled. The 
 impossibility of thinking without language, for instance, is a 
 question which, with all respect to Max MuUer's protestation, 
 we need not finally determine. 
 
 § 256, Like the word Reasoning, so ' Thought ' is used for 
 faculty, process, and product. As it is not reasoning, so neither 
 is it sense. 
 
 And whereas Conception is an ideally potential, that is to 
 say a notional, conjunction of attributes in a possible subject, 
 Judgement affirms or denies an actual conjunction of attributes 
 in an ascertained subject. 
 
 § 257. Conception has a material limitation, in that it is so far 
 psychologically determined by the nature of things that no 
 attribute can be conceived the elements of which have not been 
 actually presented to our cognizance. ' Oh, could I with Fancy 
 stray ! ' But phantasy or imagination cannot stray outside the 
 boundaries of experience.. The experience may, of course, be 
 an interior experience. Fancy is bred, begot and nourished 
 rather in the heart than in the head. 
 
 § 258. On the formal side. Conception is limited logically by 
 the requirement, or rather the necessity, that its elements shall 
 not be mutually contradictory. No contradiction is conceiv- 
 able.^ A formally self-contradictory judgement is therefore as 
 non-existent, really, as a formally self-contradictory notion (see 
 above, § 235). On the other hand, we are not able to say that 
 a concept is empirically possible, or that an assertion is 
 
 ' ' Whatever is intelligible and can be distinctly conceived implies no 
 contradiction, and can never be proved false by any demonstrative 
 argument or abstract reasoning a priori' (Hume on Miracles). 
 
122 , Conception 
 
 empirically actual, because its elements are acknowledged to 
 necessitate one another. 'Omniscience which reads the 
 thoughts of all hearts' is beyond our power of conception. 
 'Winged griffins which have the means of flight' are not 
 actual. 
 
 § 259. In all thinking we endeavour to discern the One in 
 Manifoldness. We intellectually unify the variety of impres- 
 sions received either through the 'watchful senses', the five 
 windows of the soul, or through the inward consciousness. 
 
 Apart from the unity given by general conceptions, the 
 information supplied by the inner or the outer experience 
 would be unintelligible. The concept is ' an ideal unity within 
 a phenomenal flux'. We can only 'know' by knowing 
 scientifically; and science is the evolving of conceptual order 
 out of sensory chaos. It is therefore of the highest importance 
 that concepts should be rightly framed and answer to the 
 permanent nature, the ri rjv elvai, of things. Not that a concept 
 can be true or false in itself— truth and falsehood are the 
 peculiarity of judgements — but we endeavour to select the right 
 notional category under which to place the object which we 
 desire to know; although the marshalling of each presented 
 experience under the proper head and in its true class is not 
 the logician's business, but that of the inductive intelligence. 
 For though we cannot judge without reasoning, yet bonae 
 notiones are not secured by valid ratiocination, but by capacity 
 and training in discriminating, appreciating and selecting the 
 materials put before us. 
 
 § 260. Thus, History is no mere medley or sequence of 
 chance events. It is 'philosophy taking its time'. Otherwise 
 we get but bare chronicles of a lifeless past — historia nihil aliud 
 nisi annalium confedio. Hence the historian needs insight, 
 imagination, sympathy — next best to which is antipathy. ' If/ 
 says Dr. Bradley, ' the history of a thing is ever its explanation, 
 this is because history can never be sensuous.'' What again is 
 Memory if its records cannot be grouped and classified ? A 
 palimpsest scrawled with unmeaning marks. A stimulation of 
 that part of the brain called the cortex. Or Art ? Art is not a 
 photographic transcript of ' facts ', but their interpretation, the 
 exhibition in the individual of what is universal and typical, 
 
 ' Logic, p. 493. 
 
Cognition is through Concepts 123 
 
 ■ divinely through all hindrance to find the man ' behind the face, 
 and to seek the ideal. To hold the mirror up to ' facts ' is not 
 necessarily to hold it up to nature,^ nor are things really 
 represented ' as they happen ' if they are presented out of 
 relation to other things, that is to say without suggesting a 
 universal. It is just the universal element which gives the 
 interest ; and ' un-moralized ' art is necessarily inartistic, though 
 of course it is usually for the spectator to draw the moral." 
 
 § 261. We know things, then, by bringing presentations, or 
 what are relatively such, under appropriate conceptions. ' This 
 is a flint arrowhead.' ' Pigs are not domestic animals.' ' La 
 propria^ c'est le vol.' ' Art thou that my lord Elijah ? ' ' Haec 
 est nobilis ad Trasumenum pugna,' The three last are 
 identifications. But even in an identification the subject is 
 cognized through something better known, and so possessing a 
 certain general and abstract character. ' Fit Beroe.' ' Am I 
 not thine ass on which thou ridest ? ' ' Covetousness which is 
 idolatry ' (cf. Eph. v. 5, ' a covetous man which is an idolater '). 
 No predicate can be either purely abstract or purely concrete.' 
 Nothing is conveyed by pointing with the finger and saying 'this 
 is that ', unless the ' that ' is already known, and so an identity 
 
 ' Goethe, however, when he says, ' Art never would have been called 
 Art had it been meant to be the same thing as Nature,' means by 
 ' nature ' the outward show of things before reflexion begins, isolated and 
 bare ' facts '. Plutarch writes : — '0 StfiaviSrjs tijv fiev ^aypa^lav Troirjiriv 
 (TiamSsaav jrpo<Tayop€vn, t^v 8e iroiqiTiv f(»'ypa(^mi' XaXoCcai'. 
 
 " Benn {The Greek Philosophers, i. 156-8) has an interesting dis- 
 cussion of the influence of the ideal philosophy on Hellenic imitative 
 design, which, however, at one period degenerated into ' sensationalism ', 
 while later, both in plastic and in dramatic art, it substituted abstract 
 personifications and generic types for historic or mythologic flesh and 
 blood. Yet by the help of these very a]jstractions the Greeks got back 
 into touch with living, concrete things with a fuller understanding of life's 
 meaning. Thus late arose biography ; ' and, although biographies are 
 the favourite reading of those who most despise philosophy, they could 
 never have been written without its help.' Not that the Waltons and 
 Boswells of literature intrude too many philosophic and moral reflexions 
 on us ; but sympathy,, reverence and artistic feeling enable them to get 
 behind accidents and mere ' anfractuosities '. The typical, by the by, 
 is not the average. On the other hand Dickens mistakes for strong 
 character drawing what is merely bizarre. 
 
 ' ' At no point of our experience are we presented with pure Matter or 
 with pure Form' (Mackenzie, Outlines of Metaphysics, p. 94). 
 
124 Conception 
 
 constant through various contexts. This is so even in an 
 algebraic equation — in which moreover ' equal to ' is not the so- 
 called copula, but is part of what is predicated — or in such a 
 proposition as, ' His name is John.' All thinking, then, is con- 
 ceptual. We can only ' know ' by ' understanding '. It is true 
 that, since a concept has ideally a plurality of applications, 
 universal affirmations are not convertible simply — a spade is an 
 implement, but an implement is not therefore a spade ; whereas 
 identifying propositions are simply convertible. ' Thou art the 
 man.' The man is thyself. Nevertheless, in such identifications 
 the predicate, whichever it is, is always for the moment regarded 
 as more abstract and general than the subject — 'thine ass on 
 which thou ridest ' than 'I whom thou now beatest'; 'the 
 man,' the merciless man of the tale, than ' thou sitting there ' ; 
 or else, ' thou, the great king David,' than ' the man of my tale, 
 who finds his explanation in thee '. 
 
 § 262. When, instead of looking for an appropriate concep- 
 tion under which to place an object, we seek for cases of a 
 conception already before the mind, we realize our knowledge, 
 clothing the abstract with circumstance, and learning its con- 
 crete value and significance. I form an idea of honesty; 
 but acquaintance with an honest man makes it more real. 
 Diogenes went about with a lantern looking for a man. 
 Instead of asking what a thing is, what name to give it, we 
 ask who or what answers to a name. ' Who brought the parcel ? ' 
 ' Who will o'er the downs with me ? ' But the answer to the 
 question, though the grammatical subject, is the logical predicate. 
 The postman brought this parcel (not the carried). He who 
 brought it is the postman. In all thought we begin at the one 
 end or the other. Children open a remark with the words, 
 ' Mother, you know so and so, don't you ? ' and, having fixed 
 attention on subject or predicate, proceed to supply the other. 
 
 § 263. Every predicate has itself been the subject of a 
 preliminary judgement. We know a thing by bringing it under 
 an acquired concept. But how was the concept formed and 
 placed in the mind's store-chambers ? Ultimately we shall find 
 that it is itself built up out of raw material in the shape of 
 immediate presentations to consciousness ' (the nearest approach 
 
 ^ The relation between Sense and Thought, between the particular 
 and universal, between the That and the What, says Mackenzie, is ' the 
 
Universals 125 
 
 of experience to the purely undetermined and simply given) 
 which are attended to by an act of will, and combined by an act 
 of intelligence. The particulars, not being a mere series of Thats 
 but having even in this rudimentary state a certain character and 
 determinateness which relates them to our intellect, are unified, 
 not aggregated. We are thus said to conceive (conctpere). 
 
 § 264. The Concept is itself a universal, being expressed, or, 
 as some maintain, constituted, by a Common Name applicable 
 generally to a number of objects. 'Homo,' as Gadshill says, 
 'is a common name to all men.' This universality does not 
 arise from the circumstance that the attribute connoted by the 
 name has been observed in a number of differing objects ; e. g. 
 Jlat in table, floor, field, and the like — for it is sufficient for 
 conception to have experienced the attribute once and once 
 not — , but from the abstractive nature of the Intellect. 
 
 § 265. Until Abstraction begins, Thought must be considered 
 as not born, or at least as embryonic. Antecedent to Con- 
 ception is Simple Apprehension, in which nerve modification 
 passes into Sensation, and that into Perception. Neurosis 
 becomes Aesthesis. 
 
 § 266. A pool mirrors clouds and sky, but does not retain 
 the image. The photographic plate retains the image which 
 it reflects, but is not conscious of it.* It is sensitive, but not 
 
 most fundamental antithesis in experience' {Outlines of Metaphysics, p. 93). 
 'Dualism accepts simply the antithesis as an ultimate fact ; Idealism 
 and Materialism arise from attempts to overcome it' (p. 91). 'Agnosti- 
 cism represents the despair of any ultimate solution of the problem in- 
 volved in it.' 'The fundamental forms of construction in the details 
 of the sense-material are somehow brought to unity in virtue of some 
 connecting principle' (p. loi). Contrasting perceptual with scientific 
 construction, he observes : ' In perception we forget almost that any 
 synthesis is involved. It seems at least as if the synthesis took place 
 entirely on the initiative of the material itself. The possibility of illusions 
 is the chief fact that reminds us that this is not entirely true. When we 
 find that we have made a wrong construction, we can hardly ignore the 
 fact that we have made a construction' (p. 100, cf. p. 95). 
 
 * Consciousness may be regarded as the Ego's knowledge that it 
 knows : knows not its knowledge but itself as knowing. Locke says that 
 we cannot think without knowing it : 'We might as intelligibly sa.y that a 
 man can be hungry without knowing it' {Essay on H. U., book ii., c. i.). 
 So Cousin : ' We not only feel but we know that we feel. ... To think 
 without knowing that we think is as if we should not think. . . . The 
 fundamental attribute of thought is to have a consciousness of itself' 
 
126 Conception 
 
 sentient. Even sentient creatures are not consciously aware 
 of countless impressions which their senses receive at every 
 moment. Were our powers magnified, we might hear musical 
 notes of which the vibrations now fall on our tympana, but too 
 fast or too slow to be perceived ; we might listen to the grass 
 growing, or 'die of a rose in aromatic pain'. Even those 
 impressions to which we might attend by an effort of will— 
 and volition is to some extent required for all consciousness — 
 are not necessarily registered by the mind.^ I instinctively 
 brush away a fly from my face, or close my eyelids in a dusty 
 wind, or stretch my chilled hands towards the fire. 
 
 § 267. As yet the cause of the sensation is not, or is only 
 imperfectly, discriminated from the Ego. I am conscious of 
 a modification of the Real. When consciousness of duality 
 begins, we have Perception.'' An almost blind creature, for 
 instance, is aware that something comes between it and the 
 light, or, at least, is aware that its light is now here and now 
 gone. Perception, so far, is still objective. It is awareness 
 of existence. When the mind begins to take notice of its own 
 operations, it is said to reflect, to find a unity in diversity. 
 Perception becomes Judgement. I can distinguish myself from 
 
 (H. of Modern Phil., i. 274, 275). Reid also. ' Non sentimus nisi sentia- 
 mus nos sentire ' was a scholastic phrase. To be sure, consciousness is 
 'the common condition under which all our faculties are brought into 
 operation '. Yet we often perform complicated mental feats quite absent- 
 mindedly. See Myers' ' Human Personality ' ;passim. Again, if I 
 necessarily know that I know, do I necessarily know, or necessarily not 
 know, that I do not know ? 
 
 ^ ' Facts show us that, if the attention of the mind be absorbed in other 
 things, no impulse, though it amount to the laceration of the nerves, can 
 produce in us the slightest feeling ' (Morell, Psychology, p. 107). 
 
 ' ' It may be doubted whether the element of duality is ever absent at 
 any level of conscious experience. It may be that in mere sentience there 
 is no such distinction. There may be such a condition of consciousness 
 as is described by the word coenaesthesis, in which there is mere qualitative 
 awareness without its being an awareness of anything. But it is difificult 
 to attach any intelligible meaning to such a condition ' (Prof. J. S. Mac- 
 kenzie, Outlines of Metaphysics, p. 19). Yet, ' while it is true that all 
 experience seems to reveal a fundamental antithesis [between Subject and 
 Object], it is equally true that it never seems to reveal any separation. 
 On the subjective side we never, as Hume puts it, "stumble on ourselves" 
 in separation from a world of objects by which the more purely subjective 
 state is conditioned. On the other hand the objective side seems equally 
 inseparable from the subjective ' (Ibid. p. 22). See In Memoriam, xlv. 
 
Perception 127 
 
 this or .that affectioij of my consciousness because I am not 
 always affected in the same way. In Reflexion we subjectively 
 make our own thoughts and feelings the object of our mental 
 attention. 'I smell the blood of an Englishman.' Brutes 
 cannot reflect upon their feelings, cannot classify them, but 
 at the most associate them. Association, however, is not 
 generalization. To suffer toothache, to localize the ache, to 
 submit to have it remedied, to remember' it in a way, all this 
 does not amount to an abstract conception of toothache. The use 
 of words involves conception.^ If I say, ' I feel warm,' ' I hear a 
 scream,' ' I see a man approaching,' there must at any rate be 
 already in my mind a general notion of warmth, of screaming, 
 of man, and of approaching, as well as of feeling, hearing and 
 seeing. 
 
 § 268. Perception supposes a percipient. If the Mind is 
 not a mere unretentive mirror, neither is it wax,, nor yet a 
 blank page, prepared or unprepared, which is passively written 
 upon by the senses as scribes. Lord Herbert of Cherbury 
 likened the mind to a book written within and without, but 
 waiting for experience to open it and read. This is something 
 like Plato's dva/«^o-ts,' sensuous impressions and experiences of 
 the interior sense* merely giving the occasion to knowledge. 
 But this inadequately expresses the active and creative energy 
 of the Intelligence, reacting upon the deliverance of conscious- 
 ness, combining in its secret laboratory the materials supplied 
 to it by the senses, and bringing order out of unrelated 
 impressions. 
 
 § 269. According to Aristotle, the intellectus pattens perishes 
 with the bodily organism, which supplied the matter of know- 
 ledge, whereas the intellectus agens, which gives form to 
 knowledge, is imperishable. St. Thomas makes the same 
 distinction. The one is a receptacle of sense-impressions, the 
 
 ^ Without such remembrance punishment would have no effect. The 
 flogging dominie observed that knowledge must be acquired through all 
 the senses. 
 
 ^ See Hansel's Aldrich, Ixi. n.e. 
 
 = ' Our birth is but a sleep and a forgetting,' &c. That the soul should 
 have had an ante-natal pre-existence in God would not necessitate any 
 doctrine of metempsychosis or reincarnation. 
 
 * Spinoza says : ' Nos sentimus experimurque nos aeternos esse.' 
 
128 Conception 
 
 other a recipient of ideas, comprehending as well as appre- 
 hending. 
 
 § 270, The senses by themselves do not even perceive, far 
 less conceive. As Plato remarks, we do hot see by the eyes, 
 but through the eyes. Aristotle says : — vols Oeaipei, opa, Oiyyavei, 
 oLKovei. He speaks of a Common Sentient, Iv n Kotvov a'urOrjT-qpuiv, 
 a central faculty by which the reports of the organs about their 
 own objects — and it is more correct to speak of a plurality of 
 organs than of faculties — are reduced to the unity of a common 
 apperception. Hobbes and others call it the 'common sense'. 
 But the unifying centre is rather sensibility than sense or sen- 
 sorium. A sensorium may be purely physical — grey medullary 
 substance, or the like. But sensibility is the mind receiving 
 impressions through the senses under certain subjective con- 
 ditions. The message from any part of the body to the brain, 
 apprising it of some lesion or affection, is stopped by an 
 anaesthetic. Lewes agrees that all knowledge must have an 
 a priori element, but reduces this to ' the virtual capacity of the 
 knowing mind'.' We were not born with reason, but with 
 capacity for learning to reason." Yet he is clear that the 
 faculties could not have been evolved out of sense-impressions, 
 and that what perceives is the mind. 
 
 § 371. Perception is not an activity exercised by a higher 
 faculty upon a lower, but is the Self focussing its impressions.' 
 The Ego is to itself a unity amid the world's manifold. Yet 
 we distinguish the Sensibility from the Intelligence. What 
 the former is to objects of perception, the latter is to objects 
 of thought. The intuitional activity of the mind passes into 
 an ideational activity,, in which the mind reflects upon its earlier 
 operation. ' Intuitions without concepts are blind ' ; * while, con- 
 versely, concepts without content are void. Condillac asserts 
 that ' Penser c'est sentir '. According to him all the faculties 
 are only sensation transforming itself differently. This view 
 will not stand. Yet Sensibility and Understanding cannot be 
 
 ^ H. of Phil. ii. 484. 
 
 '^ Ibid. p. 361. 
 
 ' Lamartine says : — 'Ce n'est pas moi qui pense ; ce sont mes iddes qui 
 pensent pour moi.' But he does not mean this for serious psychology. 
 
 * Lewes, H. of Phil. ii. 496. Just before (p. 494) he quotes Hegel 
 (Encykl. § 24) — ' Man is always thinking even when he is intuiting.' 
 
Conditions of Consciousness 129 
 
 parted. We neither apprehend the universal first, nor the 
 particular first, but both together, the former in the latter.' 
 
 § 272. No fact stands isolated. ' Of a pure concrete we have 
 no experience.' ^ Every perception is a bundle of generalized 
 sense-impressions. What the understanding does is to separate 
 between the here and now of a percept and its general relations. 
 It abstracts. Abstraction is the intellectualizing of a conscious- 
 ness of difference and agreement. Two (or more) presentations 
 to consciousness are perceived to be the same, yet not the same. 
 It is not at bottom of consequence whether the comparison is 
 between two (or more) objects, exhibiting a similarity in diversity 
 — as when eyes, the sky, the sea, a violet, are all noticed to be 
 blue — , or between two (or more) phases of the same object — 
 as when the sea is observed to be blue, green and grey. ' Wine- 
 coloured,' a Homeric epithet of the ocean, may be regarded 
 either as one aspect of the sea — difference in unity — , or as a 
 resembling quality between the sea and wine — community in 
 difference. 
 
 § 273. Consciousness requires transition. Bain remarks : — 
 ' To make us feel, there must be a change of impression ; whence 
 all feeling is two-sided. This is the law of Discrimination or 
 Relativity. Observation shows that unbroken continuance of 
 the same impression is attended with unconsciousness. An 
 unvarying touch or a monotonous sound ceases to be felt. In 
 an even temperature we lose all consciousness of heat or cold.' ' 
 A lizard or other creature which is exactly like its surroundings 
 is practically hidden from the observer, even though he be 
 intently gazing at it. The flame of a match is invisible in 
 broad sunlight. The music of the spheres, supposed con- 
 tinuous and perfectly harmonious, is unheard. 
 
 § 274. But all consciousness also implies some perdurance. If 
 the changes of sensation were infinitely quick, so that the sense 
 received a continual rush of fleeting impressions, the mind 
 would perceive nothing. The impressions must have some 
 unity, — as colours melting swiftly into one another are all per- 
 ceived to be colour—, and the percipient mind must have some 
 retentive power. What is wanted is not consciousness of 
 
 ' 'Alio modo [substantia] universalis est quum cogitatur, alio singularis 
 quum sentitur' (Boethius). 
 = Bain, Logic, Pt. I. p. 7. ° Ibid. Pt, I. p. 2. 
 
 K 
 
130 Conception 
 
 transition at the moment it takes place — for daylight may die 
 by fine gradations into darkness, or a hard substance become 
 soft, without our apprehending any dividing line between the 
 two — , but rather memory — Bishop Hall's ' custos rotulorum ' — , 
 enabling the mind to compare a past with a present impression. 
 
 § 275. We see, then, that consciousness is of a one in the 
 many and of many in the one. The understanding, or cogitatio 
 abstradiva, invests a point of resemblance with an intellectual 
 character, and viewing it as quality {qualitas) regards it neces- 
 sarily in the light of a universal, which is indefinitely repro- 
 ducible and entitled to a common name applicable to an indefinite 
 number of objects. Memory, if merely (as with Hobbes) a decay- 
 ing sense, could not produce general notions, nor could these be 
 generated by simple iteration of sensations. ' Music, when soft 
 voices die, vibrates in the memory.' Condillac regarded 
 memory as literally the tendency of the brain fibres to vibrate 
 in the way they have formerly done.' Hartley developed the 
 vibration theory. Erasmus Darwin taught that recollection and 
 imagination are but 'a repetition of animal movements'. An 
 exploded materialism, however, need not here be discussed. 
 There cannot be ato-Orjm's ala-Orjcrcoi's. The notice which the mind 
 takes of its own operations and acquisitions cannot be explained 
 in terms of sense — sense does not distinguish or unify. By 
 the eye, by bare inspection, we could never discriminate the 
 shape of a piece of ice from its transparency. '^ 
 
 § 276. We have endeavoured, then, in the foregoing paragraphs 
 to suggest the psychological genesis of Conceptual Thought. 
 The human understanding notionalizes impressions, and, viewing 
 every attribute as a quality, gives it a general character, and 
 thus conceives it. 
 
 § 277. It is usually said that Abstraction precedes Generaliza- 
 tion. Abstraction is the withdrawal of the mind from all the 
 qualities of an object except one " — though this is only possible 
 
 ' Logique, c. Ix. pp. 82 seq. 
 
 ^ See McCosh, Discursive Thought, p. 4. 
 
 ' ' Drobisch observes that the term Abstraction is used sometimes in a 
 psychological, sometimes in a logical, sense. In the former we are said 
 to abstract the attention from certain distinctive features of objects pre- 
 sented [abstrahere a differentiis). In the latter we are said to abstract 
 certain portions of a given concept from the remainder {abstrahere 
 
Abstraction and Generalisation 131 
 
 when those other qualities have not invariably been experienced 
 in conjunction with it : if I lived immovable and with fixed gaze 
 in a world made entirely and uniformly of blue ice, I should be 
 unable, perhaps, to discriminate cold from colour. Generaliza- 
 tion, on the other hand, recognizes a common quality or 
 circumstance in several objects otherwise diverse. But these 
 are really the same mental operation. If it is possible to make 
 abstraction of a single property of a single object, this is because 
 the other properties of the object can be varied, the one 
 remaining the same. The moon is the moon whatever its shape 
 or place in the sky. This is abstraction. Again, a child has 
 a general idea of lessons, running through the variations of 
 reading, writing, arithmetic, geography, Latin, drawing, music, 
 and the rest. (If no child ever did any lessons but sums, the 
 two ideas might seem inseparable.) Is this abstraction or 
 generalization, or both ? ' If the world were a plain with a single 
 mountain in it, I could obtain as good an abstract idea of 'moun- 
 tainous' as if I knew a hundred such. If the mountain is 
 sometimes in eruption and sometimes not, the general idea of 
 eruption is as clear to me as if the mountain were part of a 
 volcanic chain. I may live by a single river crossed by a single 
 bridge, with a single cataract, and inhabited by a single crocodile. 
 A man may never have seen but one railway. A child may 
 know but one cat. But am I or they in the least surprised if 
 river, bridge, cataract, crocodile, railway or cat be found 
 repeated elsewhere ? It is the essence of a general notion to 
 cover an indefinite number of cases. Even an object sui generis, 
 or necessarily individual, is known under various circumstances 
 and in different connexions, and so can always be regarded 
 under the aspect of unity in diversity. Yesterday's, to-day's 
 and to-morrow's moon — the moon being thought of by most 
 people as a unique object — are practically three moons. There 
 
 differ entias)' Mansel, Prol. Logica, p. 25 n. It is the former we are here 
 concerned with. 
 
 '^ Whately gives as an example of abstraction without generalization a 
 man's attending to the scent of a rose— the only one he had ever met with 
 — disregarding its colour, form and the like. But he can do this because 
 he regards the rose-fragrance as a permanent property of the flower, 
 which would possess it equally in the dark ; or because it lingers in the 
 memory, 'living within the sense it quickens.' It has thus a general 
 character, perduring through differences. 
 
 K 2 
 
132 Conception 
 
 is but one ' God that judgeth the earth '. There is only one 
 centre of the material universe (if finite). But these readily 
 become notions. 
 
 § 278. It appears, therefore, that to recognize that several 
 objects have a common attribute, and to recognize an attribute 
 as constant in one object under varying conditions, are really 
 the same recognition. To consider a quality by itself is neces- 
 sarily to view it in an abstract and general light. 'Whatever 
 is received by the intellect is supra-sensible.' ' Aristotle says : — 
 alxrOaviTai jxiv to KaO' eKoxTTOv, ■^ 8' attrOrjcn's tov Ka96\ov iariv, oiov 
 avOpmirov aXK ov KaXXtou dvOfHiyirov,^ 
 
 § 279, But though it is at bottom the same thing whether 
 I recognize a similarity between several objects, or say, 'This 
 is what I have observed before under other circumstances,' 
 it is much easier in the former case to classify and name. To 
 do this we must refer the phenomenon to an existing category. 
 We know one object only by knowing others. 'Nought do 
 they know of England who only England know.' We can only 
 say what a thing is by saying that it is something else. ' Fire 
 is a good servant.' 'This is a Norman arch.' Now every con- 
 crete falls potentially under as many classes as it has attributes. 
 An orange is round, yellow, juicy, and so forth. These classes 
 have names. But many sensations, savours, scents, sounds 
 and unique experiences have no name.' We say. It is a je 
 ne sats quoi, a nescio quid, a something or other, a kind of feeling 
 or taste, a sort of look, an indescribable perfume, about which 
 it is not easy to compare notes with other people. It is an 
 affection of a certain sense, but the differentia cannot be named. 
 In King Henry the Sixth (Part II), Simpcox, who pretends to 
 have recovered his sight by a miracle, is detected even by the 
 simple king for a cheat when he names the colour of Gloucester's 
 gown — ' Black, forsooth ; black as jet.' How was he acquainted 
 with the category ' black ' ? If a person were to set about com- 
 menting on Shakespeare, with no previous study of general 
 literature, of words, customs, institutions and history, he could 
 
 ^ Clark, Logic, p. 99. ^ An. Post. i. 100* 15. 
 
 ' Manna ('which thou knewest not, neither did thy fathers know,' 
 Deut. viii. 3) was the name given by Israel to the bread from heaven, 'for 
 they wist not what it was ' — the word meaning either ' What is it ?' or 'a 
 portion '. 
 
Origin of Naming 133 
 
 contribute little more than, 'This is a fine passage'; 'This 
 scene appeals to me/ and the like — mere blue-pencil annotation. 
 Very complicated things, as well as very simple ones, are diffi- 
 cult to name — a character, a position of affairs in history or 
 politics, a piece of mechanism, a work of literature. Uneducated 
 minds, in all classes of life, have a very limited vocabulary; 
 though in an older state of society common folk were wonder- 
 fully shrewd in noting picturesque analogies, and their talk was 
 rich with proverbial lore. 
 
 § 280. When we proceed to ask how names originated, we 
 meet an insoluble problem. Are they, since a rose by any 
 other name would smell as sweet, purely conventional ? That 
 a mark once affixed to a class of objects having a certain 
 characteristic would quickly extend itself, analogically, to 
 numerous other classes is obvious. Weather, features, a poem, 
 conduct, an ideal, a scarce-discriminated difference, are alike 
 called ' fine '. ' Sharp ' is applied to a spike, a tooth, the wind, 
 a shrewish tongue, temper, wit, musical tone, and the like. 
 Whatever satisfies the canon of taste — a plump pig or a good 
 cigar as well as Cleopatra's face or a saint's death — is called 
 'beautiful'. In the rustic idiom 'terrible' (Seti/ov) is a word 
 for anything that excites admiration — e.g. 'a terrible one at 
 Scripture and that '. But how did the name come to be given 
 in the first instance? Philologists speak of some 120 'pre- 
 dicative ' roots, to which must be added a few ' demonstrative ' 
 or 'pronominal' radicals, at the actual disposal of human 
 language.^ Max Muller holds that every one of these mother- 
 sounds expresses a general idea, and (with Leibnitz) that 
 names of individual objects or persons were originally appella- 
 tive — e.g. George Cooper, Mayfair, Lent, moon, earth — , whereas 
 Nominalist thinkers (e.g. Locke, Condillac, and Adam Smith) 
 uphold the contrary view, that all names were originally proper 
 names. Of course there are many such — e. g. palace (Palatium), 
 
 ^ Max Miiller, Lectures on the Science of Language, ninth edition, i. 
 306-10, 441, 442. With the twenty-four letters, however, the number 
 of possible biliteral and triliteral roots would amount to 14,400. The 
 actual combinations of the four-and-twenty is calculated by Leibnitz at 
 620,448,701,733,239,739,560,000 I In a monosyllabic language like 
 Chinese, there is no formal distinction between noun, verb, adjective, 
 a.dverb and preposition. A Chinaman finds it difficult to conceive a 
 language in which every syllable is not significative (ibid, pp. 332, 377), 
 
1^4 Conception 
 
 iiansom, boycott, pasquinade, Bradshaw, brougham, Gladstone, 
 lazar, maeander, currant. But how did proper names origi- 
 nate ? When we go further back we come sooner or later to 
 a root expressing a general notion. ' All naming is classifica- 
 tion/ and — except perhaps the handful of demonstrative roots 
 — 'every word is originally a predicate.* The old view that 
 brutes are without articulate speech because they cannot form 
 general conceptions seems perfectly philosophic. They are 
 aXoya, without Xoyos.* 
 
 § 281. It will occur to every one that, if it is impossible to 
 form general notions without having names to give them, if sign 
 must precede cognition, the names must have been given to 
 general notions by those who as yet had no general notions. 
 This is like the question, which came first, hen or egg ? If lan- 
 guage were literally an arbitrary convention, the philologist would 
 be posed. We are forced to believe that thought and speech were 
 evolved, or given, together, as two sides of the same thing. 
 
 § 282. The advocates, indeed, of the Onomatopoetic and of 
 the Interjectional theories of the origin of Naming consider that 
 names were supplied to man ready-made, by imitation of the 
 sounds of the world around him, or by his own involuntary 
 noises. Such words as crash, clank, crunch, hum, mugire, 
 balare, o-i'^ctv (the word used by Homer for the sound made by 
 the red-hot pine-tree when dropped into Polyphemus' eye), are 
 samples of a host of mimetic words. The nursery is rich in 
 them; so also is slang {'ticker,' 'fizz,' &c.). Max MuUer, as 
 every one knows, ridiculed this as the bow-wow theory. Ono- 
 
 ^ ' Whatever we know, we know it only by means of our general ideas. 
 Other animals have sensation, perception, memory, and, in a certain 
 sense, intellect ; but all these, in the animal, are conversant with single 
 objects only' (Max yivA^x, Lectures on the Science of Language, mafii 
 edition, i. 433). Accordingly ' the one great barrier between the brute 
 and man is Language. Man speaks, and no brute has ever uttered 
 a word' (ibid. p. 43). The writer quotes Descartes and Locke (ibid. 
 PP- 399i 405) ^s to the fundamental difference between the mind of 
 a beast and the mind of a man. Yet Locke did not regard language as 
 necessary to thought. To the ancients talking oaks (Trpocrfiyopoi Spies) 
 did not appear more monstrous than utterance from ox ('bos locutus est') 
 or horse. When Achilles' horse speaks, the portent is repressed by the 
 Erinnyes, as guardians of the cosmic order (//. xix. 418). In the Book of 
 Numbers the abuse of reason (irapacjipoi'la) by a prophet, to whom the gift 
 of utterance has been given above other human beings, is rebuked by 
 speech in the mouth of the least intelligent of ciXoya C^a. 
 
Origin of Naming 135 
 
 matopoeia accounts, he argued, for only a certain proportion of 
 words; and, 'though a language might have been made out 
 of the roaring, fizzing, hissing, gobbling, twittering, cracking, 
 banging, slamming, and rattling sounds of nature,' language as 
 we know it had a different origin. The Interjectional hypothesis 
 he called the pooh-pooh theory, for 'language begins where inter- 
 jections end'.^ Professor Sayce suggests the 'ding-dong' 
 theory — that man responds to the impressions of nature like a 
 bell that is struck. 
 
 Max Mtiller, however, makes scarcely an attempt to explain 
 how names did arise. Roots, or phonetic types, 'are simply 
 ultimate facts.' He has to fall back on a mystical or theo- 
 logical explanation. ' We might say, with Plato, that they 
 exist by nature ; though with Plato we should have to add that, 
 when we say by nature, we mean by the hand of God — ^ijo-m rot 
 
 § 283. Even though all language is 'by nature ', yet we have 
 to distinguish ' natural ' from ' artificial ' modes of expression : 
 not merely cries and gestures from grammatical speech, but 
 painting, sculpture and hieroglyphics from writing, telegraphy, 
 and the like. When we see three balls we mfer a pawn- 
 broker's; when we see a wooden Highlander a tobacconist's; 
 a bush over the door signifies a wine-shop. These are repre- 
 sentative signs.. But a bootmaker's is presentatively indicated 
 by boots in the window, a grocer's by sugar and raisins. Again, 
 some language may be purely Kara trwdi^Krjv, as a burglar's signal 
 to his accomplice, or calling for trumps at whist. Contrast 
 Blondel's minstrelsy, by which King Richard knew in prison 
 that a friend was near ; or the flute which told the besieged in 
 Montauban that relief was at hand. In the Rehearsal much 
 was conveyed by a shake of the head — ' vox quaedam est animi 
 corporis motus.' 
 § 284. Words tend in course of time to become mere tokens, 
 
 ^ Lectures, i. 419, 420. 
 
 ^ Ibid. p. 439. Some of the Greek Fathers held that paradisal Man 
 was only dowered with a power of nomenclature, not with a stock of 
 words and syntactical constructions. The origin of Grammar takes the 
 inquirer into the profoundest recesses of the human intellect. It is the 
 earliest philosophy of the race : hence the possibility of a universal 
 Grammar. The first attempt at a ' Grammaire Gdndrale et Raisonnde ' 
 was that published by Arnauld and Lancelot of Port Royal in i66o. 
 
136 Conception 
 
 losing their intrinsic and acquiring a merely conventional value. 
 Every language, it has been remarked, begins as poetry and 
 ends as algebra. A Bill ' runs the gauntlet ' of criticism. To be 
 clapped is to ' receive an ovation '; to think is to ' labour under an 
 impression ' ; a scrape is a predicament, a madman is a lunatic, 
 a smile bewitches, a debtor is bankrupt. Every second word we 
 use in modern speech is a slipshod metaphor of which we have 
 forgotten the meaning. Hence the austere educational value of 
 Latin composition. 
 
 Place-names have all, no doubt, had at one time a general 
 significance ; e. g. Cologne (colonia), Edinburgh (Edwin's burgh), 
 Bradford (broad ford), Kirkcudbright (Cuthbert's kirk), Essex, 
 le Havre, Weymouth, Bath, Wells, Haymarket, and the like. 
 
 § 285. Proper names may be used representatively as common 
 names ; as when we speak of playing the Lady Bountiful, of a 
 village Hampden, of a Daniel come to judgement, a Roland to 
 your Oliver, a modern Bayard, a little Eden. Boniface comes 
 to mean an innkeeper; Rosinante a lean nag; Edwin and 
 Angelina stand for a young married pair ; Jacques Bonhomme 
 is a French peasant ; Tommy Atkins an English private ; Ivan 
 Ivanovitch a Russian conscript. Or an individual may be 
 thought of as capable of multiplication. ' If I had business at 
 Leipzig,' boasted Luther, ' I would ride into Leipzig though it 
 rained duke Georges for nine days running.' Again, where a 
 concept is highly complex we often personify it — John Bull 
 standing for the English character. Father Christmas for Yule- 
 tide festivities, Pomona for the rural scenes of autumn. Ab- 
 stractions like liberty, empire, industry, agriculture, are con- 
 ventionalized in art by an individual figure bearing certain 
 emblems. Authority, old and blind, is pictured by the poet as 
 beating with his staff the child that might have led him, or 
 Laughter as holding both his sides. Truth is shown by the 
 sculptor tearing out the tongue of calumny. Time is an old 
 man with scythe and hourglass, or ' has a wallet at his back '. 
 Opportunity has a forelock, but is bald behind — 'fronte gerit 
 crinem, post est occasio calva.' 
 
 § 286. To say that an individual can only be conceived by 
 becoming generalized is as much as to say that there can be no 
 idea of a fact indicated as such. A united Italy is a conception, 
 but an Italy in fact united is a presentation to consciousness. 
 
Fact cannot he Conceived 137 
 
 Place can be thought of conceptually because it is not a naked 
 there or here — not even ' the point midway between Bath and 
 Bristol' — but it has local colour and circumstance, which might 
 be repeated elsewhere, or indeed may have no geographical 
 reality at all — like Utopia with its stream the Anyder, or like 
 the Hesperides, or the castles we build in Spain. Settlers in 
 new lands try, like Aeneas' followers, to reproduce the familiar 
 places of home. Less easily can time be idealized. The 
 externals of a period, no doubt, may be reproduced — cinque- 
 cento, Elizabethan, Louis Quinze ; the ' brave days of old ' 
 might conceivably return in a golden cycle ; but ' now ' or ' last 
 Tuesday ' can by no possibility be anything but now and Tues- 
 day last. Of course, since time's stream is for ever running 
 beneath the bridge, there is, in one sense, an endless succession 
 ofnows, of present standpoints. ' A fortnight hence ' to-morrow 
 will be a different date from ' a fortnight hence ' to-day. In this 
 sense there is a general idea of nuncitas. But not of the actual, 
 the asserted, demonstrative now, the 'now' to me who am 
 judging and speaking.^ I must stand off my own shadow, so to 
 speak, to make categorical indication notional. 
 
 § 287. A real event can be depicted on canvas or otherwise 
 in all its circumstances — place, persons, action and the sugges- 
 tion of date — like the past fortunes of Troy which Aeneas saw 
 on the walls of Dido's palace, or the future history of Rome 
 represented on the shield wrought by Vulcan. And what is 
 pictorial, whether it be of an existent thing, as London Bridge at 
 midnight, or a non-existent thing, as a hundred-headed giant, 
 is ideal. But a picture asserts nothing. Hence tense enters 
 into predication only as itself predicated." It does not modify 
 the assertive energy of the sentence. There are not different 
 kinda of assertion — past, present, future, perfect, pluperfect, &Ci 
 See below, § 612. 
 
 § 288. But though ' in perception the object known is always 
 a single determinate object ',' no judgement about fact can be 
 purely concrete, for every judgement involves inference. The 
 
 ^ ' So long as we keep a demonstrative, spatial or temporal, reference 
 in the thought, the subject of judgment is not cut loose from our personal 
 focus of presentation ' (Bosanquet, Essentials, p. 62). 
 
 ^ Aristotle, after defining a name as ^avfj <njij.avTiKri Kara a-vvdfjKrjv dvev 
 Xpovov, goes on to recognize tense in the verb {De Interpr. 2. i). 
 
 ' Hamilton, Lectures on Logic, i. 75. 
 
138 Conception 
 
 fact is judged in the light of theory. And, further, the proposi- 
 tion is the interpretation in words of the judgement. 'I am 
 watching the sun setting.' ' I saw the conjuror put the card into 
 the pack.' We place sensations under descriptive conceptions ; 
 and it is here that error enters. 
 
 § 289. Similarly, the very naming of an individual object is 
 never wholly concrete. It is assumptive, and in some degree 
 theoretic^ ' Your brother Richard ' assumes that you have a 
 brother, and that his name is Richard. , Simple ' Richard ' 
 assumes that there is a person so called, and that to-day's 
 Richard is the same person as yesterday's. 'EKctvos, 'that person 
 over there' assumes that there is a person over there; while 
 pointing with the finger involves the idea of digital indication. 
 To get to the primum cognitum of the pure Concrete the Ego 
 must go behind even the simplest judgement to the original and 
 speechless conviction of its own intuitional modification, of 
 Reality as determined for me. No explicit judgement can 
 be without an element of abstraction. We cannot think without 
 generalizing. 
 
 § 290. As conception implies experience, so nothing can be 
 an element in a concept which cannot be pictured to sense 
 or imagination. The notion is ovk aviv ^avracr/iaTog. Yet it 
 is in itself ideal and universal. Hence connotation precedes 
 denotation. A castle is every building which is castellated ; 
 and, though empirically the number may be limited, the limit 
 is a material one only. There might be infinite millions of five- 
 act tragedies existent, if it so happened. 
 
 § 291. The concept, then, having an ideal universality, cannot 
 be pictured or imaged as a concept, but only through some 
 representative individual of the class, which must needs appear 
 with individualizing characteristics. A clock must be shown, 
 or imagined, as grandfather clock, Dutch clock, church clock, or 
 otherwise ; circle as of a certain diameter ; flower as of some 
 shape and kind.^ The universal is realized in the individual. 
 
 ' Artemus Ward's versatile wax figure which had stood for so many 
 celebrated characters was pronounced by critics not to look like one 
 person more than another — in fact, not like anybody that ever lived. 
 This, the showman claimed, was what made the effigy so rerriarkable, 
 and well worth paying to see. Still, it could not have done duty for 
 mankind generally without being the representation of a possible 
 
Idea and Image 139 
 
 The individual is known through the universal. I know this 
 figure to be a rectangle because each of its corners is a right 
 angle. 'This rose' combines intuition with idea — either, the 
 rose concept here and now realized, or this object possessing 
 the rose attributes. 'Our dog' indicates a definite dog. 'A 
 dog of ours' the same if 'a' means 'a certain', but an ideal 
 dog if it means ' any ', 
 
 § 292. There was a street in Paris a generation ago which, 
 having been called Rue de la Reine, and then Rue de I'lmp^ra- 
 trice, had its name altered again to Rue de la Mardchale Mac- 
 mahon. Some one then suggested that, to obviate the need 
 of future changes, the street should be permanently designated. 
 Rue de la Femme du Chef du Pouvoir Ex^cutif. 
 
 § 293. Intellection of the common or constant amid diverse 
 presentations to consciousness gives us, then, the Concept or 
 Notion, the Common Name of which signifies 'possessing an attri- 
 bute', either as qualifying adjective — e. g., blue, circular— or as 
 substantive (reality quahfied thus or thus) — e. g., child, circle. 
 The connoted attribute — blueness, childhood, circularity — is 
 necessarily substantive, and can never, except seemingly in 
 identifying judgements, be a predicate. Possession of it is the 
 ground to any object for sharing in the common name and 
 coming under the concept-class, which consists of all the actual 
 and possible objects which have the attribute. 
 
 §294. 'A', 'an' (Scots ane, German ein, French un, Latin 
 unum), mean, of course, one. 'A dog is an animal' means 
 •Any one object characterized as dog is some one object 
 characterized as animal.' We shall see below under 'Judge- 
 ment' the reason for the difference here between subject and 
 predicate. 
 
 § 295. Every Concept is really a complex consisting of a 
 substantival and an adjectival element. In the ultimate analysis 
 the substantival element is Substance, or Reality, which is 
 qualified in the way indicated by the name. But, without 
 carrying analysis so far, we have little difficulty in breaking 
 up ordinary concepts into these two elements (' thrush ' is the 
 thrush kind of bird, a bird having the thrush characteristics), 
 
 individual, any more than the 'portrait of a gentleman ' in our exhibitions. 
 General names are possible, but not general images. 
 
140 Conception 
 
 while many concepts ire either compounds (as tea-caddy, engine- 
 driver, bluebell, wryneck, woodpecker), or actually consist of 
 a substantive and adjective, or a substantive qualified by a 
 dependent clause, or by another substantive used adjectivally 
 (as muffin-bell, stone wall). 
 
 § 296. Not all adjectives or adjective clauses, however, are so 
 in the sense of being restrictive and determining. They may be 
 epithetical or appositive. Contrast ' roast fowl ' with ' feathered 
 fowl ', ' good men ' with ' mortal men ', ' nobleman ' with' ' noble 
 lord ', ' learned member ' or ' learned pig ' with ' learned coun- 
 sel ', ' learned member ' with ' honourable member ', ' peace with 
 honour ' with ' meek-eyed peace ', ' the cup that cheers but not 
 inebriates' with 'wine that maketh glad the heart of man', 
 'injured innocence' with 'heaven-loved innocence', 'fallen 
 seraph ' with ' sworded seraphim '. ' Port which is unadulterated 
 is wholesome ' is not parallel to ' port, which is a red wine, 
 is shipped from Lisbon' — observe the commas. Epithetical 
 adjectives are common, of course, with proper names and in 
 poetry — 'coaly Tyne'; ' silver-streaming Thames'; 'black- 
 browed night'; 'ignis edax'; 'gold-dusted snapdragon'; 
 ' towered cities ' ; ' Genova superba ' ; ' knotty oaks ' ; ' wind- 
 changing Warwick ' ; ' great Anna ' ; ' ivy never sere.' In 
 'right reverend prelate' the adjective is assumptive, not con- 
 ditioning, except that by usage it excludes archbishops. ' Merry 
 Christmas' is not parallel to "a merry Christmas', nor 'leafy 
 June ' to ' a wet June '. Appositive expressions are of frequent 
 occurrence — 'Knowledge, the wing wherewith we fly to heaven'; 
 ' sweetest Shakespeare, Fancy's child ' ; ' spare Fast, that oft 
 with gods doth diet'; 'daisies, those pearled Arcturi of the 
 earth'; 'bluebells trembling by the forest ways.' Adjectives 
 attached to abstract names are usually ornamental — 'sour severity,' 
 'sweet seventeen,' 'youthful jollity.' In naive and childlike 
 poetry, such as Homer or the ballad, they recur with quaint irrele- 
 vance. In the Odyssey, for instance, even the traitor Aegisthus is 
 a/Av/Mov (i. 29). Complimentary titles like ' right honourable ' are 
 of this kind. And since every epithet is an assumption, such 
 adjectives follow the definite article or demonstrative pronoun, 
 and but seldom the indefinite article — ' the splendid Vandyck,' 
 'your fair daughter,' 'yonder green tree.' 
 
 § 297, Logic cannot tell whether an adjectival expression is 
 
Descriptive and Determinative Adjectives 141 
 
 descriptive or determinative, except that the voice lays a slight 
 stress upon any determining element. In pronouncing ' bonny 
 red gold/ 'dishonest rogue,' 'yellow guineas,' 'simple Susan,* 
 the emphasis is almost even, or, if anything, lies on the 
 substantive, since all guineas are yellow but not all yellow 
 things are guineas. But in 'red rose,' 'dishonest trustee,' 
 'yellow hair,' 'simple remedies,' it is on the adjective. 
 ' Green ' qualifies dress but describes grass. ' The guilty 
 boy shall be punished ' could either mean ' the boy, being 
 guilty, shall be punished ' (dStKijo-as o ttcws KoXaa-Oi^a-eTai) or ' the 
 guilty one among the boys' (5 n-ais o dSix^o-as), according as a 
 trifling accentuation were laid on the word ' boy ' or ' guilty '. 
 
 § 298. In examining the development of the Concept into the 
 Judgement, we shall see that descriptive adjectives become the 
 predicate of a universal judgement — ' mad Tom ' implies that 
 Tom is mad, ' tinkling rills ' that all rills tinkle, ' foul fiend' that 
 every fiend is foul. This is obvious in the case of appositive 
 phrases — 'sweet-william with his homely cottage-smell', 'the 
 gods whose dwelling is not with flesh.' 
 
 § 299. On the other hand, adjectival expressions which qualify 
 a noun restrictively develop as a particular judgement, and at 
 the same time imply the ' sub-contrary ' judgement. ' Well- 
 printed book', 'contented age', give us when realized 'some 
 books are well printed ', ' age is sometimes contented ', but 
 imply as a fact that some books are not well printed, and that 
 age is not always contented. 'Well-printed Aldine', on the 
 other hand, is a description, for all Aldines are printed well. In 
 'high-elbowed grigs, that leap in summer grass ' we find implied 
 not only a universal, but a convertible one. But this we only 
 know materially. 
 
 § 300. The fact that a 'sub-contrary' proposition is implied by 
 any qualifying and conditioning expression enables a person to 
 argue that if a thing is denied or condemned under a certain 
 aspect it is admitted or allowed under other aspects. Thus 
 Newman in Tract XC showed that condemnation of the dodrina 
 Romanensium concerning purgatory, pardons, &c., involves 
 recognition by the Article of a Catholic doctrine on those points. 
 \i XY's are denied some other Y's. are granted. An exception, 
 or qualification, stated as such, proves the existence of a rule. 
 ' I do not leave the office on Fridays till six ' implies that on 
 
142 Conception 
 
 other evenings I leave earlier. A dispensation implies a law to 
 the contrary. 
 
 § 301. Since universal propositions are contradicted by par- 
 ticular ones, and vice versa, epithetical positives are opposed to 
 determining negatives, and epithetical negatives to determining 
 positives — ' immortal gods ' to ' a mortal god ', ' irresponsible, 
 indolent reviewers ' to ' a reviewer who is neither irresponsible 
 nor indolent '. Wordsworth's lines — 
 
 Heaven out of view, our wishes, what are they ? 
 Obsolete lamps, whose light no time recalls, 
 Urns without ashes, tearless lachrymals — 
 
 imply that as a rule all urns contain ashes and lachrymals tears, 
 and that lamps are meant for light. But, ' obsolete ' standing 
 before 'lamps', the phrase 'whose light no time recalls ' becomes 
 merely epexegetical. 
 
 § 302. Particular negative can be true at the same time as 
 particular affirmative judgements. Accordingly, while the ideas 
 of deadly and of venial sin, of important and of unimportant 
 news, are opposed, the things can and do coexist in reality. 
 Descriptive epithets, on the other hand, suggest an assertion, 
 and therefore exclude a contradictory description. ' Royal- 
 towered Thame ' assures us that the Thames is not lined 
 throughout with gasworks, soapworks and smart villas. Con- 
 trast ' good Queen Bess ' with ' a discrowned Lear '. The latter 
 is an idea ; the former only a fiction. 
 
CHAPTER X 
 
 INTER-RELATION OF CONCEPTS 
 
 § 303. We are now, having analysed the Concept, in a 
 position to examine further the inter-relation of its elements, 
 and of concepts among themselves. For if every concept 
 consists, either openly or implicitly, of a substantival and an 
 adjectival element, that is as much as to say that every concept 
 is composed of one concept qualified by another; e.g., salt 
 water, hydrostatics, waistcoat, madman, halfpenny, hen (hen bird). 
 No doubt, an enormous number of common names are a simple 
 word (pen, book, boat, &c.). But, as already observed, every 
 such word either implies some generic class of which it is a 
 particular sort, or at least, ultimately, it is a qualification of 
 thingness or reality. Etymology will often make this clear. 
 Thus, hell is the covered (place). 
 
 § 304. Concept qualified explicitly by concept is the potential 
 definition of any simpler concept which is its equivalent. If we 
 wish to define a name we find some higher concept under which 
 to range it, some higher class under which the objects named 
 fall, and then seek so to qualify that higher concept, so exactly 
 to mark off a portion of that class, that equivalence is established. 
 Regarded extensionally as the delimitation of a class. Definition 
 may be represented by the intersection of two circles. 
 
 § 305. For different purposes, however, a concept has different 
 definitions. It may be conceived from as many points of view 
 as the thing conceived has attributes — see below, § 386— each of 
 these forming a higher concept under which it can be ranged. 
 And since each higher concept falls in turn under superordinate 
 concepts, there results a chain, or rather network, of generic 
 and specific concepts. 
 
 § 306. In defining, we select the most important and charac- 
 teristic attributes for the purpose in hand. We should be 
 unlikely to define a motor carriage as a movable machine 
 
144 Inter-Relation of Concepts 
 
 which is bound by law to carry a visible letter and number, nor 
 a postage stamp as a picture of the Sovereign an inch square. 
 But, whatever the definition I select, that is, for the moment at 
 any rate, my conception or notion of the thing. The notion is 
 thus not anything fixed, but subjective. On the other hand, a 
 definition propounded to others implies a common ground of 
 possible agreement as to the content of the notion. 
 
 § 307. Regarding definition as the intersection of two spheres, 
 it is obvious that the class defined falls wholly within both 
 those spheres. If a ship is a navigable dweUing, every ship is 
 a dwelling and every ship is navigable. Sometimes one of the 
 spheres falls entirely within the other, coinciding with that of 
 the definiendum ; in which case the attribute which marks the 
 former is a proprium of the class defined ; as if a man is defined 
 as a food-cooking animal, or real estate as landed property — 
 though, to be sure, land is sometimes unappropriated : the light 
 soil of the Sahara, for instance, or the polar regions. But 
 definition by genus and property is not good definition.* 
 
 § 308. In respect of their mutual relations. Concepts are 
 divided as : — 
 
 (i) Mutually exclusive (kind, cruel ; plant, mineral). 
 
 (2) Co-extensive (equilateral, equiangular; faithful, hereafter 
 to be rewarded). 
 
 (3) Subordinate and superordinate (wren, bird ; clock, useful 
 invention). 
 
 * It is surely by an oversight that both McCosh {Discursive Thought, 
 p. 103) and Veitch {Institutes of Logic, p. 195) assert that a differentia 
 must be convertible in extension with the species. McCosh gives as an 
 illustration, ' Mammals suckle their young ' (' Mammals are viviparous 
 animals ' would be better). Such a rule would exclude most definitions, 
 though definitions relating to natural kinds, and some mathematical ones, 
 often comply with it. We might define schooner as a two-masted ship, 
 though the sphere of ' two-masted ' falls entirely within that of ' ship '. 
 The objection to the differentia being a proprium is that, for diagnostic 
 purposes, such a definition might dispense with the genus altogether. 
 Why not say, ' a schooner is an object with two masts ' ? This would 
 bring us to definition through a commensurate attribution. ' L'fitat c'est 
 moi ' was meant to define the State. 'Homo est animal rationale' has an 
 absolute differentia if St. Thomas is right in saying that the angels are 
 not rationales but intellectuales. The Christian Platonists held demons 
 to be rational and also animal, adding ' mortal ' for the definition of man, 
 as the Greeks, to whom the gods were faa, had also done. 
 
Genus and Differentia 145 
 
 (4) Co-ordinate (wren, finch, robin ; clock, sundial, watch). 
 
 (5) Intersective (kings, philosophers ; vocal music, good 
 music). 
 
 § 309. I have hitherto tried to avoid the expressions Genus, 
 Species and Diiierentia, which belong to the classifications of 
 natural philosophy rather than to Logic. The qualified concept 
 in a definition may be called Genus, and the qualifying concept 
 Differentia. But, except in the case of a proprium, where the 
 qualifying sphere falls altogether within the qualified sphere, it 
 is impossible for the mere logician to say which is the generic 
 and which the differentiating idea. The circles intersect. 
 Differentia, therefore, may be regarded as genus and Genus 
 as differentia.' Man is a rational animal ; that is to say, he is 
 a rational among animals, and an animal among rationals. The 
 circumstance that grammatically the differentia is adjectival is 
 of no consequence logically. 
 
 § 310. Again, the subjects and predicates of ordinary speech 
 can hardly be dignified, even when we define, as Species and 
 Genera. Flirtation has been defined as attentions without 
 intentions. Flirting is a kind of attention ; but we should not 
 call it a species of that genus. At the same time, the 
 phraseology is convenient, for want of purely logical expres- 
 sions. We shall then say that every division of a whole class, 
 whether it has a name to itself or not, stands to the whole class 
 in the relation of species to genus. A white cat is a particular 
 kind of cat ; a faded scarf is a scarf under specific circum- 
 stances ; love in idleness is love circumstanced thus and thus ; 
 cupboard love is generic love so differentiated as almost to 
 destroy its character. 
 § 311. By qualifying a concept we make it more concrete. 
 
 ' In 'A quadruped is a four-footed waaa.2\' four-footed seems obviously 
 to be the distinguishing characteristic. But suppose the question to arise 
 whether a table with four legs could be called a quadruped, as one with 
 three is called a tripod. No, it would be replied ; a quadruped is a four- 
 footed animal. 'Animal' here is the logical differentia, not the genus. The 
 distinction that Genus is predicated of Species 'in the category of substance* 
 and D ifiference ' in the category of quality ' is merely grammatical, not logical. 
 'Conscience is an inward monitor' might be expressed 'is something within 
 us which warns '. A pupil-teacher is a teacher-pupil, a rainy drizzle is a 
 drizzling rain. On the other hand a libre-penseur is not necessarily a 
 penseur libre. Quarles says : — ' Be wisely-worldly, be not worldly-wise ' ; 
 and Tennyson warns us against thinking that man-woman is woman-man. 
 
 L 
 
146 Inter-Relation of Concepts 
 
 Chop is more abstract and further from experience than veal 
 chop, play than play of Shakespeare. This is also stated by 
 saying that every additional determination of a notion produces 
 an enlarged Intension or Comprehension and a contracted 
 Extension or Sphere. The new notion implies, or connotes, 
 more qualities than the old one, but applies to, or denotes, 
 fewer objects. There are more tradesmen than haberdashers. 
 The predicate, then, of a universal judgement has fewer attri- 
 butes but a wider extension than its subject — unless, indeed, 
 they chance to be convertible ; e. g., ' A modern regiment has 
 ceased to take its colours into battle.' The following exhibits 
 to the eye an intension enlarging with each new qualifica- 
 tion : — 
 
 Man 
 
 I 
 Seaman 
 
 I 
 One-armed seaman 
 
 Young one-armed seaman 
 
 I 
 Brave, young one-armed seaman 
 
 Thrifty, brave, young one-armed seaman 
 
 A number of circles enclosed one within another, of which 
 ' man ' should be the largest, would exhibit to the eye the 
 diminishing extension. 
 
 § 312. If we qualify a concept negatively, what is the effect 
 on its intension ? Does it diminish or increase it ? Obviously 
 it makes no difference whether the qualification is positive or 
 negative. 'Unkind mother' enlarges intension just as 'kind 
 mother' does. 
 
 § 313. On the other hand, a negative determination has 
 frequently an adversative suggestion — a mother, yet unkind. 
 And we cannot lay down any law that Intension and Extension 
 are necessarily in an inverse ratio. The addition of one 
 qualification to a concept may very greatly, and the addition of 
 another very slightly, diminish the number of objects included 
 in it. There are twelve times as many white metals as red. 
 Add ' sane ' to ' human being ' and the number of persons 
 denoted would not be greatly diminished. If we added 'insane' 
 
Intension and Extension 147 
 
 it would be enormously lessened (Carlyle would deny this of 
 the qualification ' fool '). Conversely, if good poets multiplied 
 among us, this would not affect the idea of good poetry. An 
 increase of population, as Mr. Stock remarks, does not diminish 
 the meaning of * baby '. All that inverse variation of Intension 
 and Extension means is that, if you ' enlarge your conception ' of 
 a term (diminish its Intension) you necessarily allow more 
 objects to come under it, whereas if you narrow your conception, 
 (add to the meaning you put upon a name), you necessarily 
 exclude objects from it which otherwise would be included. 
 Observe that an enlarged conception is not one which implies 
 more attributes, but rather one which embraces a larger variety 
 of objects. If guardians of the poor widen their definition of 
 the term 'necessitous' they diminish the qualifications for 
 relief, and make more people eligible to receive it. 
 
 § 314. We are not concerned with the actual empirical exten- 
 sion of a name. Mill truly observes : ' The Extension of a 
 concept is not, like the Comprehension, intrinsic and essential to 
 the concept, and no contemplation or analysis of the concept 
 itself will tell us anything about it. It is an abstract name for 
 the aggregate of objects possessing the attributes included in the 
 concept ; and whether that aggregate is greater or smaller does 
 not depend on any properties of the concept, but on the bound- 
 less productive powers of nature.' ' 
 
 § 315. None the less, be the extension of a concept what it 
 may, it is inevitably increased or lessened by subtraction from, or 
 addition to, the qualities implied in the name. By extension we 
 here mean the actual range of objects to which the name does, 
 or did, or will apply, not those to which it might apply.' For 
 
 ^ On Hamilton, p. 437. 
 
 ° Sigwart observes that we must 'distinguish between the logical 
 extension of the concept and the empirical extension of the name. Two- 
 footed unfeathered animal is a different concept from that of Man. They 
 are really different, and, logically considered, they have a different exten- 
 sion' {Logic, i. 271). The two classes happen to be the same. Another 
 illustration might be human beings and descendants of Noah. It is an 
 empirical accident that ' of Noah's three sons was the whole earth over- 
 spread'. This is not part of the idea of human being, though it might be 
 held that descendant of Adam is inseparable from that idea. But Sig- 
 wart's distinction pertains to Realism rather than to Logic. Unfeathered 
 bipeds might exist who would not come under the usual definition or idea 
 of Man. But the logician is indifferent to the correctness of definitions. 
 
 L 2 
 
148 Inter-Relation of Concepts 
 
 the possibility of application is unlimited — everything tabular 
 is a table — and it might be urged that one potential infinite is as 
 large as another. The fact, however, remains that the extension 
 of a divided whole is the sum of the extension of its parts ; and 
 that therefore the number of mahogany tables must be fewer 
 than the number of tables. The counter-enlargement of Mean- 
 ing and Sphere, of Depth and Breadth, means this and nothing 
 more. It does not mean that if there were twice as many sheep 
 the meaning of mutton would be halved ; or that a class con- 
 taining ten objects has three times as much intension as a class 
 containing thirty. If last week I had six apples, I have not 
 fewer now because they have gone rotten.' 
 
 § 316. The address placed on a letter, if we read it (as the 
 post office does) backwards, proceeds by successive limitations, 
 gradually narrowing down the number of possible recipients. 
 Thus : — ' Mr. William Robinson, junior, 25A, Waterloo Square, 
 South Hampstead, London, N.W., England.' The person 
 addressed lives in England, in London, in its north-western 
 district, in Hampstead, in the southern part of it, in one of the 
 squares there, in Waterloo Square, at no. 25, and of the two 
 twenty-fives at 25A. He is named Robinson, is a male member 
 of that family, bears the name William, and of the two so 
 named is the son, not the father. One person alone possesses 
 all these attributions. ' William, England ' would hardly have 
 found him ; for the wider the possible extension of a term the 
 less adequate is it as a representation. 
 
 § 317. The species dividing a class are either named by 
 prefixing the differentia to the genus — as cart-horse, carriage- 
 horse, racehorse, saddle-horse ; war-ship, merchant-ship, 
 training-ship; writing-paper, blotting-paper, newspaper — or 
 else by a substantive either suggestive of the differentia — as 
 poet, cook, artist, politician, — or a word which does not 
 suggest the differentiating quality — as ink, coal. Species 
 named by a differentiating prefix are seen at once to have a 
 greater intension than the genus — post office than office, pea- 
 fowl than fowl—; but, if we were asked which has more 
 
 ' This, I presume, is what Dr. Bosanquet means when he remarks that 
 'proper names and numbers mark the same extension as persistent 
 through intensions partially, at any rate, varying'- 
 
Genera and Species 149 
 
 meaning, ' tailor ' or ' man ', ' corporal ' or ' soldier ', ' bun ' or 
 ' food ', ' old maid ' or ' woman ', we might, perhaps, incautiously 
 say the latter name in each case. That is because the differentia 
 of ' man ' is so much more important than that which specifies 
 'tailor' (and similarly in the other cases) that we are apt to 
 forget that the lower concept includes all that the higher concept 
 means, and something more. Roses are not divided into red 
 and non-red things, but into red and non-red roses} 
 
 § 318. Not every higher concept ^ under which a class may 
 be placed, in other words not every attribute which the class 
 possesses, is part of the ordinary intension of the class-name. 
 ' Extinguished in South America ' is not the differentia of 
 ' monarchy ' as a form of government, nor ' heavy to hold ' of 
 ' folio ' as a book. The meaning or definition of a term may 
 shift for me with the momentary interest of my mind ; but it 
 cannot be supposed to change with every enlargement of my 
 knowledge — e. g., of rat, if I am told that rats desert sinking 
 ships. Nevertheless enlarged knowledge may cause me to 
 define a name, differently ; and some acquisition of knowledge 
 is a necessary preliminary to all definition. It should be noticed, 
 then, that until I know what higher concept to place a given 
 concept under, I cannot tell that the latter has a greater inten- 
 sion than the former. It is obvious that a seabird is a bird and 
 something more, but not that a gull is so. Until the judgement 
 is completed, there is nothing to show that the subject has the 
 predicated attribute. 
 
 § 319. Mill objects to the distinction between Extension and 
 Intension that it 
 
 ' is merely a bad expression for the difference between the two 
 modes of signification of a concrete general name. . . . The 
 Extension is not anything intrinsic to the concept; it is the 
 sum of all the objects in our concrete images of which 
 the concept is included; but the Comprehension is the 
 
 ' Of course we frequently attribute to a class generaliter something 
 which is not true of certain sections of it. Because Englishmen are free 
 it does not follow that Dartmoor convicts are free ; nor, because laborare 
 est orare, that the treadmill is prayer. 
 
 ''■ By ' higher ' the logician, unlike the physico-realist, does not mean 
 superior in objective dignity, but only superordinate in conception. 
 Being divided into chapters is only a ' higher ' notion than that of the 
 Bible as being more abstract. The same with 'never found now on 
 earth' compared with 'perfect holiness', or 'carnivorous' with 'European'. 
 
150 Inter-Relation of Concepts 
 
 very concept itself; for the concept means nothing but our 
 mental representation of the sum of the attributes composing it ', 
 Still, the extension depends upon the intension. What is 
 really extrinsical to the concept is, not the number of objects to 
 which the name applies, but the knowledge which we chance to 
 possess about the non-defining attributes belonging to the class. 
 We might associate blue clothes with a policeman, or snuff- 
 taking with a Scotsman, and conceivably those names might be 
 defined with 'wearing blue clothes' and 'snuff-taking' as 
 genus or differentia. But a definition is not a list of everything 
 that may be said about a subject (e. g., that cats may look at 
 kings), nor even of the ideas which we always associate with the 
 subject (e. g., that cats mew, lap milk, and so forth), but only 
 of those attributes which seem to us important, either in the 
 nature of things or for some special purpose. And definition 
 necessarily takes the form of a higher concept limited by a 
 differentia, so as to be exactly equivalent in meaning to the 
 defmiendum and to apply to exactly the same objects, neither 
 more nor fewer. 
 
 § 320. The relation of the higher and wiSer concept to the 
 lower and narrower is, when considered in extension, that of 
 logical whole to logical part. Metaphysically, Hamilton adds, 
 the relations are reversed. But this is only true between 
 defining and defined concepts, in other words between genera 
 and species. ' Tradesman ' is part of the idea of grocer, ' naval 
 officer ' of the idea of admiral, ' animal ' of the idea of man. 
 But there is no conceptual involution of 'wearing epaulettes' 
 in admiral, or of 'valuable' in old Sevres china, though all 
 admirals wear epaulettes and all old Sevres is valuable.' 
 
 § 321. Outside the hierarchy, then, of Natural Kinds and 
 Cogitable Ideas there is an infinite possibility of predication, 
 that is of ranging class under class, in which the ascending 
 and descending series cross and re-cross in every direction. 
 Sigwart ^ observes : — 
 
 ' Mill's criticism of Hamilton, viz., that two-footedness is comprised 
 among the attributes of man, but is no part of the signification of the 
 name, is therefore correct {On Hamilton, p. 434). Yet Aristotle defines 
 man not only as fwov \oyiKOV Bviyrov but as faov ne^ov Slnovv. 
 
 ^ Sigwart elsewhere observes that ' The whole of syllogistic process 
 becomes of doubtful value if, instead of regarding it as a means to the 
 
Subordination of Concepts 151 
 
 ' There is no order of succession in the subordination neces- 
 sarily given by the nature of the concepts. There is no settled 
 order of precedence according to which all concepts which have 
 a logical possibility and justification may be arranged in one 
 way. Just because concepts, as we understand them, are sub- 
 jective creations, formulae whose chief purpose is merely to 
 fix our ideas and mould them into commonly accepted and 
 unambiguous predicates, they are capable of unlimited varia- 
 tion by the many ways in which they can be combined. . . . 
 The idea of an arrangement of concepts such that the more 
 specialized concepts branch off in increasing numbers from 
 one point, the conception of the ov or something, is thoroughly 
 vicious. It presupposes that there must be a much smaller 
 number of higher generic concepts than of the more specialized. 
 But if we regard concepts as being combinations of a limited 
 number of characteristics, it depends entirely upon their inter- 
 relations whether combinations of greater or less generality are 
 the most numerous. The necessity of any fixed order, and 
 hence this imaginary pyramid of concepts, can be grounded 
 only upon the metaphysical view which regards the higher 
 concept as the real cause of producing the lower.' ^ 
 
 § 322. Realism has a great deal to say for itself, but it is not 
 Logic. It is no objection to it that it is mystical ; but only that 
 it is outside our point of view. 
 
 construction of concepts by a Socratic iwayayr), we look upon it in the 
 light of the scholastic logic ; if, that is, we accept it as based upon a 
 finished system of concepts incapable of further growth, and upon the 
 analytical judgements yielded by such a system. [If the relation of the 
 concepts is presupposed] what do we gain by the process of continuous 
 ascent to higher concepts ? If our object is to extend our knowledge by 
 means of judgements, we are moving in the wrong direction. Our predi- 
 cates become poorer and less significant ; we learn less about our 
 subjects, and lose instead of gaining by our progress. If I know that a 
 square is a parallelogram, I know much more than I can learn by erecting 
 a ladder of inferences which end by teaching me that it is spatial or divi- 
 sible, or that it is a being of some kind' (Logic, i. 357, 358). A realist 
 Logic, in other words, only uses analytic judgements, from which we gain 
 our knowledge of the world deductively. Still, much is gained by 
 analysis of notions — if, e.g., examination of the idea of free will gives us 
 the idea of moral responsibility and explains temptation. Sigwart him- 
 self says in another place : — ' We cannot regard it as an imperfection that 
 predicates, generally speaking, are poorer in determinations than the 
 concrete and fully developed subjects of which they are predicated, and 
 that they are more or less deficient when compared with the intuitable 
 reality of particular things and events' (i. 273). He is speaking of 
 analytic judgements, for he instances fruit compared with pear, clock; 
 compared with pendulum clock. * Logic, i. 273. 
 
152 Inter-Relation of Concepts 
 
 § 323. The realistic pyramid ends in a point, which is sum- 
 mum genus to all the lower species. And, even apart from 
 a hierarchical arrangement of concepts, since every predicate 
 is a subject, we may follow any series we please, step by step, 
 until at last we come to a predicate beyond which we cannot 
 go. Such diverging predicates are like the extreme twigs of 
 a tree, and are without number. And yet they have this in 
 common that they are all things. For every adjective must 
 have a substantival notion to qualify. Aristotle, followed by 
 Porphyrj', regarded each of the ten Categories as a summum 
 genus ; and the several sciences may be considered as starting 
 from some general conception — geometry, for instance, from the 
 idea of bounded extension or spatial magnitude, architecture 
 from that of building, tailoring from that of dress. But, philo- 
 sophically, there must be some element common to all nameable 
 things, an absolute Highest, pure Attribution, as yet, in the 
 abstract, unqualified and unspecified, but having potentiality 
 of being determined in every conceivable way and of being 
 predicated of every nameable object, even of opposites, but to 
 which nothing is in the relation of predicate. 'Object of 
 thought' and 'thinkable content', which have been suggested 
 as descriptions of this Highest Predicate, rather evade the 
 question what it is. 'That which — ', but what is 'that'? 
 The neuter gender seems best to convey the idea of colourless 
 attribution. The Greeks used the indefinite ti, ' a somewhat,' 
 ' a kind of neutral thingness.' 
 
 § 324. According to Hegel, the ascending scale of generaliza- 
 tion culminates in God, the Sifpreme Notion. This is to make 
 the Deity poorest in attributes instead of richest bare abstract 
 Being rather than pulsing with all life and warmth and colour. 
 It transforms God from a Person to a predicate, which is to be 
 asserted of all existences. This tea-cup, this crime, this public 
 loan, this treachery, is ultimately God. It makes Him to be 
 universal effect and attribute rather than universal cause and 
 substance. God is Truth. But truth without content, abstract 
 nakedness of truth, is meaningless. It is the Divine attributes 
 which are true, being essential. 
 
 § 325. In examining the Import of the Proposition we shall 
 see that in every attribution the determined element in the 
 subject, the unemphasized part, reappears actually or mentally 
 
Highest and Lowest Classes 153 
 
 in the predicate. 'A penny saved is a penny gained.' 'A 
 watched pot (is a pot that) never boils.' And, reduced to its 
 ultimate nucleus, the real subject and the real predicate in 
 every proposition, when all else has been stripped away, is 
 Reality. Reality qualified in this way is reality qualified in 
 that way. Gradually diminish the intension and the highest 
 predicate, the most general category of thought, will seem to 
 be 'is real'. But to be thought as actual and concrete, this 
 highest notion must be specified, qualified, determined. We only 
 know thing-stuif, the maieries rerum, in its manufactured state. 
 
 § 326. While at one end of thought we have a concept so 
 capacious and devoid of special characteristics that we can 
 find no higher concept under which to place it, a predicate 
 to all subjects, at the other end, in the descending direction, 
 we arrive at classes so narrowed in extension, and so complete 
 in all possible characteristics, that they cannot be differentiated 
 any further, or predicated of any more concrete class, but only 
 of individuals. In the language of physico-realism each of these 
 is an Infima Species. 
 
 § 327. Logically there should be an endless number of such 
 lowest species. For the combination of positive attributes with 
 negative ones is theoretically endless. Thus, to carry the 
 specification to the third step only, we get as follows: — 
 
 A 
 
 I I 
 
 B not-B 
 
 I I 
 
 not-C C not-C 
 
 I I I 
 
 D not-Z» jD not-Z) D not-D D not-Z? 
 
 giving eight lowest species, viz, DCBA's, not-DCBA's, D 
 not-CBA's, not-D not-CBA's, DC not-BA's, not-DC not-BA's, 
 D not-C not-jB^'s, and not-Z> not-C v\.oi-BA'%. Logically, again, 
 there can be no such thing as an absolutely lowest species ; for 
 the possible differentiae, applicable or inapplicable, are inex- 
 haustible. But in natural philosophy and in everyday matters 
 we get both the genus generalissimum and the species specialis- 
 simae. In an army highest genus and lowest species are, of 
 course, not commander-in-chief and private, but at the top 
 
154 Inter-Relation of Concepts 
 
 'soldier' and at the bottom field marshal, colonel, captain, 
 bombardier, drummer boy, and so forth; or dragoon, lancer, 
 sapper, artilleryman, infantryman, &c. Geometrical figure is 
 divisible as rectilinear and not rectilinear, and the former, 
 according to the number of sides, as trilateral, quadrilateral, 
 &c. Trilateral may be divided as equilateral and not equi- 
 lateral; and the latter class as isosceles and scalene. These 
 allow no further subdivision in respect of the sides — unless the 
 positive length of the sides, carrying with it an infinite differen- 
 tiation of the angles, be taken into consideration — so that for 
 the geometer, if not for the logician, these will be infimae species. 
 For military purposes, the classes mentioned above were prac- 
 tically lowest. Linesmen need not be distinguished as blue-eyed 
 and brown-eyed, though it might be necessary to divide them as 
 married and unmarried. 
 
 § 328. We are concerned, however, only with the theoretic 
 limit of specification ; and, formally, the most homogeneous 
 individuals can always be further differentiated, even were they 
 new shillings or sands on the seashore. Two identical beings, 
 says Leibnitz, do not exist. No intuitions can be so alike as to 
 be absolutely indiscernible (a.^i6.<^opa). There must be at least a 
 distinction of time and space, a differentia singularis et numerica. 
 To the quidditas can always be added a haecceitas. There is no 
 such thing, then, as a principle of individuation distinct from the 
 principle of specification. An individual presentation to con- 
 sciousness may be pointed to, but cannot be characterized save 
 in general terms. 
 
 § 329. We are always seeking in our thoughts to connect 
 individual objects by some intellectual link. Some people can 
 never remember the order of the balls in croquet, now that 
 stripes have been superseded by colours. If English streets, 
 like houses, were numbered, the effect would be unpicturesque ; 
 yet it would be easier to find a known address. ttSs -yap Xoyos 
 
 icat Traera ejn(TTfifji,-q tS>v KaOokov koI oi tSi' ecr^artov. 
 
 § 330. The schoolmen gave to Lowest Species in relation 
 to higher genera the name of species subiicibilis ; but in relation 
 to the individuals of which it is predicable in quid they called it 
 species praedicabilis. 
 
 § 331. Between the highest predicate and lowest subjects 
 stands the interlacing chain of Subaltern (i7raAAi;A.a) Concepts, in 
 
Matter and Form of Concepts 155 
 
 turn subordinate and superordinate, the dividing members of 
 any concept at each stage being the co-ordinates. 
 Porphyry divides substance thus : — 
 
 nana 
 fH^vxov (T&na 
 
 I 
 avBpamos 
 
 'SaKpa.TTjs JiKarav 'AXxt^iaSt^r k,t.\. 
 
 With Aristotle the concrete individual {rohe n) has full substan- 
 tive reality in itself, while the universal is a mere predicate. 
 But, as I have said, reality runs all through predication as 
 substratum of every assertion, so that every attribute is predi- 
 cated of reality, and every predicate is affirmed to be real. 
 
 § 332. The relation of a Concept to higher and lower concepts 
 suggests the subject of conceptual Matter and Form. These 
 names are given by Porphyry in his Etsagoge to the generic and 
 differentiating elements, respectively, of any Notion. He says 
 that, as a statue has a certain material on which the craftsman 
 impresses this or that form, so out of the raw and as yet 
 undetermined matter of a notion, say ' animal ', you, so to speak, 
 shape the species ' man ' by means of the mould or form 
 ' rational ', and other species of the same genus by other forms. 
 
 § 333- The abstract or general, then, is specified or concretely 
 realized by being differentiated. And the concrete, accordingly, 
 is not matter only, nor form only, but matter and form 
 combined. Matter is the potential, which the actualizing form 
 makes actual — ^Aristotle's hiTtXtx^ia. 
 
 § 334. It follows that what is matter plus form in relation to a 
 higher concept is matter in relation to lower ones, that genus and 
 species, abstract and concrete, are relative, not absolute, expres- 
 sions, and that the Actual from one standpoint becomes 
 Potential from another. Fruit, which is a particular kind of 
 vegetable growth, is a general concept in respect of apple, 
 peach, mulberry, and pomegranate. Spiritual exercise is the 
 
156 Inter-Relation of Concepts 
 
 matter of prayer, and prayer is the matter of public and private 
 prayer, or prayer pre-composed and unpremeditated. 
 
 § 335- In this metaphorical use of the words. Form and 
 Matter do not at all correspond to Incorporeal and Corporeal, 
 or to Mental and Sensuous. In ' fallen spirit ' ' fallen ' is form 
 and ' spirit ' is matter, just as ' suet ' is form and ' pudding ' is 
 matter in ' suet pudding *. In fact the material element of a 
 concept is, in a sense, more mental than the material and formal 
 elements combined, as being further removed from concrete ex- 
 perience — 'mechanism' than 'watch' and 'garment* than 'coat'. 
 
 § 336. The logical irptorij v\t) is thus Summum Genus, as yet 
 indeterminate and ' before a rag of form is on '. The logical 
 Form of any concept is that which characterizes and differentiates 
 it, not its whole essence or definition but the essential note by 
 which it is made to be what we conceive it (to ti ^v ctvai arj/jLoivov), 
 as distinguished from other things of the same class. It is by 
 possessing this note that any individual of the class is seen to 
 come under it and to be entitled to share in the common name. 
 The form, or differentia substantiahs, is thus a universal. Every 
 member of the generic class which has the mark belongs to the 
 species. The mark becomes a syllogistic middle term. 
 
 § 337- It must be pointed out, however, that this employment 
 of the words Matter and Form for the generic and the 
 differentiating parts of a concept, however convenient, is merely 
 figurative. It does not correspond with the metaphysical use of 
 the expressions. With Aristotle, in whose philosophy Form 
 and Matter are such pregnant conceptions. Matter is the form- 
 less and negative substratum of varying determinations, not, 
 however, in a logical and subjective, but in a physical and 
 cosmological, sense. It is the subject of development and of 
 decay.' At the other end, God is pure Form and highest 
 Essence, unalloyed with matter and distinct from the world, yet 
 the source of all movement, giving essence to all existences, 
 and so, since all movement is upward from the potential to the 
 actual, a completely realized actuality, absolute, infinite, eternal. 
 
 ' e(TTi 8e vXr) to moKiififvov y€vd<Tfa>s koI (jidopas Scktikov {De Gen. et Cor. 
 i. 4. 320^2). Aristotle explained by Matter and Form that problem of 
 Becoming which Platonism solved by the doctrine of the Divine Ideas or 
 the world-soul superinducing form upon rude material, orderly shape 
 upon primal chaos. 
 
Matter and Form of Concepts 157 
 
 In the words of Drummond of Hawthornden :— ' Eternal things 
 are raised far above this orb of generation and corruption, where 
 the First Matter, like a still flowing and ebbing sea, with diverse 
 waves but the same water, keepeth a restless and never-tiring 
 current." While, then, Aristotle regards Matter as rh oApurrov 
 irpiv opurOrjvai Kal /leratrxciv eiSovs Ttvos,'' that elementary constituent 
 which is common to all composite things, generation, the 
 imparting to subject matter of a particular form, is the work 
 of the Creator, or of human art, not the subjective conception 
 and synthesis of your or my mind. Disease is not the matter 
 of consumption and leprosy, nor skill of seamanship and 
 cookery, nor dignitary of bishop, dean, archdeacon, &c., in the 
 same sense that tallow is the matter of soap and candles or 
 animal nature of oxen and wolves. Bacon's superinduction of 
 forms upon matter was not a mental process in metaphor, but 
 the practical aim and business of experimental science. 
 
 § 338. We see, however, the ontological usage passing into the 
 logical in the conception of Socrates and Plato as possessing 
 a common subiecfa materia or essence, viz. humanity, which 
 sustains in the one case the form Socratitas, and in the other 
 the form Platonitas." The genus naturale here is the same as 
 the genus logicum. 
 
 § 339. In what sense, it is now necessary to ask, do we 
 distinguish the formal and- material in Reasoning ? Here are 
 Mansel's words : — 
 
 'The term matter is usually applied to whatever is given to the 
 
 ' The Cypresse Grove. 
 
 ' Metaph. A. 8. gSg^'iS. Lewes holds that the distinction between 
 Matter and Fonn, between potential and actual existence, is a merely 
 fictitious distinction imported by a metaphysical fallacy into the objective 
 world. 'As a fact nothing really exists till it exists ; and nothing exists 
 possibly ; for possibility is only the uncertainty of our ignorance ' {Hist, 
 of Phil. i. 317, 318). But the distinction is really imported into logic 
 from the objective world. 
 
 ' Abailard, who speaks thus, nevertheless understands the universal' 
 nature even of human beings in no realist sense. ' Sicut Socratitas, quae 
 formaliter constituit Socratem, nusquam est extra Socratem, sic ilia 
 hominis essentia, quae Socratitatem sustinet in Socrate, nusquam est nisi 
 in Socrate.' For the as yet undifferentiated nature 'nusquam pure 
 subsistit sicut pure concipitur, et nulla est natura quae indifferenter 
 subsistat' (De Generibus et SJieciebus). Carlyle has a phrase about 
 Correggio's corregiosity. 
 
158 Inter-Relation of Concepts 
 
 artist, and consequently, as given, does not come within the 
 province of the art itself to supply. The form is that which is 
 given in and through the proper operation of the art. In 
 sculpture the matter is the marble in its rough state as given to 
 the sculptor ; \h&form is that which the sculptor in the exercise 
 of his art communicates to it. The distinction between matter 
 and form in any mental operation is analogous to this. The 
 former includes all that is given to, the latter all that is given 
 by, the operation. In the division of notions, for example, the 
 generic notion is that given to be divided ; the addition of the 
 difference in the art of division constitutes the species.' ' 
 
 § 340. We seem here to be slipping back to the metaphorical 
 idea of matter and form as the generic and the differentiating. 
 Mansel certainly did not hold that we are capable of dividing a 
 notion, that is of differentiating one species from another, by an 
 act of pure thought. But elsewhere he says : — 
 
 'The thinking process is formal when the matter given is 
 sufficient for the completion of the product, without any other 
 addition than what is communicated in the act of thought itself. 
 It is material when the data are insufficient, and the mind has 
 consequently to go out of the thinking act to obtain additional 
 material.' ^ 
 
 § 341. Now in the Kantian system matter is the manifold of 
 the external world presented to our experience ; which, how- 
 ever, is only rendered possible by certain (as Kant calls them) 
 a priori conditions. The naked impressions upon our senses, 
 inner and outer, have to be clothed upon and fashioned by the 
 native Forms of the Sensibility, the result being Concepts. 
 Concepts, again, are combined one with another, or presenta- 
 tions with concepts, by the Forms of the Understanding. The 
 mind exercises its synthetic activity upon the materials set 
 before it, moulds them and forms them. ' Kant,* remarks Mill, 
 'holds that every fundamental attribute which we ascribe to 
 external objects is a Form of Thought, being created, and not 
 simply discerned, by our thinking faculty.' ' Archbishop 
 Thomson defines Form as 'the mode of viewing objects 
 presented to the mind'.* 
 
 § 342. Similarly Hamilton says that the Form of Thought is 
 the product of the operation of thought upon the faculties of 
 
 ^ Prol. Log. p. 226. "^ Aldrich, p. Ixiii. 
 
 ' On Hamilton, p. 403. * Laws of Thought, p. 33. 
 
^Formal Thinking^ 159 
 
 experience. Mill, accepting this statement, interprets it thus : 
 'By the Form of Thought we must understand Thinking itself, 
 the whole work of the Intellect. The Matter of Thought is 
 the perceptions or other presentations in which the intellect 
 has no share ; which are supplied to it, independently of any 
 action of its own. What the mind adds to these, or puts into 
 them, is Forms of Thought.' " 
 
 The Matter of Reasoning, in the same way, is the premisses 
 supplied in outline to the Reason. The Form of Reasoning is 
 the activity of the Reason upon these premisses, 
 
 § 343. This psychological sense of Matter and Form is clearly 
 different from the two other senses already mentioned, either 
 the conceptual determination of a generic notion by some differ- 
 ence, or the creative stamping of shape upon rude worlds 
 material. But in all three there is a datum and an operation 
 performed upon it. 
 
 § 344. It is still, however, not clear what is meant by formal 
 thinking, which cannot be merely the activity of thought in 
 impressing a form upon the material before it. For all thinking 
 is thus formal, or rather is itself a form impressed on matter. 
 Mansel speaks, however, of the mind having sometimes to go 
 outside the thinking act to obtain additional material — which 
 sounds like the cook refusing to make an omelette without more 
 eggs — in which case he says the thinking process is material. 
 
 § 345. A bishop, let us say, can be judged at once to be a 
 responsible ruler, because 'the matter given is sufficient for 
 the product ' ; in other words, a mental analysis of the idea of 
 a bishop supplies the predicate of the judgement. But if I am 
 given ' bishop ' and ' member of the House of Lords ', the data 
 are insufficient for judgement, and I must go outside them for 
 fresh material. 
 
 This fresh material, however, is obviously a middle term. 
 
 "* On Hamilton, p. 462. Mill adds : — ' Logic and Thinking are co- 
 extensive. It is the art of Thinking, of all Thinking, and of nothing but 
 Thinking. And since every distinguishable variety of thinking act is 
 called a Form of Thought, the Forms of Thought compose the whole 
 province of Logic ; though it would hardly be possible to invent a worse 
 phrase for expressing so simple a fact.' The view taken in the present 
 volume that the 'art de penser' is one thing and Logic quite another is 
 so different from Mill's, that the two views in conflict seem like the scuffling 
 of two blind men. 
 
i6o Inter-Relation of Concepts 
 
 So that Hansel's ' material thinking * is only another term for 
 syllogizing. 
 
 § 346. We have also seen above (§ 46) that even analytic 
 judgements, like 'A bishop is a ruler', are really mediate, not 
 immediate ; and if so there is no such thing as formal thinking 
 as distinct from reasoning. In any case the product is a 
 reasoned product. We have seen too that 'synthetic judge- 
 ments a priori', such as Euclidean propositions, are mediated. 
 
 § 347. For Logic the only formal process, then, in Mansel's 
 explanation of the phrase, which I gladly adopt, is reasoning, 
 which is necessarily formal. It moves along the lines of a 
 skeleton and abstract construction, without paying any attention 
 to the truth of the material supplied to it — and this material is 
 not, except in analytic judgements, the content of the terms 
 but only their relations in thought — or using any other material. 
 Directly it does go outside its data the reasoning is by most 
 logicians called material. That is to say, the conclusion is 
 reached on other grounds than the premisses warrant. The 
 fact that no bishop is a burglar, and that all burglars belong to 
 the professional criminal class, does not entitle me to conclude 
 that no bishop belongs to the professional criminal class. I can 
 only learn this by knowing something about the character and 
 pursuits of the episcopate ; which knowledge is not in the data. 
 The conclusion is arrived at by reasoning, so far as it is a 
 conclusion. But because the facts which support it were not 
 given, but belonged objectively and extraneously to the matter 
 given, the reasoning is called material. The expression seems 
 somewhat misleading. 
 
 § 348. We have thus distinguished the idea of Reasoning as 
 a formal process from the Form of Reasoning, which is con- 
 trasted with the Matter of Reasoning as Form and Matter are 
 contrasted in Conception and in Judgement. There cannot 
 really be such a thing as material reasoning ; nor has ' material 
 thinking' any intelligible meaning. 
 
 § 349. It remains to remind the reader that whereas the 
 material supplied to the conceiving and the judging activities must 
 be significant and have content, the Matter of any process of 
 reasoning may have symbols for terms. Yet, viewed as products, 
 the Matter of a concept or of a judgement can be expressed 
 symbolically. We can say that the propositions ' Some ^'s are 
 
Matter and Form of Syllogism i6i 
 
 Y', ' Some ATs are N', have the same Form but different 
 Matter, just as we can say this of 'Some fiddlers are blind', 
 ' Some oysters are unwholesome.' The judged Quantity and 
 Quality of a proposition are its Form. 
 
 § 350. Again, it is never enough to supply the Ratiocinative 
 activity with terms. Their outlined relations must be given. 
 For it is these relations about which we reason ; so that, once 
 they are given, the meaning of the terms may be forgotten, yet 
 we can still argue. Or the meaning may never have been 
 known to us at all. The Matter of Reasoning, then, is the 
 form of judgements. The Form of the reasoning, imposed by 
 the mind, is the inferential type, the conclusion as mediated thus 
 or thus, the argumentative construction (Mood and Figure). 
 
 Accordingly the following reasonings are alike in Matter and 
 also in Form : — 
 
 NoFisZ Noil/ is iV 
 
 Some X'a are Y Some L's are M 
 
 .: Some X's are not Z .*. Some L's fire not iV. 
 
 And the following are unlike in Matter and unlike in Form : — 
 Every F is Z Every V is Z 
 
 Every .X" is V Every Yis X 
 
 .: Every X is Z .•. Some ^'s are Z. 
 
 Syllogisms which are alike in Matter cannot be unlike in Form. 
 For, whereas a false judgement is a judgement, a wrong con- 
 clusion is no conclusion. Similarly, syllogisms unlike in 
 Matter cannot be alike in Form. In fact, Syllogism being 
 essentially formal, its Form is indiscerptible from its Matter. 
 Some, however, regard the conclusion as the Form and the 
 premisses as the Matter : in which case Baroco and Festino 
 (ex. gr.) are unlike in Matter but alike in Form. 
 
 § 351. The usual view makes the Matter of a syllogism as of 
 a judgement to be the content of the terms : in which sense we 
 say that reasoning is not affected, by the subject matter reasoned 
 of. We could not say that a conclusion is not determined by 
 its premisses. But this is to abandon the view of the Matter 
 of an operation as the data supplied to it (see above, § 339). 
 The whole subject is full of ambiguity. 
 
 We must now return to the subject of the relation of a Concept 
 to lower and higher concepts. 
 
 M 
 
CHAPTER XI 
 
 DIVISION AND DEFINITION 
 
 § 352. What result does the application of pure Reason to the 
 Division of the Concept afford ? 
 
 Hamilton observes : — ' When we determine any notion by 
 adding on a subordinate concept we divide it ; for the extension 
 of the higher concept is precisely equal to the extension of the 
 added concept plus its negation.* ^ And Sigwart says : — ' Upon 
 the fact that characteristics which are incompatible among them- 
 selves may yet be compatible with another, is based the differ- 
 entiation of concepts, and their complete development by 
 Division.' '^ 
 
 § 353- The limiting of one notion by another (e. g. horse by 
 black) implies that of the remaining extension of the former 
 concept (those horses which are not black) the limiting character- 
 istic must be denied. If some ^'s only are conceived as B, the 
 other A's are conceived as not B, 
 
 This is Division by Dichotomy, which exhibits the extension 
 of a concept in accordance with the principle of Excluded Middle. 
 It aims at distinctness, at the exp)lication of the internal consti- 
 tuents or classes which together make up the extension of the 
 common name. 
 
 § 354. Pure reason will further tell us that any ground of 
 division may be taken. Backgammon-boards either are or are 
 not ballet-dancers. Alligators either do or do not play the piano- 
 forte. Thoughts equally with mushrooms are divisible into edible 
 and non-edible kinds. Suppose that all are on the negative side 
 of the division, that is no concern of the logician's. No doubt 
 the doctrine of the Excluded Middle exposes him to more 
 derision than any other part of Logic. But substitute letters of 
 the alphabet (not disclosing their content) for concepts, and the 
 doctrine is unchallengeable. See above, §§ 150 seq. 
 
 ^ Lectures on Logic, i, 194. 
 ^ Logic, i. 280. 
 
Basis of Division 163 
 
 § 355- For Division, to be of any use, however; some principle 
 of division must be given extraneously. Boolis, suppose, are to 
 be divided according to size. Then we must be given a particular 
 size, say folio* To divide non-folio we must be given, say quarto ; 
 and so on. No doubt, if an idea be supplied, such, as the number 
 of times a sheet is folded, and also an arithmetical progression, 
 we can go on, quarto, octavo, duodecimo, &c. If the idea be an 
 absurd one — eg. to divide virtues by the number of their feet — 
 the absurdity, will not be lessened by carrying, on the successive 
 stages in an orderly method — one-footed, biped, three-footed; 
 quadruped, &c., centipede, &c., millipede, &c., virtues. 
 
 § 356. Yet whatever basis of division has been chosen must be 
 adhered to, if the differentia only of each member of the division 
 (i. e. of the cognate species) is to be stated. The cognate genera 
 are read upwards — as, non-octavo non-quarto non-folio book. 
 They fall under one another, whereas cognate species are co- 
 ordinate. Thus the following division — 
 
 (I) Book 
 
 I I . 
 
 folio non-folio 
 
 quarto non-quarto 
 
 octavo non-octavo 
 
 can be read off thus — Books are divided into folio, quarto, octavo 
 and non-octavo books. But if we divide thus : — 
 
 (II) Book 
 
 folio non-folio 
 
 Latin non-Latin 
 
 borrowed non-borrowed 
 
 then to say that we have divided books as folio, Latin, borrowed 
 and non-borrowed would be a cross-division. Having a part at 
 least of their extensions in common, the dividing concepts over- 
 lap. The real result of the division is into folio, Latin non-folio, 
 
 M 2 
 
164 Division and Definition 
 
 borrowed non-Latin non-folio and non-borrowed non-Latin non- 
 folio books — which is rather confusing, but perfectly rational. 
 In any case the last class of a division must always be negative ; 
 for theoretically a division cannot specify all the dividing mem- 
 bers. We cannot tell but what there are ' other varieties '. 
 
 § 357- If ^ ^sw fundamentum divisionis is introduced on the 
 negative side it may also be introduced on the positive side. The 
 Scottish 'Secession Church' was divided in 1747 into burghers 
 and anti-burgherS) and either of these sections was divided later 
 into new lights and old lights. Of course, if the positive side is 
 subdivided, the basis of division must necessarily be changed on 
 that side. 
 
 § 358. The following carries us three stages : — 
 
 (III) 
 
 fo: 
 
 
 
 
 Book 
 
 1 
 
 
 
 1 
 lio 
 
 1 
 
 
 1 
 -Latin 
 
 ed 
 
 borr 
 
 1 
 non-folio 
 
 1 
 
 1 
 
 Latin 
 
 1 
 
 2d 
 
 be 
 
 nori' 
 
 1 1 . 
 Latin non-Latin 
 
 1 1 
 
 borrowed non- 
 borrowi 
 
 )rrowed non- 
 borrow 
 
 1 I.I 1 
 owed non- borrowed non- 
 borrowed borrowed 
 
 But the negative side at each stage might have continued with 
 an unchanged basis of division. Thus : — 
 
 (IV) A 
 
 
 
 1 
 B 
 
 1 
 
 
 ■C 
 
 
 
 
 \ 
 non 
 
 1 
 
 ■B 
 
 
 1 
 
 c 
 
 1 
 
 ■D 
 
 
 non-C 
 
 1 
 
 i. 
 
 1 
 
 ■C 
 
 
 
 non-5' 
 
 1 
 
 1 1 
 
 D non- 
 
 C non- 
 
 1 
 C 
 
 1 
 non- 
 
 1 
 B" 
 
 1 
 non- 
 
 Such a scheme is pyramidal in shape because the higher 
 extension ramifies into the lower ones, just as the roots of a tree, 
 if combined, equal the trunk in thickness. 
 
 § 359- The division of a class, then, into its constituent species 
 can only be effected logically by successive dichotomies. The 
 rule that the dividing members shall together make up the totum 
 divisum is thus secured, the last member being, as I have said, 
 
Faulty Division 165 
 
 always negative. That they shall not more than make it up, that 
 is, that their extensions shall be mutually exclusive, can be 
 secured by pure reason if the result of the division is read off as 
 (II) above ; but if as (I), we need the aid of experience to assure 
 us that the basis of division is scientifically adhered to. 
 
 § 360. The practical rule that the differentia of any one mem- 
 ber shall not be an inseparable accident of the class divided is 
 intended to secure that the individuals shall not be all found in 
 one class. This would be the case if firemen were divided as 
 wearing helmets, wearing turbans, wearing silk hats, and wearing 
 straw hats, or birds as feathered and not feathered. Division 
 implies particular judgements; but all birds are feathered. 
 Empirical knowledge is required also to secure conformity to the 
 rule, ' divisio non faciat saltum.' The distinction between divid- 
 ing a genus by its species (animal is either man or brute) and 
 dividing it by its differentiae (animal is either rational or non- 
 rational) is superficial, or, at least, extra-logical. 
 
 § 361. False dichotomies are often humorous — as of mankind 
 
 into tailors and tailored. Byron says : — 
 
 Society is now one polished horde 
 
 Formed of two mighty tribes, the bores and bored. 
 
 Pope whimsically classified the population as men, women, and 
 
 Herveys. 
 
 § 362. When the overlapping of the dividing extensions is 
 unimportant, a cross-division may be sometimes allowed ; as if 
 authors be divided into poets, novelists, historians, divines, critics, 
 and so forth. The possible doubling of parts is accidental. A 
 novelist is not an historian qua novelist. On the other hand to 
 insert ' dramatist ' would involve Shakespeare being either not 
 a dramatist or not a poet. 
 
 What, in fact, we really were doing was the dividing not of 
 authors but of authorship into its kinds. All flesh, again, is not 
 the same flesh, being divided into flesh of men, of beasts, of 
 fishes and of birds, even though mulier formosa superne some- 
 times desinit in piseem and rational beings are feathered in 
 Cloudcuckooland. 
 
 § 363. It is only when an attribute, or abstract idea, has 
 varieties, shades and differences — as there are different kinds 
 of colour, of folly, of illness, of happiness, of consciousness, of 
 iniquity— that it may be regarded as a general concept and 
 
1 66 Division and Definition 
 
 admits of division. A stroke of illness may be called by a figure 
 of speech an illness, but we cannot call an act of madness an 
 insanity. As a rule, onily common names, names which have 
 extension, are divisible, thus excluding individual designations 
 and singular abstract names. Yetproper names also may acquire 
 a more or less general character, even while strictly confined to 
 one individual object. We speak of Elizabethan England and 
 modern England, of the old Hector and the new. On the other 
 hand to speak (topographically) of old and new Edinburgh, or of 
 upper and lower Bristol, is a material partition. The case of 
 proper names used by metonymy as common names — e. g. 
 'a spiritual Quixote,' a 'Napoleon de caf6 chantant' — need 
 not be again referred to, nor yet the case of proper names 
 transferred to classes of objects ; as, a Holbein, a Wellington, 
 a marechal Niel, a jersey, a St. Bernard. 
 
 § 364. The division of authorship, however, or of any other 
 abstraction, into its kinds must be carefully distinguished from 
 Ideal, or, as Hamilton calls it, Metaphysical, Partition,' the 
 analysis of an idea into its intensive elements. E. g. the idea of 
 progression may be broken up into that of movement and that 
 of forwardness. In this kind of division, the divided whole is 
 not predicable of, nor the name of the analysed idea applicable 
 to, each of the separate parts. Again, generous people may be 
 classed as tall and short (or not tall). But generosity is not 
 divisible into tallness and shortness, nor into tall generosity and 
 
 * But metaphysical partition is rather the resolution of a substance into 
 its attributes. 
 
 ' As there are two kinds of wholes there are also two kinds of division. 
 There is a whole composed of parts really distinct, called in Latin totum, 
 and whose parts are called integral parts. The division of this whole is 
 called properly partition, as when .we-divide a house into its apartments, 
 a town into its wards, a kingdom or state into its provinces, man into 
 body and soul, the body into its members. The sole rule of this division 
 is to make the enumeration of particulars very exact, and that there be 
 nothing wanting to them. 
 
 ' The other whole is called in Latin omne, and its parts subjected or 
 inferior parts, inasmuch as the whole is. a common term, and its parts are 
 the terms comprising its extension. The word animal is a whole of this 
 nature, of which the inferiors, as m,an and beast, which are comprehended 
 under its extension, are subjected parts. This division obtains properly 
 the name oi Division'' (Port Royal Logic, Pt. II, cap. 15). 
 
Ideal Partition 167 
 
 short generosity. Charitable persons are wise and unwise; 
 and certainly we can speak of wise and unwise charity. But 
 this is because the charitable are necessarily wisely and unwisely 
 charitable. 
 
 Concrete classes may often be represented by corresponding 
 abstractions ^ ; as when we say that society is made up of youth 
 and age, of discretion and folly, of wealth and poverty. Punctu- 
 ality is a form of politeness, and is therefore no part of the idea. 
 Again, we divide friends as constant and inconstant, and we say 
 that constancy is a part of friendship. But we cannot say this 
 of inconstancy. Yet we speak of constant and inconstant 
 friendship. 
 
 § 365. Every differentia is a limitation— ' black bread,' 
 'occasional intemperance.' But it is the sphere, not the 
 intension, of the generic concept which the addition of the 
 difference limits. Those who are both tall and generous are 
 fewer than the generous simply. But their generosity is not 
 limited and qualified by their inches. 
 
 § 366. Sigwart observes : — ' The prevailing logical terminology 
 is inconvenient, in that it employs the same expressions to 
 denote two processes so different as the analysis of a concept 
 into its characteristics and the development of opposed concepts 
 from one higher concept; these expressions being derived 
 from the act of dividing, and signifying sometimes the division 
 of the content into its elements, at others the division of its 
 extension into mutually exclusive extensions. To this is due 
 the paradox that by dividing a concept we do not get parts of 
 the concept, but concepts which each contain the whole divided 
 concept as a part. If we keep consistently to the content of the 
 concept, we are concerned with nothing but a development of 
 the characteristics contained in it. The term Division (Aristo- 
 
 ^ How entirely the use of abstractions as common names is a matter of 
 usage may be seen by observing that we speak of truths and of depths 
 but not of warmths ; of highnesses but not of lownesses ; of littlenesses 
 but not of greatnesses ; of delicacies but not of episcopacies ; of loyalties 
 but not of fidelities ; of spiritualities but not of animalities ; of colours and 
 dolours but not of valours ; of vanities but not of sanities ; of operations, 
 stations, and the like, but not of emaciations ; of sentences but not of 
 penitences ; of kingdoms but not (usually) of wisdoms ; of universities 
 but not of scarcities. The vulgar expression ' royalties ', for royal person- 
 ages, has lately come into vogue. 
 
i68 Division and Definition 
 
 telian Sialpecni) is more applicable to the sum of the particular 
 objects which fall under the concept. This sum is regarded as 
 a whole to be broken up into different groups.' ^ 
 
 § 367. Ideal Partition, indeed, is analogous to Material 
 Partition, the mental separation of an objeci into its component 
 parts ; as when we divide a ship into hull, masts, sails, and so 
 forth ; ^ or a collective term, as parliament into lords spiritual, 
 lords temporal and commons, college into head, fellows, 
 scholars and commoners. Logical Division is the enumeration 
 of the different classes of objects which together make up 
 a whole class and share in its common name. A concept is 
 divided on its extensive, analysed on its intensive, side. 
 Although I have more than once used the words notion and 
 concept as identical, notion is rather conception than concept, 
 and it might be better to reserve it for concept in its intensive 
 aspect. ' Soldier ' as a concept is either conscript or recruit ; 
 but we should not say, ' My notion (or my conception) of a 
 soldier is either conscript or recruit,' nor yet ' My notion of 
 butter is either salt or fresh '. 
 
 § 368. We have seen that logical analysis of the Form of 
 Thought can tell us what Division of a Concept means, and that 
 pure Reason shows the dividing process to be really a succes- 
 sion of dichotomies. Logic thus supplies negative safeguards 
 against confusion and accidental omission. But it can do no 
 more. Rules for dividing which shall be of positive utility are 
 extra-logical. Thus Hamilton, quoting Esser, says : — 
 
 ' Those characters of an object are best adapted for a division 
 whose own determinations exert the greatest influence on the 
 determinations of other characters, and consequently on those 
 of the notion itself; but such are manifestly not the external 
 and contingent, but the internal and essential characters ; and, 
 of these, those have the pre-eminence through whose deter- 
 
 ^ Logic, i. 280 n. 
 
 " This is sometimes called Physical Partition, an expression which had 
 better be reserved for actual anatomy and severance — such a dismember- 
 ment as that of Hood's hero — ' There he left his second leg, and the 
 Forty-Second Foot.' The Partition in the text is not the less (logically) 
 ' Material ' that it may apply to immaterial objects^ Thus Cicero gives 
 a sixfold partition of a speech — exordium, narratio, partitio (or divisio), 
 confirmatio, reprehensio (or confutatio), conclusio (or peroratio). 
 
Aristotle on Dichotomy 169 
 
 mination the greater number of others are determined, or, what 
 is the same thing, from which, as fundamental and original 
 attributes, the greater number of others are derived.'^ 
 
 A charity for widows will classify applicants according to age, 
 character, means of support, number of children, and the like ; 
 not according as they are fond of animals, tall, musical, or 
 anything of the kind. But what help can the logician give in 
 such classification ? 
 
 § 369. Dichotomous division is criticized by Aristotle on 
 various grounds. He exaggerates the importance assigned to 
 it by Plato,'' who rather awkwardly tried to construct definitions 
 by combining the highest genus with the successive differentiae 
 on which the division has proceeded, but who never intended 
 dichotomy as a substitute for syllogism. Aristotle recurs often 
 to the subject. His objections to Dichotomy are : — 
 
 (i) That by subdividing the negative arm we erect negation 
 into a positive principle, and make species often non-existent. 
 But if men are divided into those who are happy and those who 
 are not happy, the latter class are not necessarily more non- 
 existent than the former. Inkpots which are not happy are, in 
 fact, the only existing ones, and it is the positive arm, the happy 
 inkpots, which are non-existent. It will be remembered that 
 only in certain ' universes of discourse ' will ' which are not 
 happy ' be equivalent to ' which are unhappy '. Again, animals 
 either are rational or are not rational, which in this sphere 
 means, are irrational, and ' irrational animal ' is identical with 
 brute, which is a quite positive concept. Had we divided 
 brutes into rational and irrational, it is the rational brutes 
 which have no existence. 
 
 (ii) That we cannot by dichotomy demonstrate — as Aristotle 
 seems to have supposed that Plato thought we could do — the 
 essential nature of a thing. For this is indemonstrable, and 
 must be arrived at either inductively or from the authority of 
 the wise. 
 
 ^ Lectures on Logic, ii. 31, 32. 
 
 ^ See especially Pfiaedrus, p. 265 a, 266 c ; PoUticus, p. 285 a, b ; 
 Sophistes, p. 253 a, e. Aristotle rightly says, oi/c 'iari 8e Sia(J3opa a-repria-eas 
 ji (Triprjais {De Part. An. i. 3, § I ; of. Prior. Anal. i. 31 ; Post. Anal. ii. 5, 
 § 3). But what is negative in form is often positive in fact. 
 
17° Division and Definition 
 
 (iii) That dichotomy is only do-^ei/^s (rvXXoyicr/xo's. If we wish 
 to prove that man is mortal, and begin by dividing animals 
 into mortal and not mortal, we frame our syllogism thus : — 
 
 Every animal is mortal or not mortal. Every man is an 
 animal. Therefore every man is mortal or not mortal. Now, 
 to go on to say, ' Every man is mortal,' assumes the conclusion 
 instead of proving it. Such a syllogism, then, based on 
 dichotomy, leads to nothing. 
 
 The answer seems in the present day obvious, that no one 
 can ever have thought it did. And objection (ii) is equally an 
 ignoratio elenchi. 
 
 § 370. Proceeding with the analysis of conceptual relations, 
 we see that Division, by which the external connexion of classes 
 with one another is made explicit and their system is deduced, 
 has for its counterpart and converse Definition, whereby the 
 internal content of the idea is made explicit. It is the 
 analytical judgement in its complete form. Yet what is 
 external from one point of view is internal in another. Division 
 internally breaks up a class into its particular sub-classes. 
 Definition declares the external relation of a class to two larger 
 classes. 
 
 § 371. In dividing we differentiate the several members or 
 species of the divided whole, which as a notion is predicable of 
 each of them. In defining we predicate the generic notion of 
 some one of the members, stating at the same time what it is 
 that differentiates it from the other members. 
 
 § 372. As Division is a detailed enumeration of the different 
 species, considered as classes, which are together co-extensive 
 with the genus, so Definition fixes precisely the intension of 
 any species, considered notionally, by identifying it with that 
 of the generic notion differenced in a particular way. 
 
 ^Yhat is divided is a predicate, what is defined is a subject. 
 We say. Divide triangle, wealthy, friendly ; but. Define a 
 triangle, wealth, friendliness. More strictly, it is classes that 
 are divided, names or attributes that are defined.' 
 
 ' Against the doctrine that what is defined may always be regarded as 
 an attribute, the usual definition of triangle as a three-sided figure might 
 be objected. For triangularity is not trilaterality. The geometer, however, 
 is not intending to define triangularity, but only ' the being a triangle ', 
 
Genus and Difference 171 
 
 373. By dividing we are able to answer the question, Of what 
 '? Yonder ship must be classified, specified, as either 
 battleship, or cruiser, or troop-ship, or liner, &c. We define in 
 order to answer tlie question. Who, how many ? This charity 
 is left for the indigent ? But who are the indigent ? How many 
 persons ought to have it ? Indigence, therefore, must be defined, 
 the essential qualifications for being considered indigent must 
 be determined, the limits (fines), that is to say, within which the 
 name is applicable. It is not necessary, then, to enumerate all the 
 ideas which the word 'indigence ' conveys to my mind. All we 
 want is the quid and the quale, definition being in quale quid. 
 § 374. Now, if ' Ship ' be divided thus : — 
 
 Ship 
 
 I 
 
 , I . . I I I I I 
 
 battleship cruiser troop-ship liner schooner &c. 
 
 we notice that the species battleship and troop-ship are named 
 by prefixing the differentia to the genus ship ; cruiser is named 
 from the differentia only ; liner the same, but not so clearly ; 
 while schooner suggests to ordinary landsmen neither genus nor 
 difference. Sometimes a genus will give its name as suffix to 
 that of all the ^ecies composing it ; as tree may be divided as 
 yew-tree, beech-tree, oak-tree, rose-tree, apple-tree, &c. And 
 yet we also speak of yews, beeches, oaks, elms, chestnuts, and 
 the like. So we say, puppy-dog, bull-dog, sporting-dog, sheep- 
 dog, wire-haired dog (of course this is not a division), but also 
 we enumerate dogs as terriers, retrievers, spajiiels, bloodhounds, 
 greyhounds, Newfoundlands, collies, and so forth. Again, 
 boats may be classed as two-oared, four-oared, six-oared, eight- 
 oared, &c., boats, but also as canoe, dinghey, pinnace, gig, 
 skiff", &c. 
 
 § 375- Now, it is plain that whereas, say, battleship, troop-ship, 
 sheep-dog, pear-tree or lifeboat are for ordinary purposes 
 sufficiently defined already, and cruiser, retriever, terrier are 
 sufficiently differenced by their names, and only want their 
 genus to be indicated, yew-tree, elm-tree, oak-tree, on the other 
 hand, tell most of us nothing by their names except that 
 generically they are trees ; and yew, elm, oak, beech, not that 
 
 which is defined as the being a figure with three sides. ' Triangle ' is 
 used with momentary neglect of its verbal significance. 
 
172 
 
 Division and Definition 
 
 either. So again, red rose for practical purposes entirely 
 defines itself, briar-rose half defines itself, Malmaison does not 
 define itself at all. 
 
 § 376. It is not always possible, then, from the result of 
 a divisive process to reconstitute the definition of any one of the 
 dividing members or species by joining its differentia to the 
 genus ; for sometimes, as we have seen, a species has no other 
 name than the genus qualified by the difference ; sometimes it is 
 named from the difference only, or suggests it (e. g. quarto = 
 divided in four) ; sometimes it is named quite apart from either 
 genus or difference, and has a designation to itself. It is only 
 when a word is the equivalent of a complex name made up of genus 
 and differentia that, ordinarily, it has to be, and can be easily, 
 defined. Needlewoman explains itself, but sempstress not so 
 well ; forenoon, but not morning ; midday, but not noon ; plough- 
 man, but not hind ; foot-soldiers, but not infantry ; mean abode, 
 but not hovel; female bird, but not hen. 'Hen', however, is 
 sometimes a substantive name, but at other times a differentiation 
 (hen-bird). ' Ironclad ' needs further defining, for by usage a , 
 man in armour is not so described, but only ships. 
 
 § 377. As purely abstract ideas (e. g. incorrigibility, change- 
 ableness) are indivisible, so individuals are, properly speaking, 
 undefinable. We cannot define Napoleon, though he has been 
 described as a hero who was not quite a gentleman, the Corsican 
 upstart, or the little Corporal. Dr. Parr was 'the Whig 
 Johnson '. If it be objected that such phrases about individuals 
 are sometimes a kind of definition (e. g. SiofcpaTijs ka-rw 5 Sco- 
 (f>povl(rKov), it must be replied that the really individual is un- 
 nameable as well as undefinable. This or that person or thing 
 is never a single unrelated presentation to the senses, a 
 momentary impression at once forgotten. We cannot get at 
 a purely concrete Napoleon. It should be noticed that many 
 individual designations are complex and descriptive ; e. g. Pic 
 Nono,the present King, the House that Jack built, the Giant-killer, 
 the Marquis of Granby, St. Paul's Cathedral. But if it is possible 
 to find a purely non-connotative name, that name is undefinable. 
 
 § 378. Only so far as names imply generality — common 
 names and the connoted attributes — are they definable. But 
 summa genera cannot be defined, since they can be placed 
 under no higher class ; nor yet simple notions, such as ele- 
 
Highest Concepts and Simple Ideas 173 
 
 mentary sensations, for the differentia cannot be indicated. 
 We say, 'I have an undefinable feeling.' The plain man 
 cannot even say that he experiences an affection of the olfactory 
 nerve, or of the palate, nor define the tint of a ribbon by the 
 number of light vibrations which affect his retina. An idea of 
 scarlet, perhaps, might be conveyed by saying that it is a hot 
 colour. But the blind person thought it must be something like 
 a trumpet blowing. 
 
 Hamilton says : ' It is manifest that if a concept be simple, 
 that is if it contain in it only a single attribute, it must be 
 undefinable.'^ No concept is really simple; yet we may be 
 unable to name the generic, or the characteristic, quality. 
 ' Quand on me demande ce que c'est Dieu, je I'ignore ; quand 
 on ne me le demande pas, je le sais tres-bien.' '^ God has been 
 defined by negative differences : — ' Thou art great without quan- 
 tity, good without quality, infinite without number, beautiful 
 without figure, eternal without time, immeasurable without 
 space, pervading without extension, perfect without multiplicity, 
 most exalted without position.' In fact, theological definitions 
 aim less at exposition of the reality and attributes of what is 
 defined than at the exclusion of error by terms which are clear, 
 though it is impossible to develop their full connotation. Some 
 of the definitions in geometry have a negative differentia. A 
 line is length without breadth. Parallels are lines which are 
 in the same plane but can never meet, A point is position 
 without magnitude (^eo-ts dvni [nyiOov^). 
 
 § 379- The objection to defining by negation is that the 
 negative characteristic is usually so wide as to be practically 
 useless for the purpose. An East-end child defined grass as 
 'what one mayn't go upon". Frequently such definitions are 
 intended epigrammatically. Positivism has been defined as 
 Catholicism without Christianity. ' Baronet ' was defined by 
 an amusing member of that honourable order as a person who 
 is not a nobleman and has ceased to be a gentleman. (Here 
 genus as well as difference is negative.) Yet a Gentile would 
 be defined as a man of non-Hebrew race, a 'blackleg ' as a non- 
 Unionist workman. ' L'amiti6 ' is ' I'amour sans ailes '. 
 
 ^ Lectures on Logic, i. 151. 
 
 ' ' Quid est ergo tempus ? Si nemo ex me quaerat, scio ; si quaerenti 
 explicare velim, nescio ' (St. Aug. Conf. xi. 14). 
 
174 Division and Definition 
 
 § 380. Good definition is by proximate genus and ultimate 
 difference. It selects^ as genus a concept slightly more ex- 
 tended than the definkndum, but of which the intension is less 
 by as little as. possible than, that of the definiendum. Who 
 would define a lord mayor as a European who lives officially at 
 the London Mansion House, or china as a clay object which 
 the housemaid breaks ? Nevertheless, if subject and predicate 
 are given as interchangeable ideas, pure reason is unable to 
 disallow such definitions, which, moreover, for certain purposes 
 may have their uses. Every one knows the definition of a ship 
 as a prison with a chance of drowning, or of patriotism as the 
 last refuge of a scoundrel, or of a lexicographer as a ' harmless 
 drudge who busies himself, &c. The Irishman's definition of 
 a gun as ' a hole with something round it ' obviously needs 
 further determination ; but the child who defined a prodigal as 
 ' one who comes home ' had a clear picture in its mind. 
 
 § 381. When the genus seems more important than the 
 differentia,, definition will sometimes take a tentative form. 
 ' Revenge is a kind of (ns) wild justice.' An accountant is 
 'something in the City'. In defining we look to what appears 
 to be, for our immediate purpose, some striking feature. We 
 try to define everything by something better known. A fox 
 would not be defined ini the same way by a huntsman and by 
 a naturalist. Death, which to the physician is the cessation of 
 all vital functions, is to the singer of Hawthornden ' the thaw of 
 all those vanities which the frost of life holdeth together'. 
 Truth for the metaphysician is the agreement of idea with 
 ideatum ; but St. Cadoc the Wise calls it the eldest daughter of 
 God. The brain is to the poet the seat of fancy and the throne of 
 thought ; to the surgeon it is a soft substance of whitish and 
 reddish grey, &c. Every definition, whatever its syntax, is 
 \og\ca}\'^ per genus et differentiam, e.g. the definition of 'amphi- 
 bious ' as ' living on land and also in the water ', or that of 
 'innocent' as 'naked and not ashamed'. Innocence is un- 
 ashamed nakedness. 
 
 § 382. The rule against defining per ignottus is, indeed, merely 
 relative. The unphilosophic mind learns nothing from the 
 definition of Art as ' a productive habit acting in accordance 
 with reason ' ; or from that of Motion as ' actus entis in potentia 
 quatenus in potentia ', or as the identity of Space and Time in 
 
Defining ' Per Ignottus ■" 175 
 
 Place ; or from that of Time as the measm-e of motion ; or 
 from that of MoraKty as the astronomy of the heart — Bacon's 
 'georgics of the mind' — ; or from Hobbes's definition of Freedom 
 as ' political power divided into small fr^ments ' ; or from 
 Bruno's definition of God as 'monadum monas, nempe 
 entium entitas '. But to the philosopher the notions have really 
 been elucidated. The scientific definition of life as the dyna- 
 mical condition of an organism would not be that of the plain 
 man. The plain man thinks he knows what ivy is, and is, not 
 much wiser for being told that it is an epiphytic plant of the 
 genus hedera. But he toa may learn something from the defi- 
 nition of sickness as nature's protest against the misdirection of 
 her forces, or from St. Austin's phrase, ' virtus est ordo amoris ' 
 — the orderly and progressive unfolding of love. Johnson's 
 masculine grasp is hardly shown, however, in the definition of net- 
 work as ' anything reticulated or decussated at equal distances 
 with interstices between the intersections '. Mr. St. George 
 Stock gives as an example of a seemingly far-fetched defini- 
 tion the definition of a triangle as that section of a cone 
 which is formed by a plane passing through the vertex per- 
 pendicularly to the base.' But this, as he remarks^ is correct 
 from the view of conic sections. 
 
 § 383. The last example but one is a bad specimen of the 
 circulus in definiendo, or diallelon ; for what is reticulation and 
 the rest but network? This kind of see-saw definition may 
 be circuitous or the direct substitution of a synonym. The 
 shape of the earth is a geoid. A laundress is a washer- 
 woman. Nostalgia is home-sickness. An archer is a bowman, 
 St. Nicholas's clerks are thieves. One expression happens to be 
 better understood than the other, or nearer the vernacular ; 
 but, if this is to define, then a bilingual dictionary is all 
 definitions. 
 
 § 384. And yet, on the other hand, it is not for pure logic to 
 object to definition by synonym or even to circular definition. 
 All that the logician, analysing the Form of Thought, can 
 demand is that the definition shall profess to make explicit the 
 intension (for the particular purpose in hand) of a name — 
 otherwise it is only a description — and that the predicate shall 
 
 ' Logic, i. 117. 
 
176 Division and Definition 
 
 be convertible with the subject. No doubt this must be done 
 by delimiting the sphere occupied by the definiendum in a higher 
 concept. But the shortest synonym, though its whole sphere 
 is identical with that of the name tc be defined, really does 
 this, — for a washerwoman is a woman who washes ; a thief is a 
 man who thieves — , and so does the longest and most rambling 
 description — e. g. ' A kitten is a dear little soft playful creature 
 which runs after balls of wool instead of mice, and looks very 
 pretty with a coloured ribbon round its neck ' ; and so forth. 
 Such filling in of a picture appeals to the fancy rather than 
 to thought ; yet it can stand as an unscientific, untidy definition, 
 with 'creature' as genus and the rest as differentia. Aristotle 
 speaks of Sta^opai in the plural, meaning successive differen- 
 tiations till the concept is reached. Description appeals to 
 the imagination, definition to the mind. You describe an object, 
 define a notion. But the above may be a little child's notion of 
 a kitten. It is not for the logician to say. Prynne's quite 
 serious definition of heaven was ' a place in which there are 
 no stage-plays ' (Index to Histriomastix). 
 
 § 385. Further, it should be noticed that the distinction 
 between a definition per genus et differentiam and other general 
 propositions does not usually appear on the surface. How 
 are we to distinguish ' A man is a rational animal ' from ' A boy 
 is a queer creature'? Which of the following are defini- 
 tions ? — 
 
 Despotism is anarchy speaking with one voice (Patmore). 
 
 A horse is a vain thing to save a man. 
 
 A little learning is a dangerous thing. 
 
 Anima est forma substantialis hominis (Aquinas). 
 
 A book is a pleasant companion. 
 
 A triangle is a three-sided figure. 
 
 Hypocrisy is the homage vice pays to virtue. 
 
 Brevity is the soul of wit. 
 
 A pony is a four-legged animal. 
 
 The sacrifice of God is a troubled spirit. 
 
 Lux est umbra Dei. 
 The logician does not know which of these propositions have 
 the diagnostic character of definition. He does not know which 
 intended definitions satisfy the rule that a definition must give 
 the fewest attributes that will suffice for demarcation of the 
 
'Meaning' is Subjective 177 
 
 definiendum from other things. 'A square is a figure that has 
 equal sides and four equal angles ' gives just enough attributes. 
 ' An equilateral triangle is one that has equal sides and three 
 equal angles ' gives too many. ' A square is a figure having four 
 right angles ' gives too few. So does ' a draper is a tradesman ' 
 (man who trades). ' Retail tradesman * would not be sufficient 
 delimitation either. ' Industrious tradesman ' would contract 
 the sphere too much. ' Ratepaying tradesman ' would leave it 
 just where it was. But all this knowledge must be given by 
 experience. 
 
 § 386. The view taken hitherto has been that names have no 
 absolute, but only a relative, definition and meaning. A term 
 may be defined differently by different persons, or differently by 
 the same person according to the purpose in view. See above, 
 § 305. Accordingly, the predicate of any general proposition 
 (e. g. ' New brooms sweep clean ') may be logically regarded— 
 apart from what is said below, § 421 — as standing to the subject 
 in a generic relation, which might become a definition by the 
 addition of a differentia. On the other hand ' Hansom cabs are 
 the gondolas of London' and similar propositions are not 
 properly definitions (though in form they might be so), because 
 they do not profess to give the sense in which a name is, or 
 shall be, used. 
 
 § 387. The distinction then drawn between the ' subjective 
 intension ' of a term and its ' meaning or logical significance ' ^ 
 , is unsubstantial. In contrast, says Mr. Wolf, with the 'empirical 
 idea ', which is variable, ' each term has but one meaning, which 
 is the same for all and on all occasions. Its meaning or logical 
 signification is relatively independent of any particular thinker 
 or occasion,' It may therefore be described as ' the relatively 
 objective idea '? 
 
 § 388. Of course language would be worthless as a means of 
 intercourse if there were no general agreement or convention as 
 
 ^ Studies in Logic (Cambridge University Press, 1905), pp. 5-14. 
 Sigwart gives ' the warm zone is that which lies between the tropics ' as 
 a definition {Logic, i. 292). Lying between the tropics is certainly 
 not what the words ' warm zone ', as words, necessarily convey. But a 
 shipmaster, ordered by the owner to keep clear of the warm zone, might 
 well ask how he defined warm zone, and be answered with no reference 
 to temperature but only to latitude. 
 
 "^ Ibid. p. 7. 
 
 N 
 
178 Division and Definition 
 
 to the sense in which words are to be used ; and a definition is 
 usually propounded for the acceptance of another or of all. 
 Regard, also, must be had to etymology, though the Port 
 Royalists ^ seem to hold that ' parallelogram ' might be arbitrarily 
 defined as a triangular figure, if used exclusively in that sense — 
 an ultra-Nominalist position. The definition is intended to 
 express what seems to the definer the essential nature of the 
 object. He does not' select trivial and haphazard character- 
 istics. A good definition enables us to penetrate into the heart 
 of the thing — as when Bolingbroke defined history as philosophy 
 teaching by examples. Lord Russell defined * proverb ' wittily 
 as the wisdom of many and the wit of one. Conscience 
 according to the British sage is the eye of God in the soul 
 of man. 
 
 § 389. But such examples show the impossibility of a distinc- 
 tion between the ' subjective intension ' of a term and that 
 meaning which is ' the same for all '. The writer quoted above 
 himself remarks that ' convention is of a more or less relative 
 character'. At any rate the distinction is one of which Logic 
 can take no cognizance. 
 
 If meaning is objective, we come to Lotze's ' eternally self- 
 identical significance of ideas which always are what they are ' ^ 
 — the Platonic Ideas, in fact, and Realism. The logician has 
 no quarrel with Realism. But Realism is not Logic. And an 
 ' absolute meaning ' seems to be a contradiction in terms. 
 
 § 390. Definition cannot be of the nature of the thing, but 
 only of the content of the notion.' If it were of the former, 
 
 ^ Logic, Pt. I, c. vii. Mansel, however, remarks that 'the etymology 
 will in nine cases out of ten declare, not the present meaning of the 
 word, but either one that has become obsolete or some secondary notion 
 which may account for the imposition of the name, but which at no time 
 formed, strictly speaking, any part of its signification' (Aldrich, p. 186). 
 ' Priest ' means the same thing as ' alderman ' ; yet since it was taken 
 over by the Christian Church from the Synagogue it probably never 
 connoted age in any way. ' Bishop ', on the other hand, has not lost its 
 meaning of overseer. ' Gentlewoman ' and ' nobleman ' keep their 
 etymological signification ; but ' gentleman " only does so in part. And 
 no one would define ' chivalry ' with any reference to riding on horseback. 
 
 ■ Logic, § 317. 
 
 ' Nevertheless, names are the names not of ideas but of things. The 
 former view, as Bain notices (Logic, Pt. I, p. 46), ' is a species of idealism, 
 confounding together the object and the subject.' 
 
Definition is Conceptual 179 
 
 definitio ret, it would not be per genus et differentiam, but a 
 catalogue of attributes. That is, it would not be a definition. 
 Definition, in other words, is necessarily conceptual. And, 
 moreover, what does ' the nature of a thing ' mean, apart from 
 some eternal exemplar in the Divine mind? Physico-realists 
 endeavour to give some objective and absolute significance to 
 the word * essential ' by speaking of the necessary constitution 
 of certain natural kinds, possessing a permanent ground, a self- 
 centred unity, which is the basis of all minor attributes and 
 unfolds itself in varying manifestations and activities. And 
 certainly a permanent definition, propounded with no special 
 object in view, will try to express this permanent nature as 
 nearly as possible. But, none the less, definition is always the 
 analysis of a concept, and a concept is what the mind has 
 conceived. Define Liberty. What do you understand by it? 
 In what precise sense do you, or others, use the word ? What, 
 in your view, or in the generally accepted view, are the essential 
 notes of the Church ? How do you know it when you see it ? 
 Hamilton's distinction between the essential and accidental 
 qualities of a thing, that the former are those ' which it cannot 
 lose without ceasing to be ' — a 'vulgar' explanation, according 
 to Mill, marking 'a retrogression from Conceptualism to 
 Realism ' ^ — ought to run, ' which it cannot lose without ceasing, 
 in the view of the speaker, to be.' 
 
 § 391. All giants are tall and all are supposed to be feeble- 
 minded. It may seem obvious that tall stature is an essential 
 attribute, and feebleness of intellect only an accidental one. 
 But this is to make essence depend on definition, not vice 
 versa. Every very tall being is conceived by my mind under 
 the concept giant. Tallness constitutes a giant, but does not 
 ■make any one a giant in the sense that it makes him able to see 
 over people's heads. It is the formal, not efficient, cause. From 
 another point of view it might be considered essential to a giant 
 to have a sufficient supply of babies to eat ; non-essential that 
 he should carry a club. Without the former he would fail to 
 grow to be a giant. Similarly, bodily activity is essential to 
 a soldier ; good looks non-essential. Without the former he 
 would 'cease to be' a soldier, by having to leave the army. 
 
 1 On Hamilton, p. 430 n. 
 
 N 2 
 
i8o Division and Definition 
 
 But neither giant nor soldier is defined by such essentials. If 
 they were, it would be because the circumstance or attribute 
 had become part of the concept. 
 
 § 393. What is opL^ofjLevov, or delimited, then, is always the 
 marks or boundaries by which the right to a name is determined, 
 not the qualities which make the existence of an object possible. 
 An apocryphal salamander is as easy to define as a Tay 
 salmon. 
 
 § 393- 'What a thing really is ' was what the ancients meant by 
 opoi ova-uoSiji, definitio realis. But the expression has been 
 employed more recently for notional definition as distinguished 
 from so-called verbal definition.^ Modern writers, accordingly, 
 have been to some extent at cross purposes, in discussing 
 ' whether Definition is Nominal or Real '. Is it of the meaning 
 of the name (tov tC arrnJMlvu Tovvofm), or of the nature of the thing 
 (tov Tt eoTt ) ? Thus Sigwart says : — 
 
 'A definition is a judgement which states the meaning of 
 a term denoting a concept. All logical definitions are nominal 
 definitions. The demand for a real definition, containing the 
 essential characteristics, arises from the confusion between 
 metaphysical and logical problems. ... It is a return to the 
 Aristotelian demand that the concept should state the essence 
 of the thing, according to his metaphysical theory. Now that 
 we confess our ignorance in most departments of knowledge of 
 the Tt eo-Tt, in the Aristotelian sense, it would be well also if 
 logic were to relinquish the concept of the real definition.' ^ 
 
 Again, ' Kant has shown that in the empirical domain there 
 are no definitions in the strict sense, since the characteristics 
 which belong to the object — e. g., gold or water — can never be 
 exhaustively enumerated, and hence the rule that the definition 
 should be complete can never be complied with.' ' 
 
 So Whately remarks : — 
 
 'We are concerned with nominal definitions only, because 
 all that is requisite for purposes of reasoning is that a term 
 shall not be used in different senses. A real definition of any- 
 thing belongs to the science or system which is employed about 
 that thing.' * 
 
 ' \6yos ovofiuTaiSrjs. The Aristotelians used this phrase in this sense, 
 but not, probably, Aristotle in the only place where he employs it (Post 
 An. ii. 10). 
 
 ' Logic, i. 286, 288. ' Ibid. i. 106. 
 
 * Unless, however, ' nominal ' means verbal and ' real ' means notional, 
 I fail to see what Whately means by saying that in mathematics 
 
 •A-n 
 
'Real' and 'Nominal' Definition i8i 
 
 § 394. Mansel, on the other hand, says :— 
 
 'In the sense in which nominal and real definition were dis- 
 tinguished by the scholastic logicians the exact reverse is the 
 truth. Logic is concerned with real, i. e. with notional, definitions 
 only. To explain the meaning of particular words belongs to 
 the dictionaries or grammars of particular languages.' ' 
 
 Hamilton^ remarks: — 'By a real, in contrast to a verbal or 
 nominal definition, the logicians do not intend " the giving an 
 adequate conception of the nature and essence of a thing", that 
 is, of a thing considered in itself and apart from the conceptions 
 
 nominal and real definition exactly coincide ; for, he says, the name 
 (e. g. of parallelogram) expresses the nature of the thing, not all its proper- 
 ties but only its essential nature (Logic, c. i, § 7). He adds that the 
 same is true of logical, and most legal, and many ethical, terms. 
 
 ' Prol. Logica, p. 189 n. 
 
 " Hamilton, following Krug, adds a third kind of definition, the Genetic. 
 He says : — ' As examples of these three species the following three defini- 
 tions of a circle may suffice, i. The Nominal Definition. — The word 
 circle signifies an uniformly curved line. 2. The Real Definition. — A 
 circle is a line returning upon itself, of which all the parts are equidistant 
 from a given point. 3. The Genetic Definition. — A circle is formed when 
 we draw around, and always at the same distance from, a fixed point 
 a movable point which leaves its trace, until the termination of the 
 movement coincides with the commencement. It is to be observed that 
 only those notions can be genetically defined which relate to quantities 
 represented in time and space. Mathematics are principally conversant 
 with such notions ; and it is to be noticed that the mathematician usually 
 denominates such genetic definitions real definitions, while the others he 
 calls without distinction nominal definitions ' {Lectures on Logic, ii. 13). 
 Hamilton distinguishes them thus : — Nominal definitions are merely pre- 
 paratory explications. Real definitions presuppose the thing defined as 
 already existing (ov), so that the notion precedes the definition. In 
 genetic definitions the defined subject is considered as in the progress to 
 be (yiyvoiuvop). The notion, therefore, has to be made, and is the result 
 of the definition, which is consequently synthetic. 
 
 I think, with Veitch (Institutes, p. 208), that ' genetic ' definition is 
 merely a rule for giving concrete effect to a notion already conceived in 
 the mind. As regards ' real ' definition presupposing the existence of the 
 thing defined, certainly we do not know that a line of which all the parts 
 are equidistant from a given point is a line that can return upon itself. 
 But neither, if we define a mule as a hybrid between a horse and an ass, 
 does this prove that there can be such an animal. Hamilton's example 
 of a nominal (= verbal) definition seems a poor one. ' Circle' as a word 
 is not equivalent to ' uniformly curved line ' as vertebrate is equivalent to 
 ' having a backbone ', or hendecasyllabic to eleven-syllabled, or ' sugar ' to 
 a thing sucked. 
 
i82 Division and Definition 
 
 of it already possessed. By verbal definition is meant the more 
 accurate determination of the meaning of a word ; by real the 
 more accurate determination of the contents of a notion, . . . 
 The substitution of notional for real would, perhaps, remove the 
 ambiguity.' ^ 
 
 § 395. It is clear that ' signification of the name ' is an ambigu- 
 ous phrase. So also is ' real nature of the thing '. Definition 
 has no meaning if it is not notional. It is equally empirical, 
 objective and the same thing for everybody whether we say that 
 ' leopard ' means lion-pard, or describe the beast's colour, size, 
 habitat, temper, and other attributes. I do not say its 'distinguish- 
 ing attributes ', because this brings us back at once to the notional 
 standpoint, which alone is subjective. 
 
 § 396. The definition is the concept itself. Concepts of purpose 
 are therefore more easily defined than others, because the purpose 
 is usually consciously before the mind.^ A razor is a cutting 
 instrument for shaving. A house is meant to live in ; a bed to 
 sleep in ; a chair to sit upon. A ruler is for drawing straight 
 lines ; a helm for steering. Definition itself is defined by its 
 object. A picture is meant to look at and a song to please ; but 
 these circumstances are not so prominently before the mind, and 
 therefore are no part of the definition. 
 
 § 397. Besides final cause, scientific definition is often through 
 
 efficient cause. Aristotle says, to tL ia-nv elSivai ravro Jan koI 8ia 
 
 TL cdTLv.^ Such definitions state the way in which the effect is 
 produced. Aristotle, who regarded the securing of distinct 
 notions as a halting-place midway between the inductive and 
 deductive stages of demonstration, connected definition with 
 
 * Reid's Works, p. 691 n. 
 
 ^ See Sigwart, i. 274. 
 
 ^ Mansel, however, remarks: — 'Aristotle's opinion is not decidedly 
 expressed ; but it seems probable that he regarded the formal cause only 
 as available for purposes of Definition. For a material cause, properly 
 speaking, has no place in attributes but only in physical substances ; and 
 that which in the former is most nearly analogous to matter, viz. the 
 necessary condition out of which the effect arises, may in such cases be 
 identified with the formal cause. The efficient and final causes seem to 
 be excluded, as not being contemporaneous with their effects, so that 
 from the existence of the one we cannot certainly infer the other. Whereas 
 the formal cause is expressly distinguished as to n rjv elmi ' {Aldrich, 
 p. 183). He adds : — ' Aristotle's treatment of Definition has far more of 
 a material than a formal character ' (Ibid. p. 193). 
 
Definition through Cause 183 
 
 causation, and sought for definition through syllogism, the middle 
 term or cause being the definition sought. What makes a (solar) 
 eclipse ? This may mean, either, what constitutes an eclipse, or 
 else, what causes an eclipse. The logician gives the same 
 answer as the physicist — ' the interception of the sun's light by 
 the moon.' A cathedral may convey to the vulgar the idea 
 merely of a very splendid and ancient church. But it is correctly 
 defined by that which- in ecclesiastical law makes it to be a cathe- 
 dral, viz. the bishop's throne being in it. On the other hand a 
 city is said to be constituted in the same way ; yet few would 
 think of this in defining 'city'. The definition of 'island' as 
 a piece of land surrounded by water combines the formal, efficient 
 and material causes. Disraeli's epigram, 'Critics are painters 
 who have failed,' suggests the causa efficiens, but not the formal 
 cause of being a critic, viz. criticizing. 
 
 § 398. Accidents, the older metaphysicians say, are undefin- 
 able because they cannot be demonstrated by a cause residing in 
 their subject. There is nothing in the essential nature of man 
 which makes him a laughing creature ; nor, I suppose, in a chem- 
 ist's essential function which necessitates his putting coloured 
 lights in his window ; nor in the vows and religious character of 
 Carthusian monks which obliges them, or obliged them, to manu- 
 facture liqueur. But all this is far removed from the logical 
 standpoint. Accidentality, from the logical point of view, is the 
 absence of a universal, of any causal connexion. If it were only 
 occasionally and casually that the interposition of the moon's 
 body between sun and earth were accompanied by an eclipse, 
 a solar eclipse could not be so defined. 
 
 § 399. The disHke of the English mind for ideas and for 
 universals, its preference for the unrelated fact and the particular 
 judgement, is the reason why, as the late Bishop Creighton 
 pointed out, it has never been fertile in definitions. On the one 
 hand there is such a thing as an itch for over-defining,^ which 
 does not really advance scientific thought any better than the 
 hand-to-mouth thinking of the ' practical man ', content to ' mud- 
 dle through ' life's problems ' somehow '. But, though we must 
 
 ^ 'Ideal' Ward, rebelling against the nebulosity of the age, wished 
 jestingly that he might have a new papal bull laid every morning with 
 his muffin on the breakfast table. 
 
184 Division and Definition 
 
 be content in many matters with half lights, it does not follow 
 that ' mistiness is the mother of wisdom '. 
 
 § 400. More metaphysical than logical, again, is the distinction 
 between definitions of Substances and those of Attributes, the 
 cause of the latter residing in the subjects in which they inhere, 
 the cause of the former residing in themselves. Every oio-cas 
 yi/topto-zAds, it is said, must state what by why. But why a substance 
 is itself, who can say ? ' Properly speaking,' writes Mansel, 
 'all Definition is an enquiry into Attributes. Our complex 
 notions of Substance can only be resolved into various Attributes, 
 with the addition of an unknown substratum — a something to 
 which we are compelled to regard these Attributes as belonging. 
 Man, for example, is analysed into Animality, Rationality, and 
 the something which exhibits these phenomena. Pursue the 
 analysis and the result is the same. An unknown constant must 
 always be added to complete the integration.' ^ 
 
 §401. Definition, instead of being by cause, is sometimes /ler 
 effectum. A fool is known by his much laughter, and might be 
 defined as one who laughs excessively; for definition is not 
 seldom a response to the question. How am I to distinguish such 
 and such a class from others ? A gentleman has been defined 
 as a man who can wear a fur-coat without looking like a theatre 
 manager. The object of definition is mental demarcation. No 
 doubt, on the other hand, it is generally understood that a defini- 
 tion claims to have a universal interest and to get below the 
 surface of things. What is meant generally by this or that 
 attribute — e. g., the being a gentleman ? 
 
 § 402. Such a question is answered either dtvisively, by taking 
 a wide generic idea and adding successive differences till it is 
 contracted to the exact sphere of the concept to be defined. 
 Or else by the reverse method. The individuals, or subordinate 
 classes, to which the name required to be defined is applied, are 
 compared, and by finding wherein they agree we obtain our 
 definition. What do I mean by ' a thorough gentleman ' — putting 
 aside for the moment the element of gentle birth ? I think of 
 five or six persons to whom I should instinctively apply the 
 expression, and reflect what they have in common. Excluding 
 one quality and then another for which I esteem them, I fasten 
 on some point that seems essential — unselfishness or magnan- 
 ' Aldrich, p. 192. 
 
Which precedes,. Division or Definition? 185 
 
 imity, it may be, combined with a certain distinction of manners. 
 This inductive method examines attributes rather than, as the 
 divisive method does, extensions. If the definition is faulty, it 
 is in the divisive method because there are some members of the 
 class which are not covered by the definition, or else because 
 there are some members not of the class which are included in 
 it ; in the inductive method it is because there is some part of the 
 definition which does not apply to one or more of the constituents 
 of the class, or in respect of which it is inadequate to express 
 the characteristics which they have in common. 
 
 § 403. Some logicians distinguish between ' Analytic ' and 
 ' Synthetic ' definition — the former explicating the content of 
 a notion, the latter stating the limits within which a name is 
 applicable. If it be asked. What is man?, analytic definition 
 replies, Man has the attributes of animality with rationality ; 
 synthetic definition replies, Man is any rational animal — that is, 
 all rational animals, and they only, are entitled to the name man. 
 The distinction, hovyever, if it is worth making, is merely the 
 distinction between a statement expressed intensively and the 
 same expressed extensively. Humanity is essentially rationality 
 with animality. Man is essentially whatever is rational and at 
 the same time animal. Every definition is analytic, and in every 
 definition, not in ' synthetic ' ones only, the defmiendum may be 
 regarded from one point of view as the real predicate. Toast is 
 baked bread. All baked bread is toast. 
 
 § 404. What has been said in the last paragraph but one about 
 the divisive and the inductive ways of obtaining a definition 
 bears on the question whether Division precedes Definition or 
 Definition Division. It is plain that Specification and Generaliz- 
 ation are mutually inverted operations. For if ships are divided 
 as warships and non-warships, and the former class are divided 
 again as ironclads, cruisers, gunboats, destroyers, and so forth, 
 then, inversely, we compare these objects, when put before us, 
 and find that they are all alike ships (higher genus), and that 
 their characteristic (the differentia of their immediate genus) is 
 the being used for warfare. Now suppose that, instead of divid- 
 ing ships according as they are or are not used for war, we had 
 given the dividing members names which did not explain them- 
 selves but needed definition, viz, navy and not-navy, the former 
 being as before divided further as ironclad, cruiser, gunboat, 
 
i86 Division and Definition 
 
 destroyer, and so forth. Comparing these objects together, with 
 a view to defining navy, and finding that they are all ships, and 
 ships used for war, we should take this as the definition of navy. 
 Or, possibly, the same comparison might have given us the 
 definition, 'ships belonging to his Majesty.' 
 
 § 405. The matter, then, may be looked at either way. If we 
 are finding a definition inductively, the division is supposed given, 
 for we found the meaning of ' navy ' by comparing the dividing 
 members of the concept. From this point of view Division pre- 
 cedes. Divisionem excipii Definitio. But we may proceed in the 
 opposite order. Dividing the class ' ship ' by any pair of contra- 
 dictory attributes we like, in this case navy and not-navy and 
 being given the definition of navy as ships used for war, we 
 proceed with this knowledge to divide navy empirically into 
 different kinds of vessels intended for war, as ironclads, cruisers, 
 and so forth. Mansel, therefore, taking this point of view, 
 prefers to say, Definitionem excipit Division 
 
 § 406. Hamilton says : — ' Division supposes the knowledge ot 
 the whole to be given through a foregone process of Definition 
 or Declaration, and proposes to discover the parts of this whole 
 which are found and determined, not by the development of the 
 Comprehension, but by the development of the Extension.' ^ 
 Aristotle prescribes the other order, in which Division prepares 
 the way for Definition, securing that no member of the class to 
 be defined is omitted in the induction.' Plato also defined by 
 dividing, though. Dr. Wallace remarks, ' his method of discover- 
 ing the character of an object by continual dichotomy really 
 assumes what is to be proved. It arbitrarily takes one of two 
 classes under which it seeks by successive divisions to bring 
 the particular conceptions.' * 
 
 § 407. The material on which thought is to work must always 
 be given extraneously to the thinking act. Until the concept 
 to be divided has been defined, division is barren ; and until 
 a class has been divided, no induction can take place with 
 a view to definition. 
 
 P. L. p. 194. 
 
 Lectures on Logic, ii. 25. 
 
 An. Post. ii. 13. 96^15 and 97''7. 
 
 Outlines of Ai-isiotle^ s Philosophy, p. 35. 
 
Division and the Predicables 187 
 
 § 408. Division and Definition involve, as we have seen, three 
 relations between concepts, Genus, Differentia and Species, of 
 which the two former are together equivalent to the latter, and 
 constitute a definition. 
 
 § 409. The Greek dialectic turned very largely on Definition, 
 the fourfold division of Predicates answering to the modern 
 division of attributes into those which do, and those which do 
 not, define. 
 
 Attributes 
 
 I I . 
 
 defining non-defining 
 
 I " I I. J 
 
 generic (= genus) specific (= differentia) proprium accidens 
 
 § 410. Looking at the matter from the other side, the Heads 
 of Predicables (at -Kkvre) are connected with Division. In the 
 whole to be divided {genus), each dividing member (species) is 
 separated from the others by its differentia. Each species is 
 equivalent, extensively and intensively, to the genus qualified 
 by its own difference. But a species may also be co-extensive, 
 though not co-intensive, with some other concept, or, in other 
 words, be the sole possessor of some attribute which is not its 
 differentia in the division, and therefore not part of its definition 
 as given through that division. Such attribute is called a 
 proprium of the species.' A warship is a king's ship, but ' war- 
 ship ' does not mean ' king's ship '. Cats mew, and they alone ; 
 or, if the sea-mew be objected, they alone among quadrupeds. 
 But ' cat ' and ' a thing that mews ' have not, from the ordinary 
 point of view, the same intension. One conceptual relation 
 remains — that of accidens. This, from the logician's standpoint, 
 is an attribute possessed by a part only of the species; as 
 whiteness by some geraniums and not others. Such an 
 
 ' 'AvayKij yap irav to irepi rivos KaTTjyopovfi,evov rjroL avTtKaTtjyopelcrdai. 
 Tov Trpayfiaros r) fo], koi fi fiev avTtKaTr]yopelTai, opos r) ibiov hv eirf el fiev 
 yap arjiialvei to tI rju elvai, tipos, el de p.!] arjpuivei, i&wv' toCto yap rjv iBwv, 
 TO avTiKarrjyopovpevov pev, p.fj ampcdvov Se to tI rjv eivai (Ar. Top. i, 8. 
 
 los*;). 
 
i88 
 
 Division and Definition 
 
 Accident, however, may become the differentia of a further 
 division of the species into sub-classes.^ 
 
 § 411. Logic can only recognize the Predicables as relations 
 in predication. Property and Accident call for a little further 
 consideration from this point of view. Porphyry " distinguishes 
 four kinds of Property, thus expressed by later writers : — 
 
 (i) That which belongs to the subject soli sed non omni. As, 
 homo grammaticus est. Only men, yet not all men, can learn 
 grammar. 
 
 (2) The same omni sed non soli. As, homo bipes est. All men 
 are bipeds ; but so also are other creatures. 
 
 (3) Omni et soli, sed non semper. As, homo canus est. All 
 men, and only men, get grey, but only during part of their 
 lives. [Bald would be better than grey, for dogs and horses get 
 grey.) 
 
 (4) Omni, soli et semper. As, homo risibilis est. Man, man 
 only, and man always, is apt to be moved to laughter. 
 
 The two last kinds must, for our purpose, be combined in 
 one, (3) becoming ' Man, and man only, is liable to get bald '. 
 We have then to distinguish three relations : — 
 
 ^ Mr. Stock {Logic, p. 105) gives the following scheme, based on 
 Aristotle's division : — 
 
 Predicate 
 
 I 
 co-extensive with Subject 
 
 \ 
 
 I 
 
 not co-extensive with Subject 
 
 co-intensive 
 
 with Subject 
 
 {opos) 
 
 I 
 
 not co-intensive 
 
 with Subject 
 
 (rSiov) 
 
 I 
 
 partially 
 
 co-intensive 
 
 with Subject 
 
 {yivos) 
 
 I 
 Defini- 
 tion 
 
 Synonym 
 
 I 
 
 not at all 
 
 co-intensive 
 
 with Subject 
 
 (Accident, 
 
 Designa- 
 tion 
 
 I 
 Genus 
 
 I 
 
 Differ- 
 ence 
 
 "I 
 
 Generic 
 property 
 
 Descrip- Peculiar 
 tion property 
 
 It is impossible that a predicate should not be co-extensive, and yet be 
 co-intensive, with its subject ; for this would imply that certain objects, 
 either in the subject or the predicate class, possessed all the qualities 
 belonging to their class without possessing the qualities belonging to the 
 other class, which are, however, ex hypothesi, the equivalent of them. 
 
 " Eisagoge, v. I. 
 
Property 189 
 
 (i) Quod speciei soli sed non omni convenit. 
 
 (2) Quod speciei omni sed non soli convenit. 
 
 (3) Quod speciei omni et soli convenit. 
 
 Of these the second kind is merely the ordinary universal 
 affirmative judgement, and Subject and predicate are simply 
 species and genus. All men are bipeds, and so are all geese. 
 Two-footedness, then, is only a property in the loose sense in 
 which the attributes of a thing are called its properties. The 
 first kind is the judgement, 'Only X'% are y]'='All Fs are X' — 
 except that we are given the fact that not all X'^ are Y. It may 
 appear at first sight that Y should be regarded in such a case as 
 a proprium, especially if the X's which are not Y are very few-— 
 e. g., ' It is peculiar to man to have the use of speech.' ' But in 
 strictness Y is a peculiarity, not of X, but of a sub-species 
 of X 
 
 § 412. The only predicable relation which really expresses an 
 IZiov, or specific difference, is omni et soli. Subject and predicate 
 must have the same extension, and the proposition be con- 
 vertible. It is true, as we shall see under Quantification of the 
 Predicate, that this relation cannot be expressed in any pro- 
 position about ' every X '. Strictly speaking, Logic cannot 
 recognize Property. The examples, for instance, given above 
 of the fourfold Porphyrian distinction are all alike in form. 
 How are we to know that 'homo risibilis est' expresses a 
 different relation from ' homo grammaticus est ' ? On the other 
 hand, the relation can be expressed in a compound proposition ; 
 e.g., 'All X's, and they only, are Y', or in some other way. 
 Thus we might say, ' A shop where a bush is displayed and a 
 shop where wine is sold are the same thing.' 
 
 § 413. The relation of a genus, a difference or a property 
 to a species is a general and causal one. Accident, as a 
 Predicable, is when the relation of predicate to subject is only 
 occasional and so accidental. It is an accident whether a 
 feather is yellow or any other colour, whether a picture is good 
 or bad. 
 
 § 414. The predicate is therefore accidental in particular 
 and also in 'universal-concrete' propositions, there being no 
 
 ' See Ar. Hist. Anim. iv. 9, 16. ' Since man from beasts by words is 
 known, Words are man's province ' (Pope, Dunciad). 
 
igo Division and Definition 
 
 causal connexion or rule suggested, ' Some potatoes come from 
 abroad.' 'All these potatoes come from abroad.' 'Some boys 
 are tall.' ' Tom, Dick and Henry are tall.' It is true that the 
 tallness results from something in the constitution of the tall 
 boys, and the having been grown abroad may be inferred from 
 the nature of the potato. But this does not make any 
 difference to the particularity or generality of the propositions. 
 For example, ' Some clocks are always right ' is a particular 
 proposition, and being always right is an accident contingently 
 true of clocks, though it involves a general judgement about 
 certain unnamed clocks. 
 
 § 415. Logical books speak of a kind of accident called 
 Inseparable Accident. There can, I submit, be no such thing. 
 We may be uncertain whether a seemingly invariable con- 
 comitance has a universal character or not. Is it an inductive 
 generalization or only a fact true within the limits of our 
 observation ? But it is impossible to suppose that two 
 phenomena which never have been, are, or will be found 
 separated are entirely without causal connexion, however 
 obscure it may be. The examples usually given are that the 
 mammals are always the warm-blooded creatures, and horned 
 animals are the ruminants. An 'inseparable accident' is for 
 the logician identical with property.' 
 
 § 416. Accident is commonly defined as a quality which might 
 be absent from an object in this or that case without destroying 
 
 ' Porphyry professes to disregard metaphysical questions. Yet, like 
 other writers, he bases his doctrine of the Predicables on a scheme of 
 natural kinds. A man, he says, may be 'more or less ' angry, but he 
 cannot be more or less animal or rational. That is because in the former 
 case we have only the possibility of a particular judgement. A man 
 (like every other man) is always animal and rational, but only occasion- 
 ally angry. Besides, an emotion has degrees, a nature is constant. Sig- 
 wart also ignores the difference between the universal and the particular 
 when he says that ' it is only concepts within the same category which can 
 be subordinated to one another, and to speak of red as superordinate to 
 rose, or intentional as the superordinate concept to murder, is only con- 
 fusing' (Logic, i. 269). Not all, but only some, roses are red. If, on the 
 other hand, all murders are intentional, murder might well be defined as 
 intentional homicide, or be classed in an ethical treatise under the generic 
 head of intentional acts, with ' homicidal ' for differentia. ' Among the 
 characteristics,' says the Professor on the same page, ' there is always one 
 which determines the nature of the synthesis by giving the category.' 
 
Accident 191 
 
 our essential idea of it. Sleeves are essential to a coat, but not 
 sleeve-buttons. A bad sixpence is no sixpence ; a sixpence, how- 
 ever, would be as much a sixpence if the superscription were 
 in English rather than in Latin. But the superscription being 
 in Latin must be regarded as a property of British coins — unless, 
 indeed, any other State uses that tongue. On the other hand, 
 it would be logically an accident if this, that, or the other 
 sixpence had a hole in it. A particular judgement only is 
 involved. But all sixpences bear a legend in Latin. So it is 
 a property, not an accident, of a triangle that its angles are 
 together equal to two right angles. If it is of the essence of 
 a square to be rectangular but the accident of a table, this is 
 because there are round tables, hexagonal tables, and so forth. 
 For the same reason it is essential to a table to be flat, 
 accidental to be of this or that shape. 
 
 § 417. Undoubtedly the flatness of a table is determined by 
 the physical necessity of things. Nevertheless, the usual treat- 
 ment of the Predicables a parte rei is extra-logical. Such 
 names as genus, species, essence, property, accident, are 
 borrowed from Ontology. They look to the constitution of the 
 universe rather than to the form of the predication. Aristotle 
 does not objectify the Heads of Predicables as the schoolmen do. 
 To him they are 'the Four Differences' — originally three, but 
 iStov was subsequently broken up by him into Definition and 
 Property. The Aristotelian point of view, however, is only 
 semi-logical. Mansel gives the traditional doctrine in the 
 following form : ' — A predicate expresses either^ 
 (i) the whole essence of its subject (Species) ; or 
 
 , ■. . r i.u f the material part (Genus) 
 
 (2) part of the essence \ , . , ,X.^ , 
 
 I the formal part [Difference) ; or 
 
 {3) something joined to the essence \ . , , , . , ^ 
 
 \ contmgently (Accident). 
 
 § 418. What, however, can we know about whole essences 
 and part essences ? ' Essence ' for Logic is subjective only — 
 not the necessary basis of the definition (about which basis we 
 can form no judgement without a material knowledge of some 
 things, or all things), but given by the definition. Even 
 property, until the definition is given us, can only be dis- 
 tinguished from definition as simple commensurate from 
 ' Aldrich, p. 67. 
 
ig2 Division and Definition 
 
 complex commensurate attribute. In metaphysics, on the 
 other hand, property is a secondary attribute which flows 
 exclusively from the essence of the object it belongs to— either 
 from the genus (e. g., man being animal is appetitive), in which 
 case it is called Generic Property, or from the differentia (e. g., 
 man being rational is progressive '), in which case it is called 
 Specific Property. Aristotle says that man is <^v(ret troi/Svao-rwdv, 
 and (jtva-u TToXiTLKov. But the question what flows from the nature of 
 any object — e. g., that mammals do not lay eggs — is quite extra- 
 logical. As well say that because a scarecrow is defined by its 
 final cause, that of frightening birds by a human semblance, we 
 must know that it wears clothes, and that this is an inseparable 
 accident of a boggart, which never undresses, but the separable 
 accident of a man, who does.^ What, by the by, shall we say 
 about a tailor's dummy, which only exists for the purpose of 
 being clothed and yet is not always so ? The inner and 
 essential nature of things is beyond the logician's ken. Is a sloe 
 more essentially black than an Ethiopian ? If habitat has made 
 the one black, soil may have made the other. And how is pure 
 reason to say what secondary attributes flow from the essence 
 of the subject to which they belong ? It is not of the essence of 
 a lobster to be red ; yet boiling educes the redness from some- 
 thing in the creature's constitution. 
 
 § 419. In the above elucidation of the inter-relation of 
 concepts, Species has been regarded as the subject of which the 
 rest are predicable. But the schoolmen made Species itself 
 a Predicable [species praedicabilis), taking as starting-point the 
 individual substance.' That which the individual is always and 
 
 ' Progress, Man's distinctive mark alone — 
 
 Not God's and not the beasts'. God is. They are. 
 Man partly is, and partly hopes to be. — (Browning.) 
 
 ^ Apart from the question of there being any humans who wear abso- 
 lutely no clothing at all, wearing clothes is a property — at any rate among 
 terrestrial beings — of mankind. Or, if horses and Dutch cows be objected, 
 we may say, putting on clothes. ' An animal who, in a civilized condition, 
 wears clothing ' would be a logical definition of man. 
 
 ' Aristotle, remarks Bain {Logic, App. A. p. 17), established 'a gradu- 
 ated scale of Entia, each having its own value and position, and its own 
 mode of connexion with the common centre ', viz. the individual object, 
 ToSe Tt, hoc aliquid, to which all the higher Entia belong as predicates, 
 and without which none of them has any concrete reality. The Realists, 
 adopting the same scheme of ontological classification, contended on the 
 
Predicahles not Heterogeneous 193 
 
 necessarily is his essence, or flows from it. That which a thing is 
 at one time and not at another is accidental — e. g., the tempera- 
 ture of a given piece of water, or the posture of Agamemnon. 
 This rose was fresh yesterday, but is withered to-day. 
 
 § 420. It has been objected to the Heads of Predicables, e. g. 
 by Professor Minto, that the list is heterogeneous. Genus and 
 Species being the names of classes. Difference, Property and 
 Accident the names of attributes. But Extension and Intension 
 are only two aspects of the same thing, and we have already 
 noticed (§ 309) that Genus and Difference may often gramma- 
 tically change places. Species as the subject of predication 
 must, no doubt, be regarded primarily as a class of things, since 
 it is of things that attributes are predicated, but not as species 
 praedtcabilis. The predicate of any particular proposition is 
 accidentally predicated. The predicate of any universal proposi- 
 tion, whatever its grammatical form, may be genus, differentia 
 or property. 
 
 § 421. These expressions, however, should only be used in 
 reference to an act of definition. Logic has been unduly 
 narrowed by attention being fixed on a limited scheme of 
 concepts, classified in correspondence to a fixed order of the 
 universe or the Cogitable Ideas ; whereas the field of general 
 assertion is really boundless. Nevertheless, there is order in 
 the universe,' and things have proper places into which 
 
 other hand that the individual is what it is only by participation in the 
 universal. Just actions are so because they are stamped with the charac- 
 teristics of justice. Justice is not merely a compendious name for a circum- 
 stance in which a number of actions happen fortuitously to agree. Prob- 
 ably, as regards a certain range of concepts we are all at heart realists — 
 justice, beauty, goodness and the like. Either we must hold a universale 
 ante rem, an eternal cogitabile, or be driven, step by step, to base every- 
 thing on Chance. Bain, however, maintains that there is no idea of 
 Government in the abstract {Logic, p. 178). Certainly we only recognize 
 the universal in the particular ; yet such recognition implies a priority in 
 idea. This Trendelenberg derides as ' the ancient hysteron-proteron of 
 abstraction '. 
 
 ' ' Were the various properties of things loose and unconnected, it 
 would be impossible to reduce the Concrete Generals to anything like 
 order. As an infinitely worse consequence, it would be found impossible 
 to arrange natural objects into natural classes. For, the number of 
 qualities in all objects, material and mental, being innumerable, we might 
 fix with equal propriety on any one as the ground of the arrangement, and 
 there could be no agreement among those investigating the kingdoms of 
 
 o 
 
194 Division and Definition 
 
 ordinarily to fall. So that, though we perforce use these 
 expressions (see above, § 386), it seems strange to speak of 
 'sweeping clean' as genus (or differentia) to 'new brooms', 
 because it would not probably occur to us as part of a definition. 
 Nor is ' cheaper than it used to be ' part of the usual analysis 
 of the idea of bread. Such predicates, though stated universally, 
 are not part of that symmetrical arrangement of the world 
 according to which we observe that a great number of con- 
 comitant and incidental attributes group themselves round one 
 especial characteristic. On the other hand, the logician is 
 incompetent to say what is a natural and what is an arbitrary 
 and artificial classification. For him there is no fixed scheme 
 of genera and species. Everything may be conceived under 
 as many aspects as it has attributes, and may be defined 
 therefore in an equal number of ways. 
 
 § 422. Before leaving this division of our subject, something 
 should be said about the sign of Negation as attached to Con- 
 cepts. Aristotle says that contradiction does not apply to simple 
 concepts, Kara ij.rfiiij.iav a-vfj.TrXoKrjv Xeyo/xeva, but involves predica- 
 tion. 
 
 A negated notion has no meaning out of predication, i. e. 
 apart from an implied or expressed assertion. If a notion 
 could be entirely simple, it could not be affirmative or negative. 
 For there is no such thing as an idea which states or denies. 
 So far from not-horse shutting out the idea of horse, or ovk 
 avOpmiro^ of avOptoTroi, each idea involves and calls up the other, as 
 an idea. They are mutually creative. All that can be affirmed 
 or denied is attribution to a subject. 
 
 § 423. But, since every concept is the complex of a higher 
 concept qualified by another concept (see above, § 295), it 
 necessarily contains within it an element which may be 
 expanded as a relative clause. An iron bar is a bar which is 
 made of iron, warm weather is weather of which warmness may 
 be predicated, a newspaper is a paper which gives news ; and 
 
 nature. Or rather . . . the God Who made all things has, happily for our 
 understanding and our practical convenience, instituted an order among 
 the separate qualities of objects, so that it is possible to arrange them 
 into orders which have such marks as enable us to fit them into our 
 material systems' (McCosh, Laws of Discursive Thought, p. 34). 
 
Negation attached to Concepts 195 
 
 even simple nouns like fork or stool are analysable into factors 
 — an implement which is furcated, an article which is called a 
 stool ; or, be the definition of the name what it may, at least it 
 has one, and that a complex. 
 
 § 424. If now we attach a mark of negation to the concept, it 
 is not the entire concept which is negated — for this is impossible 
 — but only the relative assertion contained in it, the inherence of 
 the qualifying in the substantive part, ' Unhappy pair ' means 
 a pair who are not happy .' 
 
 § 425. Accordingly, simple nouns substantive, not explicated 
 into their elements, do not usually admit the prefixing of a 
 negative sign. We do not say un-dirt or not-kettle. Whereas 
 adjectives, which are not concepts by themselves but wait to 
 qualify a substantive, do take the negative. We say illegal 
 but not un-law, unfaithful but not unfaith — though these harsh 
 expressions, it is true, have been used. Undoubtedly non is 
 often used with simple substantives — a non-voter, a non-gentle- 
 man (we could not say ungentleman, though we say ungentle 
 man and ungentlemanly). But in such cases the negated 
 word is understood quasi-adjectivally, a qualified notion being 
 understood — a non-voting citizen, a person who is not a gentle- 
 man. Or the termination supplies the substantive element. 
 In non-voter, disloyalist, nonjuror and many like words, the 
 termination er, ist, or, remains unnegated. 
 
 §4^6. For a similar reason attributes commonly allow a 
 negative prefix — imbecility, imperfection, nonconformity, 
 illegality, injustice, irreverence, inhumanity, disreputableness. 
 Only the adjectival part of the word is negated. Unfriendliness 
 is the quality of not being friendly, dissatisfaction is the 
 condition of not being satisfied. Even adjectives and participles 
 are not wholly annulled by being negated. ' Unfriendly ' keeps 
 My' (sc. like) undestroyed, 'unloved* keeps 'ed.* A verdict 
 which is unjust has still a certain character in relation to 
 morals. A noncommissioned officer is an officer who, though 
 without a commission, is qualified by some character or other. 
 Compare unceremoni-ous, unmerci-ful, inattent-ive. The sub- 
 
 ^ Hughlings says : — ' In a negative name the negative sign plays the 
 part of an adjective, in a negative proposition of a predicate ' {Logic of 
 Names). But the negation does not qualify the whole notion— e. g., wireless 
 telegraphy is a kind of telegraphy. 
 
 o 2 
 
196 Division and Definition 
 
 stantive is oiJtws ex""' constituted if not in this way then in 
 another. Adjectives usually suggest some sphere of discourse. 
 If a thing is said to be not blue, it is suggested that it has some 
 other colour, not-obstinate is understood of character, not-pretty 
 of outward form, ungentle of speech or manners. Not-oviparous 
 denies ovi but not parous. 'The book is not James's' leaves 
 the possessive case-sign un-annulled, and implies that it belongs 
 to some one else. In ' not unlikely ' not destroys the un only, 
 and leaves the likely. 
 
 § 427. The element on which the force of the negation falls is 
 that on which stress is laid by the voice. ' Not four-footed ' 
 might mean two-footed, or it might mean four-handed, like an 
 ape. If I deny that a spear is silver-headed, I may intend 
 that it has a head of gold, or that it has a shaft of silver. 
 Obviously silver-headed would not be negated by golden- 
 shafted, for the spear might be both. A sacrament which 
 'bonos vivificat' at the same time 'malos mortificat', though 
 malos is the contrary to bonos and mortificare to vivificare. 
 
CHAPTER XII 
 JUDGEMENT 
 
 § 428. In treating of Conception before Judgement we have 
 followed the older and more obvious arrangement. But 
 modern writers, regarding the Judgement as the logical,' and 
 the Sentence as the grammatical, unit, are for the most part 
 inclined to invert this order, and to regard the notion as only 
 an analytic element of judgement. 
 
 § 429. Every act of consciousness involves a comparison. A 
 concept, says Sir William Hamilton, ' is nothing but the result 
 of a foregone judgement or series of judgements fixed in a sign.'" 
 Mansel remarks : — ' We judge individual objects to resemble 
 one another before we gather them into classes. . . . According 
 to Hobbes a proposition is but the addition of two names so 
 coupled together that he that speaks conceives both to be names 
 of the same thing. ... He has overlooked the fact that 
 apprehension is primarily the analysis of judgement, not 
 judgement the synthesis of apprehensions.' ' 
 
 § 430. Mill, while welcoming Hamilton's view, asks how it 
 agrees with the Hamiltonian doctrine that in judging we bring 
 one notion under another notion. If a judgement is involved 
 in every mental act, and if, as is generally agreed, every 
 concept is built up by a succession of judgements and can be 
 resolved into these again, how can the judging act be a 
 comparison of concepts ? Such an inconsistency, Mill observes, 
 'coming from a thinker of such ability, almost makes one 
 despair of one's own intellect and that of mankind, and feel as 
 
 ^ ' An assertory predication is the unit with which Logic concerns itself 
 (Minto, Logic, p. 43). ' We do not enter upon logical development proper 
 till we come to deal with the evolution and affiliation of jiSdgements' 
 (Bosanquet, Logic, i. 7 1). ' The sentence is the significant unit of language ' 
 (ibid. p. 40). 
 
 " Lectures on Logic, i. 1 17. 
 
 ^ Aldrich, p. xliii. 
 
igS Judgement 
 
 if the attainment of truth on any of the more complicated 
 subjects of thought were impossible.' ' 
 
 § 431. Mill's own teaching is that judgement is not a com- 
 parison of concepts, but of the intuitions and presentations of 
 experience. We obtain the judgement ' Water rusts iron ', not 
 by comparing our ideas of water, iron and rusting, to see 
 whether they agree, but by examining the facts, to see whether 
 they co-exist.^ 
 
 § 432. This is surely to overshoot the mark. Bare examina- 
 tion of facts, that is of presentations to consciousness, could 
 never assure us that water rusts iron, but only that a certain 
 individual presentation is at this moment, or (if memory be 
 granted us) was at some past moment or moments, accompanied 
 by another presentation. To these presentations we cannot yet 
 even give names ; whereas the proposition ' Water rusts iron * 
 implies the possession of the ideas of water and of rusting iron. 
 And though we might indicate the subject by pointing to it, or 
 saying 'this object', no general judgement can be formed about 
 it unless the predicate is a concept fixed in a common name. 
 Mere experience of co-existences is not knowledge. Fact 
 must be brought under notion. For Nature to ' stand up and 
 say. This was a man ', she and we must have some general idea 
 of what ' man ' means. 
 
 § 433. If this be so, we still have judgement pre-supposing 
 conception, as much as if Hamilton's view of judgement as the 
 analysis of a notion were correct. Yet, on the other hand, it is 
 common ground that a concept is a fasciculus or integration of 
 judgements — or at least of comparisons. Yes; but such com- 
 parisons are ultimately only the inchoate beginnings of judgement 
 — -an awareness in which subject and predicate are as yet not 
 distinguished. 
 
 § 434. The question before us resolves itself into the con- 
 troversy as to the relative precedence of sensible and intelligible, 
 of individual presentations and cogitable universalia. In truth, 
 'judgement and idea go pari passu.' ' 
 
 If thought be analysed back and back into its dim rudiments, 
 we come at last to a perceptive consciousness of impressions 
 
 ^ On Hamilton, pp. 422-5. ^ Ibid. p. 426. 
 
 ' Bosanquet, Logic, i. 34. 
 
Precedence of Judgement and Concept 199 
 
 which is not yet judgement, and a grouping of unreflective 
 beliefs which does not yet amount to conception. The Epicurean 
 expression ' iudicia sensus ' is open to objection ; for sense and 
 judgement, though in an embryonic stage they may be 
 indistinguishable, can never be the same thing. To judge is 
 to interpret. Similarly, belief may be involved in sense — as 
 contrasted, for instance, with plant sensitiveness — ; yet 'sensory 
 beliefs' is really a contradiction in terms. All we can say is 
 that the ultimate constituents of thought refuse to be further 
 dissected. A sensation as such can be neither true nor false, 
 though James Mill says, 'To have a sensation and to believe 
 that I have it is the same thing,'* 
 
 § 435. A young child draws back its hand quickly from a 
 red-hot coal or bar with a cry of pain. So far there is only 
 perception, by which the externality of the cause of the sensation 
 is distinguished from the sentient self: which perception is a 
 rudimentary judgement. ' An impression on my consciousness 
 is real.' At other times, touching boiling water or a highly 
 heated dish, the child again recoils with the same cry of pain. 
 But now it is able to separate the burning sensation from the 
 visible presence of fire, and so to abstract the idea of extreme 
 heat. The process of forming this conception was based on the 
 previous 'sensory judgements', and the latter involved the 
 beginnings of predication, that is of the recognition of qualities 
 in things, which recognition is rudimentary conception. 
 
 § 436. But it should be obvious that this question concerning 
 the priority of Conception and Judgement is psychological, not 
 logical. The logical Proposition presupposes, and is analysable 
 into. Terms. The logical Term, on the other hand, does not 
 suggest analysis into propositional elements. Terms, in fact, 
 may be replaced by mere alphabetical symbols. It has been 
 necessary to inquire at some length into the psychological 
 structure of the Concept in order that we may understand the 
 
 * Lewes(see above, p. 83n.) regards ' primaryjudgements of sensation and 
 intuition' as'identical' judgements. Although they are 'sensible experiences 
 of indubitably a posteriori character', yet 'all identical propositions are 
 necessarily and universally true ' ; and ' all judgements, to be absolute, 
 must be identical' {Hist. Phil., ii. 463, 541). Accordingly, 'the whole 
 stress of Verification consists in reducing propositions to identity or 
 equivalence' (i. Ixii)— that is, ultimately, either to a sensation or to a 
 necessity of thought. 
 
200 Judgement 
 
 import of Judgement as conceptual. And in doing so we have 
 found that Conception involves and presupposes a faculty of 
 Comparison. But as a logical product the proposition is com- 
 pounded of terms, not the term of propositions. 
 
 § 437. The terms of a proposition together form an idea 
 which the proposition asserts (or denies) to be true in certain, 
 or in all, cases. The notion of S being P, of a P S, has 
 actuality in experience. In vivid narrative events are often 
 turned into pictures which, as all art is, are in themselves 
 universal yet are to be understood as predicated of reality in 
 the case described. Before ' Water, water everywhere, but not 
 a drop to drink ' we must understand ' there was '. In the lines, 
 ' Cannon to right of them, &c., volleyed and thunder'd,' on the 
 other hand, the tenses might be replaced by present participles, 
 ' volleying and thundering.' Compare the pictorial descciption 
 at the beginning oi Enoch Arden. 
 
 § 438. A notion, then, or ideal conception, is an undeveloped 
 judgement, and becomes a judgement by being asserted to be 
 real. Thus, ' anima naturaliter Christiana — est.' Reality, then, 
 'is the ultimate subject in every judgement.' 'Judgement,' 
 writes Dr. Bosanquet, following Bradley, ' is the reference of an 
 ideal content to Reality,' ' a qualification of Reality by some 
 ideal content.' ' Again, ' Every judgement, perceptive or 
 universal, might be introduced by some such phrase as, 
 " Reality is such that — '' ; " The real world is characterized 
 by-."'^ 
 
 § 439. ' A proposition,' writes Hughlings, ' is the exhibition 
 of a compound name in analysis or synthesis ; and the copula 
 asserts that the names it is interposed between may together 
 form one compound name or be together replaced by one 
 simple name.' " The Concept has the same elements as the 
 Judgement, without that which is the essence of the judging 
 act, assertion or belief* 
 
 ' Logic, i. 288 ; ii. i. 
 
 2 Ibid. i. 78, 79. 
 
 ' Logic of Names. 
 
 ^ Mill says that the element of belief or assertion of reality is ' an 
 essential element in a judgement, but may be either present or absent in 
 a concept ' (Logic, i. 420). I submit that it is essentially absent from 
 a concept ; whereas judgement is ' a conscious reference to what actually 
 exists ' (Ueberweg). Not, as we shall see, that in a general proposition 
 
How Concepts develop into Judgements 201 
 
 § 440. Implicitly the same ; for at first sight the Concept lacks 
 the element of quantification. But it is important to notice (see 
 above, §§ 298, 299) that the General Notion develops, not into 
 the General Proposition, but into the Particular. 'A lame 
 horse ' implies a contingent possibility about horses. If all 
 horses were lame, we should not trouble to qualify ' horse ' by 
 * lame '. Accordingly, the General Notion involves both a 
 particular affirmative and a particular negative judgement. It 
 does not develop into a pre-indesignate proposition — ' Horses are 
 lame ' — but into ' Some horses are lame, and some horses are 
 not lame '. ' Cold weather ' implies that weather may be cold, 
 but need not be. ' Mad dog ' suggests an exception. So that, 
 whereas every ideal conception, involving no assumption of fact, 
 is potentially universal, the judgement of experience wrapped 
 up in it is necessarily concrete and therefore partial. The idea 
 of hot water is referred to existence in the form, ' Some water is 
 hot,' or ' This water is hot', but not in that of 'All water is hot '. 
 Even a simple name, like ox, suggests that some animals only, 
 or some things only, are oxen. 
 
 § 441. On the other hand epithetical, appositive, or non- 
 determining attributives involve a general proposition, stating 
 inherence universally in a subject. 'Roaring cataract' — all 
 cataracts roar. ' Man that is born of a woman ' — all men are 
 born of a woman (this, by the by, is a convertible proposition). 
 The elements of the concept are not merely compatible. 
 
 § 442. It is a corollary from this distinction that in a general 
 proposition the idea in the subject-term cannot be qualified by 
 the predicate, in the sense of being determined by it {qualitas = 
 differentia) seeing that in such propositions subject qualified by 
 predicate (e.g., mortal men) is co-extensive with the subject 
 alone (men). In other words, a general proposition asserts 
 that subject and predicate must form a compound name. 
 
 § 443. General propositions about an individual correspond 
 
 the content of the subject-term is asserted to be real. But, given the 
 condition which it expresses, then the reality of the consequent is affirmed. 
 In other words, Reality is asserted categorically to have a certain nature. 
 It is this assertiveness which is ^^form common to all judgements, the 
 content of the terms being its matter. But form and matter cannot in 
 judging be sundered ; for assertion requires something to be asserted. 
 Without the terms, the assertion is not unlike the smile which, in Lewis 
 Carroll's book, remained after the Cheshire cat's disappearance. 
 
202 Judgement 
 
 in the same way to an epithetical designation. Will Legge is 
 honest — honest Will Legge ; London is vast — vast London. 
 Particular propositions about an individual are easier to throw 
 into notional form in Greek, with the help of a participle, than 
 in English. Yet we can speak of Philip drunk ($iXt7nros ix^&v<s 
 uy) and Philip sober. Phrases like 'An excited House of 
 Commons shouted ' are possible because we conceive of many 
 Houses of Commons, not merely of one with many moods. 
 Still, we might say ' a restored Cologne Minster '. 
 
 § 444. The essential Form of Judgement is Assertion or Assent, 
 involving, of course, its opposite. Denial or Dissent. What is 
 always asserted, or denied, is the reality of a compound notion, 
 not simply existence in the speaker's mind, but objective reality.' 
 The universal or occasional inherence or non-inherence of an 
 attribute in a subject is affirmed. 
 
 § 445. We start, of course, from the idea of the subject being 
 there. This is hypothesized in the general proposition, assumed 
 in the particular, singular, and concrete-universal. ' Fairy god- 
 mothers are benevolent.' The truth of the proposition is in no 
 way dependent on the existence of fairy godmothers in rerum 
 natura or anywhere else outside the common consciousness of 
 speaker and listener. If, and when, they exist, they are benevo- 
 lent. But ' Three fishers went sailing ' assumes the existence of 
 fishermen, ' Some flowers are wild ' that of flowers. If I say 
 ' Harry is returned ', or 'AH my teeth are gone ', I must mean in 
 the one case that there is such a person as Harry, in the other 
 that I once had teeth. ' My eye teeth have not yet come ' asserts 
 non-existence in actuality, but implies potential existence. Even 
 'Some fairies are benevolent ' implies the at least /iterary existence 
 of fairies ; a class familiar to the persons I am addressing is 
 being spoken of. If it be objected that the same is true of fairy 
 godmothers, we can easily find propositions about subjects which 
 are quite 'in the air'. ' Whoever has learned the Encyclopaedia 
 Britannica by heart is able to guess acrostics.' ' One who has 
 
 ' ' Mere presence in the individual mind is not the existence in question. 
 And indeed to speak of it as such would be to enter upon a vicious circle 
 which would stultify the judgement ; for it is essential to the judgement 
 to affirm a reality outside itself, and it would be too ridiculous that your 
 judgement should refer merely to the content of mine as the reality 
 asserted, and mine in turn to that of yours' (Bosanquet, Logic, i. 192). 
 
Elements of Judgement 203 
 
 never known the slightest care or trouble has lost the discipline 
 of life.' In the following line of Prior's — 
 
 He alone is blest who ne'er was born — 
 the subject cannot be supposed ' existent ' in the ordinary sense. 
 
 § 446. Judgement, then, asserts that benevolence in all fairy 
 godmothers (so far as they exist), or that wisdom in some rulers 
 (assumed to exist), is real. A general judgement declares the 
 reality of a fact about a hypdthetically existing subject ; a par- 
 ticular judgement declares the reality of a possibility about an 
 actually existing subject ; a concrete universal or singular judge- 
 ment declares the reality of a fact about an actually existing 
 subject. 
 
 § 447. ' In judgement,' says Dr. Bradley, ' we do not refer one 
 idea to another, but the subject is always reality.' ' ' The tradi- 
 tional subject, predicate and copula are mere superstitions. 
 The ideal matter which is affirmed in the judgement no doubt 
 possesses internal relations, and in most cases (not all) the 
 matter may be arranged as subject and attribute. But this 
 content is the same both in the assertion and out of it. . . It is 
 impossible that this internal relation can itself be the judgement ; 
 it can at best be no more than a condition of judging.' ^ 
 
 § 448. I presume the last words mean that, if there were no 
 internal relation between the elements of the complex idea which 
 is asserted to be real, there would be nothing to assert. Reality 
 could not be asserted of a perfectly simple fact. But that 
 internal relation must always combine a substantive and an 
 attributive element.' In every case the compound idea of which 
 
 1 Logic, p. 14. 
 
 ' Ibid. p. 22. 
 
 ' Similarly Bosanquet says that ovofia and piy/xa, noun and verb, have 
 been ' transmuted into subject, copula and predicate. . . . The judgement, 
 however complex, is a simple idea. The relations within it are not rela- 
 tions between ideas, but are themselves a part of the idea which is predi- 
 cated. In other words, the subject must lie outside the judgement, in 
 order that the content of the judgement may be predicated of it. If not, 
 we fall back into. " My idea of the earth goes round my idea of the sun ". 
 What we want is, " The real world has in it as a fact what I mean by 
 earth-going-round-sun" (Logic, i. 80, 81). In every judgement, even 
 though immature or impersonal, ' there is a starting-point, or point of 
 contact, with the ultimate subject,' viz. Reality ; which point of contact 
 ' is present in a rudimentary form in the simplest perceptive judgement ' 
 (i. 82). 
 
204 Judgement 
 
 reality is asserted or denied involves attribution to a subject. 
 But, apart from the iconoclastic precipitateness of this writer, 
 logicians must, I think, subscribe to his doctrine of the Real as 
 the ultimate and underlying subject of all assertion. And this 
 is equivalent to its being also the universal predicate. For in 
 all judgement we assert an ideal combination to be real. 
 Regarded, on the other hand, as subject we judge (in Bosanquet's 
 words) that 'the Real is such that, under the ideal condition 
 which forms the immediate subject of the judgement, it will 
 furnish the ideal consequent which is expressed in its pre- 
 dication '.' 
 
 § 449. Reality, then, being conditioned as Y, is Z (i. e. is 
 Z reality). But we may take some smaller universe of dis- 
 course, X, assumed as real; and then Y X{X conditioned as Y) 
 is Z (i. e. is Z X). Assuming horse as a real class, we say, 
 ' A thoroughbred horse (horse conditioned as thoroughbred) is 
 a stayer (a staying horse).' Mr. A. Wolf says : ' One can 
 generally tell what particular portion or aspect of reality it is 
 that elicits the several judgements from us. For instance, the 
 judgement, "equilateral triangles are equiangular," is forced on 
 us by a consideration of the nature of space. The nature of 
 space is such that, given an equilateral triangle, it would need 
 be equiangular as well.'^ 
 
 § 450. Impersonal verbs and sentences with an unexpressed 
 subject have in the background some well-understood sphere of 
 discourse within reality ; as, 'pluit ' ; ' It is finished'; ' Ite, missa 
 est.' The interjection or ejaculation, the utterance of pain. or 
 triumph, those cries too with which Mary calls the cattle home, 
 have self or some other immediately presented reality for 
 subject — 6a.Xa(T(Ta ! Shame ! Nonsense ! and the like. 
 
 § 451. But while the Real is the ultimate subject of all judge- 
 ments, giving the expressed subjectof the judgement a substantival 
 and extensional significance, Dr. Bradley and his follow£;rs go 
 too fast in denying the necessity of the threefold construction of 
 the idea as predicated of reality. Subject, 'copula' and predi- 
 cate are still essential elements. For the idea which is asserted 
 to be real is, as we have seen, a complex. It is the idea 
 of X being Y, 
 
 ^ Logic, i. 282. ^ Studies in Logic, p. 62. 
 
CHAPTER XIII 
 IMPORT OF THE PROPOSITION 
 
 § 452. What now is the import of the idea of ' X being Y', 
 whichj as asserted to be real, becomes the proposition ' Jf is y ? 
 
 Should it be found that the verb 'to be' is never a mere 
 grammatical copula, but always retains the notion of existence, it 
 will afterwards have to be determined, first, whether exist- 
 ence necessarily means actual existence in rerum natura ; and, 
 secondly, what it is that is asserted to exist, the subject, or the 
 predicate, or both, or the one as qualified by the other. Again, 
 it is important to ask whether the existence is absolutely or 
 hypothetically asserted. 
 
 § 453. The ordinary view of the ' copula ' is the one stated 
 thus by Veitch : — ' The is with which knowledge begins is totally 
 different from the logical copula, the is of comparison. The 
 former implies a judgement of real existence ; the latter implies 
 nothing more than a judgement of congruence or harmony 
 between terms.' ' 
 
 § 454. Sigwart, on the other hand, pertinently asks : — ' How 
 does it happen that the verb " to be ", which is the expression of 
 actual existence, assumes a formal function whereby it loses its 
 meaning — nay, even seems to contradict it [as in the sentence, 
 " A centaur is a fiction of the poets "] ? The remarkable thing 
 is not that the ambiguity [as Mill asserted] has been so little 
 noticed, but rather that all known languages agree in having it.' " 
 
 § 455. It cannot be supposed that, when thought and language 
 lay in the same womb, the simplest and most primary of verbs ' 
 
 ' Institutes, p. 77. 
 
 ^ Logic, i. 100. 
 
 ' Sigwart remarks that in ' cinnabar is red ' the verb is serves to show 
 that red is a predicate, and not (as it might seem to be if merely juxta- 
 posed with cinnabar) a mere attributive. (In English, however, the 
 adjective part of a notion usually precedes the substantive.) But, he 
 says, ' in so doing it is a mere vehicle for the copula, not the copula itself; 
 it does not constitute the judgement, but merely prepares the way for it ' 
 
2o6 Import of the Proposition 
 
 was to be born with two entirely diverse meanings, or rather 
 was to express at one time the metaphysical idea of existence 
 {as, life-breath, bhu, beget), and at another nothing at all, but 
 to have instead of a meaning a mere function, and that a 
 superfluous one — the establishing of contact, or asserted co- 
 existence, between juxtaposed thing and notion. The phe- 
 nomenon, whatever its explanation, extends to all persons, 
 numbers, tenses, moods and participles — am, art, is, are, wast, 
 be, being, been, io-oixai, fuerimus, and so forth. Consider, for 
 instance, the force of the inflected ' copula ' in the words, ^re 
 TTore cTKOTOs, vvv 8e <^Ss iv K.vpL<a. 
 
 § 456. Mr. A. Wolf, in his treatise on ' The Existential 
 Import of Categorical Predication V replies that, granting that 
 the original, etymological meaning of the substantive verb 
 implied existence, and' existence only, this merely shows that 
 the mind of primitive man was entirely occupied with what were 
 believed to be real objects. ' But once the avowedly non-existent, 
 too, received attention and was made the subject of judgements, 
 then the copula, extended by analogy to those judgements also, 
 must have become modified in meaning and implication. For 
 
 {Logic, i. 94). But, 'how does it happen that it is just the verb to be 
 which we use in this way ? ' He replies : — ' The explanation is not diffi- 
 cult. As Ueberweg (p. 162) rightly notices, it is a rule taken for granted 
 that the things of which we speak exist ; there is no need of any 
 express assertion ; we are not interested to know Ma^ things are but what 
 and how they are. When now it is desired, not merely to express predi- 
 cation by mere juxtaposition, but to give the form of the verb to the prer 
 dicate, the verb to be offers itself just because it is so general and has by 
 itself no content. It is always presupposed ; but, in order that we may 
 know what we wish to know, we need to have it determined more exactly 
 as " being this " and " being thus ", just as the statement of existence is 
 determined more exactly as "being here " and " being now ". The predi- 
 cate red, which by its form already denotes something appertaining to 
 something else which exists, now appears as a modification of Being, being 
 red' (ibid. p. 100). 
 
 This fits in with the view advocated in the text, that the interest of 
 a proposition lies in the predicate, in the kind of existence possessed by 
 the subject. But for the expression ' a vehicle for the copula ' I would 
 read, ' a vehicle for the assertive energy of the judgement.' A mere 
 copula, or coupling word, is, as I endeavour to show below, a fourth 
 wheel to the propositional tricycle. 
 
 ^ Studies in Logic (1905). 
 
The 'Copula^ 207 
 
 obviously the original meaning of " is " could not transform 
 a non-existent into an existent subject.' ' 
 
 § 457. The last words assume what has still to be argued, viz. 
 that is, meaning exists, in a categorical sentence implies the abso- 
 lute existence of the subject. But, apart from this, Mr. Wolf's 
 theory of the transformation of is from a verb of existence into 
 a mere logical symbol appears to be far from satisfactory. In 
 the first place, he does not explain what primitive man meant 
 by ' Oxen exist slow-footed ', or ' Your brother exists dead '. 
 Secondly, primitive man must have sometimes spoken of things 
 known to be non-existent and merely hypothetical : how did he 
 express his thought then ? Thirdly, it is far from clear how an 
 implication of existence could have become ' extended by analogy ' 
 to judgements where non-existence is understood, or at least not 
 excluded. But this, says Mr. Wolf, 'is what has actually 
 happened. The substantive verb sometimes still has the same 
 meaning as " exists " ; at other times it is simply a sign of pre- 
 dication without any existential implication whatever' ; ^ — which, 
 again, is to assume the point to be proved, 
 
 § 458. It is true that the Greeks distinguished between ectti, 
 exists, and i<m, is. Also that we commonly lay a stress on is 
 when it means existence; on est in 'Homerus est', but not in 
 ' Homerus est poeta '. Sometimes the two senses are combined 
 in the same sentence ; e. g. — 
 
 'Rather than be less, cared not to be at all' {P. Lost). 
 
 'I had as lief not be, as live to be 
 
 In awe of such a thing as I myself (J. Caesar). 
 
 'Omne ens est unum.' 
 
 'There is that is destroyed for want of judgement' (Proverbs), 
 
 ' God is, and is a rewarder of them that seek Him ' (the Greek 
 verbs are la-nv and yCverai). 
 
 ' Parvi sunt foris arma, nisi est consilium domi ' {Cic). 
 
 ' The courts are open, and there are deputies.' 
 
 ' Which is, and which was, and which is to come ' (o &v Koi 6 rjv 
 /cat o £jO;^oyxcvos). 
 
 ' I should have been as though I had never been ' (/o6). 
 
 ' Whatever is, is right.' 
 
 ' Esse est percipi.' 
 
 ' Nihil est incorporale nisi quod non est ' (Tertullian). 
 
 1 Op. cit, pp. 74, 7S. ^ Ibid. p. 75. 
 
2o8 Import of the Proposition 
 
 ' One is with our father, and one is not.' 
 Where the existence is denied, as in the last two examples, 
 no emphasis need be laid on is, so that ' one is not ' might mean 
 ' is not with our father '. 
 
 Other examples of the verb 'to be ' implying absolute existence 
 are such as these : — 
 
 'Je pense, done je suis.' 
 
 'Times have been.' 
 
 'Troia fuit.' 
 
 ' The child is not ' (no is in the Hebrew). 
 
 'Esse aliquos Manes . . . nee puerlcredunt.' 
 
 la ovra. 
 
 ' The powers that be.' 
 
 ' To be or not to be.' 
 
 ' The thing that hath been is the thing that shall be.* 
 
 It was said to the early Christians, ' non licet esse vos ' — you 
 have no licensed existence, ea-n, translated ' is possible ', is really 
 of this class — ovk lanv oLKeiv, &c. ('there is no living,' &c.). We 
 have to notice the large class of sentences beginning with (in 
 English) ' there is ' — e. g., ' Verily there is a reward for the 
 righteous ' ; 'est modus in rebus ' ; ' sunt lacrimae rerum ' ; ' Of 
 making of books there is no end.' 
 
 And yet ' there is ' (correlated to ' where is ? ') must mean the 
 same thing as ' is there ', in which phrase is may be either 
 ' existential ' or ' copulative ' (is a thing situated yonder). Take 
 this — ' seges est ubi Troia fuit ' ; or TertuUian's saying, ' ubi 
 tres, Ecclesia est ' (which might be expressed, ' ibi Ecclesia 
 est '), or ' animus est ubi amat ' ; or Horace's words : — 
 
 Est hie, 
 Est ubi vis, animus si te non deficit aequus. 
 In ' Where there is smoke there is fire ' the quasi-impersonal 
 and the local sense of ' there ' are indistinguishable. It seems 
 strange to be obliged to hold that est is existential in ' non est 
 peccatum nisi contra conscientiam ', but copulative in ' omne 
 peccatum est contra conscientiam ' ; existential in ' est unum 
 necessarium ', but copulative in ' unum est necessarium '. Can we 
 fundamentally distinguish ' Nothing is a departure from law' from 
 Tennyson's ' Nothing is that errs from law ' ; or 'AH might have 
 been well ' from ' Cold to all that might have been ' ; or ' Rachel's 
 children are not here' from 'Rachel's children are not'? 'Is 
 
The ' Copula ' 209 
 
 there a man with soul so dead ? ', &c., is equivalent to ' Breathes ' 
 or ' Lives there a man ', &c., and again is equivalent to ' No man 
 is so dead of soul ', &c., where is may be called a copula, unless 
 we like to regard it as existential. 
 
 § 459, It should be further observed that the subject introduced 
 by ' There is ' is never undetermined, but is always united to a 
 relative clause or qualifying description.' ' There is a tide in the 
 affairs of men which taken at the flood,' &c. This equals, 
 ' A tide exists in the aifairs of men, of such a kind that,' &c, 
 ' There was an old woman ' must be completed by ' who lived in 
 a shoe '. ' There are odd people in the world.' ' Est in con- 
 spectu Tenedos.' ' Est regio in terris.' ' There is a vale in Ida, 
 lovelier,' &c. ' There ' points to the coming qualification. In 
 other words, actual existence is predicated not absolutely, but 
 under such and such a mode. So ' sunt qui dicant ', &c. Even 
 the most absolute predications of existence seem to wait for some 
 further, elucidation. 'There is a land of pure delight* — but we 
 go on, ' Where saints immortal dwell.' 
 
 § 460. In many cases it is difficult to distinguish 'existential' from 
 'copulative' being. E. g. ' Cupio dissolvi et esse cum Christo.' 
 'Est deus in nobis.' iraa-a iroXts <\>va-iL ia-riv (Ar.). 'Amicitia 
 est inter pares ' (cf. ' inter pares non est potestas '). ' All power 
 is from God.' ' Quid est Imperatori cum Ecclesia ? ' ' Nihil est 
 in intellectu nisi prius fuerit in sensu.' ' De rebus non apparen- 
 tibus et non existentibus eadem est ratio.' 
 
 What shall we say, further, of expressions like 'in eo est 
 ut . . .' ' It may be that ...,'' fama est,' ' mos est,' ' opinio est,' 
 or the frequent substitution in Latin of verbs like existo, fio, 
 appareo, evado, audio, reperior, appellor, reddor, &c., for 'copula, 
 tive' suml The Hebraism 'to be called' ('He shall be called 
 the Son of God') means, ' His real nature shall be.' 
 
 § 461. What is ' coupled ' to a subject has frequently no gram- 
 matical congruity with it ; e. g. ' ea dedecori sunt nobis ' ; ' sum 
 
 * Bosanquet erroneously calls all that follows ' There is ' a predicate. 
 Hughlings is, I think, ' getting warm ' when he remarks that, ' if the 
 logical copula is to be taken to be anything more than a sign of predica- 
 tion, it must be taken as predicated of the subject ; and the following 
 noun or adjective is predicated of the copula ' {Logic of Names). The 
 latter statement is crude ; but he seems to mean that the existence which 
 • is ' predicates of the subject is a qualified, not an absolute, existence. The 
 predicate is an ' appredicate '. 
 
 P 
 
2IO Import of the Proposition 
 
 derisui inimicis meis ' ; ' hoc mihi volenti est ' ; ' omnia sunt 
 recte ' ; ' adolescens in lubrico aetatis est ' ; ' necessitati a me est 
 parendum ' ; ' interest (= inter rem est) ut te videam ' ; ' aeternas 
 poenas in morte timendum est.' And what is coupled by the 
 verb 'to be' in relative and interrogative clauses, such as 
 ' quod non est, simulat, dissimulatque quod est ' ? In ' quae 
 sit natura lucis ambigitur ' it seems very far-fetched to say that 
 * sit ' couples in thought ' quae ' to ' natura '. 
 
 § 462. In direct questions the 'copula'is usuallyplaced first— 'Is 
 your bag ready?' ; — also after 'nor', 'yet ' and other conjunctions. 
 In some statements the predicate comes first, then the ' copula ', 
 and the subject last; as, 'stulti sunt qui putant,' &c., or 'Blessed 
 are the poor.' In others, even in English, the ' copula ' comes 
 last in the principal clause ; e. g. " All equal are within the 
 Church's gate'; 'All that therein is'; 'Follow the thing that 
 good is ' ; ' The King of Love my shepherd is ' ; and of course 
 very frequently in Latin prose. Also in legal language the 
 verb. 
 
 § 463. I venture to think that a slight examination of idiomatic 
 forms begins to undermine the very existence of a merely coupling 
 part of speech, a conventional mark of predication. Nor does 
 one seem to be wanted. In every language it is frequently 
 omitted ; e. g. ' beati pacifici ', ' traditores proditores,' ' place 
 aux dames,' 'praemonituspraemunitus," Forewarned forearmed,' 
 'uomo awisato mezzo salvo,' 'First come first served,' 'The 
 more the merrier,' 'Unkist unkind,' vhap apurrov, 'omnis homo 
 mendax,' ' homo homini lupus.' In Latin and Greek the copula 
 is dispensed with in elaborate as well as in pithy sentences. In 
 English it is not seldom missing, especially in verse, when the 
 -sentence begins with the predicate ; e. g. ' Happy the man 
 who ', &c. 
 
 § 464. I argue below (§ 612) that we must distinguish in the 
 word ' is ' between the element of assertiveness and that of 
 asserted 'being'. Any verb will serve as a vehicle for the 
 assertive energy of judgement. Not so a mere 'copula'. If 
 'to be ' essentially implies existence, it is easier to understand 
 -that in propositions secundi adiacentis, such as ' God loves us ', 
 ' Evil pursueth sinners,' ' Rira bien qui rira le dernier,' the 
 idea of existence would become merged in the p^/xa expressing 
 action or passion, than that a functional copula should do so. 
 
The ^Copula* 2n 
 
 The view that the verbal idea is here predicated directly, in 
 which case the verb 'to be ' is not necessarily implied at all in 
 propositions like 'Pigs grunt', 'Fire burns,' is considered 
 infra, § 498. Philologically, every proposition is the juxta- 
 position of a verbal idea with a noun. 'John comes' is 'John 
 come-he'; 'I am glad' is 'Ibeing-me glad'; 'sOl splendet' is 
 * sol splende-ta ' ; <ni TuirTcts is <rii TUTTTci-trv. But in Greek the 
 verbs in -/it exhibit the original structure of predication best. 
 The juxtaposition, at any rate with a certain stress of voice, 
 implies an asserted relation between a subject and a notional 
 category. 
 
 § 465. Even quasi-imperatives sometimes dispense with the 
 substantive verb. ' Sweets to the sweet ' ; ' Losers finders ' ; 
 a-yia ayiois. Selden, on 'salus reipublicae suprema lex', says 
 that ' esto ' is the understood word. 
 
 § 466. Language is only fossil history because it is embalmed 
 thought. The simplest explanation of the so-called copula is 
 that, whatever part may be conventionally assigned it in gram- 
 mar, it always retains logically its primary meaning of existence} 
 
 But not existence unconditional. What is predicated is exis- 
 tence after a certain mode. Even in the cases in which existence 
 seems to be asserted absolutely (e.g. 'The child is not ' ; ' There 
 are such things as angels ' ; ' The supernatural exists ') we must 
 usually understand 'in the world' or some other obvious deter- 
 mination. In ' Troia fuit ' the past tense supplies a qualifying 
 idea. Esse in ' esse quam videri ' clearly awaits an attributive.^ 
 
 § 467. But yet again, even the qualified existence is only 
 
 ^ ' Is ', no doubt, acquires this or that force in predication, according 
 to the character of the proposition and the nature of the predicate. In 
 •Hoc est Corpus meum' it carries a different significance from that which 
 it has in 'The field is the world'. But the logician cannot decide such 
 matters. 
 
 ' No doubt, assertions of existence may be regarded as relational — 
 X exists = Jy is existent. But this = exists as existent, which again 
 might be phrased, ' exists as existing as existent.' And so on. Sigwart 
 says : — ' Herbart finds in the concept of Being complete unconditioned- 
 ness and absence of relations ; and against this Lotze rightly shows that 
 what we think of in the concept of Being is just this fact of standing in 
 relations ' (Logic, i. 77). Only, Being cannot stand in relation to itself. 
 
 And so again 'A" exists ' cannot mean ' Whatever existence A" has, it has 
 it ', or, ' If anything is X it exists ' ; for ^ in such a sentence is necessarily 
 concrete. We cannot first hypothesize existence a,ijd then assert it. 
 
 P2 
 
212 Import" of the Proposition 
 
 asserted of the subject on the hypothesis or assumption of the 
 subject having existence of some kind. ' All X'%, ' means ' what' 
 ever ^'s there are.' ' All authority is from above ' asserts that 
 whatever authority exists exists from above. ' Salt is good ' 
 means that salt, wherever found existing, is found existing as 
 good. A proposition in the form ' A mountain made of " one 
 entire and perfect chrysolite" would be worth more than all 
 Essex arable ', implies the non-existence of its subject. Yet it is 
 still true that if it existed it would have an existence determined 
 as worth more than arable Essex. Even ' Queen Anne is dead ' 
 implies that the mode of existence or being possessed by Queen 
 Anne is that of deadness. 
 
 § 468. I have purposely taken an illustration which presents 
 difficulty, and which suggests other propositions in which the 
 existence or being asserted is non-existence. For example — 
 
 No existing MS. of Livy is complete. 
 
 Nihil est quicquid in saeculo est. 
 
 An idol is nothing in the world. 
 
 The King is a thing of nothing. 
 If, however, anything can be said to be a thing of nothing, there 
 is no reason why a subject of discourse should not be said to 
 have its being as non-existent (e.g. '"Gorgons and hydras and 
 chimaeras dire " are non-existent '). And this goes further than 
 ' exists as dead ' ; for a dead person may have a very real 
 existence in the love and recollections of his friends or in the 
 works which follow him, to say nothing about any other state of 
 existence. But we shall have to return to the question whether 
 existence in predication means actual, palpable existing in space 
 and time or only objectivity in thought. 
 
 § 469. To return. The interest of every statement resides in 
 the predicate. We do not want to know that a thing exists, but 
 how it exists.^ A predicate, then, is logically adjectival, and 
 grammatically agrees with its subject in gender, number and 
 case. It expresses the mode in which the subject has its being, 
 not has being, simply, but has whatever being it has.^ ^-ness, 
 
 ' ' All judgement whatever is an attempt to make explicit the nature of 
 Reality' (Bosanquet, Logic, i. 146). Yet Judgement does not say baldly, 
 ' Reality is Y,' but, ' Reality, conditioned as X,\sY' (All ^ is F). 
 
 ^ Cf. 'Then shall every man have his praise of God' (i Cor. iv, 5, 
 R.V.). Some will have none. 
 
The ' Copula * 213 
 
 where it exists, does not exist without V-ness. As the substratum 
 of a judgement, not of existence, but of co-existence, however, 
 the verb ' to be ' may in a sense be regarded as coupling ideas, 
 and so as a copula. 
 
 § 470. But this neutral and non-committal import of is = exists 
 applies not only to general and abstract, but also to particular, 
 singular, and concrete universal propositions, though in these 
 the existence of the subject is assumed. ' Some birds are tune- 
 less ' ; ' My brother is married ' ; ' All the cups are broken.' 
 The subject in each case is said to be, to have whatever being 
 it has, in a certain way. It is the same, too, with negative 
 judgements. 
 
 § 471. The circumstance, then, to which we must next attend, 
 that some kinds of judgement imply the existence of their sub- 
 jects, while others do not, is not really affected in any way 
 whatever by the question whether the verb 'to be ' does or does 
 not always mean to exist. It is to the subject, and to the form 
 of the sentence, that we must look to ascertain whether it is 
 ' existential ', not to the ' copula '.* 
 
 § 472. Many pages have been written on the existential 
 import of propositions. Yet the matter is really a simple one. 
 Concrete propositions do, while abstract propositions do not, 
 imply that their subject actually exists. The former are assump- 
 tive, — they take as granted the empirical and concrete existence 
 of the thing spoken of— John ; five sailors ; our garden ; some 
 islands ;- all the chairs. The latter are hypothetical and general 
 in character — all good men ; a tidy garden ; the wise ; African 
 lions ; eternity ; to die ; and a number of forms of direct 
 hypothesis — ' If you are a good boy you shall have a penny.' 
 
 § 473. To make the point turn on mere quantity is crude. It 
 is usually said that, in afiSrmative forms at any rate, universal 
 
 ^ Sigwart adheres to 'the proposition, so strongly emphasized by Kant, 
 that the predicate io be adds nothing whatever to the content of the idea 
 as such. Whether I say "A is ", or "A is not ", my thought of A is just 
 the same ; the meaning of the statement itself demands that neither 
 more nor less shall be present in the actual world than just the A thought 
 by me. Thus " being " forms no part of the subject-idea, no " real predi- 
 cate ", as Kant says ; it merely expresses the relation of the A which is 
 thought to my faculty of knowledge ' (Logic, i. 76). In the same way 
 Hume says: — 'The belief of the existence joins no new ideas to those 
 which compose the idea of the object' {Treatise, I, iii. 7). 
 
214 Import of the Proposition 
 
 judgements leave the existence of the subject undecided, while 
 particular ones imply it. Yet ' all the water-babies ' is at least 
 as 'existential' as 'some water-babies'. What can totality 
 or numerical more or less have to do with the matter? Mr. 
 Wolf, finding that the quantitative divisions cross one another, 
 comes to the conclusion that ' no line of formal demarcation ' 
 is to be trusted.' I do not think, however, that an elaborate 
 examination, such as he offers, of a number of various kinds of 
 judgements is necessary. It is an easy principle to be grasped 
 that what is named as concrete and perceptive is assumed to 
 exist ; whereas an ideal content, having an abstract and notional 
 reference, leaves it an open question whether, empirically, 
 there are any objects which answer to the conceptual conditions 
 of the name. Every concrete proposition is thetic, positive and 
 assumptive ; every general proposition is hypothetic and sup- 
 positive. 
 
 § 474. Negative judgements follow the same rule as affirmative 
 ones. ' No parallel lines meet ' is abstract ; ' None of the lines 
 on this paper meet ' is concrete. So are, ' Some of the lines do 
 not meet,' and, ' This pair of lines does not meet,' 
 
 § 475. The only difficulty which arises is when a general 
 statement is made about a concrete thing or things. ' This pair 
 of lines will never meet.' ' St. Paul's is always open.' 'Some 
 men have greatness thrust upon them.' ' Some people,' ob- 
 serves old Robson in Cynthia's Lovers, 'are always talking 
 about matrimony.' But even in such propositions, though, no 
 doubt, the existence of the subject is assumed, there is a 
 hypothetical and abstract element too. ' If this pair of lines 
 be traced to any point.' ' If St. Paul's be visited at any time.' 
 ' If you listen to the talk of some people at any moment.' And 
 so forth. 
 
 § 476. An abstract character belongs also to propositions 
 beginning with ' all of the ', when followed by a determining 
 clause. 'All the clothes that { = whatever clothes) I have on 
 my back ' might be said by a naked man, and ' You are welcome 
 to all the gold mines I ever possessed ' by a beggar. In such 
 propositions ' the ' is not simply demonstrative, but marks the 
 antecedent to a relative clause coming afterwards. Again, ' All 
 the gifts of Nature are for our good ' is not purely concrete ; for 
 ' Studies in Logic, p. 124. 
 
The ' Copula ' 215 
 
 • the gifts of Nature ' means, ' the gifts which Nature bestows, 
 whatever they be.' 
 
 § 477. As regards Singular Judgements, Mr. Wolf says : — 
 ' It is noteworthy that, as regards existential implication, Dr. 
 Venn and Dr. Keynes class singular propositions with particular, 
 not with universal, propositions.*' They ought rather to be 
 ranked with concrete universals, — ' The earth goes round the 
 sun ' with ' All the planets go round the sun ', not with ' Some 
 planets are uninhabitable ' nor with ' All planets have a visible 
 movement '. 
 
 § 478. A distinction is drawn in this matter by some writers 
 between categorical and hypothetical judgements. The categori- 
 cal judgement, accordingto Bosanquet, 'affirms the existence of its 
 subject.' " Dr. Venn declares that the hypothetical form implies 
 a doubt. The former writer seems to use the word 'categorical ' 
 in the sense of concrete. We have seen that a categorical 
 general proposition affirms hypothetically only. It does not 
 differ essentially from one expressed in full hypothetic form — 
 ' Every YX \sZ' from ' If ^ is Y it is Z '. It is true that, 
 when a doubt has to be expressed, the latter form of sentence 
 is usually employed. ' If X were Y it would he Z ' necessarily 
 implies doubt, and something more. But, as Mr. Wolf observes, 
 'the hypothetical form, as such, expresses neither peculiar 
 certainty nor peculiar doubt, but simply connexion of content.' ^ 
 To add ' if any exist ' to a general proposition, whether expressed 
 in full hypothetic form or not, is superfluous. But such a doubt 
 may find a place in an assumptive proposition — e.g. 'Some of 
 my eggs, if I have any, are for you.' 
 
 § 479, The question of existential implication in the subject of 
 judgement has been usually confused with that of the existence 
 of the subject as qualified by the predicate,* 
 
 ' Studies in Logic, p. 119. " Essentials, p. ii6. 
 
 ' Studies, p. 79. 
 
 * The late ' Lewis Carroll ', in his whimsically ingenious Symbolic 
 Logic (pp. 165-170) deprecates the 'bated breath' with which those 
 whom he refers to by the (he hopes inoffensive) title of ' the Logicians ' 
 have usually spoken of the Copula. His own dealing with it, though 
 parrhesiastic enough, trips over the confusion, here pointed out, between 
 the implication of the absolute existence of the subject (implied by ' some 
 of the ', ' none of the,' in his amusing but misleading illustration) and 
 the assertion of the determination of a hypothetical subject by the predi- 
 
^i6 Import of the Proposition 
 
 The universal negative general proposition, E, from this 
 point of view, appears to have a dissimilar implication from the 
 universal affirmative proposition A, which stands isolated. 
 
 A — ^All men are mortal. 
 
 E — No men are immortal. 
 
 / — Some men are wise. 
 
 O — Some men are not wise. 
 Now, / may be expressed thus — 'There are some men who are 
 wise ' ; * and O thus — ' There are some men who are not wise * ; 
 and E thus — ' There are no men who are immortal.' But A 
 cannot take the form, 'There are all men who are mortal.' 
 
 O, like /, affirms, not denies, existence. We do not say, 
 ' Some dangerous snakes are non-existent ' (unless we mean, 
 are extinct), but ' Some snakes exist which are not dangerous '. 
 E denies existence — ' No elephants fly ' : flying elephants are 
 non-existent.^ A cannot affirm existence. 'AH elephants are 
 
 cate. He argues, for example, that / and E cannot both assert or imply 
 existence, being contradictories. So that, if ' Some ^'s are F' implies 
 that there is a class of X's, ' No ^'s are Y' implies that there is no such 
 class ! The contradiction, however, is not between the two subjects (X 
 in either case) but between what is said of them. ' Lewis Carroll ' 
 further contends that, if /asserts existence, A ' makes the same assertion, 
 since it necessarily contains a proposition in /'. But this is a confusion 
 of thought. 'Air, no doubt, includes ' some ' of the same thing ; and if, 
 after alluding to ' some seven-leagued boots ' (in a way which implies that 
 there are such things), I go on to speak of 'all seven-leagued boots', 
 I may be presumed to be still thinking of them as actual objects. But 
 ' some ' of one thing is not contained in ' all ' of another. 'Some' in fact 
 may be larger than ' all '- It may stand for ten, and ' all ' only for four. 
 * Some ' must express a positive quantity, but ' all ' may stand for any 
 quantity down to and including zero. 
 
 ^ This is a more correct phrase than ' There are some wise men '. For 
 some is properly partitive ; and, if ' some men ' means a portion of the 
 human class, ' some wise men ' should mean a portion of the wise-men 
 class. The French ily a is noticeable. ' II y a fagot et fagot ' (Molifere). 
 Balzac says : — ' Dans tout homme de gdnie il y a un enfant.' Usually 
 partitive de follows — e. g. ' II a de jolies peiritures '. 
 
 " Dr. Case {Encyclopaedia Britannica, art. ' Logic ') quotes and 
 criticizes Brentano, as having tried to put all reasoning upon an 'existen- 
 tial ' footing by turning universal affirmatives into negatives. Thus — 
 
 All men are mortal. 
 
 All professors are human, 
 
 Therefore all professors are mortal 
 becomes 
 
 There is not a not-mortal man. 
 
The ' Copula ' 217 
 
 heavy ' : all heavy elephants are — what ? To fall into sym- 
 metrical place with the other forms, A must universally deny 
 existence — 'There are no such things as non-heavy (light) 
 elephants.' K hypothetically denies, categorically affirms. A 
 categorically denies, hypothetically affirms. 
 
 § 480. An affirmative general judgement, however, does seem 
 to stand on a footing of its own. The reason is that the some of 
 particular judgements stands for a fixed number of objects, 
 whether known or unknown. And the none of the universal 
 denial is a definite limit or starting-point, which cannot be less 
 or more, whether the universal be general or concrete. But the 
 all of a general affirmation represents what is potentially un- 
 limited. It is the distributive aspect of an ideal totality, and 
 what it stands for varies with the size of the total. Unlike 
 some, a few, thirteen, many, but like most, almost all, half, two- 
 thirds, omnitude is necessarily a relative idea. In a concrete 
 universal judgement the total to which ' all ' (like those other 
 expressions) is relative is an ascertained one. In an abstract 
 universal judgement it is unknown. 
 
 § 481. We can say, then, ' Four hundred million Chinamen 
 exist,' meaning that Chinamen exist to the number of 400,000,000. 
 Or we can say, 'No ungentlemanly Spaniards exist,' putting 
 their number at zero. But ' All gentlemanly Spaniards exist ' 
 makes no sense. Is it that they exist to the extent of a//? But 
 all what ? Not to the extent of all Spaniards, which would give 
 a good meaning ; but ' Gentlemanly Spaniards exist to the extent 
 of all gentlemanly Spaniards ',' which gives no meaning at all. 
 
 There is not a not-human professor, 
 Therefore there is not a not-mortal professor. 
 Had the minor premiss been, ' Some professors are human,' we should 
 have had in Darii — 
 
 There is not a not-mortal human, 
 
 There is such a being as a human professor, 
 
 Therefore there is such a thing as a professor who is not immortal. 
 
 A syllogistic system of this kind would be rather contra-existential 
 than what is usually meant by existential, its major premisses all denying 
 existence. In common speech such reasonings are usual enough. 'There 
 is not a plumber in the town that I have not tried, and not one that I have 
 tried who has not been a failure. It follows {Barbara) that there is not a 
 plumber in the town that has not been a failure.' And so in other moods. 
 
 * Notice that ' No X is V means that no ^ is a YX, no X is an Jf 
 existing in the mode Y. 'Every X is Y' on the other hand cannot 
 naturally be explicated in the form, ' Every ^ is a YX ' (as though X were 
 
2i8 Import of the Proposition 
 
 Or thus— given the notion YX (the notion of X being Y), we 
 can say, ' No instance of it exists,' or, ' Some instances of it 
 exist ' ; but we cannot say, ' Every instance of it exists,' nor yet, 
 'Some instances of it do not exist.' ^ Here A and O group 
 together, while E goes with /. 
 
 § 482. Concrete universals and singulars, like general proposi- 
 tions, assert merely the mode of the subject's existence, even 
 while that existence is assumed. Given 'Jenkins herds swine', 
 we can say, 'There exists one Jenkins, a swineherd,' but not 
 'There exists swineherd Jenkins'. 'None of the knights are 
 faithless ' will not give us ' None of the faithless knights exist'; 
 though ' No knights are faithless ' is equivalent to ' No faithless 
 knights exist '. 
 
 § 483. The question which has just been discussed is, it will 
 be observed, no more affected by the meaning of the ' copula ' 
 than the existential character of the subjects of propositions was 
 affected by it. It does not matter whether we begin, ' Any X'^ 
 which may exist,' or, 'Some of the ^'s which do exist': in 
 either case the proposition goes on — ' have that existence in the 
 form of y.' But since every judgement can be expressed as an 
 explicit affirmation (/, O) or denial {A, E) of existence — even 
 the concrete universal affirmative ' All my friends were kind ' can 
 be phrased ' There did not exist among my friends one unkind 
 one ' — this is further evidence that the idea of existence underlies 
 every statement, and that it is absurd to say that in ' No head 
 masters are uneducated men ' are is existential, while in ' All 
 head masters are educated men ' it is a mere hook and eye. 
 
 § 484. To glance briefly at the question, what is meant by 
 judged existence. I do not think that, for logical purposes, any 
 distinction can be made between actual existence to the senses, 
 apprehended by inner or outer intuition, and existence in fancy 
 or literature. Existences of the latter kind are an objective 
 fact, when we judge anything about them, as much as those 
 which can be touched, tasted and handled. I state something 
 
 being identified with the Y portion of itself), but only in the form, ' Every 
 X is an XY^ is a F existing in the mode X. 
 
 ' We might, it is true, say that every possible case of X being Y is 
 actually realized, or that some possible cases are not realized. But 'every 
 YX'' means ' every X that is Y\ not ' every X that might be Y'. (In 
 such a sentence as, ' All the dancing men have partners,' ' dancing ' is used 
 idiomatically.) 
 
The ' Copula ' 219 
 
 about basilisks, not about my notion of basilisks, and the state- 
 ment, however playful, is propounded as a judgement about those 
 creatures. If I say that Hamlet killed Polonius, or that some 
 elves have bats' wings, the reference is to an assumed reality, 
 as between me and the person to whom I speak, not less than if 
 I stated something about Charles Dickens or about a species of 
 rabbits ; nor would a proposition respecting Cymbeline or King 
 Arthur be more ' existential ' if I were thinking of, or referring 
 to, those princes as historical personages. Every proper name 
 assumes existence. The elaborate disquisitions, therefore, of 
 Mr. Wolf and others on existence and reality appear to me to 
 be a waste of ingenuity. If a distinction between being (wapf ts) 
 and existence (oio-ta) be insisted on, in that case the logical 
 proposition is not concerned with the latter, but only with the 
 former. No doubt, actual existence in rerum natura may be 
 explicitly asserted or denied. But the propositions, ' Centaurs 
 are a fiction of the poets,' ' Briareus was a purely imaginary 
 being,' ' Earthly perfection is nowhere to be found,' assert some- 
 thing of centaurs, Briareus and earthly perfection, not about 
 names, or about my subjective individual idea of those things. 
 
 § 485. The existential implication of predicates does not 
 require much discussion. The predicate of a general proposi- 
 tion is not hypothetical like the subject, but assumed as a known 
 category; yet it is not implied that there is necessarily an 
 empirically existing class corresponding to it. I nxay say, 
 ' Every three-headed giant eats and drinks ' ; or I may say, 
 'Every three-headed giant ought to marry a three-headed 
 giantess.' I must not be supposed to assert by implication that 
 there is in actual experience a general class on which that duty 
 lies. A predicate is merely a notion, either already existing in 
 the mind, or one the elements of which are already possessed. 
 
 § 486. The predicate of a concrete or perceptive judgement is 
 equally notional. But if the subject is assumed to exist, the 
 qualities attributed to it must be thought of as existent. And, 
 generally, so far as any subject exists, what is truly asserted of 
 that subject must exist also. Only, the existence of the predicate 
 is not necessarily limited to that of the subject. 
 
CHAPTER XIV 
 
 IMPORT OF THE PROPOSITION (continued) 
 
 § 487. Having discussed the nature of the ' Copula ', we 
 are able to proceed with our analysis of the Import of the 
 Proposition, 
 
 It has been pointed out that general propositions assert some- 
 thing of the subject on the supposition of the subject being there. 
 Its actual existence is not necessarily assumed. Nevertheless 
 no subject can be resolved into pure conditionality. Reality as 
 the ultimate subject underlies the supposed case. But moreover, 
 within Reality, there is always some lesser sphere or universe 
 of discourse which is assumed. Thus, in ' Hard words break no 
 bones', ' words ' is the sphere, the existence of which is assumed, 
 while ' hard ' is the condition of what is asserted about this 
 sphere. Words, if hard, or though hard, break no bones. 
 ' Liars need long memories.' Of men (a known class), if they 
 are liars, the need of long memories may be predicated. 
 
 It may not be always easy to name the sphere of an assertion — 
 e. g. ' Love laughs at locksmiths.' But it is always there, or, 
 in the final resort, as has been said, the sphere is the Real. 
 The universe of discourse is the largest circle in the subjoined 
 diagram ; the condition the smallest. 
 
 If the sphere of discourse ('men') fell within the circle which 
 represents the predication (' needing long memories '), it would 
 
A Sphere always assumed 221 
 
 not need to be conditioned (all men need them). It would 
 intersect that circle if other beings than men needed long 
 memories. 
 
 § 488. It is plain, then, that this assumptive element of the 
 subject runs through the whole proposition, and, even if unex- 
 pressed; underlies the predicate. Thus — No YX is Z(A watched 
 pot never boils) is equivalent to. No YX is ZX (No watched 
 pot is a pot that ever boils). Conversely, No ZX is YX (No 
 pot that ever boils is a watched pot). Again, No Y is ZX 
 (No watched object is a pot which ever boils) ; and No ZY — 
 or no YZ — is X (Nothing which, being watched, also boils is 
 a pot). 
 
 § 489. The constant and assumed element in a proposition is 
 the substance in which both the subject or conditioning attribute 
 and the predicate attribute inhere ; and the asserted or denied 
 coinherence of two attributes in a common substance is that 
 synthesis which we call predication. In every affirmation is 
 a consciousness not of identity but of unity. For logical pur- 
 poses we can speak of a plurality of substances. But in the 
 final analysis the one and sole substratum of all varying 
 determinations is the Real ^ ; since apart from the deter- 
 mining qualifications all substances must be thought as entirely 
 alike. 
 
 § 490. The qualification of Reality is either notional or phe- 
 nomenal. The latter is asserted in the proposition, which must 
 be either true or untrue. Aristotle says : Xoyos airoc^avrtKos 
 oil irSs aXk' Iv <a to aXrjOeueiv ^ xj/evSea-Oat VTrdpxei,.^ Observe that 
 while the combination of two elements in a notion (e. g. friendly 
 act) implies the possible coinherence of the corresponding 
 attributes in the same substance, the conceptual combination of 
 a negated idea with another element (e. g. unfriendly act) does 
 not imply the impossibility of their coinhering, but only the 
 possibility of their not coinhering, in one substance. 
 
 When the impossibility of coinherence is asserted, we have 
 the universal negative. So that we can either say, with Herrick, 
 
 ^ Theologically, God the Word, the Image of the Father's substance, 
 upholding {(fiipav) all things by the utterance (pfjua) of His potentiality 
 (duva/uf). Hied. i. 3. 
 
 « £>e I»f., 4. 
 
222 Import of the Proposition 
 
 ' No man at one time can be wise and love,' or, ' No wise man 
 falls in love,' or, ' No man who falls in love is wise.' No X is 
 both Y and Z. That is, no YX is Z, and no XZ is Y. If any- 
 thing is both Fand Z, it follows that it is not X. 
 
 § 491. Coinherence is sometimes expressed by ' and ', ' Give 
 him an inch and he will take an ell.' ' Divide et impera.' 
 'Scratch a Russian and you find a Tartar.' 'Tange montes 
 et fumigabunt.' ' Lang and lazy ' (i. e. long people are lazy). 
 Sometimes an antecedent and a consequent clause are juxtaposed 
 without and — e. g. ' brevis esse laboro, Obscurus fio.' 
 
 Give me but what this riband bound, 
 Take all the rest the sun goes round. 
 
 Or 'toUe periclum, lam vaga prosiliet frenis natura remotis '. 
 
 § 492. Coinherence does not imply that the subject and predi- 
 cate ideas stand on an equal footing. In universal negative and 
 particular affirmative propositions, which are convertible simply, 
 no priority can be assigned to either, though the point of view 
 is different according as we judge no S to be P or no P to be 5; 
 some 5's to be P or some P's to be 5. But in universal affirma- 
 tives, the hypothetical antecedent must be regarded as having 
 logical priority to the consequent. Bosanquet maintains that 
 the subject is not earlier than the predicate.' ' It is absolutely 
 impossible that priority in time should subsist between the parts 
 of a completed judgement . . . You cannot have an 5 first, and 
 then tack a P on to it.' ^ Of course, nothing can be a subject 
 without expecting a predicate, the two ideas being correlative. 
 But equally no one can be a mother without eo ipso having a son 
 or daughter. There priority in time comes in. But what we 
 are concerned with is rational precedence. No doubt a would- 
 be predicate often waits for a subject. 'The bell tolls, some 
 one is dead ? Who is it? The mayor.' Grammatical subject, 
 however, is here logical predicate. — 'The dead person is the 
 mayor.' Compare, 'The soul that sinneth, it shall die.' We 
 are dealing, however, rather with general propositions ; and in 
 
 ' In the Concept some languages, as French and Latin, put the 
 adjective after the substantive, the generic idea coming first and then 
 its quahfication. In English, on the other hand, the quality first presents 
 itself to the mind, the subject in which it inheres lying beyond in the 
 background. 
 
 ^ Logic, i. 85, 86. 
 
Coinherence 223 
 
 these it is clear that the conditioning idea takes in the order 
 of reason precedence of that which is predicated. 
 
 § 493. Yet, in another sense, the predicable content — though 
 not yet as predicated — comes first, for in judging (at any rate 
 in concrete judgements) we place what is more immediately 
 presented to our cognizance, and perhaps is now experienced 
 by us for the first time, under a notion which.we already possess. 
 Knowledge is the bringing what is less known under what is 
 better known; otherwise the judgement, which is meant to 
 elucidate what is obscure in the subject, would bring no light to 
 the mind. Representing a judgement, then, as SJ, where / is 
 that which is judged about the subject, S precedes /. But 
 representing it as Sis P,P the predicable but not yet predicated 
 content, is actually possessed earlier than S. 
 
 § 494. All judgement, then, brings object under concept, the 
 That under the What. This is so even in assertions about ab- 
 stractions so vague as to be inconceivable, such as Infinity,' and 
 in the identification of singulars — ' Thou art the man ' ; ' The 
 person you see there is the Duke of Omnium ' ; ' This station is 
 Weedon.' The predicate must possess some general significance 
 for the person addressed, or the statement would be wasted. A 
 bare 'hoc est illud' is really impossible. To point with the 
 finger to two objects neither of which recalled any idea at all to 
 the person for whose benefit they were being identified, would 
 be meaningless — a page of algebraic equations to a little child 
 not more so." One presentation to consciousness cannot be 
 predicated of another. Individual designations must have 
 acquired some significance. But the question how far proper 
 names are connotative is a large one. 
 
 ' Hamilton says: — 'We think, we conceive, we comprehend, a thing 
 only as we think it as within or under something else; but to do this 
 of the infinite is to think the infinite as finite.' There is here, surely, a 
 confusion of thought. If something is predicated, for instance, of spatial 
 infinity this is to place it within boundaries of thought, but not within 
 boundaries of space. Has the Infinite no attributes ? 
 
 '^ Or the following, which catches my eye in the law column of an 
 Edinburgh newspaper, to myself : — ' Lord — , Act. — . Alt. — . The 
 Lord Ordinary having considered the closed record, proof and produc- 
 tions, repels the claim on the fund in tnedio for the claimants, No. 14 of 
 process: Sustains the claim for the claimants; and ranks and prefers 
 them accordingly in the said fund in medio in terms of the condescend- 
 ence and claims. No. 15 of process : And discerns.' 
 
224 Import of the Proposition 
 
 § 495. The subject of a universal judgement is less well known 
 and narrower than the predicate, or in other words is nearer to 
 perception and further from conception. If a concept, it is 
 a lower concept. But it may be merely denominative or 
 indicative, without connotation, A lecturer in chemistry may 
 begin : ' I am going to tell you something about this object 
 which I hold in my hand (or these objects which you see on the 
 table), which you do not, perhaps, recognize, and of which, 
 probably, you do not even know the name.' On the other hand, 
 the predicate must be a concept ; must, that is, even when the 
 name of a single object, have some conceptual and general sig- 
 nificance. Thus : — 
 
 I am a lord indeed, 
 And not a tinker, nor Christophero Sly. 
 
 § 496. The subject is essentially at bottom substantival, even 
 when a grammatical adjective or participle. ' Beati pacifici ' — 
 blessed are the peacemakers ; ' seniores priores ' — elder persons 
 go first. Neuter plurals often stand as subject — e. g. ' mediocria 
 firma.' And the predicate is essentially adjectival, even when 
 a grammatical substantive ('traditores proditores ' ; 'Tu es capi- 
 taine ' ; ' This is food '), or when regarded from the point of view 
 of extension (' Penwipers are useful things ' ; * She is a widow ' ; 
 ' This is a bad business '). In considering the Categories, we 
 shall notice a number of different grammatical forms by which 
 a predicate may be expressed. 
 
 § 497. This adjectival character is less obvious where the 
 ' copula ' unites two abstract qualities — e. g. ' Unity is strength.' 
 What, however, is here predicated of unity is not strength, or 
 the being strong, but identity with strength. Unity in the 
 abstract exists as strength in the abstract. The corresponding 
 proposition about a class is ' The united are strong '. 
 
 § 498. No doubt the thing predicated of a subject is always an 
 attribute — in this case not ' strong ' but ' the being strong '. 
 'The grapes are sour' — sourness is attributed to the grapes; 
 grapes possess the attribute of sourness. It follows that the sub- 
 stantive verb usually called the copula is not really a ' mark of 
 attribution ' — if so, the subject would come last, not first— but 
 expresses an assertion that what existence or being the subject 
 has it has under a certain adjectival mode or qualification. The 
 grapes have their being (verbal noun) as sour, as being (present 
 
' Congruence and ConflicHon ' 225 
 
 participle) sour.^ This adjectival mode is usually called in 
 logic, as in grammar, the predicate ; and it is in that sense that 
 we say that the predicate of a proposition is always notional, in 
 other words an adjectival concept, signifying possessing an 
 attribute. Whatever is real as X is real as Y. If reality 
 possesses the attribute -X'-ness it possesses the attribute F-ness. 
 'Pro'posti.ions secundi adiacentis — 'sol splendet '; 'Dogs bark'; 'I 
 ran' — may be analysed into the same elements. Sometimes a sen- 
 tence lies in a single impersojial verb — e. g. <raXirL<7ti, The trumpet 
 shall sound.^ On the other hand the original of ' I will put my 
 trust in Him ' is lyia la-ofiai Tr€iroi6u>? ett' avrZ. The necessity of 
 logically resolving all propositions into the terlu adtacentis form, 
 called by the schoolmen orafio perfeda, follows from the doc- 
 trine that all predication whatsoever brings, a subject under 
 a general notion. See below, § 612. 
 
 § 499. We are now in a position to scrutinize Hamilton's 
 view of the Import of the Proposition.' He says, following 
 Locke : ' To judge is to recognize the relation of congruence or 
 of conflictio'n in which two concepts, or two individual things, or 
 a concept and an individual, compared together, stand to each 
 other. This recognition, considered as an act of internal con- 
 sciousness, is called a Judgement ; considered as expressed in 
 Language it is called a Proposition or Predication.'* The 
 congruence or agreement of two ideas Hamilton explains as 
 their capability of being ' connected in thought ', of being com- 
 
 ■^ This modal character is especially observable in tertiary predicates — 
 e. g. Seiwa Tamn/ua Saifjitov tSaiKev, or KaWta-ros avfjp iiro "lAtov ^Kdiv Nipeiir. 
 
 ' I Cor. XV. 12. (ToKiny^, however, occurs in the preceding clause. 
 Bosanquet remarks : ' The reason why the Verb is appropriated to the 
 act of predication is that it is a miniature sentence .... By convention, or 
 explicitly in the person-ending, it includes within itself a reference to 
 given reality, and can therefore stand alone as an enunciation, which no 
 Other part of speech can do' {Logic, i. 84). He adds : — 'An adjective 
 implies a reference to something else ; but the something may be a mere 
 idea. ... It is in the demonstrative force of the verb that we must look 
 for its fundamental predicative force.' The copula he calls ' a mere sign 
 of afHrmatiori '. 
 
 ' I have not troubled in this book to keep the names Judgement and 
 Proposition distinct, for it is seldom that the one is not also the other. 
 However, as every judgement is an interpretation of the facts of sense, so 
 every proposition, by which judgement is translated into speech, is an 
 interpretation of an interpretation. 
 * Lectures on I^ogic, i. 225. 
 
226 Import of the Proposition 
 
 bined in the same presentation of sense or representation of 
 imagination. He instances learning and virtue, beauty and 
 riches, magnanimity and stature^ 
 
 § 500. Congruence and confliction, however, only give us two 
 judgements, the particular affirmative and the universal negative, 
 in which subject and predicate may -be transposed. Some 
 learned people are virtuous and some virtuous people are 
 learned. The attributes may go together ; they are capable of 
 being combined in the same person. Again, no learned people 
 are lazy and no lazy people are learned. The attributes cannot 
 be combined in the same person. We want a word to indicate 
 that attributes need not be combined, which would give us the 
 particular negative judgement — some learned persons are not 
 rich. If, further, it could be implied by any form of thought 
 that attributes are necessarily combined, we should have a con- 
 vertible universal affirmative judgement (the admissibility of 
 which has to be discussed later), as when one of the Apologists 
 says that to Christians every foreign country is a fatherland and 
 every fatherland a foreign country. 
 
 § 501. Where, however, in this scheme is room to be found 
 for the ordinary universal affirmative judgement — ' Comparisons 
 are odious ' ; ' Queen Anne is dead ' ; ' The learned are always 
 diligent'? Subject and predicate in such judgements do not 
 stand on the same level. The judgements are not convertible. 
 Not all diligent people are learned, nor all dead people are 
 Queen Anne, nor all odious things are comparisons. Yet 
 Hamilton explains agreeing or congruent as ' coinciding ', ' con- 
 ceived as one,' capable of being 'blended into one '." But just 
 afterwards he says : — ' We may articulately define a judgement 
 or proposition to be the product of that act in which we pronounce 
 that, of two notions, thought as subject and predicate, the one 
 does or does not constitute a part of the other, either in the 
 quantity of Extension or in the quantity of Comprehension.' ' 
 
 § 502. It is clear, however, that throughout Hamilton's ex- 
 position of the import of propositional assertion he is thinking 
 only of the subordination of species to genera in a classified 
 scheme of things, where the higher or including class is always 
 part of the definition of the lower or included class. The 
 
 ' Lectures on Logic, \. 213, 214. 2 j^jj p_ 227. 
 
 ' Ibid. p. 229, 
 
' Agreement of two Notions ' 227 
 
 predicate, he says, forms one notion with the subject, and is 
 judged to be ' one of the constituent characters of the [subject] 
 notion '. Thus polar is part of the notion electrical. In other 
 words the Hamiltonian view ignores all judgements except 
 analytical ones. Judgements of experience are not a comparison 
 of notion with notion but a bringing of fact under notion. 
 ' Mary had a little lamb ' is a proposition concerning Mary, not 
 concerning my idea of her. No doubt it is what I know of her 
 which makes me say she had a lamb. But this knowledge is 
 empirical merely. Or take this rustic saying — ' Lang and lazy. 
 Black and proud, Vair and voolish. Little and loud.' Long 
 people have been noticed to be lazy, dark people to be proud. 
 Folly has been found to co-exist with fair complexions and loud- 
 ness with low stature. No doubt a causal connexion is implied. 
 But there is nothing in the notion of length which implies 
 laziness, nor will analysis of blackness as an idea show it to 
 contain, as one of its constituents, pride. 
 
 § 503. To find by comparison that two notions agree in some 
 respect is not to form a judgement having the one as subject and 
 the other as predicate. Puppies and calves, ex vi notionum, 
 agree in being young, but puppies are not calves nor calves 
 puppies. Yet Jevons speaks of the relation of subject and 
 predicate as ' a relation of sameness or difference ', and Mr. A. 
 Sidgwick contends that ' every proposition asserts the manner 
 in which two nameable things are related to each other ; e. g. as 
 resembling or differing '.^ It is true that negation is a judgement 
 of disagreement. Even a slight point of difference enables me 
 to say that house sparrows are not hedge sparrows, and that 
 Blenheim spaniels are not King Charlies. But affirmation — e. g. 
 "'A turnip is a root'— is not the statement of a resemblance. 
 If a certain resemblance justifies a judgement, turnips are 
 potatoes, since both are roots. We judge that S is not P on 
 the ground that the one is M and the other is not M ; but we 
 cannot judge that S is P on the ground that both are M. 
 
 § 504. Again, judgement is the result of a comparison between 
 some circumstance or quality known to belong to a thing and a 
 notion ; which circumstance or quality does not conform to the 
 notion in one or more respects only, but in all. Yonder orb is 
 a planet because it moves round the sun — such being the 
 ^ Fallacies, p. 35. 
 Q2 
 
228 Import of the Proposition 
 
 definition of planet. It would not be enough that the circum- 
 stance observed of the subject should agree with one of the 
 constituent and essential characters of the predicate notion; 
 e.g. visible moving as implied in planet, for comets move 
 visibly. If I say, 'Soap is useful, because it is detergent,* 
 usefulness is part of the notion of detergence, not detergence 
 of usefulness.' 
 
 A whist-player looks first at the turned-up card, and then 
 goes through his hand to see if any of his cards resemble it, and 
 so are trumps. He could not ascertain this merely by scru- 
 tinizing his hand, unless some suit, as clubs, were necessarily 
 trumps. The latter case corresponds to the analytic judgement, 
 in which scrutiny of the subject idea enables us to frame a 
 proposition — e.g. that those whom we commend or blame for 
 their actions must be regarded by us as having free will. But 
 in the other case the suits in the player's hand are as yet 
 unrelated to anything until the turned-up card has been glanced 
 at. And so I cannot affirm that sugar fattens until I have on 
 the one hand considered what fattening means, and on the other 
 sifted the facts which I happen to know about sugar. This is 
 the ordinary synthetic judgement. 
 
 § 505. Hegel observes that judgement is the notion particu- 
 larizing itself, and the predicate fills the subject, regarded as in 
 itself void, with content. His example is, ' God is all-powerful.' 
 If we learn this attribute of God by His acts, the proposition is 
 synthetic. If without all-mightiness we should not think of a 
 Being as truly God, it is analytic. 
 
 § 506. Professor Carveth Read remarks ^ that there are three 
 leading schools of logicians, the Nominalist, the Conceptualist 
 and the Materialist. The first (e. g. Whately) regards Logic as 
 
 ' It may be objected that 'useful' is no part of the actual notion 
 (=definition) of 'detergent', any more than it is of soap in the rational- 
 ized judgement, ' Brown Windsor is useful, because it is soap.' Of course 
 I am arguing against, not for, Hamilton's point of view. But sooner or 
 later, in assigning ground for ground, we must come to an analytic, or at 
 least self-evident, judgement. In other words, every judgement rests 
 ultimately on an identity in difference, one, that is, in which the middle 
 and major terms are found to be identical. If we had gone on : ' What is 
 detergent has the property of making foul linen clean, and whatever does 
 this is essentially useful,' we should be on the way, at any rate, to such 
 identification of notions. 
 
 ^ Logic, p. 10. 
 
Views of Logicians 229 
 
 concerned with the consistent use of words. The second (e. g, 
 Hamilton) regards it as securing consistency in the relations of 
 thoughts, and as concerned with judgements rather than with 
 propositions. The third (Mill, Bain, Venn, &c.) look to Logic as 
 securing true statements about the relations to one another of 
 facts. Mr. Read does not mention the view which regards 
 judgement as ordinarily asserting a relation not between name 
 and name, nor yet between thought and thought, nor yet 
 between fact arid fact, but rather between fact and thought — the 
 bringing^ of experiences under conceptions. 
 
CHAPTER XV 
 
 ANALYTIC OR EXPLICATIVE JUDGEMENTS 
 
 § 507. Examination of the view of predication as notional 
 inclusion has led us to speak of Analytic (Decompositive) as 
 contrasted with Synthetic (Compositive) Judgement. The dis- 
 tinction, already pointed out by Hume and by Locke in discuss- 
 ing 'Identical Propositions', was emphasized by Kant. Analytic 
 Judgements have also been called Explicative, Elucidatory, Im- 
 mediate,^ Necessary, Essential, in contrast with Informative, 
 Mediate, Contingent or Accidental Judgements. Nominalist 
 writers distinguish propositions as Verbal and Real. 
 
 § 508. By ' verbal ' Locke means not only propositions in 
 which 'the same term, importing the same idea, is affirmed of 
 itself — e. g. 'A four-post bedstead is a bedstead with four posts' — 
 but 'all propositions which affirm genera of species are barely 
 verbal ' — e.g. ' Lead is a metal ', metal being already part of the 
 essential notion of lead. 
 
 The expression ' verbal ', however, should clearly be reserved 
 either for propositions which are actually tautologous, where, 
 that is to say, the predicate is simply a repetition, iisdem verbis, 
 of the subject — as in Ben Jonson's line, ' A wooden dagger is a 
 dagger of wood ' — ,or for propositions which explain the meaning 
 of a word — e.g. ' Parsimony is thrift ', ' A mercenary is a soldier 
 who fights for pay ' (' only for pay ', an Englishman, proud of the 
 King's army, would prefer to say) ; ' Pyrotechnics are fire- 
 works.' 
 
 § 509. Locke avers that tautologies of the form 'Whatever is, is', 
 ' Right is right and wrong is wrong,' ' The law is the law,* and 
 the like, are mere 'trifling with words. It is but like a monkey 
 shifting his oyster from one hand to the other ; and, had he but 
 words, might, no doubt, have said, "Oyster in right hand is 
 
 ^ That no judgement can be immediate is maintained throughout this 
 book. To our rudimentary perceptions the name 'judgement ' must be 
 denied. 
 
Verbal Propositions . 231 
 
 subject and oyster in left hand is predicate," and so might have 
 made a self-evident proposition of oysters, i. e. oyster is oyster ; 
 and yet with all this have not been one whit the wiser or more 
 knowing.' ^ 
 
 § 510. It is strange, if verbally identical propositions are not 
 worth making, that they are so frequently made. ' Man is man,' 
 sings Enid, ' and master of his fate.' ' Son' lo ' — ' I am I.' ^ We 
 point out that business is business, that boys will be boys, that 
 ^Love is love, in beggars or in kings'. It has been already 
 shown (§ 45) that such tautologies are not worthless truisms, 
 inasmuch as subjects are directly denominative, and in danger of 
 being thought merely in extension, as class-names. Predicates, 
 on the other hand, are primarily thought in intension ; and the 
 repetition of the subject expression in the predicate calls atten- 
 tion, therefore, to the attributes connoted by the name, ■n)v 
 a-KOL^-qv a-Kd^r]v Xeyet. ' Let your yea be yea and your nay nay.' 
 If I say, ' A picture should be a picture,' I mean that it should 
 be pictorial, and not a mere transcript or photograph. 'A man's 
 a man for a' that ', reminds the reader of the humanity of every 
 person, however lowly, who bears the name ' man '. When the 
 patriarch exclaims, ' If I am bereaved of my children I am 
 bereaved,' he has acutely before his imagination the significance 
 of bereavement. Pilate's o yeypa^a yeypa<jia insists on the perfect 
 tense. It is finished, and cannot be re-opened ; like Dryden's 
 couplet — 
 
 Not heaven itself upon the past has power ; 
 
 But what has been has been, and I have had my hour. 
 
 Similarly ' Nous verrons ce que nous verrons ' emphasizes the 
 future tense and the impossibility of prediction. The cottage 
 mother's philosophy, on the other hand, about infantile dis- 
 orders — ' If children are going to have things they will have 
 them, and if not they won't ' — converts mere futurity into an 
 irreformable decree of Providence. When Tennyson writes, 
 ' No, she never loved you truly ; love is love for evermore,' he 
 implies that what goes by that name is not truly love unless it 
 
 ' Tke Human Understanding, bk. iv, c. viii, § 3. Hegel also main- 
 tains that the proposition A\% A\% necessarily frivolous. 
 
 ^ The ineifable Name represented by the Tetragrammaton JHVH is 
 thought to mean, ' I will be that which I will be.' 
 
232 Analytic or Explicative Judgements 
 
 has the characteristics of true love, such as constancy. Byron 
 
 writes — 
 
 To see my name in print — 
 A book's a book, although there's nothing in't. 
 
 And the line quoted just now from Jonson is seen to convey a 
 meaning when we add its fellow — 
 
 A wooden dagger is a dagger of wood ; 
 Nor gold nor ivory haft can make it good. 
 
 In ' Gilded chains are chains still ' the mind is recalled to a part 
 of the subject which might be in peril of being obscured by 
 another element of it. 
 
 § 511. Such propositions are not to be classed with 'Blue-nosed 
 baboons are baboons with blue noses ', or with ' Midsummer-day 
 is the day in the middle of summer ' (contrast ' Midsummer-day 
 is June 24th '). Judgements in which the predicate is a mere 
 "repetition of the subject -are not judgements at all. Nothing is 
 judged. They are only propounded in jest, and then, usually, 
 under the thin disguise of a verbal change. Schoolboys say, ' I'll 
 •not do it again — till next time." The Americans are fond of this 
 form of humour; e.g. ' He was born early in life in the town of 
 X' ; or 'I lay, expecting every moment to be my next'. But 
 the old nursery rhymes employ it most audaciously — as in the 
 case of the plaguy old woman unquiet, Mvho lived upon nothing 
 .but victuals and drink ; victuals and drink were the whole of her 
 diet. One rhyme advises us to go to bed early and keep our 
 feet dry, in which case we shall live till we die ; and another 
 gives John Boldero's counsel to wives and maids, how to make 
 their candles last for aye. What delightful exemplifications, 
 too, of absurd truism and seeming verbal contradiction there are 
 in the famous twelve-line Gammer Gurton about the ' three 
 children sliding on the ice all on a summer's day'. Compare 
 what Charmian in Antony and Cleopatra says of ' the pretty 
 worm of Nilus '— ' His biting is immortal. Those that do die 
 of it do seldom or never recover.' On the other hand, ' A great 
 cause of night is lack of the sun ' might convey information to a 
 troglodyte. The common remark ' I am not so young as I was ' 
 is a truistic reminder of the significance of advancing years. 
 
 § 513. Examples of verbal paradox and seeming contradiction 
 were given in § 133. But the affirmative tautology, ' If I perish, 
 I perish,' has not an exact .negative counterpart, seeing that w^ 
 
Verbal Propositions 233 
 
 can significantly affirm, but cannot deny, of any notion its 
 essential content. Propositions such as ' Poverty of spirit is 
 not poor-spiritedness ', or ' A sportsman is not a sporting-man ', 
 call attention by a slight verbal variation to a difference in the 
 usage of words. Possibly a word has come to be used quite 
 technically — e.g. 'The Speaker does not speak.' Or we may 
 think it is in danger of becoming conventionalized — ' It is the 
 duty of an Opposition to oppose,' not merely to sit on the 
 Speaker's left. ' Conseirvatives ought to conserve,' not merely 
 to belong to the Carlton Club or the Primrose League. But we 
 could not say, ' He who speaks does not speak,' or ' Those who 
 conserve do not conserve '. ' Liberals ' — but not ' Those who are 
 liberal ' — ' are not liberal.' 
 
 ' No true disciple of mine,' said Ruskin, ' will ever be a 
 Ruskinian.' The only immortal tongues are the ' dead ' ones — 
 compare, ' Comme ils sont jeunes, ces antiques ! ' A condition of 
 ^crisis', some one has said, is normal in the Church. All 
 ' improvements ' (e. g. in village architecture) have long been for 
 the worse. There is an art, we say, in being ' natural '. A ' half- 
 truth ' is not half the truth, but ' is ever the blackest of lies '. 
 Free trade in land has often meant land monopoly. The cynic 
 -said that the ' equality of the sexes ' is the supremacy of woman ; 
 the humorist that for an impromptu speech he required a fort- 
 night's notice. ' I am their leader,' remarked a statesman 
 bitterly; 'I must follow them.' A London tailor gave as a 
 reason to a customer for the non-delivery of a suit that his men 
 had gone to walk in the procession of the Unemployed. 
 
 Tacitus is fond of epigrammatic paradox, such as the well- 
 known — ' praefulgebant Cassius atque Brutus eo ipso quod 
 effigies eorum non visebantur'^ — they were conspicuous by 
 their absence. The predicates are clearly used in a separate 
 sense from that of the subjects in the definition of the equal 
 state as that in which everybody is somebody and nobody is 
 'anybody. 'Then we are in order,' cries Jack Cade, 'when we 
 are most out of order.' We have all experienced the wisdom 
 of the saying, ' There is no time to-day for short cuts.' Of course 
 poetry constantly challenges our attention to something para- 
 doxical in the expression ; as in Milton's line — 
 
 I waked ; she fled ; and' day brought back my night, 
 * Ann. iii. 76. 
 
234 Analytic or Explicative Judgements 
 
 or Quaries's verses ' To my heart ' — 
 
 Mine wert thou never till thou wert not mine. 
 Sacred rhetoric especially uses this figure ; e. g. TertuIIian's — 
 ' quae maior voluptas quam fastidium omnis voluptatis ? ' 
 
 § 513. But Locke also includes under ' trifling propositions ' 
 those that are usually called Analytic, which, having a predicate 
 more extensive than the subject, explicate the content of a name, 
 not verbally in terms of itself, but by recalling one or more of 
 its essential characters. These, he maintains, like Identical 
 Propositions, ' teach us nothing.' 
 
 Locke does not mention an intermediate class of propositions, 
 those which appeal to the etymological meaning of a word 
 rather than to the conceptual content of a notion. The Stoics 
 pointed to the derivation of ' virtue ' to show that it consists in 
 manhood. A layman is not simply a non-expert, but one who 
 has duties and privileges as a member of God's Xads ; but again, 
 since a Xads is not a S^/aos, those duties and rights are not 
 necessarily democratic. Towns whose names end in ' mouth ' 
 (e. g. Plymouth) are, we can be sure, or were at some time, sea- 
 ports, and on a river. Ruskin enlarges on the gulf between 
 franchise, the quality of the Franks, and the parliamentary 
 thing.^ At the equinox there are twelve hours of daylight. 
 A magpie talks and is coloured black and white. A reason 
 must be rational. An archdeacon performs archidiaconal 
 functions. This happens, by the by, not to be true ; though in 
 England and elsewhere, till about the end of the twelfth century, 
 an archdeacon was actually chief of the diaconate. But it is 
 often a real elucidation of a name, and a help towards recovering 
 its true sense, to throw it into adjectival form, or to substitute 
 the form it has in the original or some other language. A 
 mischief-maker is 'diabolical'. An apostle has an apostolic 
 commission.^ There is an ethical tinge in 'womanly' and 
 
 ^ Bible of Amiens, pp. 10, 60. 
 
 ^ This will not always do, however ; for of the words ' churchman ' and 
 ' ecclesiastic ' it is the latter whose meaning has become deflected. The 
 technical use of ' churchman ' (as used, for example, in the Declaration 
 prefixed to the XXXIX Articles, or in Tennyson's lines to F. D. Maurice) is 
 now almost obsolete. No doubt, it might be held that an ecclesiastic is a 
 person in a special relation to the formal assembly called the ecclesia, just 
 as a domestic is not any member of the domus but one who has a function 
 in it. A churchman (in- the old-fashioned sense) attends to the church as 
 a coachman does to the coach. 
 
' Frivolous ' Propositions 235 
 
 • womanliness ', and in ' feminine * (though not in ' female '), 
 which is absent from 'woman'. A preacher may usefully 
 remember that he has to be a praedicator, a judge to be judicial, 
 a worshipper to worship, a servant to render service. If it be 
 debated whether law is essentially positive or natural, the 
 etymology of ' law ' (A.-S. laid down) might be pointed to. It is 
 not much use, however, as a rule, to look to the meaning of 
 proper names to learn anything about general characteristics — 
 e. g. Philippi or Philadelphia. And changes of meaning are for 
 ever slipping in between the same word in subject and predi- 
 cate ; so that we could not argue that a cowboy, or a postboy, is 
 a boy, and therefore ought to be at school. 
 
 § 514. Condillac regards propositions containing a verbal 
 identity as frivolous, but not those in which there is an identity 
 of ideas, or rather a reminder that one "idea is included in 
 another. Of such analytical judgements, however, Locke main- 
 tains that they ' add no light to our understandings, and bring 
 no increase to our knowledge '. But. their not adding to the 
 sum of our knowledge need not imply that they do not illuminate 
 our minds. Explicative judgements certainly enable us to recall 
 and appreciate better the knowledge we have already put by in 
 store. They bring home to our mind, and make subjective, 
 knowledge which was before only dimly realized, lying, as it 
 were, outside us, yet within hail. Thus Epictetus writes : ' He 
 that expecteth nothing cannot be disappointed.' ' The Saturday 
 Review,' we might reflect, ' appears, no doubt, at the end of 
 every week.' 
 
 Many examples of conceptual analysis will be found in the 
 more argumentative Epistles of the New Testament. Thus St. 
 Paul, speaking of election, reminds the Roman Christians — 
 £t Se yapni, ovKeri ii Ifyyiav hrii fj X^'P'S ovKen yiveTat X"P'^ (^i* ^) — 
 ovKCTi is only partly temporal here ; iam non in the Vulgate, not 
 non mm. Again, ' Where no law is, there is no transgression ' 
 (iv. 15 : cf. V. 13). ' To him that worketh the reward is not 
 reckoned as of grace, but of debt ' (iv. 4). 'If children, then 
 heirs '(viii. 17). So also in the Epistle to the Hebrews — 'In 
 that He saith, A new covenant, He hath made the first old ' (viii. 
 13). ' Where a testament is, there must also of necessity be the 
 death of the testator ' (ix. 16).* Or conceptual implication is 
 
 1 Compare also Heb. ii. 6, 8, 10, 11, 14, 17; iii. 3; iv. lo, 14; v. i, 
 
236 Analytic or Explicative Judgements 
 
 denied. ' Because they are Abraham's seed, they are not there- 
 fore all children' (Rom. ix. 7). 
 
 § 515. Of course all argument, and all education, must be at 
 bottom a priori — an appeal to common ground as to the meaning 
 of concepts.' Sometimes an analytical proposition is meant to 
 startle, yet none the less sets out from an assumed agreement. 
 E. g. ' Civilization is man's natural state ' ; ' Protestantism can 
 be the possession of only one man at a time ' ; ' Every Socialist is 
 a conscious or unconscious Tory ' (contrast, ' Every woman is 
 at heart a Tory'). Sometimes we try to arrest attention by the 
 truisticor affectedly moderate form of a proposition — e.g. ' satis 
 quod sufficit '; 'There's a great deal of human nature in mankind.' 
 
 § 516. All propositions stand for something gained to the 
 mind. But only synthetic propositions convey information. 
 We cannot therefore regard as analytic those propositions 
 which, on the authority of the speaker or of a dictionary, tell us 
 for the first time what a name, not ought to mean but, means. 
 ' A vertebrate creature is one that has a backbone.' ' The Chan- 
 cellor of the Exchequer is the minister who manages the 
 finances of the kingdom.' ' Browne's Pseudodoxia Epidemica is 
 his Vulgar Errours.' ' Effervescence is fizzing.' ' Essex is the 
 land of the East Saxons.' ' Remuneration,' says Costard; 'oh, 
 that's the Latin name for three farthings.' To make them 
 analytic, we must understand in propositions a scilicet, a ' to be 
 sure'. ' X is necessarily {rfirj) Y' ; ' X cannot, of course, be 
 Z.' ' Lord ! Then I must be thy lady.' Analytic propositions 
 are always persuasive rather than assertory. 
 
 § 517. Definitions (which Bain and others class as verbal) 
 are either propounded authoritatively, as at the beginning 
 of any science — in which case they give information, and ^re 
 therefore synthetic." Or they are put forward for acceptance 
 suggestively, and as stimulating reflectiveness.^ Those definir 
 
 13; vi. 7, 16; vii. 7, II, 12, 26; viii. 3, 4, 7, 24; x. 4, 18, 29; xi. I, 
 14 ; xiii. 17 ; Gal. iii. 18 ; and many other passages. 
 
 •* See Aristotle, Post. An. I. i. I. 
 
 ^ '" A city is a large town possessing a cathedral," ' says Sidgwick, ' is 
 not a thesis set up for proof, but the registration of a postulate in order to 
 let the full extent of our assumption be openly known' (Fallacies, p. 1 19). 
 Some cities, e. g. Llandaff, St. David's and Ely, are not large towns. 
 
 ^ Isaac Barrow, asked by the Bishop's chaplain, Quid est fides ? 
 answered. Quod nan-vides. Quid est spes ? Magna res. Quid est 
 
Locke's View 237 
 
 tions which we gradually, by much reflexion, work out for 
 ourselves are the ones which do most to clear our thoughts. If 
 propounded to a person ignorant of Latin, the proposition, 
 ' Three men make (constitute in thought) a triumvirate,' though 
 a definition, would be as synthetic as ' Foiir people make (con- 
 stitute in fact) a game of whist '. 
 
 .§ 518. Locke, as we have seen, insists that to predicate of 
 a term either the whole or any part of its content is to trifle — 
 e.g. 'AH gold is fusible ', for fusibility is already comprehended 
 in ' the received signification of gold '. ' Gold is yellow ' also. 
 He gives ' A palfrey is a neighing, ambling animal ' as another 
 example of triviality ! But while in Locke's view it is trifling to 
 say that man has corporeity, sensibility, rationality, risibility, 
 power of movement, to say that man has a notion of God or is 
 liable to be cast into sleep by opium is ' an instructive proposi- 
 tion '. The generic may not seriously be predicated of a species, 
 for it is part of the definition of the species. 
 
 Locke's point of view is inconsistently Realist. He assumes 
 first that the definition of everything is fixed and known to 
 everybody — so that everybody knows without being told that 
 a whale is not a fish, nor a bat a bird, and that lead is, while 
 brass is not, a simple metal — ; and, secondly, that, a name being 
 once defined, it is trivial to reflect upon and draw out any, part 
 of its meaning — e. g. the rational nature of man. Cousin applies 
 the word Identical to propositions 'in which we affirm of a thing 
 what we already know of it '. But we never do this, in the 
 sense that subject and predicate have, prior to the affirmation, 
 exactly the same value and significance to the conscious intelli- 
 gence. Every judgement is framed for the enrichment or 
 clarifying of our own mind, or another's. Starting like Locke 
 from a presupposition of definite and unchallengeable concepts, 
 Kant also regards ' Gold is a yellow metal ' as analytic. But he 
 does not go so far as to call it puerile. Propositions of the kind 
 would not be so common if they were not worth stating. If 
 they do not instruct, they remind, or make something clearer. 
 
 § 519. But it is a paradox to deny the name 'instructive ' to 
 reflective and expository judgements, based upon the analysis of 
 a complex notion into its simpler constituents. Take the follow- 
 
 caritas ? Magna raritas. Only the first of these answers can be called 
 a definition— a superficial one compared with Heb. xi. i. ' 
 
238 Analytic or Explicative Judgements 
 
 ing. ' Freedom of the will being denied, there can be na 
 morality.' 'Immediate inference is a contradiction in terms' 
 (the view advanced in this book). ' " Miracles do not happen." 
 No; for if they did they would not be miracles.' That is, 
 the raison d'etre of a miracle is to be exceptional and rare. 
 ' Imitation has no place in morals ' (Kant means that an act, to 
 have an ethical character, must proceed from some inward 
 principle). According to Philo, to know that God exists is to 
 know Him to be one, perfect, simple, immutable. Or again, 
 reflexion on what is meant by Unity leads to the conclusion 
 that the Oneness of the Godhead does not mean an everlasting 
 loneliness and singleness, but rather an internal consociation 
 and co-operation within a unique Being. Ridley says : — ' Com- 
 memoratio non est rei praesentis, sed praeteritae et absentis ' — 
 to which it has been replied that dva/xvi^o-is has not necessarily 
 this connotation. Buonaparte observed that a throne is but 
 boards covered with velvet — though his acts belied this con- 
 temptuous analysis. 
 
 § 520. It depends on the way in which a proposition is put 
 forward whether it is, or is not, to be called analytical. It must 
 claim that character in order to have it. Even as a judgement 
 in the mind it must be consciously based on the analysis of an 
 idea. And as propounded to another it must appeal to that 
 person's reflectiveness. Yet it might be analytic for the speaker 
 but not for the hearer, to whom it might come as assertion and 
 information. A great deal of lecturing is of this kind. Again, 
 what is self-evident to one mind is not so to another. The 
 content of any idea is relative to men's apprehensions.^ 
 
 § 521. Again, the content of an idea, or, more strictly, the 
 connotation of a name, varies with circumstances. We amend 
 and modify our conceptions. Definition has no absolute and 
 objective stability. New attributes are taken up into the general 
 notion. Old ones are sometimes discarded. If characteristic 
 
 ' There is no ' scientific frontier ' between names. ' The meaning of a 
 word,' remarks Mr. Sidgwick, ' is very much like the " market value " of 
 an article — a matter to be settled between the parties concerned.' In 
 theory words ' postulate definition of outline, whereas as a fact complete 
 definition of outline does not exist in nature ' {Fallacies, pp. 133, 134). If 
 ' night ' is defined as the hours between sunset and sunrise, then 'When the 
 sun sets, who doth not look for night ? ' is analytic. But in the ' land of the 
 midnight sun ' the expression itself is at variance with that definition. 
 
*^Synihetic to-day, Analytic to-morrow ' 239 
 
 they some to seem essential to it — that is, either part of the 
 actual definition per genus et differentiam or derivable from it, 
 and peculiar and proper to the object. Locke gives five 
 essential characters of man. Why only five ? 
 
 § 522. Accordingly, ' what is synthetic to-day may be analytic 
 to-morrow.' But in saying this, we must not be supposed to 
 assent to the common view that every extension of knowledge 
 passes into the notion we have of things. Thus Sigwart 
 observes : — 
 
 ' The more perfect the knowledge, and the richer therefore the 
 meaning of words [but ' therefore ' begs the question], the less 
 room there is for syntheses, in which something new is learned. 
 In the end, synthetical judgement would be limited to that sphere 
 which can never be denoted by words— to the particular fact as 
 it is for any one who has not observed it for himself.' ^ 
 
 He quotes Schleiermacher as limiting the synthetic judgement 
 proper to the sphere of particular facts, and remarks that the 
 distinction is only relative, because the concept is always in 
 process of being formed ; so that ' Ice melts ' by being enun- 
 ciated at once becomes an analytic proposition. Bain takes 
 much the same view,^ and Thomson also. Lewes says : — 
 
 'Synthetic judgements are only analytic judgements in the 
 making. A synthetic judgement becomes analytic as soon as its 
 elements are integrated. Propositions which at first were 
 hypothetical became at last truisms.' ' 
 
 § 523. Such a view renders worthless the distinction between 
 analytic and synthetic judgements. If it be true, no synthetic 
 judgement can be framed mentally more than once ; indeed, on 
 Socrates' obstetrical view that all experience and learning is but 
 recollection, not even once. The moment any circumstance is 
 ascertained, it is bound up in the bundle of our conception, or 
 recognized as being already there. 
 
 § 524. But this is the confusion already adverted to between 
 the way we conceive a thing and the circumstances we happen 
 to know about it. I discover that herrings make good manure. 
 I am informed that English judges are only removable on the 
 petition of Lords and Commons to the Throne. I find that our 
 cricketers usually get their bats at a certain manufacturer's, and 
 
 ' Logic, i. 114, ^ Logic, Pt. I, p, 70. 
 
 * Hist, of Phil. ii. 472, 473. 
 
24P . Analytic or Explicative Judgements 
 
 use balls of a certain weight. Some one suggests to nre that 
 toothache is cured by decapitation. I observe that cheating 
 never prospers, or that beggars are liable to get into the hands 
 of the police, or that barristers virear bands. But is it to be 
 supposed that from that moment those items of information form 
 for me part of the connotation of the names herring, English 
 judge, Oxford Eleven, toothache, cheating, beggar, and barrister 
 respectively; part, that is to say, of these concepts, so that 
 without them the designations herring, &c., would cease to be 
 applicable?' St. Austin says: 'Gratia nisi sit gratis, non est 
 gratia.' But would the Archbishop of Canterbury cease to be 
 Archbishop of Canterbury if he were no longer a member of the 
 Board of Trade or of the Council of the British Museum? 
 
 § 525. A proposition which every one at once recognizes as 
 true need not be analytic. And, on the other hand, there are 
 propositions which rake painfully in the bowels of a conception, 
 and which are likely to win their way to acceptance slowly, if at 
 all, to which we must certainly give the title. An illustration 
 of the former kind is, ' Custom-houses are a drawback to the 
 pleasure of travelling.' Of the latter — ' Art is not a transcript 
 of mere " fact " ' ; or, ' Things are not true apart from a per- 
 cipient mind.' An analytic judgement is always an appeal, 
 always ad hominem. It assumes a common ground of agree- 
 ment or admission between speaker and hearer. But at the 
 same time it invariably makes a demand, sometimes a severe 
 one, upon .the reflective powers. A circumstance may be so 
 familiarly known about an object as to be inseparably associated 
 with it ; yet if it is no part of the notion it cannot be appealed to 
 in an analytical judgement. E. g. ' The Guards, as you know, 
 
 ■• Sidgwick, having correctly laid it down that ' an analytical proposition 
 is one which cannot be denied without contradicting the postulated 
 meaning of the name employed as subject ', deals, I think, inadequately 
 with Bain's assertion [Deductive Logic, p. 70) that ' all newly discovered' 
 properties are real predications on their first announcement, although 
 immediately on being communicated they- become verbal'. Sidgwick 
 says that this is ' in one sense, no doubt, perfectly true ; but the expres- 
 sion needs to be interpreted with care', seeing that 'as a rule, when 
 using a name, we can only have before us quite a small part of its total 
 meaning ' (Fallacies, p. 126). Only if every circumstance we chance to be 
 acquainted with about a thing is part of the meaning of the word, is Bain 
 right. Possibly he is using ' properties ' in a restricted sense — e.g. it is 
 a property of a pyramid to be the form of greatest stability. 
 
Analytic and Synthetic 241 
 
 wear bearskins.' Ruskin, on the other hand, analytically insists 
 that the Guards ought not to do police duty in Ireland. Five 
 people out of six would be quite unable to say what a Quaker is 
 essentially, but every one recalls certain peculiarities of speech 
 and dress which nevertheless are no part of the connotation of 
 the name. ' Teetotallers do not drink champagne ' is analytic. 
 ' Mahometans do not drink champagne ' is not. 
 
 § 526. The confusion between our essential notion of a thing 
 and the list of circumstances we happen to be acquainted with 
 concerning it causes Veitch (among others) to say : — 
 
 ' Logically all judgements are analytic ; for judgement is an 
 assertion by the person judging of what he knows on the subject 
 spoken of. To the person addressed the judgement may con- 
 tain a predicate new — a new knowledge. But the person 
 making the judgement speaks analytically, and analytically only ; 
 for he sets forth part of what he knows belongs to the subject 
 spoken of . . . Logically, every predicate is analytic. It is ex- 
 planatory of what is already conceived in the mind of the subject. 
 It is explicit of the implicit.' ^ 
 
 § 527. Bosanquet holds that ' every judgement is both analytic 
 and synthetic'; for 'judgement always involves identity in 
 difference'.'' His illustration is, 'Caesar crossed the Rubicon.' 
 But to turn over our stock of knowledge about an object and 
 select one fact is not analysis of a concept.' 
 
 Bradley more truly remarks that ' every judgement is essen- 
 tially synthetic '. As already shown, analytic judgements amplify' 
 our consciousness by drawing' attention to something in the 
 subject which has been imperfectly noticed. Even where the 
 expression is tautologous — e. g. ' Such a gratuitous insult was 
 quite undeserved ' — the predicate is fuller of explicit content 
 
 ^ Institutes of Logic, pp. 237, 238, 253. 
 
 ^ Logic, i. 99. 
 
 ' Sigwart (Logic, i. 109, lie) contends that while 'This liquid is sour' 
 is synthetic, because the liquid has first to be tasted, ' This rose is yellow ' 
 is analytic, because, if asked ' Which rose ? ' I answer, ' The yellow one.' 
 Surely not. The answer would be, ' The one I hold in my hand,' or 
 ' The one in the middle of the bowl '. Bain {Logic, Pt. I, p. 6"]) maintains 
 that ' Homer wrote the Iliad'' is a verbal proposition, because we know 
 nothing else about Homer — so that it is as though we said, 'The writer of 
 the Iliad wrote the Iliads But either ' Homer' is the true predicate — ' It 
 was Homer — not a syndicate — that wrote the Iliad' ; or possibly an ill- 
 informed person, recalling the name 'Homer', might ask, 'What did 
 Homer do ? ' ' Homer wrote the Iliad.' 
 
242 Analytic or Explicative Judgements 
 
 than the subject : in this illustration the meaning of ' gratuitous ' 
 was not distinctly before the speaker's mind. As Lewes says, 
 'All judgement is predication, and all predication is synthesis.'' 
 Still, it may be well to keep the name Synthetic for the Kantian 
 sense of propositions which bring the hitherto unknown into 
 relation with the body of ascertained knowledge. 
 
 That every judgement is in a true sense synthetic is itself an 
 analytic judgement. 
 
 § 528. Particular propositions truly such — that is, where the 
 attribution is not regarded as unconditionally valid ^ — are neces- 
 sarily synthetic. For if the predicate were part of the essential 
 notion of the subject it must have been predicable universally. 
 Individual propositions may be quasi-analytic. ' Our giant will 
 want an unusually big bed.' '.The policeman here is sure to 
 keep order.' 'The Primus will of course take the chair.' 
 ' Yonder flagship carries the Admiral.' But identifications are 
 usually synthetic. ' The Prince of Wales is the Heir Apparent.' 
 ' The flagship is the Bucentaure.' Non-connotative terms, if any 
 are strictly such, cannot be the subjects of an analytic judge- 
 ment. But in 'Caesar's wife must be above suspicion' 'Caesar's 
 wife' is tantamount to a common name. Proper names, as 
 shown above (§ 494), are never without some degree of general 
 significance. If Caesar acted otherwise than in a certain way, 
 he would not be Caesar. Men went down before Lancelot's 
 spear at a touch, 'but knowing I am Lancelot.' Juliet asks, 
 ' Wherefore art thou Romeo ? ' 
 
 § 529. It should be observed that an analytic judgement is not 
 so called because it analyses, but because it is based and grounded 
 on an analysis. To assert, or judge, that a notion contains certain 
 elements is the psychological counterpart of asserting, or 
 judging, that a chemical substance or a landscape contains 
 certain elements. The analysis is pre-supposed and appealed 
 to by the 'analytic ' proposition. It lies behind it. This appeal 
 to something acknowledged constitutes the force of the 'scilicet', 
 'eo ipso,' 't]^' 'naturally,' 'of course,' 'necessarily,' ' ex vi 
 termini' or other such phrase, which is either expressed or 
 
 ' Hist, of Phil. ii. 474. 
 
 ° In ' One of the players has to sit out ', or ' semper aliquid certi pro- 
 ponendum est ', or ' Many will always be on the side of right', or 'Some 
 of my friends can invariably be relied on to help me', there is this uncon- 
 ditional validity. See below, §§ 555, 556. 
 
The Analysis Presupposed 243 
 
 understood in every analytic proposition. Or the assumed basis 
 of such a proposition is itself predicated of it — e. g. ' That " hope 
 which is seen is not hope " is implied in the very meaning 
 of " hope ".' ' That " by civility we are distinguished from brute 
 beasts led by sensuality " appears from the actual terms them- 
 selves.' To deny an analytical proposition is to destoy the 
 conception analysed. Goodness is part of the notion of God. 
 Then ' If the gods do evil they are no gods '. 
 
 § 530. Psychological analysis, then, has for its subject the 
 content of a notion or the meaning of a name. It is thus more 
 abstract than the analytical judgement logically based upon it. 
 Being a child implies being an heir. All children, then, (of the 
 kind intended) are heirs ; and if we are children (of God) we are 
 heirs (of God). The subject of an analytical judgement may be 
 an abstraction — e. g. ' Patriotism has necessarily, to some extent, 
 a self-regarding motive.' But the appeal is to what is still more 
 abstract, viz. the connotation of the name 'patriotism', the 
 resolution of the idea. This lies behind any 'analytic' statement 
 we make about the thing. But analysis of the idea, again, may 
 appeal to a dissection of the word (patria, one's own country), 
 Kant remarks that we think the connexion of subject and pre- 
 dicate in analytical judgements through identity. But the fact 
 of the identity has to be given by a prior analysis. 
 
 § 531. If this be so, it does not seem exact to speak of the 
 analytical judgement as a reuniting of the elements obtained by 
 analysis of a concept.^ To do so, writes Sigwart, 'no way 
 contradicts the essence of the judgement, which is to be a 
 oTJi'^ecris vrnitmrav. For the analysis, or decomposition, is only 
 the preparation for the act of judgement, not the act itself; the 
 work of judgement is to restore union between the elements 
 which have been thus distinguished.' In the same way Lewes 
 observes that the concept being shown by psychology to be 
 a synthetic integration of perceptions, ' or their combination into 
 a whole,' and analysis having resolved the concept into its 
 constituent elements, the analytical judgement is a redintegration 
 of the concept which has been resolved.^ But what analysis 
 does is to break up an idea — e. g. ' Being a sailor connotes living 
 
 ^ ' Of a presentation,' is Sigwart's expression (Logic, i. 104). He is 
 speaking of so-called immediate judgements. 
 2 Hist, of Phil. ii. 472. 
 
 R 2 
 
244 Analytic or Explicative Judgements 
 
 on the waves ' — , whereas the analytical judgement based on it 
 does not reconstitute the idea, but fills up the picture of an 
 object — ' A sailor, of course, lives on the waves '. The former 
 tells us what a name implies. The latter tells us what a thing 
 therefore is. The analysis mediates the analytical judgement. 
 It is its logical ground. Thought gives the one. Reason draws 
 the other. Thought explicates the conception. Reason bases 
 on the result the judgement concerning the corresponding thing 
 or things.^ 
 
 § 532. And so we see once more that not even analytical 
 judgements are 'immediate'. Pure reason can no more say 
 what is in a concept than it can say what is in a comet. The 
 idea that a logician ought to know, without being told, what the 
 essential characters of a notion are springs out of the inveterate 
 confusion of Reason and Judgement. If a mind were to be 
 created stored with universal knowledge, still the distinction 
 would remain between propositions as known and propositions 
 as proved. Yet even Mansel asserts that 'analytical judging 
 is formal, synthetical judging is material '.'' It will be remem- 
 bered ' that ' the thinking process is formal when the matter 
 
 ^ In dreams, by some mechanism of the brain, a new circumstance 
 often seems to become known to the dreamer by which a preceding 
 complication is set right or puzzle explained. But lock and key were 
 really made together. The explanation must have been latent there 
 in the sub-consciousness before, or in the moment that, the com- 
 bination which requires solving formed itself in the sleeper's mind, 
 just as the answer to a riddle must precede the question. Thus, what 
 has the semblance of a newly presented fact of experience was really 
 part of the cerebral presupposition. This may seem analogous to the 
 predicate of an analytic judgement being presupposed in the subject. It 
 could not be explicatively enounced unless it were already there. Yet we 
 must not confuse psychic working with rational process. The analytic 
 judgement does not recall by an act of memory, but concludes on the 
 ground of a previous analysis. It infers that, if a characteristic is part of 
 an ideal content, it is actually found in the corresponding objects. 
 Therefore it is logical rather than psychological. 
 
 '^ Lectures and Reviews, ed. Chandler, 1873, p. 50. 
 
 ' Dean Mansel's words are : — ' Formal judging is possible whenever 
 one of the given concepts is contained in the other. If Q contains the 
 attributes OP I can by a law of thought alone determine "All Q is /"'. 
 The law in this case is the principle of Identity, of which the most general 
 statement is, "Every A is A" or " Every concept is identical with itself".' 
 He goes on : — 'Hypothetical and disjunctive judgments are also some- 
 times analytical, and the result of a formal process. For example— if, 
 
Analytic Judgements not ^Formal' 245 
 
 given is sufficient for the completion of the product, without any- 
 other addition than what is communicated in the act of thought 
 itself. It is material when the data are insufficient, and the mind 
 has consequently to go out of the thinking act to obtain additional 
 materials.' ' But no analytical judgement is possible unless the 
 concept is given to reason as already explicated by a previous 
 analysis, which constitutes its rational ground. It takes the 
 form, not, ' A notion composed of ar-ness and jv-ness and s-ness 
 involves ^-ness,' but ' The thing X, because the notion of it is 
 composed of a;-ness and jc-ness and s-ness, is z\ The simple 
 
 having given the judgments "-4 is B ", "C is Z>," I can form solely by an 
 act of thought without experience the judgment, " If A is B, C is D," the 
 process is formal. This I can do when the concepts zx^ given as standing 
 in the relation of operating cause and resulting effect.' But either this 
 knowledge of a causal connexion is given in an extraneous and additional 
 experience — which Mansel supposes not to be the case — or it somehow 
 resides in the judgements ^A is B', 'C is D,' which therefore must be 
 given in some such form as 'A being B is always accompanied by C 
 being D ', or 'A being B always causes C to be Z) '. But where is the 
 advance in thought from suph data to the proposition, 'It A isB, C\s D'} 
 There can, in truth, be no such thing either as formal judging or material 
 concluding. If a ' conclusion ' has been reached by some process outside 
 of, and apart from, the daia, it has not been, in relation to the daia, con- 
 cluded at all, though of course it must have been arrived at from some 
 premisses. Mansel quotes De Morgan's ' challenge ' inference : — 
 
 Every man is an animal. 
 
 Therefore every head of a man is the head of an animal. 
 
 Is this reasoning, he asks, material or formal ? If material — drawn from 
 our knowledge of the subject matter — what business has it in a work on 
 formal logic ? If formal, it can only be reached by supplying what is 
 formally missing. Or, to take another syllogism propounded by De 
 Morgan — 
 
 1 8 out of 21 F's are X's. 
 
 15 out of 21 K's are Z'i. 
 Therefore 12 Z'% (qu. 12 at least?) are X's. 
 
 The reasoning here is valid enough. But, Mansel asks, is it valid in 
 consequence of its form or of its matter ? He proceeds to fill in the 
 missing steps. I submit, however, that the mere non-enunciation of all 
 the steps of an argument does not make it material. It is ' material ' when, 
 the premisses being all given, it is not based upon them. ' Twelve Z's 
 are X's' would be a 'material inference' (so-called) if it were obtained 
 not by reasoning from the data but by inspection of the facts— which is 
 like 'demonstrating' a theorem in Euclid by a yard-measure, or getting 
 the result of a sum right by copying it from the Answers, 
 1 Op. dt. p. 49. 
 
246 Analytic or Explicative Judgements 
 
 pronunciation of the subject term cannot by itself justify a 
 judgement. 
 
 §533. There is a class of 'necessary judgements' in which 
 the subject cannot be conceived as not involving the predicate, 
 yet the impossibility is not a logical consequence of the definition 
 which we have chosen to give to the subject, but is psychological. 
 Such are Kant's 'synthetic judgements a ^r/or/' — e.g. the axiom 
 that a straight line is the shortest way between two points (unless 
 this be the definition of straight line), or that a figure with three 
 angles has three, and only three sides. That a triangle is 
 trilateral Locke considers a trifling proposition, like ' Saffron is 
 yellow ' ; whereas he considers the statement that the external 
 angle of any triangle is larger than either of the opposite internal 
 angles as a ' real truth ', since the predicate ' makes no part of 
 the complex idea signified by the name triangle '. (' Triangle ' 
 is usually defined as a three-sided figure.) Kant rightly gives 
 the name ' synthetic ' to all non-defining geometrical, arithme- 
 tical and algebraic propositions, whether axiomatic or derived. 
 E. g. ' The circumference of a circle is more than three times 
 the length of the diameter.' ' The figures composing multiples 
 of nine always, when added together, make nine, or a multiple 
 of nine ' (9 x 70 = 630 ; 9 x 46 = 414 ; 9x71= 639 ; &c.). 
 ^{a + bY = a^ + 2,ab + W.' Such propositions are necessary ; 
 but the necessitation is not logical, but psychological, proceeding 
 from those intuitions of Time and Space, those pure Concepts or 
 Categories of the Understanding, which Kant places among the 
 a priori conditions of knowledge^ — occasioned and confirmed, 
 but not originated, by experience. Such synthetic judgements 
 a priori are not, as Hume contends, ' analytical judgements.' 
 
 ' A body has extension ' is analytic. 
 
 ' A body has attraction ' is empirical. 
 
 ' A body cannot be in two places at the same time ' is synthetic 
 a priori. (But a ' ubiquitarian ' Lutheran might deny this 
 proposition.) 
 
 ^ A priori signifies with Kant, not rational deductiveness from cause 
 to effect, but a constructive limitation arising from the constitution of the 
 human mind. Lewes (who calls mathematical propositions analytic) 
 describes the Kantian distinction of a priori and a posteriori as ' a logical 
 distinction without psychological validity ' {Hist, of Phil. ii. 463, 484). It 
 is surely just the opposite. It expresses a psychic limitation, which is 
 outside the scope of Logic. 
 
The Appealing Vocative 247 
 
 § 534. A class of quasi-analytical propositions are those which 
 contain an appealing vocative. ' It is good and joyful, brethren, 
 to dwell in unity/ ' My son, give me thy heart.' ' Men of 
 Israel' would prepare a Hebrew audience, and 'Quirites' a 
 Roman one, for patriotic exhortation, of which the vocative 
 clause is the ground. So again, 'Britons, strike home.' (It 
 should be noted that the grammatical imperative is logically 
 a proposition— /wfeo, fas est ut, oportet, debes, -ndum est, or the 
 like, being understood.) 
 
CHAPTER XVI 
 GENERAL AND CONCRETE PROPOSITIONS 
 
 § 535- Synthetic judgements are either general {' Salt is 
 good') or concrete ('The grapes are sour'). 
 
 If analytic judgements are those in which something is 
 predicated of a subject on the ground of a psychological analysis 
 of its idea (e. g, 'All planets move'), General or Abstract Judge- 
 ments are those in which something is predicated of a subject 
 on the ground of an empirical analysis of its nature (e.g. 'All 
 planets move elliptically '). A connexion of cause, rule, or 
 principle is understood — e. g. ' The noblest mind the best con- 
 tentment has.' 'A merry heart goes all the way.' 'XaXeTro, 
 TO. KoXa..' 'Securus iudicat orbis terrarum.' 'II faut souffrir 
 pour etre belle.' ' Toute civilisation est d'origine aristocratique.' 
 ' Truth never goeth without a scratched face.' 
 
 § 536. In a Concrete Judgement the ground of the predica- 
 tion does not reside in the subject- term,' but in the contingent 
 circumstances of the particular objects which are for the moment 
 being spoken of. ' All planets (i. e. all the known planets) move 
 from west to east.' Again, all brooms sweep ; but only some 
 brooms, or this broom, or all the brooms in a particular place, 
 sweep clean — by reason, namely, of something in their nature, 
 such as newness. If this characteristic be added, we get a 
 general proposition — all new brooms sweep clean.' 
 
 ^ In ' Some neglected infants die' 'neglected' is part of the cause of 
 death, but not the entire cause. For in that case all neglected infants 
 would die. If the contributory cause, ' because they are weakly,' be 
 expi'essed, a general judgement is at once suggested — ' All neglected 
 infants which are weakly die.' 
 
 ' Sidgwick considers that 'every proposition may be viewed as saying 
 that one thing indicates, or does not indicate, a certain other' — whether 
 implication be intended (analytical judgement), or the circumstance that 
 one fact is material evidence for another (synthetic). As, however, under 
 the latter head ' indication ' (symbolized by ->) has to cover assertion 
 both of law and fact (abstract and concrete propositions), he admits 
 
Ground Indicated 249 
 
 § 537. The ground of a general proposition may be indicated 
 expressly in the subject. ' The hireling fleeth because he is an 
 hireling.' Or some element of the subject suggests it — 'A 
 rolling stone gathers no moss' — because it rolls, and rolling 
 things gather nothing. 'The early bird finds the worm' — 
 because it is early, and what is early finds what is about. 
 A major premiss is appealed to in the background. The general 
 proposition here unfolds into the syllogism without going outside 
 the statement for a middle term. All BA's are C because B'& 
 are C (and every BA, of course, is B). 
 
 § 538. But more often the middle term must be sought, 
 inductively or otherwise, outside the proposition. ' Blessed are 
 the meek.' Why? 'For they shall inherit the earth.' All 
 A'b are C, because they are B, and every B is C. 
 
 § 539. An epithetical, equally with a determining, element in 
 a subject will often indicate the ground of predication — e. g. 
 ' Royal Windsor has great historic interest ' ; ' Mortal men 
 should prepare for eternity ' ; ' Uncertain riches are not to be 
 desired.' But the ground, being assumed, runs the risk of 
 petitio principii. 
 
 Sometimes the connexion of thought is adversative. ' Threat- 
 ened men live long'; 'Mortal man recks little of eternity'; 
 ' The daughter of a hundred earls, you are not one to be desired ' ; 
 * Great kings love tarts like other folk ' (Elia) ; ' The cobbler's 
 wife goes worst shod'; 'Hard words break no bones'; 'The 
 wicked flee when no man pursueth.' In such propositions one 
 element of the subject often supplies the ground, and another 
 element the adversation. Thus, 'Faithful are the wounds of 
 a friend ' ; ' Blind Love will find out the way.' All BA's are 
 C because they are A, and in spite of their being B. But 
 
 a ' certain harshness ', and that to find ' indicates ' in ' Bavius is a fool ' is 
 clumsy. Yet he holds that 'no word appears better suited for the 
 purpose' {Fallacies, pp. 59-61). But in most concrete propositions there 
 is nothing whatever in the subject to indicate that the predicate is to be 
 expected, for an indication must refer to some law or general connexion 
 behind it. Sidgwick himself says that in a concrete proposition the 
 subject does not indicate the predicate ' except by virtue of the special 
 circumstances bound up with the thing most prominently denoted there 
 as subject ' (ibid.). Besides, it is more natural to regard predicates as 
 indicating subjects {ratio cognoscendi). E.g. 'A bad workman blames 
 his tools.' 
 
250 General and Concrete Propositions 
 
 in a negative adversation the subject is often a single word— 
 e. g. ' Compliments butter no parsnips.' 
 
 § 540. In such a proposition as the famous * canis vivus 
 melior est leone mortuo ' (Elizabeth was the former and Mary 
 the latter) the ground is indicated in subject and predicate 
 together ; and there is also an ' albeit ' in both. A live dog, 
 because alive and though a dog, is better than a dead lion, 
 because dead and though a lion. 
 
 § 541. It will be observed that every general proposition 
 involves an if and also a because. ' Every X is Y' means that 
 if anything is X then, because it is X, it is Y. 'A burnt child 
 fears the fire ' is equivalent to ' If a child has been burnt, then 
 for that reason it fears the fire'. But the 'for that reason' may 
 need a good deal of further explicating. Thus, the proposition 
 ' Months without an "r" in them are not good for eating water- 
 cress playfully suggests a causal connexion, though the unfitness 
 of the months May to August for the purpose has nothing to do 
 with spelling. 
 
 § 542. ' Causal connexion ' must be taken as covering every 
 kind of universal relation between subject and predicate involving 
 a rule, principle or generalization. Logic is only concerned 
 with subjects and predicates, in the two relations of general 
 statement and concrete fact. To the metaphysician 'A green 
 Yule makes a fat churchyard ' is the same statement as ' A fat 
 churchyard is caused by a green Yule '. But the logician looks 
 to the form of the predication. 
 
 § 543. He is not concerned therefore with the distinctions — 
 often difficult to discriminate — in the relation of predicate to 
 subject which underlie the verbal expression.^ This, as we 
 saw above (§ 218), sometimes expresses a sign (' Creaking boots 
 have not been paid for '), but more often one of the following 
 ontological relations : — 
 
 ^ De Morgan (Formal Logic, p. 49) observes that the Copula is used 
 in different senses according as names, ideas, or objects are intended, 
 (a) 'Man is animal.' The name 'animal' can be applied to whatever 
 objects ' man ' can be applied to. 0) ' Is ' signifies the possession of 
 constitutive characteristics (' Three are a quorum ' ?). (y) ' Is ' signifies 
 identity with an external object. ' Man is one of the animals.' Touch 
 him and you touch an animal. We identify the objects, but not the 
 names or the ideas. These distinctions, however, are superficial and of 
 no logical value. 
 
Connexion of Subject and Predicate 251 
 
 Condition. The righteous shall be rewarded. 
 
 Possession of attribute. Porcelain is brittle. 
 
 Class-reference. A lion is a large cat. 
 
 Activity. Evil pursueth sinners. Water finds its own level. 
 
 Character. The raven chides blackness. 
 
 Production of effect. The good are happy (simultaneous). 
 Fire melts wax (gradual). 
 
 Equation. 6x is gy. 
 
 Identification. Maro is Virgil. \/i6 is 4. 
 
 Definition. Dirt is matter out of place. 
 
 § 544. The above relations, except the first and last, belong 
 also to Concrete Propositions, in the form, however, of mere 
 empirical antecedence and accidental fact. ' The fire is out ' ; 
 ' Three men are at the door ' ; ' Some people can eat meat un- 
 cooked.' But in ' The blind man fell into the ditch ' a narrative 
 judgement indicates a cause. 'Existential' judgements are 
 usually concrete, but not always — e. g. ' In much wisdom is 
 much grief (Eccl. i. 18). 
 
 §545. Regarded from the point of view not of the subject, but 
 of the predicate, the significance of predication may be described 
 as class-inclusion, genus, difference, attribution, inherence, 
 quality, concomitance, co-existence, effect, consequence, sign, &c. 
 
 McCosh remarks : — 
 
 ' The logician does not require to consider what is the nature 
 of the dependence of the consequent on the antecedent, whether 
 it is in things or in thought, whether it is or is not the relation of 
 cause and effect, or whether the relation of cause and effect is 
 necessary or contingent. He leaves all these questions to the 
 investigator or the metaphysician. To him the relation of the 
 two [propositions] is given, and he has to consider the discursive 
 thought involved in the relation.' ^ 
 
 § 546. The propositions here spoken of are the antecedent 
 and consequent in a Hypothetical Judgement. If A is B, it is C. 
 Or, if A is B, C is D. But, as will be shown, the ordinary 
 categorical judgement, if general, is essentially hypothetical. 
 ' Every BA is C ; i. e. If any A is B, it is C — , and for ' the two 
 propositions ' we can substitute ' the two terms '. Logic does 
 not go into ontological questions. It is satisfied with the state- 
 ment that given, or assuming, an antecedent condition, a certain 
 
 ' Laws of .Discursive Thought, p. 107. 
 
252 General and Concrete Propositions 
 
 consequence will hold good. The ' hypothetical or abstract 
 affirmation of necessary connexions ' (Bosanquet) is the universal 
 judgement. At bottom a categorical general proposition like 
 ' Every bullet has its billet ' is analogous to — 
 
 If Candlemas Day be fine and fair, 
 Ye've half the winter to come and mair.^ 
 
 'Who sleeps dines' is equivalent to 'If any one sleeps, he 
 dines '. 
 
 § 547. If any philosophic distinction is to be drawn between 
 a categorical general proposition and a hypothetical, it must be 
 by reserving the latter name for the subjunctive mood in the 
 past tense, suggesting the improbability of the condition being 
 realized. ' If all the sea were ink, and all the trees were bread 
 and cheese, what should we do for drink ? ' But even so, the 
 distinction is only on the surface. ' If any A were B it would 
 be C can be expressed in the form, ' Every BA would be C 
 
 ' The north wind brings snow ' is general. ' The north wind 
 doth blow' is concrete. The former proposition expands thus — 
 If the wind be a north one (blow from the north) we shall have 
 snow. Supply now the minor premiss, ' The north wind doth 
 blow,' and the conclusion follows, 'We shall have snow.' As 
 regards a judgement like this, 'All living things are now asleep,' 
 we notice that what is asserted is a concrete circumstance, and 
 yet the judgement has not been arrived ait perceptively, by 
 enumeration, but as a deduction from an abstract judgement. 
 ' All living things sleep at midnight. This is midnight. Then all 
 living things sleep now '. But ' sleep ' here is not concrete, ' are 
 sleeping,' but abstract, 'are of a kind to sleep,' 'may be expected 
 to sleep.' From this conclusion we get, by the raiio essendi, 
 ' All living things, then, are now asleep.' 
 
 § 548. Conversely, every hypothetical proposition is a general 
 one. The same is the case where there is an antecedent clause 
 introduced by when, where, as often as, or similar conjunctions. 
 ' Ubi amor, ibi Trinitas ' ; ' Where the bee sucks, there lurk I ' ; 
 ' When the age is in, the wit is out ' ; ' While there is life there 
 is hope ' ; ' When the cat 's away, the mice do play ' ; ' Wher- 
 ever we tap organic nature, it seems to flow with purpose' 
 
 ' Si sol splendescat, Maria purificante, 
 Maior erit glacies post festum quam fuit ante. 
 
Numerical Quantifications 253 
 
 (Romanes). The form ' No X is Y' is illustrated by ' It is not 
 night when I do see your face '. Such conjunctions do not lose 
 their local and temporal significance — e. g. ' dum spiro spero ' — ; 
 but, says Sigwart, 'we cannot state that two events will happen 
 together in the future, or that they will always and unconditionally 
 take place together, unless there be some necessary connexion 
 between them.' * 
 
 § 549. A general proposition imports that in every case where 
 the antecedent condition exists the consequent is found. But 
 many general assertions seem to have a quantification which is 
 less than universal. The following are some examples (see 
 also below, § 581) :— 
 
 Half a loaf is better than no bread. 
 
 One swallow does not make spring. 
 
 Multi homines unus populus. 
 
 No two minds think alike. 
 
 Ten to one is no impeachment of valour. 
 
 Three generations make a gentleman. 
 
 Three removes are worse than a fire. 
 
 Fifteen millions of people must give way to forty (Napoleon). 
 
 Two of a trade never agree. 
 
 A corsaire corsaire et demi. 
 
 One half the world does not know how the other half lives. 
 
 Two 's company, three 's none. 
 
 Two blacks do not make a white. 
 
 Much cry, little wool. 
 
 A little leaven leaveneth the lump. 
 
 One soul outweighs the world. 
 
 Two straight lines cannot enclose a space. 
 
 Duobus litigantibus, gaudet tertius. 
 
 Ten thousand difficulties do not make one doubt. 
 
 A thousand years in Thy sight are as one day. 
 
 Better fifty years 'of Europe than a cycle of Cathay. 
 
 Much study is a weariness of the flesh. 
 
 If the last example meant that a great deal of study is a 
 weariness, but not all, it would be a particular judgement. 
 It would be particular if ' Many waters cannot quench love ' 
 meant that a large proportion cannot, but others can. Cf. 
 ' Much rain wears the marble ', ' Of making many books there 
 
 ' Logic, i. 218. 
 
254 General and Concrete Propositions 
 
 is no end^, in like manner. Equally ' Nine tailors make a man ' 
 would be particular if the meaning were that of all tailors only 
 nine succeed in making a man. ' Too many cooks spoil the 
 broth ' would be particular if the words signified that more cooks 
 than we could wish spoil the broth. Or 'A little learning is 
 a dangerous thing ' if it were meant that all the rest is not so. 
 
 § 550. In the above propositions, the numerical or quantitative 
 expressions do not quantify the judgement, but are themselves 
 a qualifying and hypothetical part of the subject. E.g. 'Five 
 sparrows are sold for two farthings ' is equivalent to ' Whenever 
 five sparrows are sold they are sold for two farthings.' Compare 
 'ubi tres ibi Ecclesia'. ' If tailors be nine they make a man': 
 contrast ' Nine tailors are out of work'. ' Much,' 'five,' ' nine,' 
 and the like, are here collective, not distributive. ' Unus homo 
 nullus homo ' is equivalent to ' Every case of unus homo is a case 
 of nullus homo '. ' Many hands make light work ' is not a plural 
 but a singular proposition — 'many' being collective, as in 
 ' Many a little makes a mickle '. ' Where there are many hands 
 they make light work.' Similarly, ' One fool makes many,' or 
 'Haifa truth is ever the blackest of lies'. 'The many fail, the 
 one succeeds ' may be regarded either as antecedent and con- 
 sequent — ' Where the many fail the one succeeds ' — or as two 
 particular propositions, either of which, however, is a generaliza- 
 tion. (' Cf ' A few pray ever, many not at all '.) ' They that run 
 in a race run all, but one receiveth the prize ' is, taken as an 
 entire proposition, general (TravTes /a€v . . cTs 8e). But of the 
 clauses taken separately, the former is universal, the latter 
 particular. 
 
 § 551. General propositions maybe expressed in thousands of 
 different forms. A variety of examples is given in Appendix 
 K. The word 'all' itself introduces a number of universal 
 relations. Thus — 
 
 1. All the rocks are dangerous. 
 
 2. All the rocks are now submerged by the tide. 
 
 3. All rocks are fragments (rocks are always fragments). 
 
 4. The rock is all porous. 
 
 5. The rock is always slippery. 
 
 I and 2 are concrete universals ; ' but in the former case a 
 
 ' It should be noticed that Aristotle seems to use the word 'universal' 
 of abstract judgements only, where there is an essential connexion between 
 
General Statements about Concrete Things 255 
 
 permanent quality, in the latter a temporary circumstance, is 
 predicated. 4 and 5 also have a concrete subject ; but in 4 a 
 unity of continuous parts is asserted of it, in 5 a unity running 
 through successive moments. 3 alone is a general proposition 
 of the normal type. ' All ' is collective in Byron's lines : — 
 
 All that tread 
 The globe are but a handful to the tribes 
 That slumber in its bosom. 
 
 But 'totus mundus stultizat' (Francis II to the Hungarian Diet), 
 like the French ' Tout le monde s'amuse ', has a distributive 
 sense. 'All the world's a stage 'is best classed as collective. 
 Equally ' All the men were about twelve ' (Acts xix). 
 
 § 552. A single point of time must be concrete. Yet the 
 proposition may contain an abstract and general element. 
 E. g. ' All the children in France are at this moment learning 
 geography.' Marks of time may be recurrent. ' May 29th is 
 Oak-apple Day'; 'July 2nd is the day my brother died.' 
 'July 2nd, 1866 ' would be merely narrative. 
 
 § 553. The more or less of abstract character attaching to the 
 subject of a proposition, and determining the proposition as 
 abstract or concrete, need not appear in the expression. We 
 can say, 'A wet June puts all in tune,' or ' A wet June spoilt the 
 hay-crop last year'. ' A ' signifies one of a class. The definite 
 article often expresses a type. We can say, 'The lion is the 
 king of beasts,' or ' The lion inhabited Palestine in David's time'. 
 Take next an 'abstract ' notion.* ' Procrastination is the thief 
 of time ' (general). ' Procrastination lost him his one chance ' 
 (concrete). Infinitives and verbal nouns are abstract. But we 
 can equally well say, ' Their strength is to sit still,' or ' Their 
 
 subject and predicate. 'K.aBoKov 8e Xcya 6 hi Kara iravros re {mapxn kol koS" 
 avTo Koi 17 avTo (An. Post. 73 b, 26). See also Sigwart, Logic, i. 175. 
 Sigwart observes : ' The statement that it is false that all men are sinners 
 (in the sense of sinfulness inherent in their nature) does not tell us that 
 some men are actually not sinners ; and the empirical judgement " All men 
 are sinners" might still be true, "because all have sinned" ' (p. 174). 
 
 1 It is not the ' abstract ' name which makes the abstract judgement. 
 As Sidgwick points out {Use of Words, p. 254), the distinction between 
 abstract and concrete refers to judgements only, and not properly to names 
 apart from their context in predication. Yet we can hardly avoid giving 
 the name abstraction to the mental process which obtains the idea of 
 blueness from blue objects, of untidiness or punctuality from untidy or 
 punctual people. ' Angle, angular, angularity ' is the order of abstraction. 
 
25S General and Concrete Propositions 
 
 strength was to sit still'; 'Seeing is believing,' or 'Seeing was 
 believing ' ; ' Writing makes an exact man,' or ' Writing made 
 him an exact man '. The line ' solamen miseris socios habuisse 
 doloris ' makes equally good sense whether we understand ' est ' 
 or 'fuit'. 
 
 § 554. Particular expressions like sometimes, often or seldom, 
 do not destroy the general and abstract character of a proposition 
 if the quotiens, instead of quantifying it, is made part of the 
 predicate.^ E. g. ' All children are occasionally troublesome ' ; 
 • dormit aliquando, numquam moritur, ius ' ; ' nemo mortalium 
 omnibus horis sapit ' ; ' Every good servant does not all com- 
 mands ' [Cymbeline) ; ' interdum stultus bene loquitur '; ' Great 
 poets sometimes nod.' But this, said of any individual poet, — 
 ' aliquando bonus dormitat Homerus ' — would be more naturally 
 regarded as particular. ' The wicked sometimes die repentant ' 
 must be particular ; for no one dies more than once. So also, 
 ' Second thoughts are not always best,' or ' Misfortunes seldom 
 come singly '. 
 
 § 555- -^nd yet these particular judgements are in a sense 
 generahzations — Hke Escalio's 'Some rise by sin, and some by 
 virtue fall',* or 'Time pleases some, tries all'; or 'One man 
 holding truth, A million fail, confounding oath on oath'; or 
 'Souvent un beau desordre est un effet de I'art'. I can reflect 
 on them, and apply them to this or that case. If it be an 
 observed truth that the wicked sometimes die penitent, then this 
 case of a wicked man dying may be such a case. I can apply 
 the generalized possibility to the minor term before me, and 
 conclude that the possibility, the chance, attaches to it. Again, 
 long experience has taught that ' there 's something comes to 
 us in life, but more is taken quite away' — in form, a pair of 
 particular judgements. But I apply the aphorism as a guiding 
 principle to my own career. 'Some innocents scape not the 
 thunderbolt ' is said, in Antony and Cleopatra, with reference to 
 an immediate occasion. Compare, ' Many are called, but few 
 chosen.' The universal and its constituent particulars are 
 combined in Euripides' lines — 
 
 ttSs Tts avTov Tov TTcXas fiSXKov ^iXet, 
 ot fLiv SiKo.iw'S, 01 Se Kat KepSovs 'j(a.piv. 
 
 ^ It may, in fact, become in the predicate a qualifying adjective; e.g. 
 ' rarus venit in cenacula miles ' ; ' deorum est cultor infrequens.' 
 
Generality in Particular Judgements 257 
 
 § 556. Particular propositions may often be regarded as the 
 result of ah induction. For though there can be no causal 
 relation between the predicate and the particular subject, as 
 stated, yet the latter may be understood to answer to a whole 
 nameable class of things. Thus, ' Some rational beings are 
 mortal ' is a generalization, if ' some ' means a certain understood 
 class, viz., all men.^ We can subsume under a formally particular 
 judgement, either, as suggested above, by throwing the occa- 
 sionalness into the predicate, or else by regarding the proposition 
 as itself predicated of the implied sphere of the subject term. 
 Thus — ' Eleven of the twenty-two players in a game of cricket 
 field while two are batting.' This becomes a general pro- 
 position in the form — ' In every game of cricket it is the case 
 that eleven,' &c. Minor premiss — ' This is a game of cricket.' 
 Similarly, ' All the rowers in a coxswainless four must be good 
 watermen ' is a concrete universal as it stands — though to each 
 of the four rowers there attaches a general obligation-^; but 
 expressed thus, ' In every coxswainless four all the rowers,' &c., 
 it is abstract. 'Some are born to greatness' may be stated 
 thus : ' It is always found that some,' &c., or, ' It is found of 
 mankind generally that some,' &c. 
 
 § 557. The essence of a general judgement is invariableness 
 in the bond between antecedent and consequent. Where the 
 former is found the latter will be found. Accordingly, 'Tout 
 comprendre c'est tout pardonner ' is not a whit more universal 
 for the word tout, for which any other quantity might be sub- 
 stituted—half, a little, nothing. So in the proposition, ' Whether 
 one member suffer all the members suffer with it ; now ye are 
 the Body of Christ and members in particular,' the universality 
 of the first clause does not lie in ' all ' but in the asserted 
 connexion. The latter clauses are also general, in spite of the 
 
 ^ Every generic statement may be represented, with reference to a 
 higher genus, as specific and particular ; e. g. ' All negroes are woolly- 
 haired ' tells us that some men are so. But the converse does not follow, 
 that every particular proposition may be replaced by an inferior general 
 one, or, in other words, that every ' some ' stands for a nameable species 
 or group. Thus, some European nations are Roman Catholic, viz. the 
 Latin ones (though this is not quite exhaustive), and here a causal 
 connexion is suggested. But the some European nations who are 
 Calvinistic do not form any racial group, and the statement is purely 
 enumerative and accidental. For an effect is not always traceable to 
 a single cause, but may have different causes in different cases. 
 
 s 
 
258 General and Concrete Propositions 
 
 phrase 'in particular'. Also 'The members of that one Body, 
 being many, are one Body ', in spite of ' many ' in the subject, 
 and ' one ' in the predicate. The proposition is collective. We 
 have seen that there is the same assertion of invariable connexion 
 in seemingly numerical judgements like ' Where two fires meet 
 they do consume ', or ' ubi tres medici duo athei.' ' If two of 
 you shall agree, &c.' 
 
 § 558. A general statement is sometimes an appeal to past 
 experience. Thus — 
 
 Men Were deceivers ever. 
 
 Nemo repente fuit turpissimus. 
 
 Your chestnut was ever the only colour. 
 
 Fear and Savoy have never met. 
 
 Who ever loved that loved not at first sight ? 
 
 Jamais Breton ne fit trahison. 
 
 Nature did never betray the heart that loved her. 
 
 § 559. A law or rule can often be expressed by an imperative 
 and indicative, or by two imperatives, with or without and 
 between them. 
 
 Vive plus, moriere (Ovid; be good and you will die all the same). 
 
 Laugh and grow fat. 
 
 Give a dog a bad name and hang him. 
 
 Go a borrowing, go a sorrowing. 
 
 Love me, love my dog. 
 
 Speak truth and shame the devil. 
 
 Give him an inch and he will take an ell. 
 
 Lege, lege ; aliquid haerebit. 
 Or by a simple imperative, the condition lying in the verb 
 itself — e. g. * Take care of the pence ' (if of anything) ; ' ut 
 migraturus habita ' : if you make your dwelling make it as one 
 who must quit it — or in some other part of the sentence ; e. g. 
 TO. Tuiv Oeuiv xpv </>¥""> 'tota vita discendum est vivere' (Seneca). 
 ' Principiis obsta ' may be expanded either thus — If you are 
 making a stand make it at the outset ; or thus — If you find 
 mischief being hatched crush it. 
 
 § 560. Since generalization is essentially predictive, such a 
 proposition is often stated in terms of futurity — e. g. ' A friend 
 will be proved in adversity'; 'Wonders will never cease'; 
 ' Care will kill a cat ' ; 'Murder will out'; 'A lover's eyes will 
 gaze an eagle blind.' ' Dead men tell no tales ' may be expli- 
 
No Statement is purely Concrete 259 
 
 cated as ' If a man is dead he tells no tales ', or ' he will tell 
 no tales '. Similarly ' Least said, soonest mended.' 
 
 § 561. A general proposition may be in reciprocative form — 
 
 Les esprits forts se rencontrent. 
 
 Iron sharpen'eth iron. 
 
 Sensationalism and nominalism always go together. 
 
 A fool and his money are soon parted. 
 
 Friends have all things in common, 
 Subsumption of a minor is not always easy in such cases — e. g. 
 after ' Great minds think alike ', we cannot go on, ' His is a great 
 mind ; therefore it thinks alike ' — rather, it thinks like other 
 great minds. A complex minor is wanted for St. Augustine's 
 ' non aliunde beata civitas aliunde homo '. 
 
 § 562. From what has been already said it will be plain that, 
 while the distinction between abstract (or general) and concrete 
 judgements is most important — the one implying a de iure con- 
 nexion of principle, the other only a de facto and accidental 
 conjunction of experience — it is not always easy to draw in 
 practice. For, in the first place, no statement can be purely 
 concrete — even ' The clock struck one ' or ' Against the Capitol 
 I met a lion ' asserts something which, being once true, remains 
 true in and through the variety of all future experiences ^ ; the 
 assertion moreover must be based on some intellectual ground, 
 and this is necessarily universal. And, secondly, while each 
 member of a class spoken of generally may be afifirmed to do or 
 suffer something once and only once (e. g. ' The world woke one 
 morning to find itself Arian '), on the other hand a particular 
 or concrete subject may have a general predication — e. g. ' Some 
 generals are always fortunate,' ' None of my sons ever tells 
 a lie.' Such propositions are an enumeration of separate 
 generalizations. 
 
 § 563, Still, there is a clear distinction between ' Guineas are 
 yellow' and 'This guinea is light'; between 'Two men form 
 
 ^ A singular subject, even when associated with a mark of time, is an 
 identity persisting through differences. As Dr. Bosanquet says, in a 
 perceptive and narrative judgement like ' Caesar crossed the Rubicon ' 
 we are referring to a subject known to us not simply as at a particular 
 moment fording that river, but as the conqueror of Gaul, the rival of 
 Pompey and the true founder of the Roman monarchy. Otherwise the 
 mention of his name would be meaningless, and the proposition an 
 identical one. 
 
 S 2 
 
26o General and Concrete Propositions 
 
 a duumvirate ^ and ' Two men formed a duumvirate ' ; between 
 ■ All fat melts with heat ' and ' All the fat is in the fire ' ; between 
 * All the brothers of our family go into the army ' and ' All my 
 brothers are in the army ' ; between ' Brutus is an honourable 
 man ' and ' Brutus helped to kill Caesar '. 
 
 Clearly, ' I shall die rich ' is less a generalization than Pascal's 
 'Je mourrai seul' (a better reading, however, is 'On mourra 
 seul ' ). ' Les Juifs subsistent toujours ' is more ambiguous. Is 
 it a fact or a law ? ^ 'Is there corn in Egypt ? ' was in Jacob's 
 mouth a concrete question. 'Is there no balm in Gilead?' 
 implied that it was to be expected there. When Buonaparte 
 said, ' Every soldier carries a marshal's baton in his knapsack,' 
 he said it generally. But ' Every soldier is carrying a wounded 
 comrade ' would be concrete. ' Every soldier is carrying so 
 many pounds' might be either, according as it were arrived at 
 enumeratively, or as an inference from some regulation of the 
 drill-book. ' No general is over seventy ' might be said after 
 scanning the Army List, or else through acquaintance with a 
 rule about superannuation. ' The rain it raineth every day ' is 
 perceptive. ' In Scotland it rains every day ' might be a grum- 
 bling generalization. 'The British Empire is never at peace' 
 suggests a causal connexion. But Lord Palmerston's ' I never 
 could make out where the British Empire is not' was an 
 enumeration. 
 
 § 564. In English, as an analytic language, it is often easier 
 to distinguish general from concrete judgements than in more 
 synthetic tongues. ' Canes latrant,' e. g., has to stand for ' Dogs 
 bark ' and for ' The dogs are barking '. ' Squalent abductis arva 
 colonis' might mean either 'If the husbandmen are taken away 
 fields get foul,' or, ' Because the husbandmen have been taken 
 away the fields are getting foul.' On the other hand, in the 
 past tense, the auxiliary verb in English, by spreading out the 
 
 * 'All great auks are now e^jtinct.' Is this general or concrete? 'All 
 auks ' is in a sense enumerative — though negatively ; for we have not 
 counted the extinct auks, but only know they are extinct by never finding 
 one — since the class of auks, by the force of the judgement, is limited to 
 the auks which have actually existed. There can be no more. On the other 
 hand, we are saying something generally about auks, that auk-existence 
 is at an end. We are not saying that the auks which empirically have 
 existed are dead ; but that it is impossible that any auks should be found 
 by us again. 
 
Abstract Character of Space and Time 261 
 
 action ante and post, may give a rather more general character to 
 a statement than a bare aorist. Compare ' The wind blew keen ' 
 and 'The wind was blowing from the east'. There is no 
 frequentative aorist in English. 
 
 § 565. It should be observed that, while a point of space has 
 continuance in time before and after, a point of time has conr 
 tinuance in space in all directions. Both, therefore, admit 
 of abstract predication. Always, at this place, such a thing 
 happens. Everywhere, at this moment, such a thing exists. 
 ' The Jungfrau is always hard to climb.' 'To-day is a general 
 holiday.' 
 
CHAPTER XVII 
 
 QUANTIFICATION 
 
 § 566. The foregoing discussion of General and Concrete 
 Judgements brings us to a further elucidation of the Quantify 
 and Quality of Propositions. 
 
 For purposes of inference, the logician has not only to ask 
 whether the subject of the proposed major premiss is quan- 
 titatively definite or indefinite, but whether, as quantified, it is 
 a specified class or object. For ' twenty-six ' is a definite quan- 
 tity, while 'some' or 'a few' is indefinite (dSidpio-Tos). But 
 ' Twenty-six children are ill ' can no more stand as a major 
 premiss (except in equational or ' ultra-dimidiate ' reasonings — 
 (discussed below) than ' A few children are ill ' can. What reason 
 demands is a universal, a statement, that is, about all of a sphere 
 or denomination, whether the circumscription of that sphere be 
 in itself determined or not. It may be an unlimited class, or 
 a class whose limit is known, or even a known individual — all 
 children, all the children, the ten children, both children, this 
 child, John. Such statements can stand as a major premiss, and 
 admit the subsumption of a minor term, which has to be brought 
 under, or identified with, the middle term. 
 
 Take the following inference. ' I won both my games of 
 chess ; one was against X ; I therefore beat X.' Or this, 
 ' Either Y or Z will be the new dean. Y is my oldest friend 
 and Z is my cousin. It follows that either my oldest friend or 
 a cousin of mine will be the dean.' Here ' both my games of 
 chess ' and ' Either F or Z ' are expressions relating to all the 
 members of a class limited to two. The latter, or disjunctive 
 expression, will be considered later. 
 
 § 567. Hamilton's Classification of mental Judgements ^ in 
 respect of quantity may be exhibited thus :— 
 
 ■" Lectures on Logic, i. 243-5 ; 11-278. 
 
Suggested Schemes 263 
 
 Of a whole undivided 
 
 (universal or general 
 
 (I) Definite, or De- ] Propositions) 
 
 terminate (of circum- 
 
 scribed sphere) j qj ^ ^^j^ j^jj^i^ibie 
 
 (individual or singular 
 propositions) 
 
 A single object (Cati- 
 line) 
 
 A collection of single 
 objects (the Twelve 
 V Apostles) 
 
 (2) Indefinite, or Indeterminate (of ) _ p^Hrnlar Prnnn^itiotK! 
 uncircumscribed sphere) \ " Particular i-ropositions. 
 
 But he overlooks the case of numerical (including singular) 
 particular judgements, which cannot be called indefinite as 
 regards quantity.^ 
 
 § 568. I suggest the scheme of Judgements according to 
 Quantity which is given on the following page. In that scheme 
 I have used the word 'total' rather than 'aggregate", because 
 (as Bosanquet points out, Logic, i. 225) an unknown or unlimited 
 aggregate is a contradiction in terms. By an undetermined total 
 I mean that we can predicate about all men, some men, five 
 men, some man, without knowing how many men exist. On 
 the other hand, the expressions all the men, all nine men, 
 some of the men, five of the men, five of the nine men, 
 Clearchus, all imply a definitely determined extension. The 
 class might be further specified, e.g., 'three of the Seven 
 Sleepers of Ephesus.' ' Every ' stands ambiguously for * all ' 
 (abstract), or for ' all the ' (concrete). 
 
 § 569. A minor term can be subsumed under the subject of (A), 
 propositions or identified with the subject of a {B). proposition. In 
 other words, the propositions which fall under {A\ or {B) can be 
 
 ' 'The whole distinction consists in this, that in Universal and in 
 Individual Judgements the number of the objects judged is thought by us 
 as definite, whereas in Particular Judgenients the number of such objects 
 is thought by us as indefinite ' {Lectures on Logic, i. 246). ' Indefinite ' has 
 further to be distinguished from ' Pre-indesignate ', by which name ' Pre- 
 indesignate ' Hamilton merely intends an accident of expression — e. g. 
 ' Fools mock at sin ' ; ' Scotsmen take snuff'. In the' Prior Analytics 
 Judgements are divided into Universal, Particular, and Indefinite. 
 Mr. Stock {Logic, § 49) has revived this distinction. It seems, however, 
 unnecessary to take account in a classification of Judgements of those 
 whose quantity is undetermined, or which are expressed elliptically. We 
 need not know how many 'all' or ' some ' represents, but we must be told 
 whether a judgement is universal or particular. 
 
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Marks of Quantity 265 
 
 used as major premisses, but not those which fall under (C) ', 
 except as explained above (e. g. §§ 555, 556). 
 
 The usual triple division of propositions into universal, parti- 
 cular and singular, evidently needs further elucidation. 
 
 §570. All, every, in a general proposition, signifies not only 
 complete distribution, but an ideal boundlessness of potential 
 application. All the, every one of the (unusquisque) in a concrete 
 universal proposition signifies what Hamilton calls 'definite 
 omnitude'.'' The words which express universality and par- 
 ticularity need careful discrimination — as, omnts, totus, cunctus, 
 universus, singuli, nuUus non, unusquisque, iravn^, oi irai/res, Ikoctto's, 
 •n-as Tts. Again, aliquis, quidam, quisquam, nonnulli, &c. ; Ttves ov, 
 ov ■Tra';, &c. The English marks of quantity are especially 
 meagre and ambiguous. Frequently, of course, a universal has 
 only the indefinite or definite article, or a possessive pronoun 
 (' Your lion is a wild fowl '), and some languages, as Latin, lack 
 even the article.' 
 
 ^ Yet 'some man', even though unidentifiable, might stand as the 
 subject of two affirmative premisses (Darafiti), so long as it were known 
 to be the same ' somebody ' in both. Thus — ' Somebody or other stole 
 my umbrella and afterwards sent it back again. It follows that thieves 
 occasionally have consciences.' The empirical school of writers, in their 
 anxiety to dissolve knowledge entirely into experience of separate facts, 
 set up Darapti as the type of inference — ' X is K and also is Z. Then 
 there is a possible association of Fand Z' (see Bradley, Logic, p. 44). 
 
 " 'AH the X's' assumes that there are X's — hence the great 'the' 
 {a&z.Vj oi •petitio principii. Yet 'AH the KAT's '—All the ^'s which are Y 
 — is less assumptive and more hypothetical. ' All the children must leave 
 the camp ' takes it more for granted that there are such, than ' All 
 children under ten must leave' would do. The latter combines an 
 assumptive with a hypothetical element. This combination is most often 
 found in imperative sentences. 
 
 ' The true Universal or Abstract Judgement cannot be enumeratively 
 exhaustive, for the ' allness ' is not gained by counting up to the point at 
 which an already ascertained totality is reached — as in ' Five of the (twelve) 
 months', 'All the (seven) Champions' — but is the intellectual apprehension 
 of a general principle or law. Such a law may be discovered from a 
 single positive and a single negative instance. It is essentially ideal, not 
 empirically finite. The ' all ' of the generic judgement has no limit in 
 thought, though it may have one actually. Bosanquet regards ' Man as 
 such is mortal ' as the type, and ' All men are mortal ' as a transitional 
 form between this and a collective judgement (Logic, i. 169). He calls 
 'AH men are mortal' exhaustive, and maintains that in it 'form and 
 meaning are at variance '. He fails, I think, to notice that it is not ' all ' 
 but 'aU the' which conveys the idea of completed enumeration. An 
 
266 Quantification 
 
 §571. Quantitative expressions may form part of subject or 
 predicate without affecting the proposition — e. g. ' We are each 
 all Dane in our welcome of thee ' (cf ' totus in illis ') ; ' He is every 
 inch a king ' ; * saepe cadendo gutta cavat lapidem.' ' What is 
 occasional and exceptional may be ignored ' is not a particular 
 judgement, nor in the proposition, ' That which has been held 
 always, ever3rwhere and by all is true,' does the semper, 
 ubique et ab omnibus add anything to its universality. 
 
 The qualification of a notion by a quantitative idea, or the 
 idea of duration or. totality, is of course common — e. g. ' a uni- 
 versal hiss ' (Milton) ' ; ' unceasing praise ' (Sterne speaks of ' an 
 unceasing wife ') ; 'everlasting night' ('in aeternam clauduntur 
 lumina noctem'); 'An eternal sin' (St. Mark iii. 29, R.V.); 
 ' an ever-victorious army ' ; ' a perpetual curate * ; ' Hope springs 
 eternal ' ; ' All partial evil universal good ' ; ' universa vanitas 
 omnis homo vivens'; 'A thing of beauty is a joy for ever.' 
 'There is no smoke without some fire' is universal, not particular. 
 
 § 572. The marks of the Particular Judgement are, in English, 
 such as some, several, many, most, a few, five, one in twelve, 
 a large number, the majority, nearly all, usually, mostly, not all, 
 some not, many not, scarcely any, seldom, not often, not always. 
 Or phrases like 'Instances have been known of, &c. ; or, 'There 
 are who,' &c., cf. ' interdum vulgus rectum videt, est ubi peccat.' 
 ' There is a friend that sticketh closer than a brother ' is parti- 
 cular if no known individual is intended, singular if otherwise. 
 'All the months but one' is particular. 'All the months but 
 March ' is concrete-universal. So 'Ye are clean, but not all', 
 was concrete-universal to the Speaker, who knew who the eleven 
 clean ones were, but particular to the hearers, who did not. 
 
 § 573' The following are various examples of particular pro- 
 positions — though from another point of view, as we have seen, 
 many of such judgements may be regarded as generalizations 
 within a large sphere of discourse (It is a rule found true oi A'& 
 that some of them are B's) : — 
 Non omnia possumus omnes. 
 Man in the aggregate lives principally in Asia. 
 
 ' all ' gained by counting must be in relation to an ascertained totality ; 
 for enumeration cannot be the warrant of its own completeness. In an 
 abstract judgement we might count on the fingers for ever without attaining 
 to all-ness. How many in such judgements is alH 
 
Particular Judgements 267 
 
 The Austrian empire consists chiefly of health i*esorts. 
 
 We are not cotton-spinners all. 
 
 En rdalit^ peu de personnes ont le droit de ne pas croire au 
 Christianisme (Renan). 
 
 Some truths are found in each school, but not all in any 
 (Heylin). 
 
 Non omnis fert omnia tellus. 
 
 The poor in a loomp is bad. 
 
 All flesh is not the same flesh. 
 
 Ridentem dicere verum Quid vetat ? 
 
 Loan oft loseth both itself and friend. 
 
 Great men are not always wise, neither do the aged understand 
 wisdom. 
 
 Something is rotten in the state of Denmark. 
 
 We find 
 Many for many virtues exceUent, 
 None but for some, and yet all different (R. and Juliet). 
 
 Non semper erit aestas. 
 
 When I shout Murder! I am not always being killed 
 (Carlyle). 
 
 Cucullus non facit monachum (not necessarily). 
 Nihil est ab omni parte beatum. 
 
 'Tis seldom when the bee doth leave her Jiome 
 In the dead carrion (Henry IV). 
 
 Geniuses do not grow on every hedge. 
 
 ov)^ airavra tm yigpa Kaxa. 
 
 The race is not always to the swift. 
 
 Monarchs seldom sigh in vain. 
 
 They rode back but not, Not the six hundred. 
 
 Fades non omnibus una. 
 
 Non quicquid morale est bonos mores facit. 
 
 The Few shall not for ever sway. 
 The Many moil and sorrow (Massey). 
 
 Non omnis moriar, multaque pars mei Vitabit Libitinam. 
 
 With which compare — 
 Some parts may perish ; dye thou canst not all ; 
 The most of thee shall 'scape the funerall (Herrick); 
 
 or, Non totus obit, petiit pars caelica caelum; or, Quid moror 
 altera ? (sc. pars mei). 
 
268 Quantification 
 
 In Hellenistic Greek, as in Hebrew, 'not all' often means 
 ' none ' — e. g. o5 StKaiw^ija-eTat TTttcra o-ap|. The Vulgate imitates 
 this idiom — ' non iustificabitur omnis vivens.' Again, ' non 
 est impossibile apud Deum omne verbum ' ; ' non confundar 
 irv' aeternum '. At Eph. iv. 29 we have ■ttSs A,oyos o-awpos Ik toS 
 cTTo/xaTos vjuiiv fj-r] iKTropevc(rdw, where, however, ttS.? precedes /xij. , , 
 
 § 574. Bosanquet observes : — 
 
 'The Plural Judgement, or the Particular of traditional logic, 
 differs in no essential respect from the Singular. It is not, 
 however, accurately described as a mere aggregate of singular 
 judgements. ... I cannot doubt that the plural judgement is 
 a single act of thought. It is not an aggregate of judgements, 
 but a judgement about an aggregate. Therefore the number 
 is to be regarded as a predicated content or determining con- 
 dition attributed to a whole consisting of the units which have 
 been counted up to the point at which the plural judgement is 
 taken.'' 
 
 § 575. The expression ' singular judgement ', however, is 
 ambiguous. We must proceed to examine it. In the scheme 
 suggested above there is a Singular judgement under Universals 
 and a Singular judgement under Particular^ 'Tiberius Caesar' 
 I class with 'all the Caesars', but 'one of the Caesars' with 
 ' four ', or ' many ', ' of the Caesars '. 
 
 Ueberweg states the distinction correctly. He says : — 
 
 ' Singular subjects are to be subsumed under Universal when 
 the subject is definite and individually designated (Caesar, this 
 man), but under Particular when indefinite, or designated only 
 by a general notion (e. g., a man, a great general).'^ 
 
 Hamilton remarks : — 
 
 ' That Individual Judgements do not correspond to Universal 
 Judgements merely in virtue of the oneness of their subject, is 
 shown by this — that if the individual be rendered indefinite, the 
 judgement at once assumes the character of particularity. For 
 example, the propositions, A German invented the art of printing, 
 An Englishman generalized the law of gravitation, are to be viewed 
 as particular propositions. But if we substitute for the indefinite 
 expressions a German and an Englishman the definite expres- 
 sions Fust and Newton, the judgement obtains the form of an 
 universal.'" 
 
 ^ Logic, i. 160, 161. 2 System of Logic, § 70. 
 
 ^ Lectures on Logic, i, 247. 
 
Singular Judgements, how Classed? 269 
 
 § 576. But the erroneous reason which, he says, ' logicians in 
 general ' give for always classing Individual with Universal pro- 
 positions, viz. that ' in both something is predicated of a whole 
 subject, and neither admits of any exception ', would not be 
 erroneous at all if the fact were true. 'Some member of the club 
 has taken my umbrella ' is a proposition about one object, but what 
 is predicated is not predicated of the whole subject (club mem- 
 bers), but of a particular portion of it, viz. one member. The 
 possible extension of the subject term is not exhausted. This 
 will be at once obvious if we take a universal — 'All the members 
 of the club are respectable.' What is predicated is ' predicated 
 of the whole subject', viz. (indefinitely) members of the club. 
 ' The whole of all the members of the club ' would be nonsense. 
 The subject of a proposition is the term about which any thing 
 is predicated, apart from quantification} Through not noticing 
 this, Hamilton goes on to say: — 'A Particular Judgement, like- 
 wise, predicates something of a whole subject, and admits of no 
 exception ; for it embraces all that is viewed of the subject, and 
 excludes all that is viewed as not belonging to it.' It is surely 
 paradoxical in the extreme, as well as meaningless, to say that 
 ' A few novels are worth reading ', states something about a whole 
 subject, and that ' Not many mighty are called ' is an assertion 
 admitting of no exception. 
 
 §577. A Singular subject, then, is to be classed with Univer- 
 sals if individually designated and pointed to — but with concrete, 
 not abstract, universals. If I say, ' All my uncles are dead,' or 
 'My uncle Henry is dead', I can point to a miniature and say, 
 ' That is an uncle of mine,' or * That is my uncle Henry '. It 
 follows that the person whose picture that is is no longer alive. 
 But if I said, ' All of my uncles but one are dead,' or ' One of my 
 
 ' It should be noticed that whereas in ' All horses are quadrupeds ', 
 ' Some horses are timid,' ' Six horses are lame,' the subject is ' horses ', in 
 propositions stated with reference to a pre-determined total, such as ' All 
 the horses, Six of the horses, Some of the horses, are lame ', the subject is 
 not 'horses' but 'the horses'. In 'Two of the six horses are lame' it is 
 ' the six horses '. In fact, the distinction between abstract and concrete 
 universals — 'all ^'s' and 'all the A's' — disappears if this be borne in 
 mind. In the concrete as in the abstract proposition ' all ' will mean ' all 
 possible' — an ideal universality. 'AH my furniture is sold' means all 
 things, whatever they be, which can be described as my furniture, all 
 possible instances of it, are sold. 
 
270 Quantification 
 
 uncles is dead ', the production of the portrait would allow no 
 inference to take place. 
 
 § 578. 'Singular-universals ' have for subject a proper, or quasi- 
 proper, name — Dr. Johnson, Bath, the Blue Mountains, the 
 Medea — ; or a common name used as a proper designation — hall, 
 chapel, dinner, jSao-tXevs, &c. — ; or a name marked out by the 
 definite article or a demonstrative pronoun or in some other 
 way — the oldest member of the House, my mother, last Friday 
 week — ; or a personal pronoun — 'Je suis moi-meme la matiere de 
 mon livre'( Montaigne) — ; or an abstract or quasi-abstract noun — 
 philanthropy, music, fate, art — ; or a collective noun or imper- 
 sonation — man, John Bull, The definite article, of course, 
 frequently designates a class of objects; in which case the 
 proposition is general. Distinguish ' The cleverest boy gets all 
 the prizes ' and ' The cleverest boy got all the prizes '. 
 
 § 579. Sigwart remarks : — ' A concept can never be called 
 singular because there happens to be only one thing correspond- 
 ing to it in empirical reality,' any more than the logical nature 
 of the concept would be affected if there were no object whatever 
 corresponding to it. Only concepts whose characteristics 
 involve the uniqueness of the corresponding object can be called 
 singular. In this sense the centre of the material universe is 
 a singular concept.' " But the form of thought is not affected by 
 the empirical correctness or incorrectness of our conceptions. 
 ' My guardian angel ' is a singular expression even though in 
 fact I have none, or have ten legions. 
 
 § 580. Sigwart, distinguishing singular judgements as indi- 
 vidual ('CalHas is rich'), numerical ('One planet has a ring') and 
 particular (' There is such a thing as a comet which has broken 
 up '), and noticing that the first can, but the other two cannot, 
 be classed with Universals, objects to the ' customary plural ' of 
 the Particular Judgement. 'One man is sinless' is as particular 
 as ' Some men are sinless '. He might equally object to the 
 ' all ' of universal judgements. Nor would ' A is always B','A 
 is sometimes B ' fit every case of a singular proposition. Yet ' A 
 is in this case B ' goes with ' .(4 is in all cases B ' ; and ' .<4 is in 
 one case B ' goes with ' .(4 is in some cases B'. 'I think there 
 
 ^ There was a man who boasted that his father was the only provost 
 of Dundee who had ever swum the Hellespont. 
 ' Logic, i. 271. 
 
'Singular Judgements 271 
 
 be six Richards in the field ' and ' unus homo nobis cunctando 
 restituit rem ' rank together. 
 
 § 581. ' Every single day has its blessing ' is a general, not 
 a singular, proposition. So is 'singulos dies singulas vitas 
 puta' (Manchester al Mondo). Also the following (cf. above, 
 § 549) :— 
 
 One touch of nature makes the whole world kin. 
 
 One soweth, another reapeth. 
 
 Una instantia cadit inductio. 
 
 One good turn deserves another. 
 
 One fire drives out one fire, one nail one nail {Coriolanus). 
 
 One man's meat is another man's poison. 
 
 Ab uno disce omnes. 
 
 If two ride the same horse, one must sit behind. 
 
 One tale is good till another is told. 
 
 Through the ages one increasing purpose runs. 
 
 One may steal a horse, while another may not look over 
 the wall. 
 
 One man can do only one thing (Plato). 
 
 One crowded hour of glorious strife Is worth a thousand 
 years of ease. 
 
 Any stick will do to beat a dog with. 
 
 § 582. Bearing in mind the broad distinction between proposi- 
 tions which can be used as major premisses and those which 
 cannot, it is impossible to agree with Sigwart when he says : — 
 
 'We have no ground for. treating particular and universal 
 judgements as special kinds. There is no more reason in the 
 ordinary logic for regarding judgements having ' all ' for a pre- 
 dicate as a special kind, than there is in mathematics for regard- 
 ing judgements having the predicate ' equal ' or ' infinite ' as 
 a special kind. Hence it is an arbitrary proceeding on the part 
 of the traditional Logic to ask of every judgement whether it is 
 particular or universal.' 
 
 He goes on to observe that — 
 
 ' The Particular Judgement, as ordinarily treated, is one of the 
 most unfortunate and inconvenient creations of Logic' ' Some 
 A's are B implies an empirical knowledge of part of the exten- 
 sion of the subject. Such a formula was rational enough 
 according to the view of Nature taken by Aristotle; a view- 
 which starts from the idea that a fixed and immutable order of 
 
272 Quantification 
 
 concepts has realized itself, and is constantly realizing itself, irr 
 the forms of Nature, and that our empirical knowledge surveys 
 the realization of the concept in all its essential differences." 
 But when the later Logic, dealing only with conceptual relations, 
 and totally disregarding the material realization of the concept, 
 took up the Aristotelian distinction [between universal and par- 
 ticular] and made use of its formulae — or rather of a bad 
 translation of them — the result was a host of absurdities. . . . The 
 Aristotelian to/I virdpx'^i.v, jjurj TravTL virapx^iv, is generally translated 
 by the formula ' Some ^'s are B ' ; but the plural here can have 
 a meaning only when applied to things which are particular and 
 definite, and can therefore be counted ; in which case it pre- 
 supposes a narrative judgement treating of the actually existent. 
 . . . When, however, we are dealing with abstract subjects, whose 
 extension does not consist in a plurality of things, the formula 
 leaves us in the lurch. Must we say, ' Some virtue is justice ' 
 or ' Some virtues are justice ' ? ' 
 
 § 583. Certainly Logic has been cramped by its inherited 
 formulas. But Sigwart's protest against the formula of the 
 Particular Judgement does not seem important. We must have 
 a formula ; and ' Some A's are B ' is more generally applicable 
 than ' Some A is B'. It is true that semper and nonnunquam, or 
 similar adverbs, can nearly always be used, but omnes, aliquot 
 and aliquod not always. Yet we can say ' Some philanthropy is 
 misdirected ' when the subject is an abstract expression, and the 
 proposition quasi-general, as well as ' Some boys have got the 
 measles '. 
 
 § 584. It should be observed, on the other hand, that as all 
 and some qualify a subject, so always and sometimes cannot have 
 an absolute significance, but mean in all cases, in some cases, 
 of the occurrence of the subject. ' Motor cars are for ever getting 
 out of order' does not mean that eternity is filled with such 
 phenomena, but that wherever there is a motor car there is 
 getting out of order. On the other hand, quantitative expressions 
 which have an absolute significance, as five, several, a few, can 
 be separated from the subject. ' Twenty passengers are injured ' 
 —the injured passengers are twenty in number. 
 
 § 585- Quantity, then, though adjectival, does not qualify the 
 subject in the same way that a determining adjective does. 
 ' Gold mines are valuable ' could not be expressed in the form — 
 ' The valuable mines are gold ones.' It should be noticed that 
 
 ' Logic, i. 166, 167. 
 
' Some ' 273 
 
 when quantitative expressions like all and some are exhibited 
 as predicates, their distributive force becomes a collective one. 
 * All cats, some cats, love milk ' — the cats who love milk are the 
 whole number, are a portion, of the class. And whereas 'All men 
 are mortal ' stands for 'are men-mortals', are the human section 
 of the class mortal, this, with 'all' as predicate, becomes, 
 'Mortal men are ail men.' 
 
 §586. Employing the usual signs A and / (Afflrmo) for 
 universal and particular affirmative propositions, and E and O 
 {tiEgO) for universal and particular negative propositions, 
 respectively, A indicates that a dictum must always^ be found 
 true, / that it may be, E that it cannot be, and O that it need 
 not be. 
 
 Or grouping each with its contradictory, A implies that the 
 dictum is necessary, O that it is not necessary, E that it is 
 impossible, and / that it is not impossible. Grouping by con- 
 traries, A and E indicate what is always the case, declare the 
 rule; while / and O indicate what is occasional and excep- 
 tional. 
 
 § 587. / and O do not contradict one another ; — to tlvC, says 
 
 Aristotle, t£ ov rivX Kara T^i/ Xefti/ avriKeuraL /jt-ovov.^ But if 
 
 ' some ' meant ' certain ', the same individuals in both pro- 
 positions, or if the two subjects overlapped — as, ' Most ^'s 
 are Y,' ' Most X's are not Y' — there would be contradiction. 
 ' Some ' must usually be taken to mean ' some at least '. But if 
 a stress is laid on the word, ' some only ' is probably intended. 
 "^Some people think so '■ — meaning that others do not. In this 
 case / and O imply one another. Sigwart censures ' the thought- 
 less habit of substituting the plural " some " for oi ttSs and tis '.' 
 5ras_and ov TToii, says Aristotle, are opposed, ovSek and Io-ti tis.. 
 
 § 588. Though particulars are contradicted by universals, and 
 ' many *■ and ' a few ' are marks of particularity, ' not many ' 
 (= few)' and ' not a few' (= many)* are also particular. Again, 
 affirmatives are contradicted by negatives^ But if ' some ' has the 
 
 ^ Yet while 'All, or some, ^'s are V can be expressed, 'X's are 
 always, or sometimes, Y,' ' All, or some, of ike X's axe Y' requires ' in all 
 instances ', ' in some instances.' ' Some sailors can swim ' = ' Sailors 
 can sometimes swim''. ' Some of our sailors, can swim' = ' Our sailors 
 can in, some cases swim/., 
 
 ^ An, Pr. ii. 15, b-^iT. ^ Logic,, i. 173.. 
 
 T 
 
274 Quantification 
 
 sense of 'some only' (non quivis)} it is contradicted by A 
 iquivis) rather than by E {non ullus). It is the ' only ' which is 
 negated. Sometimes the 'only' when denied is not expressed. 
 ' Not once or twice in our rough island story ', &c. ; i. e. often, 
 ' Not all ' may mean ' not even all ' — as in * Not all the waters of 
 the rough, rude sea ', &c. ; where ' all ' is collective. 
 
 § 589. When the incompatibility of contradictories is expressed 
 disjunctively, the expression is apt to be ambiguous. ' Either 
 every X is Y or it is not ' may mean (i) Every X either is or is 
 not Y; or (2) Either every JT, or not every X, is Y. 'Either 
 some X's are Y or they are not ' can only mean ' Either some 
 ^'s, or not any X's, are Y'. For ' Some ^'s either are or are not 
 y would be an otiose proposition, since this must be true of 
 all .;^'s. 
 
 § 590. NuUus is ne-ullus (ne-unulus), nemo ne-homo, ouSei's oill 
 cTs, none ne-one. Nulli and nonnulli are opposed, rts and orJris, 
 omnis and non omnis. For omnisvie can write nemo non ornullus 
 non.^ Let it be observed, however, that ' omnis X est Y' is not 
 equivalent to 'nullus non-X est Y', but to 'nullus X non est 1". 
 Yet Bishop Stubbs's saying, 'There are two sides to everything 
 — except Reading station,' may be expressed thus: 'nullum 
 non-^ non est Y.' And Maine's remark, ' Except the blind 
 forces of Nature, nothing moves in this world which is not Greek 
 in its origin,' is of the form — 'nullum non-.X' non- Y" est Z'. 
 More simply — 'omne non-XZ est Y'. 
 
 § 591. Interrogations expecting a contradictory reply are 
 answered, A hy O, O by A, E hy I, I by E. Have all gone ? 
 No, not all. Are there some who have not gone ? No, all 
 have gone. Is there no wine ? Yes, there is some. Is there 
 any wine ? No, not any. 
 
 § 592. In O propositions, ' Some X's are not Y,' the negation 
 is thought as attaching to the predicate, not to the quantification 
 (yet for ' Some are not ' we might say ' Not all are '), for it is not 
 
 ' But such a proposition is really a double one — ' Some men only are 
 black ' affirms that some men are black (contradicted by^) and some are 
 not black (contradicted by A). 
 
 ' The latter is sometimes igiore natural than the former. ' Every one 
 of the seventeen prisoners answered to his name ' might be omnis or 
 nullus non. But ' Every one of them has escaped ' would be learned, not 
 by counting up to seventeen, but by seeing the guard-room empty, with 
 not a prisoner in it. 
 
' Some ' 275 
 
 particularity which is denied but universality. We shall see 
 that an O proposition can only thus be converted — Some non- Y's 
 are X. 'Some ^s are not Y' is of the same form as 'Eight 
 X'a are not Y'. ' Not eight ^'s are Y' means ' Less than 
 eight '. In an E proposition, it is, in the given sphere of dis- 
 course, the same thing whether we say, 'No children are 
 experienced' or 'All children are inexperienced'. 
 
 T 3 
 
CHAPTER XVIII 
 NEGATION AND MODALITY 
 
 § 593. If a quantified proposition be denied, the denial must 
 be taken to apply to the quantity only, unless emphasis has been 
 laid on some other word. If I demur to the proposition 'All 
 men are born good', I may perhaps mean that all men are 
 rather born bad or imperfect. 
 
 § 594. In every proposition it is the word or element in which 
 the mind is directly interested which is the real mental predicate, 
 and which feels the force of any negation, even when it comes 
 first in the sentence.' Thus ' All that glistens is not gold ', or 
 ' Every cloud engenders not a storm ', is an O proposition. 
 Compare ' ex quovis ligno non fit Mercurius ', or ' All things are 
 not expedient', or 'Every one cannot (non cuivis contingit) go to 
 Corinth'. In Symmachus's striking expression, 'uno itinere 
 non potest perveniri ad tam grande secretum,' uno is emphatic 
 — not by one road only. In ' They shall not plant and another 
 eat thereof the negation is directed against they and another. 
 Compare ' Men make cities, not walls '. An unintelligent reader 
 might emphasize the word ' cities '. Where a proposition has 
 no marks of quantification, however, the interest is usually in 
 the predicate. Denial then may merely demur to the truth of 
 the predication. E. g. ' The Gracchi were patriotic '. No, they 
 
 ■" For Tras ov see Winer, Greek Grammar, p. 196. The parts of the 
 judgement do not lie evenly in the mind, and the denial falls upon that 
 element on which a mental or vocal emphasis is laid. Thus, ' Thou 
 bearest not the root, but the root thee.' ' The fathers should not provide 
 for the children, but the children for the fathers.' For whatever part of 
 the grammatical sentence the stress falls on is the logical predicate. 
 Even ' the ' may hold this position. ' Ivanhoe is the book to give a boy.' 
 Among books to give a boy Ivanhoe holds a unique place. In Latin, 
 emphasis falls on any word which is in an unusual place — a pronoun, for 
 instance, placed first — ' Vester, Camenae, vester in arduos ToUor 
 Sabinos.' ' Me, me, in me, convertite ferrum.' The French idiom is more 
 analytic than the English — ' The first step only is the costly one ' — ' Ce 
 n'est que le premier pas qui coute '. 
 
The Force of Negation 2']'] 
 
 were not (ils ne /'^taient pas). That this need not necessarily 
 be read, ' No, they were unpatriotic,' is shown by the re-affirm- 
 ing rejoinder, ' Yes, they were.' Such emphasis on the ' copula ', 
 Unless it draws attention to the tense (' fuimus Troes,' ' This was 
 my son '), is the denial of denial. 
 
 § 595. In English ' not ' is usually placed after the ' copula ' or 
 auxiliary verb — ' He is not mad ' ; ' I do not play ' ; ' you cannot 
 go ' — , and in rhetorical or poetical speech after the fyqfm — 
 ' I care not ' ; ' He descended not.' The English tendency is 
 to attach the negation to the predicate. In most languages 'not' 
 stands before the verb. In French, however, ne before a verb, 
 with pas, rien, or personne after it, negates the latter, as in our 
 ' not a soul ', ' not a doit,' ' not an inch.' In English ' not ' or 
 ' never ' before the so-called copula usually negates the tense ; 
 as in Pope's line, ' Man never is, but always to be, blest.' We 
 might say, rather clumsily, ' She not had been, but still was, 
 very ill.' 
 
 § 596. The view of negation expressed by Sigwart seems, 
 then, clearly to be correct, though Bosanquet calls it ' monstrous '. 
 It is, Sigwart says, always directed against a tentative or 
 suggested synthesis:' Accordingly negative judgement is not 
 co-ordinate and equally primitive with positive. It 
 
 ' pre-supposes the attempt, or at least the thought, of an affirma- 
 tion — that is, it pre-supposes the positive attribution of a predi- 
 cate, and has a meaning only in contradicting or annulling such 
 an affirmation. Or rather, the primitive judgement should not 
 be called affirmation at all ; it would be better described as 
 positive. The simple statement, ' A is B,' is an affirmation only 
 when opposed to the negative judgement, and in so far as it 
 rejects the possibility of a negation,' 
 
 He goes on : — 
 
 ' When we consider that only a finite number of predicates 
 can be affirmed of every subject, while an incalculable number 
 can be denied, it is at once evident that the negation has no 
 meaning except in opposition to an attempt at a positive state- 
 ment. . . . No one could say. Justice is not five-cornered, unless 
 there was a chance of some one saying it is''. . . It is impossible 
 
 ' Logic, i. 122 seq. 
 
 ^ ' Negation pre-supposes an idea suggested as true of Reality within 
 a state of facts judged to be true of Reality. . . . The suggestion which 
 denial pre-supposes is not a mere floating content, but a suggested 
 qualification of reality' (Bosanquet, Logic, i. 295, 296). This is clearly 
 
278 Negation and Modality 
 
 to lay down universally and exhaustively what must necessarily 
 be denied of any subject.' 
 
 Kant is wrong in thinking that an 'aoristic ' predication (Aris- 
 totle's pij/xa ddpto-rov) is possible ; as if ' The soul is not mortal ' 
 could mean 'belongs to the infinite sphere of things outside 
 mortal ' (i. e. has one or more of the infinite number of attributes 
 which are not mortality). He says himself that 'negative 
 propositions have the peculiar faculty of simply averting error'. 
 
 § 597. To the question whether the negation affects the 
 copula Sigwart answers that it is so far true that the negation 
 does not lie in the elements of the judgement, but only in the 
 manner in which they are referred to each other. But it is 
 incorrect to oppose a negative to an affirmative copula. The 
 copula represents a unifying mental act ; and the negation, 
 'which holds subject and predicate apart, and prevents the 
 attainment of unity, cannot be a kind of unification. A bond 
 which divides is nonsense.' In negative as in affirmative 
 judgements, the copula expresses the positive judging relation 
 between subject and predicate, the attributing of the predicate 
 to the subject. But it is just this attribution which negation 
 declares to be false. ' The copula does not convey the negation, 
 but is the object of it. There is no such thing as a negative, hut 
 only a negated, copula.' The negation follows the different 
 forms of the positive judgement, and may apply to any part of 
 the grammatical subject or predicate, wherever the true logical 
 predication lies — e. g. ' It is not in my left hand ' ; ' Charles is not 
 coming, but Edward ' ; ' My poverty but not my will consents.' 
 This again shows that it is unable by itself to constitute any 
 definite relation. It merely annuls another statement, and is 
 not directly and independently significant. 
 
 § 598. Aristotle makes affirmation correspond to a composition 
 or unification (cruyiccto-^ai), and negation to a division or severance 
 (Sirifyrja-Oat). But the predicate cannot be thought as a separate, 
 self-existent idea. Spinoza's formula, ' determinatio est negatio,' 
 makes everything to be what it is because it is not something 
 else. A Is B because it is not C, not D, not E, not F, In 
 predicating an attribute, however, we are not asserting our 
 
 seen in sentences like — ' Not as the offence, so also is the free gift' ; ' He 
 is not a Jew which is one outwardly ' ; ' num, quia frater meus es, gratis 
 servies mihi ? ' 
 
The Force of Negation 279 
 
 psychological inability to think anything without discriminating 
 it from other things. We are declaring what the real nature of 
 the subject is. Sigwart might have insisted more plainly that 
 * A is not non-5 ' can only mean, ' is not something which is 
 incompatible with B.' The import of negation is not ' I do not 
 affirm X to be Y', but ' I affirm that X is not Y'. In Greek ou 
 ^ij/ii is the Latin nego, which means ' I assert that not '. 
 
 § 599. From this view that Negation is ' a judgement concern- 
 ing a positive judgement that has been essayed or passed, and 
 only indirectly concerning the subject of the judgement ' ' Dr. 
 Bradley dissents, but I think without cause. It may, however, 
 be objected, If 'X is not Y' means ' It is not the case that X is 
 y ', does not the problem remain where it was ? Have we not 
 simply made the proposition ' X\& Y' the subject of a negative 
 judgement, and how then are we to avoid a regressus ad 
 injimtum ? ' I assert the proposition affirming the truth of the 
 affirmation " that .<^ is F is true " to be untrue ' — and so on. 
 The only answer we can make to this objection is that 'is 
 untrue ' is not just ' is true ' negated, but that ' contrary to fact ' 
 is an ultimate and simple idea, necessarily implied in the notion 
 of unreality. Falsity, like sin, is a metaphysical entity, and not 
 a mere correlative in thought.'^ 
 
 § 600. The attachment of 'not' to the predicate, moreover, 
 only shifts the question for a moment ; for ' not sheep ' means 
 ' that which is not sheep ', and ' unwholesome ' means ' what is 
 not wholesome ' ' — where subject and predicate have reappeared. 
 We have seen that it is only in certain appropriate ' universes of 
 discourse' that not-Y (negative) means un-Y (privative). When 
 
 ^ Sigwart remarks that, if ... is ' states the subject's existence, ' is not ' 
 must deny it, which, he says, is certainly not the case. I have shown 
 above that the verb 'to be ' does connote existence, but not absolutely. 
 'Xhas lis mode of existence as K' 'X is not Y', then, does not mean 
 X is non-existent as Y', but '■ X has its existence as not-K' (or 'It is 
 untrue that X has its existence as F'). Sigwart correctly says: 'The 
 negative judgement in itself states no more concerning existence and 
 non-existence than the afifirmative judgement.' 
 
 ^ Ueberweg dissents from Aristotle's endeavour to find a form of 
 metaphysical existence as a correlate to negation, viz. separation^arro- 
 diams TLVos airo Tiyrfs. 
 
 ' Hobbes held that all assertion is affirmation. ' Pigs are not sheep ' 
 means 'Pigs are not-sheep', as 'Some berries are not wholesome' 
 means ' are unwholesome '. 
 
28o JSlegation and Modality 
 
 it is said that Art is non-moral tliis must not necessarily be taken 
 to mean immoral. Our acutest faculties are non-rational, but 
 not irrational. 
 
 § 6oi. Attached to the subject, ' not ' has no influence on 
 the predication^e. g. ' It is easy not to write an epic poem ' ; ' Not 
 to relent is devilish ' {Ric. II). In Dryden's line, ' Not to wish 
 is not to be deceived,' the second ' not ' must be taken into the 
 predicate — non-JT is non-F— and cannot be understood as 
 qualifying ' is ', which here means ' is equivalent to '. Of the 
 same form are propositions like ' No pains no gains ', ' No cross 
 no crown,' ' Point d'argent point de Suisse,' ' Not in Kent not 
 in Christendom,' ' No penny no paternoster.' Since ' No Jf is 
 y can be expressed thus, ' X is not any Y,' we get judgements 
 such as ' Exchange is no robbery ', ' Self-praise is no recommen- 
 dation,' ' Force is no argument,' ' Killing no murder.' Kmerson 
 declares that nature is no saint. 
 
 § 602. To sum up. In ' No X is Y' it is neither the subject 
 which is negated (non-X is Y), nor the universal quantity of the 
 judgement (Not every X is Y), but the attribution of Yto any X 
 whatever. Take any Xyou please, to say that it is Yis untrue. 
 Accordingly, Every X is non-Y. Only let it be remembered 
 that a notion cannot be entirely negated, but only the inherence 
 of its adjectival in its substantival element.'^ An orange is not 
 black (coloured), — but it has some other colour ; or at any rate 
 there is some substratum of reality which remains undenied. If 
 a predicate were negated in all its parts, ludicrous judgements 
 might be the result. E. g. ' Piteous appeals never reach the 
 rich philanthropist — in vain ' ; 'It never rains — but it pours.' 
 Waller the poet declared that he was unable to read Chapman's 
 Homer — without rapture. We have to look always for the 
 emphatic element in a proposition ; i. e. for its interest. ' He is 
 not badly wounded ' might mean (i) he is wounded, but not 
 badly ; (2) he is badly shaken, or frightened, not wounded ; (3) 
 he is killed ; (4) he is unhurt ; or (5) it is some one else who is 
 badly wounded. 
 
 ' Bosanquet says that the attribute to which is attached the interest 
 that guides the selection of the content used in judging ' cannot precisely 
 coincide with the content denied ; for, if so, no result in which we had 
 an interest would spring from the denial ' (Logic, i. 302). But surely the 
 logical reason is somewhat deeper, and lies in the essential form of all 
 thought. 
 
Proving a Negative 281 
 
 § 603. An idea is always denied as to its entire extension, from 
 which the subject is wholly excluded, but only as to part of its 
 comprehension.^ A square is not a triangle ; but it has- angles. 
 A triangle is not a square ; but it has sides. 
 
 § 604. It is often said that it is difficult to prove a negative. 
 Sir Thomas Browne says that there are no toads, but there are 
 spiders, in Ireland. He had seen a spider there. It is, however, 
 not more difficult to prove a negative than an affirmative — that ' No 
 Scot can see a joke ' than that ' Every Englishman is illogical ', 
 that 'Earth hath not anything to show more fair' than that 
 ' This is the fairest view on earth ' — ; but it is harder to prove 
 a universal proposition than a particular fact. It is only because 
 particular propositions commonly present themselves in a positive 
 form that the opposing universal, with its difficulty of proof, 
 seems usually to be negative. It is easier to show that James 
 came yesterday than that he did not do so, because the former 
 assertion relates to a single event and point of time, and is 
 evidenced by a stick left behind, or a footprint found, while the 
 latter is a general proposition relating to a whole day, and 
 insufficiently proved by stick or footprint not being found. The 
 distinction, then, is between general and concrete affirmations, 
 not between affirmative and negative.'^ These are always inter- 
 changeable — e. g. ' Every one knows ' with ' nemo nescit '. Some- 
 times, no doubt, an enumerative affirmative universal is more 
 quickly verified than a negative — e. g. ' They are all wounded ' 
 than ' They are none of them wounded '. But at other times we 
 convince ourselves more quickly of a negative ; e.g. that not a seat 
 in the concert-hall is occupied — which is seen at a glance — than 
 that every seat is occupied. 
 
 ^ See above, §§ 423 seq. The Port Royalists put it thus : ' The negative 
 proposition does not separate from the subject all the parts contained in 
 the comprehension of the attribute, but only the total and complete idea 
 composed of all these attributes.' To the agriculturist 'not cereal' 
 probably means roots ; as in the tale of the early- Victorian incumbent 
 who had planted the churchyard with oats. The Archdeacon : ' This is 
 very wrong.' The Churchwarden : ' I told en 'twas wrong, and that it 
 should have been turmets.' 
 
 ' Peter Ramus, aged twenty, for his Master's degree at Paris, under- 
 took to demonstrate the thesis, 'Whatever has been said by Aristotle 
 is false' — to prove which every sentence in Aristotle's writings would 
 have to be scrutinized. But the thesis would have been the same in the 
 form, ' Nothing that has been said by Aristotle is true.' 
 
282 Modals 
 
 MODALS 
 
 § 605. Having considered the Quantification of propositions, 
 and also the import of Negation, we are led next to examine the 
 import of Modified Assertion. 
 
 Some modal expressions are seen clearly to attach to the 
 predicate ; others must be considered as qualifying, and as 
 extraneous to, the whole judgement. 'He is happily married' 
 has a different meaning from ' He is, happily, married ' ; ' He is 
 unfortunately circumstanced ' from ' Unfortunately he is dead '. 
 We distinguish adverbial expressions like ' He is plainly dressed', 
 ' grievously sick,' or ' easily convinced ', from ' He is plainly 
 wrong', 'Seemingly he is mad,' and the like. The latter class 
 of adverbs is modal. ' That he is wrong is plain ', &c. 
 
 §606. It is the same distinction which we drew above (§ 571) 
 between quantifying adverbs which are most naturally taken as 
 affecting the predicate only, and those which can themselves 
 become predicates with the dictum as subject. Of the former 
 class are such as ' Sou vent femme varie ' ; ' The dead are always 
 right ' ; ' Les absents ont toujours tort ' ; ' Kings are scarcely ever 
 at leisure ' ; ' They were half-and-half patriots ' ; ' The excellence 
 of the classics lies chiefly in their uselessness ' ; ' The crew were 
 mostly tipsy.' But in ' Kings are scarcely ever cowards ', 
 'Women are often braver than men,' 'The dead are always 
 buried in woollen,' ' The crew were mostly Portuguese,' the 
 adverb might stand outside the proposition — e. g. ' That women 
 are braver than men is in many cases true,' &c.^ . 
 
 §607. The question of Modality, however, arises rather in the 
 
 ' Bosanquet contests Kant's doctrine that ' modality affects only the 
 copula in judgement, and that therefore, though a measure of assertiveness, 
 it is indifferent to the content affirmed '. Both this and the opposite 
 view, that 'modality is a peculiarity of the content affirmed which does 
 not affect the essential act of predication ', ' by separating the asserrive- 
 ness of assertion from the content asserted, represent judgement as an 
 arbitrary and irrational activity. . . . Logical, unlike psychological, certainty 
 depends on reasoning, and is therefore incapable of more or less, and 
 is the chief element in the assertiveness of judgements. It follows that 
 modality is, as Kant said it was not, a characteristic of the content 
 affirmed, but is also, for that very reason, as the modems say it is not, 
 a measure of the assertiveness of assertion. Whether modality must be 
 said to affect the "copula" at all, or the "copula" only, depends on what 
 we mean by the copula ' {Logic, i. 377-9). The traditional logic regards 
 
Modification of the ' Copula ' 283 
 
 case of problematic judgements and those asserted to be neces- 
 sary. Do words like perhaps, possibly, probably, undoubtedly, 
 necessarily, constitute a 'modification of the copula'? Not, if 
 by the copula is meant the assertive force of the proposition. 
 'Mankind,' says Pascal, 'are necessarily mad, and not to be 
 mad is a new kind of madness.' Now ' necessarily-mad ' can 
 have no meaning out of predication. Does then ' necessarily ' 
 here qualify the word 'are'? Or does it govern the whole 
 judgement? That all men are mad is necessarily true. It 
 is not the ' copula ' which is modified ; nor yet the content 
 regarded in itself as a notion; but the content as affirmed. 
 A problematic judgement asserts the subjective mode under 
 which the dictum is regarded as real. The proposition is 
 qualified by a reflective estimate of its more or less of certainty. 
 
 §608. Necessity and probability, as Mansel observes, are 
 products of the act of thought — states of mind, not modes of 
 reality. Psychologically, then, the connexion between predicate 
 and subject is judged problematically. But logically and ration- 
 ally the connexion admits of no degrees. If the one cannot be 
 asserted of the other, it cannot. This is the meaning of the 
 Principle of Excluded Middle (see above, §§ 156 seq.), which lays 
 no emphasis on the content of subject or predicate, but, be the 
 content of ^ and Vwhat it may, asserts that either ^ is Yor X 
 is not Y. 
 
 § 6og. The way in which this or that mind regards a proposi- 
 tion must not be confused with the objective relation of its terms. 
 The subjective confidence or hesitation of the person who judges 
 is a judgement about the judgement — that it is certain or uncer- 
 tain, probable or improbable. Modi sunt relationes ad intellectum. 
 ' Every judgement,' says Bosanquet however, ' may be called 
 assertory in virtue of its psychological reference to self-feeling.' ^ 
 
 § 610. Every judgement is an inference (see § 26). Now an infer- 
 ence cannot but be necessarily drawn. If 5 is probably M and 
 M is P, we may ' probably conclude ' that 5 is P. But this means 
 that we are obliged to conclude that S is probably P. A ' reason- 
 
 the ' copula ' as formal, empty, and indifferent. But, ' if we extend the 
 notion of the copula to include the material or logical grasp by which 
 a complex content is fitted on to a complex Reality, then we may say that 
 Modality is a matter of the Copula.' 
 ' Ibid. p. 389. 
 
284 Mo dais 
 
 able inference' is, qua inference, cogent and binding on the 
 mind which draws it. Butler pointed out that men are logically, 
 and therefore morally, bound to follow Probability, if there is no 
 doubt where the probability lies. 
 
 §611. The doctrine of Chances, in the same way, does not 
 measure the degree of expectation which the individual forms in 
 his mind, but rather the rational ground for supposing that the 
 event will or will not happen as afforded by the knowledge which 
 we possess. Relatively to this knowledge it is a fixed ratio, 
 'The probability of an event,' says Poisson, 'is the reason 
 we have to believe that it has taken, or will take, place.' 
 ' Probability,' says Boole, 'is expectation founded upon partial 
 knowledge.' It would be more correct to say 'justified by' 
 rather than 'founded on' ; for the chances are what I ought to 
 think them, not what I do think them. A peradventure might 
 be calculated mechanically' — So/cel eTvat ahCa filv y rixq, aSi;Xos 
 tl av&pwTTLvrj SiavoLo. (Ar. Phys. ii. 4, § 8). 
 
 § 612. The answer to the question whether the ' copula ' is 
 modified by tense and mood — ' Were I not Alexander I would 
 be Diogenes'; 'Si Cato reddatur Caesarianus erit' — depends 
 on the distinction which I have urged between the verb ' to be ' 
 and the assertive energy of which it is the vehicle. Mill says 
 that the futurity of ' The sun will rise to-morrow ' cannot belong 
 to the predicate since there are not different kinds of sunrising. 
 And, though we might reply that the predicate really is ' a thing 
 which will rise to-morrow", this only postpones the issue. 
 When we have resolved 'Supper will be ready' into 'Supper 
 is a thing which will be ready ', we have still a ' will be ready ' to 
 consider. 
 
 § 613. I think it must be agreed then that the verb ' to be ' is 
 
 . ' Chance is the ratio of the favourable events to all the events, favour- 
 able and unfavourable. Quetelet says that the chance of an event which 
 
 has happened n times happening over again, is ; the adverse chance 
 
 is — ; — . For example, if a man were for the first time to go to the seaside 
 
 and witness on n days the rise of the sea. But see Cajoir, History of 
 Mathematics, p. 340. Mellor {Higher Mathematics, p. 491) gives this 
 formula: — If an event can happen in a ways and fail in b ways, the 
 
 probability of the event happening is =, failing -, . 
 
 a-\-b ° a-^-b 
 
Modification of the ' Copula "" 285 
 
 inflected in thought by tense and mood. But, if the view taken 
 above is correct, the verb ' to be ' is always in thought substan- 
 tive and never has a mere artificial copulative function. It is 
 therefore itself asserted of the subject. On the other hand, this 
 assertiveness of the judgement admits of no temporal or modal 
 modification. It is in immediate contact with the judging ego. 
 Every judgement starts from what is necessarily present — ' I 
 judge ' or ' I assert '. 'The real is such that' — . Sir Thomas 
 Browne observes profoundly that ' Reality, like Eternity, has 
 no distinction of tenses'. Assertion, then, even when not 
 grammatically oratio indkativa, must always be pivoted on the 
 conscious now. 
 
 ^ Logically, says Mansel, ' all thought is the consciousness of present 
 mental acts, and its object is not the past event but the present concept 
 of it. The office of the copula is to declare the present co-existence of 
 two concepts in the representative act of thought ' {Prol. Logicd), 
 
CHAPTER XIX 
 
 IMPLICATION OF JUDGEMENTS 
 
 § 614. Having so far elucidated the character of Judgements, 
 we are able to consider what changes can be made in the form 
 "of a proposition without change of its meaning ; in other words, 
 what differently worded propositions are implied in it. In par- 
 ticular, we have to examine the way in which, when a proposition 
 is converted, its quality (affirmative or negative) governs the 
 quality of the terms. 
 
 § 615. Of the four kinds of Judgement, A, E, I, and 0, the 
 second and third convert ' simply ', the first only ' per accidens ' 
 —All X'a are Y; Some Y's are X. Yet, since 'All X's are Y' is 
 equivalent to ' No X's, are not- Y' (this change is called Obversion), 
 A and E are seen to contain precisely parallel implications. 
 Thus : — 
 'All X's are y ' No X's are Y' 
 
 contain the following implications respectively : — 
 Some ^'s are Y Some ^'s are not-V 
 
 [Some y's are X] [Some not- Y's are X^ 
 
 No X's are not Y All Z's are (No ^'s are not) 
 
 not-y 
 No not- y's are X No Y's are X 
 
 All not- y's are not-Z All y's are not-Z 
 
 [Some not-Z's are not-Y] [Some not-X's are Y'\ 
 
 In these two sets of propositions, wherever Y appears in the 
 one not-y appears in the other. The propositions in square 
 brackets are logically contained in the original proposition, but 
 are meaningless apart from the assumption of the actual exis- 
 tence of the subject. For the existence of such a class of things 
 is assumed in any predicate, but conditional in any subject 
 (see above, §§ 471 seq.). When subject and predicate change 
 places, the condition and assumption shift also.^ Thus, we can 
 
 ' A friend objects : ' Of course, if you use terms which do not correspond 
 to reality, you will naturally get propositions which fail to do so also.' 
 But my point is that the original proposition is not unreal in the same 
 
opposition 287 
 
 say without reserve that all existing mermaidens live in the sea, 
 but not that some existing denizens of the sea are mermaids. 
 The difficulty, however, ceases within an ascertained sphere of 
 discourse— e. g. from ' Mermaids in books always comb their hair ' 
 we can safely infer that some who comb their hair in books are 
 mermaids.^ 
 
 § 616. Every judgement, A, I, E, or O, may be expressed in 
 four simple equipollent modes, from any one of which any of the 
 other three may be obtained. Each is contradicted by a corre- 
 sponding judgement — an ^4 by an O and an O by an ^4 ; an / 
 by an E and an E by an I. The / modes stand in a weakened 
 relation to the A modes, and the O modes in a weakened relation 
 to the E modes. The O judgements correspond exactly to the 
 /judgements, and the E to the A judgements, with the reciprocal 
 exchange of Vfor not- V" and of not- V for Y. Again, while Con- 
 version preserves the affirmative or negative quality of the 
 converted judgement, and also, in the scheme given below, its 
 universal or particular quantity, but interchanges subject and 
 predicate, Obversion, on the other hand, keeps the same subject, 
 with the same quantity, but changes the quality of the judgement, 
 and therefore the quality of the predicate. Thus : — 
 
 Contradictory Propositions. 
 A and its equivalents. O and its equivalents. 
 
 1. Every X is Y {5) Some X 's are not Y 
 
 2. No X is not-V (obverse (6) Some X's are not-F(ob- 
 
 of i) verse of (5) ) 
 
 3. No not-y is X (converse (7) Some not- F's are X (con- 
 
 of 2) verse of (6) ) 
 
 4. Every noi-Y is not-^ (ob- (8) Some not-Y's are not 
 
 verse of 3) not-X (obverse of (7) ) 
 
 way that its converse is unreal. ' Dragons are not ruminant beasts' is 
 not so odd a proposition as ' Some non-ruminant beasts are dragons '. 
 
 ' Yet the sphere may be a misleading one. For example, if 'Every 
 human is mortal ' be expressed thus, ' Every human animal is a mortal 
 animal,' we get by obversion, ' No human animal is an immortal animal,' 
 and from this, by simple conversion, ' No immortal animal is a human 
 animal ' ; which is again obverted as, ' Every immortal animal is a non- 
 human animal,' and this, when converted per accidens, gives us the 
 paradoxical proposition, ' Some non-human animals are immortal animals.' 
 In speaking originally of mortal animals we implied that they were only 
 a portion of the animal class, and that ' mortal ' was a dififerentia. 
 
288 Implication of Judgements 
 
 I and its equivalents. E and its equivalents.. 
 
 5. Some ^'s are not not- F (i) Every ^ is not- Y" 
 
 6. Some X's, are Y (obverse (2) No ^ is F (obverse of (i)) 
 
 of 5) 
 
 7. Some y's are Jf (converse (3) No Yis ^(converse of (2)) 
 
 of 6) 
 
 8. Some F's are not not-X (4) Every y is not-.<Y' (obverse 
 
 (obverse of 7) of (3) ) 
 
 The respective corresponding numbers counterchange Y and' 
 not-y. 
 
 § 617. It is obvious that an A can always by Obversion be- 
 turned into an £ judgement, and an E into an A; an I into an- 
 O, and an O into an /. A cannot, as it stands, be converted" 
 simply, and O cannot, as it stands, be converted at all — that is, 
 ' Some X's are not y implies nothing about Y. But it is the 
 same judgement as ' Some not-F's are X'. And 'AH ^'s are Y" 
 (its contradictory) is the same judgement as ' No not- Y's are X', 
 the contradictory of ' Some not- Y's are X'. O, then, can only 
 be converted by becoming an F proposition. It is true that 
 ' Some students are not persevering ' may be phrased thus : — 
 'The persevering students are a portion only of the student 
 class ' (see below under Quantification of the, Predicate, §§ 662 
 seq.). But this is not a true conversion. 
 
 Mr. A. Sidgwick'" speaks, of 'the important and far-reaching 
 law of Counter-indication '. If the presence of S indicates the 
 presence of P (Every S is P), the absence of P indicates the 
 absence of S (No not-P is S). And if the presence of 5 indi- 
 cates the absence of P (No S is P), the presence of P indicates 
 the absence of S (No P is S).. We might, add that if the absence 
 of S indicates the presence of P (Every non-S is P), the absence 
 of P indicates the presence of S (Every non-P is S). Also, if the 
 absence of S indicates the absence of P (No non-S is P), the 
 presence of P indicates the presence of S (No P is non-S). 
 
 § 618. ' No news is good news ' is an ^ proposition (Every non-X 
 is Y). If it meant that the news which comes is never good, 
 news it would be E (No X is Y). ' Nothing venture, nothing- 
 have ' may be regarded either as A or as E (Every non-X is. 
 non-Y, or No non-X is Y), according as the. second negative is 
 
 ' Fallacies, cap. iv. 
 
Expombles 289 
 
 attached to the predicate or not. The first ' nothing ' does not 
 affect the point at all. Compare the 'non posse peccare maius 
 est quam non peccare ' of St. Thomas, where neither non affects 
 the quality of the judgement (= Every non-^^ is Y). 
 
 'Vita sine litteris mors est' is of the A form ('All non-ZX is 
 Y'). ' Omittance no quittance ' is either A or E. ' He is all 
 eyes and no sight ' may be represented by ' X is non-Z Y'. ' Good 
 wine needs no bush ' is a simple E proposition. The following 
 are more complex universal negatives — ' There is no living, none, 
 if Bertram be away' (no non-ZX is Y). 'Can't be no other way but 
 he must die ' (the same). Similarly ' ubi non est sacerdos non 
 est Ecclesia' (St. Jerome), and 'I am nothing if not critical'. 
 ' No ZX is y represents such a judgement as ' Nothing comes 
 amiss, so money comes withal '. ' Who gives not lives not ' is 
 ' no not-ZX (or no non-X| is Y'. The formula for ' A prophet 
 (X) is not without honour (Y) save in his own country (Z) ' will 
 be ' No non-Z.<Y' is non-F'. More simply, Every non-YX is Z — 
 every unhonoured prophet must be looked for in his own 
 country (i. e. and there only). 
 
 § 619. The limiting word 'only' (jjiovoi) attached to a subject, 
 or ' the only ' (ol fiovoi) attached to a predicate, both in affirmative 
 and negative assertions, requires subject and predicate to change 
 places in order that the proposition may be expressed in the 
 ordinary logical form. Thus ' Only X is Y'. ' Only the sense 
 matters ' = ' The sense is the only thing that matters ' = ' AU that 
 matters is the sense ' (All Y is X). Yet the order is preserved 
 if the proposition be expressed in E rather than in A form — 
 ' Nothing but the sense matters ' (No not-X is Y). ' Deus solus 
 fruendus est, reliqua utenda ' = 'All that is to be enjoyed is God' = 
 ' Nothing that is not God is to be enjoyed '. Again, negatively, 
 ' Not only X is Y.' ' Not only blows hurt ' = ' Blows are not the 
 only things that hurt ' = ' Not all things that hurt are blows '. 
 But this, which is an O, can be expressed as an I, proposition in 
 the form, ' Some things which are not blows hurt ' (Some non-.Z''s 
 are Y), which again preserves the original grammatical order. 
 
 On the other hand, ' only' preceded by the definite article or 
 possessive pronoun marks the subject affirmatively, the predicate 
 negatively. ' Phyllis is my only joy' = ' My only joy is Phyllis ' 
 = 'Only Phyllis is my joy' = 'All my joy is Phyllis ' = ' Nothing 
 but Phyllis is my joy '. ' Only the brave deserve the fair ' = 
 
3^9® Implication of Judgements 
 
 'The only ones who deserve the fair are the brave' = 'All who 
 'deserve the fair are brave ' = ' None but the brave deserve the 
 fair'. Again, ' Phyllis is not my only joy' (or ' My only joy is 
 tncJt Phyllis') = 'Some joy of mine is not Phyllis' = 'Some not- 
 iPhyllis (something besides Phyllis) is my joy'. 
 
 ' Alane ' is equivalent to ' Only the ' — ' The brave alone,' &c. 
 •'In Mm alone 'twas natural to please.* Compare the Latin 
 Mnus — ^'hic unus servat fidem'; 'uni aequus virtuti.' But it 
 :Stands for ' the only ' rather than ' only the ' in sentences like 
 ' una salus miseris nullam sperare salutem '. ' Alone ' also has the 
 ■meaning of absence of associates — ' He drank two bottles alone.' 
 ((See also below, § 6go.) 
 
 'Only" has also a purely adverbial use (/iovov). 'Tears are 
 only salt water.' This maybe expressed in the singular, 'A tear 
 is only salt water ' ; or particularly, ' Some tears are only salt 
 water.' And negatively, ' Tears are not only salt water.' What 
 is spoken of is the nature and composition of each individual 
 of the class. It is nothing else than salt water. Such a use 
 of ' only ' cannot always be easily distinguished from the other— 
 e. g. * We only meet to part ' — each of our meetings is simply 
 a parting; or, all our meetings are partings, — whenever we meet 
 it is to part. 
 
 § 620. In the above examples of implicated judgements is 
 there any illative process ? There has been a change of expres- 
 sion, a shifting, perhaps, of the mind's attitude ; yet the meaning 
 remains the same, or at least — in the case of the converted 
 statement of A, and that of certain weakened implications — is 
 part of, and contained in, the meaning of the original judgement. 
 The logical connexion of the terms has not been modified. 
 ' Nothing which is X is Y' and ' Nothing which is Y is X' are 
 not merely rationally equivalent — for it might be urged that the 
 conclusion of a syllogism is the rational equivalent of the com- 
 bined premisses, but is nevertheless inferred from them — ,' but 
 are the same assertion, viewed from different standpoints. 
 Nothing is both X and Y, both Y and X. Nothing being X is 
 also Y. Nothing being Y is also X. No one combines the 
 
 ^ I am hardly disposed to admit this ; for it is just the rational combina- 
 tion of the two premisses, and elimination of the middle term when it has 
 done its work, in which the inferential process consists. There is nothing 
 like this in so-called ' immediate inference '. 
 
' Immediate Inference ' 291 
 
 characters of bully and brave man. And similarly with particular 
 judgements. Some persons are at one and the same time both 
 knave and fool (/), both knave and wanting in wits (O). Where 
 is the processus mentis, the advance in thought, from convertend 
 to converse? It is objected that the same judgement cannot 
 have two subjects. But the logical judgement can have varied 
 grammatical expression. Are not ' Pictures brighten a room ' 
 and 'A room is brightened by pictures' the same judgement 
 rationally ? ' He did it ', with an emphasis on ' he ', is the same 
 judgement in my mind as ' It is he who did it '. 
 
 § 621. Whatever difficulty exists arises about the converse 
 per accidens, or, as it is called, ' by limitation,' of ^. ' Some Y's 
 are X ', which is contradicted by E, is clearly only a part of what 
 is asserted in ' All X's are Y', which is contradicted by O. If 
 'All X's are Y' meant 'Everything is at once X and Y', it 
 would convert simpliciter. But it means ' Everything which is 
 X is at once X and Y', or ' Y and X'. The subject is hypo- 
 thetical — 'If anything is X' — and does not stand on a level 
 with the predicate. Only when we obvert 'Every X '\%Y' to 
 ' Nothing which is X is not Y' do we obtain an equivalent 
 converse, ' Nothing which is not Y'ls X' ; just as an O proposi- 
 tion, ' Some things which are X are not Y,' can be expressed, 
 ' Some things which are not Y are X' 
 
 § 622. But ' Some Y's, are X ', implied in 'All X's are Y', can 
 only be regarded as obtained inferentially from that judgement 
 if the axiom that the greater contains the less be considered as 
 a mentally supplied major premiss. In which case the inference 
 is mediate, not immediate. The same is the case with ' Three 
 (at least) are dead ' obtained from ' Five are dead ', and with the 
 judgement that a hole large enough for the cat to enter by is 
 large enough for the kitten. Hamilton (ii. 269) calls ' inference 
 of Subcontrariety ' by the name ' Integration '. 
 
 I have already argued (§§ 37 seq.) that the phrase ' Immediate 
 Inference ' is a contradiction in terms. It is admitted that all 
 inference must have a ground. Every statement must have 
 a sufficient reason. But it is urged that a ground or reason is 
 not necessarily a middle term. The original proposition is itself 
 the ground for the one based on it. Having made a statement 
 we are entitled, in virtue of that statement, to proceed to another, 
 just as in mediate inference, having made two statements con- 
 
 u 2 
 
292 Implication of Judgements 
 
 nected by a middle term, we are entitled, in virtue of those 
 statements, to proceed to a third. 
 
 § 623. I submit, however, th^at the two cases are not alike. 
 A pair of premisses, united by a middle term, usually called the 
 ground, present in combination a rational character, and contain 
 an energy bound to issue in inference, in obedience to an 
 ultimate law of Reason, examined in the earlier part of this 
 book. But a simple judgement has in itself no rational character. 
 It is merely intellective. Not wedded to another, it remains 
 unproductive. If another judgement professes to have been 
 inferred from it, the challenge, By what law? claims an answer. 
 In the case of a conclusion from premisses, there is no difficulty 
 about assigning the law of the process. ' Syllogistic reasoning,' 
 says Whately, ' is in truth all reasoning.' ^ 
 
 Not admitting Conversion to be illative, neither can we ascribe 
 that character to Obversion. E. g. 'No X is not Y' (It never 
 rains but it pours) is not an inference from ' Every Jf is Y' 
 (Whenever it rains it pours), but the same logical judgement. 
 
 § 624. To return to the implication of judgements. The 
 bearing of the doctrine of Quantified Predicate on the conversion 
 of ^ will be considered later (§ 672). If, however, we complete 
 and fill up the predicate of a universal affirmative, All X's are Y, 
 by annexing to it the subject as qualifying difference, All X's are 
 XY, predicate and subject become identical in extension. 'All 
 whales are mammals ' means all whales are whale-mammals, 
 form the cetacean section of the mammal class. But not ' are 
 mammal whales ' ; for Y is at least as large a class as X, and 
 cannot determine it as differentia. Yet if the subject have 
 a qualifying and a substantival element, the latter is the sub- 
 stantival element of the predicate also. 'A penny saved is 
 gained ' — a penny saved is a penny gained. Boiled turkey is 
 spoiled turkey. The predicate has a wider extension, presuma- 
 bly, than the subject, though 'turkey spoiled' is narrower than 
 ' turkey ' alone. Compare, ' The word of the Lord is a pure 
 word ' ; ' A vote given to my antagonists is a vote given to the 
 enemies of England.' See above, § 488. 
 
 § 625. On the other hand, it is immaterial whether we say 
 ' Some X's are XY', or ' Some ^'s are YX ' — ' Some kings are 
 royal sages', or 'Some kings are philosopher kings'. It is 
 ' Logic, Introduction. 
 
Implication Shown by Diagrams 293 
 
 immaterial whether we say ' No X's are XY', or ' No X's are 
 yX'^'No women are female voters ', or ' No women are vote- 
 possessing females '. 
 
 § 636. Using the language of Predicables, in / judgements 
 either X or Fmay difference the other ; in O judgements either 
 X or not-Y; in E judgements neither. / and E are therefore 
 convertible simply ; O after obver.sion only. In A judgements, 
 Y is genus to X, unless it chance that they coincide in exten- 
 sion. According 'All ^'s are Y' converts in the form 'Some 
 y's (at least) are Jf'. 
 
 § 627. The following Diagrams will exhibit to the eye the 
 Implication of Judgements. The darker portions show the 
 quantification of X, whether in convertend or converse.^ 
 
 Every X is Y. 
 
 A 
 Some Y's (at least) are X. 
 not Y, &c. 
 
 No X's are 
 
 Y' ■ 
 
 or 
 
 This is contradicted by 
 
 O 
 
 Some X'a are not Y. Some not- Y's are X. 
 
 or 
 
 No ^'s are Y. No Y's are X. 
 All X's are not-Y", &c. 
 
 • I do not mean that ' Some Y's axe. all ^'s ' is a possible judgement 
 (see below, under Quantification of the Predicate) ; but only that, having 
 been given the number of X's that are Y, we know, when we conversely 
 include a portion of the Y class among the X's, how many X's we 
 happen to be speaking about. 
 
294 
 
 Implication of Judgements 
 
 This is contradicted by 
 
 / 
 
 Some Z's are Y. Some Y's (at least) are X. 
 
 
 or 
 
 X ^ 
 
 /and O, being compatible with one another, have the same 
 diagrams, with the darker parts reversed. A and E, being 
 contraries, are entirely dissimilar. In A, X is wholly included 
 in Y. In E, Xis wholly excluded from Y. In /, ^is partially 
 included in, and in O, X is partially excluded from, the sphere 
 
 of y. 
 
 I have preferred to employ rectilinear diagrams instead of 
 the usual circles ; for, if the two classes X and Y chance to 
 make up together the entire extension of Z (as male and female 
 are all human beings), this cannot be shown by circles, though 
 it might be shown by segments of circles. 
 
 § 628. If ^ is true, / is true, E is false and O is false. 
 
 If A is false, / is doubtful, E is doubtful, O is true. 
 
 If £■ is true, O is true, A is false 'and / is false. 
 
 If E is false, O is doubtful, A is doubtful, / is true. 
 
 If / is true, A is doubtful, E is false, O is doubtful. 
 
 If / is false, A is false, E is true and O is true. 
 
 If O is true, E is doubtful, A is false, / is doubtful. 
 
 If O is false, E is false, A is true and / is true. 
 
 In a complex proposition we argue from the truth of an ante- 
 cedent to the truth of its consequent, and from the falsity of a 
 consequent to the falsity of its antecedent. If Mis TV, X is Y; 
 M is A^, then Z is Y; Z is not Y, then M is not N. But in the 
 above implication of judgements it has been erroneously asserted 
 that we argue from the truth of an antecedent to the falsity of a 
 consequent, and from the falsity of an antecedent to the truth of 
 a consequent. E. g. if A be true, O is false ; and if A be false, 
 O is true. But it is not A and O (for example) that are ante- 
 cedent and consequent respectively, but the parts of the state- 
 ment about their relations ; viz. if A be true (antecedent), O is 
 false (consequent). We proceed to argue — A is true (it is true 
 that A is true). Then O is false (it is true that O is false). 
 
Antecedent and Consequent 295 
 
 is not false (it is false that O is false). Then A is not true (it is 
 false that A is true). 
 
 § 629. For the Opposition of Singular Judgements, in which 
 Contrary and Contradictory appear to be identical, see above, 
 § 143 seq. The earth is flat ; the earth is not flat. Brutus killed 
 Caesar ; Brutus did not kill Caesar. Freedom shrieked when 
 Kosciusko fell ; Freedom did nothing of the kind. Yet where 
 any question of degree can enter, the ordinary forms of Opposi- 
 tion reappear. E.g. 'The earth is not altogether flat'. This 
 is an O proposition, contradicting A, ' The earth is (altogether) 
 flat.' 'This egg is not good. Yes ; it is good in parts.' 
 
 § 630. We have seen that 'Every X is Y' implies that every 
 non-Y is non-JT (contrapositive implication), but yields no 
 general proposition about non-Jf or about Y, 
 
 This is the most summary form of the doctrine that the 
 falsity of a consequent carries with it the falsity of the ante- 
 cedent, but that the truth of the consequent allows us to infer 
 nothing about the antecedent, and the falsity of the antecedent 
 allows us to infer nothing about the consequent. For though 
 in metaphysics 'sublata causa tollitur et effectus,' the effect only 
 disappears as an effect of that particular cause, but may still be 
 found as a phenomenon, seeing that phenomena may have 
 more causes than one. 
 
 Yet ' Every .X^ is Y' yields the implicated propositions, ' Some 
 Y's are X' and ' Some non-X's are non-F'. This is as much as 
 to say that, where a consequent is found true, this sometimes 
 implies the truth of the antecedent, and that if an antecedent is 
 falsified there is to that extent a greater possibility of the conse- 
 quent not being found true. 
 
 § 631. An A proposition may be expanded in the conjunctive 
 form — If A is B, C is (always) D. 
 
 An / proposition expands in the form — HA is B, C is some- 
 times D. 
 
 An E proposition thus — If A is B, C is not (never) D. 
 
 An O proposition thus — If A is B, C is sometimes not D. 
 Now from A we can go on — ' If C is not Z>, A is not B '. But 
 from E the assertion that C is not D yields no further judge- 
 ment. The denial of the consequent is here ' C is D '. From 
 / we get, ' If C is D, A is sometimes B,' and from O, ' If C is 
 not D, A is sometimes B.' 
 
296 Implication of Judgements 
 
 The denial oi A being B affords no result in either A, E, I 
 or O. 
 
 The antecedent, of course, might have been, '\{ A is not B' 
 and the consequent, 'C is not D.' 
 
 § 632. In the above expansions, / and O deny any necessary 
 causal connexion or invariable sequence. The antecedent ' If A 
 is B' becomes then in meaning concessive rather than hypo- 
 thetical. Even if ^ be 5 it does not follow that C is never D, 
 that C is always D. 
 
 § 633. The signs of quantity {always, not always, never, some- 
 times) do not qualify in each case the consequent in itself, but 
 the consequence, the nexus. Thus, if ^ is i? it may happen 
 that C is D — not, it must happen that C may be D. E.g. 'If 
 persons are injured sometimes the law can do nothing for them '. 
 Yet the 'sometimes' (or other mark of quantity) will occasionally 
 be merged in antecedent or consequent. E. g. ' If a man be- 
 comes a judge he is sure sometimes to make mistakes'. 'If a 
 clock never goes, it is useless.' 
 
 § 634. One more case of Implicated Propositions arises in 
 what are called Added Determinants. In these, a proposition 
 being granted, it is assumed that a new qualification of the 
 subject involves a similar qualification of the predicate. If a 
 watch is a piece of mechanism, a watch that will not go is a 
 piece of mechanism that will not go. If James is a seaman, 
 James's uncle is a seaman's uncle (has a nephew who is a 
 seaman). 
 
 This is on the principle that any qualifying or determining 
 element in the subject of a proposition reappears, actually or 
 tacitly, as a similar element of the predicate. Thus, beef is 
 food ; then boiled beef is food, viz. boiled food. 
 
 § 635. But care must be taken that the added determinant has 
 an absolute and not a relative significance. Horseflesh is food; 
 but it does not follow that the best horseflesh is the best food. 
 The oldest clergyman is not necessarily the oldest human being, 
 nor a big frog a big animal. 
 
 Again, even when the determinant has an absolute meaning, 
 it can only be safely added to a universal judgement. If some 
 men are Europeans, we cannot proceed to say that some black 
 men are black Europeans ; though it would accidentally be true 
 that some deaf men are deaf Europeans. 
 
Added Determinants 297 
 
 Diagrams, which the student can draw for himself, would at 
 once make it obvious that, in the case of a universal judgement, 
 the subject, however qualified and differenced, falls entirely 
 within, or entirely without, the sphere of the predicate. But 
 that in the case of a particular judgement we cannot be sure 
 that this is so. 
 
 § 636. ' Complex Conception ' is somewhat similar to Added 
 Determination. But on neither — in spite of the textbooks — can 
 an ' immediate inference ' be founded. 
 
CHAPTER XX 
 
 EXTENSION AND INTENSION 
 
 § 637. The Conversion of Propositionis raises two matters 
 for discussion. One is Extension and Intension in predication. 
 The other is the Quantification of the Predicate. 
 
 In converting propositions we seem hitherto to have viewed 
 them as regards their Extension only — transferring the quanti- 
 tative sign from the subject of the convertend to its predicate. 
 
 § 638. The extension of the predicate Y or not- Y must ration- 
 ally be at least as broad as that of the subject X. 'Quotquot Z 
 sunt X tot sunt Y.' And the Y's which coincide with the X's 
 are not merely equal in number to them (so that if the twenty- 
 two cricketers dine together the diners number at least twenty- 
 two) but identical with them. A proposition is not an 
 equation. 
 
 § 639. It must be borne in mind, however, that expressions 
 like all, some only, most, half, all but four, are relative. If all or 
 most or a half of the ^'s are Y, it does not follow that the sphere 
 of the predicate covers all, most, or a half of the F's. Yet any 
 absolute numerical determination of the subject, from nought 
 upwards, will govern the predicate also. 
 
 §640. 'Every X vs, Y' implies that only F's, only things 
 which are Y, are X. It does not imply that only F-ness is to 
 be attributed to the X'&. They have other attributes, such as 
 Z-ness. If every X, then, is Z, only things which are Z are X. 
 It follows that the spheres Y and Z are at least partially co- 
 extensive. If all Cretans are liars, and all 
 Cretans are seafaring men, then (granting 
 the existence of Cretans) some liars are 
 seafaring men and some seafaring men 
 are liars, although the two connotations, seafaring and lying, 
 have nothing in common. 
 
 Even if the extensions of subject and predicate happen to coin- 
 cide, the attributes connoted are not, except in definitions, the 
 
 
 
 
 Y 
 
 El 
 
 z 
 
 
 
 
Hamilton' s Doctrine 299 
 
 same, though they may be causally inseparable. All equilateral 
 triangles are equiangular; but having equal sides is not the 
 same thing as having equal angles. 
 
 § 641. Prior to quantification, the subject concept in a general, 
 or abstract universal, affirmative proposition cannot have a 
 wider extension than the predicate — there cannot be more men 
 than mortals; on the other hand, in a negative or particular 
 judgement there is nothing to show which of the two concepts 
 is the larger. Horses are not cows. Some horses are affec- 
 tionate. Some horses are not affectionate. We cannot, comparing 
 horses with cows, with affectionate, or with non-affectionate, 
 creatures, determine in each case which is the bigger class. 
 But in a concrete-universal judgement — 'All my camels, all the 
 five camels, are stolen ' — , while we have no data for comparing 
 the extensions of ' camel ' and ' stolen ', ' my camels,' ' the five 
 camels ' must be fewer, or at least not more in number, than 
 stolen things. 
 
 § 642. Only, let the caution be again observed, that so far as the 
 two concepts are united in predication, the classes do not merely 
 overlap but are identified. As Dr. Bradley says, ' Hope is dead ' 
 does not mean that in hope and a fraction of dead things there 
 is exactly the same sum of units.' They are identical. 
 
 If some men are negroes, some negroes are men, and the 
 ' some ' stands in both cases not only for the same number but for 
 the same individuals. There could not be one hundred million 
 of men negroes, and another hundred million of negroes men. 
 
 § 643. We have now to ask what is the effect on the conver- 
 sion of judgements of viewing them not in Extension but in 
 Intension, not quantitatively but qualitatively. 
 
 Hamilton considered that the intensive force of propositions 
 had been ' marvellously overlooked ' by logicians.'^ Undoubtedly, 
 
 ^ Logic, p. 24. 
 
 ^ ' If the reasoning under either of these two quantities were to be 
 omitted, it ought, perhaps, to have been the one which the logicians 
 have exclusively cultivated. For the quantity of extension is a creation 
 of the mind itself, and only created through, as abstracted from, the 
 quantity of comprehension ; whereas the quantity of comprehension is 
 at once given in the very nature of things. The former quantity is thus 
 secondary and factitious, the latter primary and natural ' {Lectures on 
 Logic, i. 217, 218). On the other hand, a synthetic judgement can be 
 stated as a relation between classes, but not as the relation of one 
 
300 Extension and Intension 
 
 to say that a subject is contained in a certain class is to say that 
 whatever has the attributes connoted by the subject has the 
 attributes connoted by the predicate expression. And con- 
 versely, possession of the predicated attribute or attributes 
 sometimes at least carries with it possession of the attribute 
 or attributes of the subject expression. That is, if everything 
 qualified by X-ness has the attribute of Y-ness (every X is Y), 
 some at least of the objects possessing Y-ness have necessarily 
 the quality of ^-ness — ^that is, if any objects have it. 
 
 § 644. But, equally, the attribution of a quality to any object 
 implies that that object is part of, or a member of, a class whose 
 extent may or may not be ascertained, of objects characterized 
 by that quality. Conceivably there may be but a single object 
 so characterized. The class consists of one. Yet an extension 
 consisting of one object is still an extension and not an intension. 
 E. g. 'Joshua captured Jericho without a blow'. 
 
 § 645. It seems plain, then, that all predication is simul- 
 taneously in extension and in intension (see above, §§ 189 seq.). 
 ' London is a big city ' ranks London among big cities, and 
 at the same time describes its character. ' Big city ' connotes 
 a quality. Yet ' a ' ( = one) is numerical. No doubt. Extension 
 rests on Intension rather than Intension on Extension.' A rower 
 is one who rows. Yet some have held that language began 
 with proper names — chance designations of individual objects 
 — which were afterwards extended to similar objects, and so 
 acquired a connotation.^ The process still goes on to some 
 extent, proper names becoming common nouns and verbs — e.g. 
 pandar, hansom, sally-lunn, jeremiad, maudlin, bowdlerize, 
 
 connotation to another — this is the import of the analytic judgement ; or it 
 expresses the relation of a connoted attribute to a class. ' Blessed are ye 
 poor ' — blessedness is attributable to you who are poor. 
 
 ' 'A concept cannot denote unless it first of all indicate [this word 
 should surely be reserved for pointing to objects], or connote. So that 
 connotation is the ground of denotation. . . . The attributes in the com- 
 prehension of a concept are fixed ; they do not vary. But the species, 
 classes, or individuals contained within the extension vary according to 
 our principle of division' (Veitch, Institutes, p. 100). 
 
 ^ Jevons ascribes to proper names a maximum of intension, refusing to 
 distinguish them from names of singular objects. E.g. 'My mother'; 
 ' The earth's centre ' ; ' The victor of Austerlitz.' Such names ' indicate 
 content as such, but content that is in its nature unique'. But see 
 Bosanquet, i. 50. 
 
Notional Whole and Part 301 
 
 macadamize, macchiavellian, quixotic, thrasonical, orrery, out- 
 herod Herod. Not all names of individuals are so connotative 
 as the Puritan ' Obadiah Bind-their-kings-in-chains-and-their- 
 nobles-with-links-of-iron' or 'Hew-Agag-in-pieces-before-the- 
 Lord '. But ancient proper names had usually some significance 
 — Rufus, Redgauntlet, Deerslayer, or Scriptural names. 
 
 § 646. So far it is not easy to see what ' discovery ' lay in 
 Hamilton's contention, though no doubt the traditional state- 
 ment of propositions and syllogisms was couched too exclusively 
 in. extensional shape. And this in spite of the essentially 
 qualitative character of the Aristotelian reasoning, ever seeking 
 for the one in the many, for the form or cause which alone, and 
 not empirical quantitativeness, determines the validity and 
 scientific cogency of an argument. Moreover, in ordinary talk 
 class-reference is less usual than the ascription of an action or 
 quality. ' The blind man beat the dog ' only remotely suggests 
 inclusion in a category of dog-beaters. No one on hearing that 
 nature abhors a vacuum calls up a picture of a class of vacuum- 
 abhorring objects, and then places nature among them. 
 
 § 647. It is as opening out an order of inverted reasoning that 
 Hamilton laid most emphasis on the intensive aspect of predica- 
 tion. Either subject or predicate may be viewed as a containing 
 whole,' and 
 
 'it is manifestly a matter of indifference, in so far as the 
 meaning is concerned, whether we view the subject as the whole 
 of comprehension which contains the predicate, or the predicate as 
 the whole of extension which contains the subject. . . .The copula 
 is, est, &c., equally denotes the one form of relation or the other. 
 Thus, in the proposition man is two-legged, the copula here is 
 convertible with comprehends or contains in it; for the proposi- 
 tion means, man contains two-legged. That is, the subject man, 
 as an intensive whole or complex notion, comprehends as a 
 part the predicate two-legged. Again, in the proposition man 
 
 ' See below, §§ 821 seq. ' That there are two logical wholes, and con- 
 sequently two grand forms of reasoning and not one alone, as all logicians 
 have hitherto taught, I shall endeavour to convince you ' (Lectures on 
 Logic, i. 262). However, he inclines to think that Aristotle's doctrine 
 ' has reference indifferently to both ' (p. 219). Mill rejects the ' discovery ' 
 as ' an excrescence and encumbrance ', a ' mere superfoetation on Logic ', 
 ' requiring the ground to be gone over twice, with a perpetual struggle to 
 express all the fundamental principles of reasoning in a manner combining 
 both points of view' {On Hamilton, p. 508). 
 
302 Extension and Intension 
 
 is a biped the copula corresponds to contained under; for this 
 proposition is tantamount to, man is contained under biped. 
 That is, the predicate biped, as an extensive whole or class, 
 contains under it as a part the class man.' 
 
 § 648. Hamilton is here again misled by his doctrine that 
 judgement is a comparison of two notions or ideas, and not 
 rather of a thing with a notion. Conceivably two-leggedness 
 may be part of the definition of man ; but directly we leave the 
 established hierarchy of concepts, with their analytical impli- 
 cations, notional inclusion is certainly not the import of the 
 proposition. Is there no difference between 'The flagship is 
 the Victory ' and ' The flagship is the vessel on which the 
 Admiral hoists his pennon ' ? If lions are said to lack and 
 suffer hunger, or bows and arrows to be antiquated weapons, or 
 millers to wear white hats and have broad thumbs, how is the 
 predicate comprehended in the subject as an intensive whole ? 
 The brave, we say, are modest, and princes are punctual. But 
 modesty is not part of the idea of valour, nor punctuality of that 
 of princehood. Cracking nuts may possibly be part of the con- 
 cept squirrel, for squirrels are rodents; but not running up 
 trees. Veitch illustrates his master's teaching by a quasi- 
 analytic judgement — ' The river runs '.^ But Hamilton goes so 
 far as to say that in ' Caius is a man ' ' The term Caius contains 
 in it the term man'. If it does, the proposition is a feeble 
 truism — scarcely deserving the name of analytic — , and in that 
 case is no type of the ordinary synthetic judgement. 
 
 § 649. How would Hamilton bring Particular Judgements 
 under the idea of notional inclusion — 'Some women are 'badly- 
 dressed ' ; ' Two passers-by were killed ' ; 'A riot is taking 
 place ', and the like ? If the predicate were notionally compre- 
 hended in the subject, the judgements would be universal. And 
 how would he deal with judgements in which a 'nevertheless' 
 is understood — such as ' Some women are very tall ' or ' Many 
 rogues have a conscience ' ? 
 
 §650. Accordingly, even if 'is' could mean 'contains' — 
 Hamilton elsewhere makes all predication, even when in Com- 
 
 ^ Institutes of Logic, p. 225. 'Running' he says, 'is part of the 
 whole concept of river. This is the relation of whole and part in thought, 
 as much as the relation in extension of the subject to the predicate as 
 a whole. Why then should Logic neglect this ? ' 
 
Conversion 303 
 
 prehension, to be equative, Comprehension or Intension being 
 defined by him as Internal Quantity ' — , the converse of X is Y' 
 could not, except in analytic judgements, be ' F-ness is contained 
 in ^-ness '. Nor is this in logic, whatever it be in grammar, a 
 conversion at all, any more than ' Boys are troublesome ' has 
 for converse ' Troublesomeness is a characteristic of boys '. In 
 fact — since the converses of A, I and O propositions are all 
 particular — the only kind of judgement in which 'intensive' 
 conversion is possible is the analytic E judgement. Thus 
 ' Kings are not subjects' — the idea of being a king excludes the 
 idea of being a subject, which converts into ' the idea of being 
 a subject excludes the idea of being a king'. 
 
 In the affirmative analytic judgement, in which the subject 
 and predicate are respectively species and genus, the subject as 
 to part of its intension is equivalent to the predicate ; and the 
 predicate as to part of its extension is equivalent to the subject. 
 But, as it is not an extensive conversion to say ' Part of the 
 class Y is equivalent to X, and X is part of the class Y', so 
 neither is it an intensive conversion to say ' Part of the idea of 
 X-ness is equivalent to F-ness, and Y-ness includes the idea of 
 X-ness '. These are in either case one and the same judgement, 
 not even looked at from different standpoints. It is all one to 
 say ' The notion of sovereign power includes that of incapacity 
 to commit any legal wrong ', and ' Incapacity to commit any 
 legal wrong is included in that of sovereign power'. If a pony 
 is a small horse, pony minus smallness = horse, and horse plus 
 smallness = pony.^ But these propositions are not convertend 
 and converse. 
 
 § 651. Similarly with the ordinary synthetic judgement. 'X 
 belongs to the class Y' has not for converse 'F-ness is always 
 found among the properties of things which possess ^-ness.* 
 These are the same judgement viewed in extension and in 
 intension. The real conversion (of A) is between, ' F-ness is 
 
 ^ Op. cit. i. 142, 144. 
 
 '^ Species — differentia = genus, and genus + differentia = species. This 
 is true of intension, not, of course, of extension, since differentia does not 
 augment but diminish the sphere of the genus which it qualifies. As 
 based on conceptual abstraction, the genus gives only a partial and in- 
 complete idea of the species, and the notion only a partial and incomplete 
 idea of the nature of any individual. The differencing points must be 
 omitted in what is general. 
 
304 Extension and Intension 
 
 always found among the properties of things that possess 
 ^-ness,' and '^-ness is sometimes found among the properties 
 of things that possess Y-ness '. 
 
 § 652. There are four possible ways of stating a proposition ; 
 viz. (i) both subject and predicate in extension ; (3) both subject 
 and predicate in intension ; (3) subject in extension and predicate 
 in intension ; (4) subject in intension and predicate in extension. 
 Yet it is often difficult to make any distinction. The mind 
 necessarily intends both, though the one may be more promi- 
 nent in thought than the other. Mill remarks : — .'When I say 
 the sky is blue, my whole meaning is that the sky has that 
 particular colour. I am not thinking of the class blue, as 
 regards extension at all. I am not caring, nor necessarily 
 knowing, what blue things there are, or if there is any blue 
 thing except the sky. I am thinking only of the sensation of 
 blue.'^ This is a better illustration than his other one, 'All 
 oxen ruminate,' for the speaker might very well be meaning to 
 class oxen with ruminant animals. Even in describing the sky 
 as blue, a scene-painter might be mentally ticketing it as one of 
 the objects for which he would require a particular pot. And 
 in any case the name ' blue " implies a comparison of existing 
 things agreeing in that colour.^ Intension, it must be repeated, 
 does not stand for attribute, but for possessing attribute. All 
 that can- be said is that the subject of a judgement is thought 
 primarily in extension, for it is reality qualified thus and thus of 
 which we assert anything ; and we do not usually ascribe attri- 
 butes to attributes ' but to the possessors of attributes. On the 
 
 ^. On Hamilton, pp. 497, 498. 
 
 ^ On the other hand, a complex conception need not have been 
 experienced so long as its elements recall familiar things. It was not 
 necessary to compare a number of different people having blue beards 
 before getting the idea of barbe-bleue. 
 
 ^ Yet an attribute can stand as subject, e. g. ' Slowness in a horse is 
 undesirable ' ; or (analytically) ' Slowness excludes hurry '. St. Paul has 
 a chapter on the characteristics of Charity. Sidgwick {Use of Words, 
 p. 254) accuses Mill of departing from his own account of the nature of 
 connotation when he says that an attribute may sometimes be said to 
 have attributes. But a name need not be ' connotative ' for that which it 
 designates to have attributes. Individual objects have attributes. An 
 abstract name is the name of a connotation ; yet it is not itself connotative 
 but notative. McCosh says: 'Abstract Notions have Comprehension, 
 for they embrace qualities ' {Discursive Thought, p. 1 2). Untidiness, 
 
Class Inclusion; Number 305, 
 
 other hand what is ascribed to them is not things but qualities, 
 and so the predicate is primarily thought in intension. Yet this 
 necessarily involves inclusion in an actual or potential class. 
 
 § 653. Such inclusion is sometimes directly expressed.. For 
 example — 
 
 Fies nobilium tu quoque fontium. 
 
 I guessed you one of those Who eat in Arthur's hall. 
 
 lubes esse in amicorum numero. 
 
 Divitiae numerantur in bonis. 
 
 In the catalogue you go for men. 
 
 Sum ex Mbris. 
 
 Aramis was one of the Three Musqueteers. 
 
 He is in the school Eleven ; in the Grenadiers. 
 
 He is one of six. 
 
 Lust and envy are two of the darkest sins. 
 
 He belongs to the criminal class. 
 
 And every proposition, in fine, of which the predicate is a 
 noun substantive — 'Plain-dealing is a jewel'; 'Pickpockets are 
 criminals.' 
 
 A predicate, again, may be an individual, a numerical totality, 
 or an abstraction. 'Attila was the Scourge of God,' 'L'Empire 
 c'est la paix,' 'laborare est orare,' 'Omission is prohibition,' 
 ' Possession is nine points of the law,' ' We are seven,' ' Love is 
 to be all made of fantasy,' ' I am Cinna the poet, not Cinna the 
 conspirator,' ' This crust is all I have.' 
 
 § 654. The expressions major and minor term imply container 
 and contained, but in extension only. 
 
 § 655. An adjectival predicate primarily expresses intension, 
 yet an adjective is incomplete without a substantive. Number 
 has the peculiarity of being adjectival, and yet of connoting 
 extension. In 'the five virgins' and 'the foolish virgins', 
 'five' and 'foolish' are not similar qualifications. For each of 
 the virgins was foolish, but each was not five. We say, ' three 
 blind mice'; but a blind mouse is not a three mouse.^ Number, 
 
 however, does not imfly any quality; it is a quality. In the text 
 ' ascribe to ' means, of course, ' predicate of.' Attributes of a predicate 
 are often ascribed to those of the subject as effect to cause. London eggs 
 are indifferent because they are characterized by staleness. 
 
 ^ Bosanquet says : ' In the proper name there is still the semblance or 
 fiction of a general Intension. In the number even this fiction has 
 
 X 
 
3o6 Extension and Intension 
 
 therefore, as a predicate, must, in converting, be regarded as 
 a totality. ' Thy servants are twelve men ' — a body of twelve 
 men constitutes thy servants. 
 
 § 656. The variety of grammatical forms in which predicates 
 can be expressed is the only interest, as I imagine, possessed 
 for pure Logic by the famous Categories, or to use their Latin 
 name, Predicaments. 
 
 As attribution necessarily implies an extended subject, so 
 everything about which we speak must always be conceived as 
 possessing intensive attributes or activities. A subject has to be 
 regarded under some aspect. The concrete is only known by 
 being brought under the general. The sensible individual and 
 the cogitable universal come into explicit existence in thought 
 together. Now Aristotle, with the Nominalists, denies the 
 separate and prior existence, ante rem and extra rem, of the 
 universal thus predicated, and regards it in his doctrine of 
 Categories as a mere predicate, having but an adjective being. 
 And, without deciding any metaphysical question, this must be 
 the way in which the mere logician regards it. Only, we have 
 so far considered the ultimate subject of predication to be not, 
 as Aristotle holds, the particular sensible, toSe «, but Reality 
 determined in this way or that. To Reality thus determined we 
 attribute in judgement a further determination. 
 
 § 657. For us, then, the Predicaments have only a gramma- 
 tical significance ; and, if we were considering Thought apart 
 from Language, we might pass them by altogether. They are 
 arrived at by breaking up propositions, and observing how 
 many grammatical shapes predication can take. The predicate 
 is not considered subjectively in relation to the subject (as 
 genus, property, accident), nor objectively in relation to the 
 ' copula ' (as inherence or result, answering to the nature of the 
 subject as causa immanens or causa transiens), but in itself, aveu 
 (TVfnrXoKTJ^, apart from assertion, yet as capable of being asserted. 
 We have therefore no concern with ' syncategorematic ' parts of 
 speech, such as preposition, article, or most adverbs, which can 
 only be predicated in connexion with categorematic parts of 
 speech. 
 
 disappeared, and nothing remains but the place of the particular in an 
 aggregate of particulars, united solely by a common denomination' 
 {Li?£:ic, i. 50). 
 
The Categories 307 
 
 § 658. Aristotle, it is true, can hardly have regarded his 
 scheme as simply ' an enumeration of the different grammatical 
 forms of the possible predicates of a proposition', for Grammar 
 was practically as yet unborn ; and, moreover, to a Greek there 
 was an intimate union between forms of words and the reality 
 of things.^ Names expressed the various modes of Being's 
 manifestation. Yet the Aristotelian Categories do roughly 
 answer to ten principal grammatical forms capable of standing 
 as predicates. The predicate can be a substantive (i. e. ' second 
 substance ', regarded as genus, &c. ; e. g. ' Lions are cats '). 
 This is Aristotle's ovuLa, answering the question tL Icrn ; It can 
 be an adjective of quantity (answering the question ttoo-ov ;) ; of 
 quality (ttoTov ;) ; or of comparison (irpos Tt ;). It can be an adverb 
 of place (answering the question ttov;); or of time (ttote;). It 
 can also be a verb, either neuter (/ccto-^at), or middle (ex^iv), or 
 active (Troieiv), or passive (irao-xeiv). But the significance of 
 Keia-Oai and ex^iv is disputable. 
 
 § 659. Adverbs of time seem to be quasi-categorematic like 
 those of place — ' Mon pays est la oii je prie le mieux '; ' It was 
 two years ago.' No doubt, adverbs can only stand as predicates 
 when capable of being expanded in an adjectival form. ' Hinc 
 illae lacrimae ', — those tears are (things which come) from hence. 
 The motto of the Earls of Ellesmere is ' Sic donee ' — which has 
 been paraphrased, ' Bridgewater House will do till I reach the 
 celestial mansions.' A sentence may be expressed in a single 
 adverb — ' Softly,' ' Gently,' ' Up ! he cried.* In ' PlutOt mourir 
 que de changer ' ' plutot ' is rhetorically concise. 
 
 ^ According to Bacon, Aristotle ' constructed the world out of his 
 Categories'. The Rev. Mr. Grundy {Arisioie/iam'sm, p. ii^) observes: 
 'That the Categories were metaphysical or ontologioal is true, in the 
 modem acceptance of the terms, but not so according to the conception 
 of Aristotle. They denoted real existence, however closely they were 
 connected with the thought and its expression, but real existence in its 
 varieties of manifestation ; while the Aristotelian metaphysics are occupied 
 with existence as a whole. Yet the Metaphysics, perhaps the latest of 
 Aristotle's works, presuppose the logical treatises, and expressly refer 
 back to them (iii. 3). . . . The interest which attaches to nine of the 
 Categories is antiquarian. One and all, except the first, mark the 
 outlines of a coast which has shifted, so as to be no longer recognizable. 
 But those waves of thought which have swept away the old landmarks 
 still beat restlessly about the adamantine barrier which shuts in the 
 mystery of existence.' 
 
 X 2 
 
3o8 Extension and Intension 
 
 § 660. It must be confessed, however, that the Aristotelian 
 Categories are chiefly interesting, after all, to the metaphysician, 
 and help us very little in sorting the immense variety of idio- 
 matic phrases and syntactical collocations by which predication 
 is actually expressed in language. Here are a few samples : — 
 
 Like people like priest. 
 
 Ecce Homo. 
 
 Away with such a fellow from the earth ! 
 
 The way to heaven is by weeping-cross. 
 
 Comes iucundus in via pro vehiculo est. 
 
 Sic itur ad astra. 
 
 Throw dirt enough and some will stick. 
 
 Woe unto thee, Chorazin. 
 
 II faut aimer les choses divines pour les connoitre. 
 
 Safe bind safe find. 
 
 Ne iudicate ne iudicemini. 
 
 It is seven miles to London. 
 
 To horse ! Ad arma ! 
 
 Plus je me sens franfais, plus je me sens humain. 
 
 Two Czars are one too many for a state (Dryden). 
 
 Clever men are as common as blackberries ; the difBculty is 
 to find a good one (Huxley). 
 
 II faut si peu a I'homme et pour si peu de temps. 
 
 Mos pro lege. 
 
 LXX is 70. 
 
 The chariots of God are twenty thousand. 
 
 Ubi aves ibi angeli. 
 
 § 661. The practical difficulty of converting some of these 
 propositions affords good exercise. For example, ' Throw dirt 
 enough and some will stick ' converts to ' One case at least of 
 some dirt sticking is when you throw enough of it '. ' Ubi aves 
 ibi angeli ' becomes ' Birds are sometimes where angels are '. 
 The line from Dryden becomes ' One case of there being one 
 Czar too many for a state is when there are two '. ' To horse ! ' 
 becomes something like this : — ' One occasion for bidding you 
 mount is now.' 'Judge not, that ye be not judged' means 
 ' Your not judging others is an invariable condition of not being 
 judged'; which converts thus: — 'One condition of your not 
 being judged is not judging others.' If a cavil be raised that 
 imperatives are not propositions, we answer that this is only 
 
Imperatives, Interrogatives, and Interjections 309 
 
 true grammatically. From the point of view of Logic every 
 enunciation is categorical, and can become a major or minor 
 premiss. ' Go ! ' means ' You are to go *, eundum est. Tlie only 
 exception is interrogations, which are either a suspended asser- 
 tion — ' Tu m'aimes, n'est-ce pas ? ', ' Thou lovest me ? ' — or an 
 incomplete assertion, leaving a blank, as it were, to be filled up 
 by the person questioned — ' When did you come ?' ' You came — 
 when ? ' ' The time at which you came was — ? ' Until these 
 dicta in the air come down to earth, and become assertive, they 
 are only notional, and so cannot stand as premisses. But many 
 questions indicate the expected reply, and therefore acquire 
 various degrees of assertiveness, e. g. ' What is the use of 
 writing ? ' ' Where are the snows of yester year ? ' ' Will you 
 not come ? ' 
 
 An Interjection is usually said to be not Aoyos but (^wvij. But, 
 regarded logically, exclamations like ' Ah ! ' ' Fie ! ' ' Alas ! ' 
 ' Fudge ! ', ' Dear me ! ', and the like, are judgements and may be 
 expanded into propositions. 
 
CHAPTER XXI 
 QUANTIFICATION OF THE PREDICATE 
 
 § 662. This is another question which arises under the head 
 of Prepositional Implication. 
 
 It is certainly remarkable that, after censuring previous 
 logicians for having ' marvellously overlooked the reasoning 
 in Comprehension', Hamilton should have proposed a second 
 reform in the process of reasoning which, by reducing the 
 judging act to an equivalence of singulars or aggregates, ignores 
 Comprehension altogether.^ 
 
 § 663. ' The common doctrine,' he observes, ' remounting to 
 Aristotle, takes into view only the subject, and regulates the 
 quantity of the proposition exclusively by the quantity of that 
 term.' This comes of ' an incomplete analysis, resulting in 
 confusion and multiplicity '.' ' The New Analytic is intended to 
 complete and simplify the old, — to place the keystone in the 
 Aristotelian arch.' ' The quantity, not only of subject but also of 
 predicate, is ' always understood in thought ', and it is a ' simple 
 logical postulate, to state explicitly what is thought implicitly', 
 ' The preindesignate terms of a proposition, whether subject or 
 predicate, are never on that account thought as indefinite (or 
 indeterminate) in quantity.' " 
 
 § 664. Hamilton continues : — 
 
 ' The whole doctrine of the non-quantification of the predicate 
 is only another example of the passive sequacity of the logicians. 
 
 ^ ' All judgement,' writes Hamilton, ' and consequently all reasoning is 
 simply an equation of its terms, and the difference of subject and predicate 
 is purely arbitrary ' (Lecttires on Logic, ii. 298). Again : ' A proposition 
 is simply an equation, an identification, a bringing into congruence, of 
 two notions in respect of their Extension ; for it is this quantity alone 
 which admits of amplification or restriction, the Comprehension of 
 a notion remaining always the same, being always taken at its full 
 amount' (ibid. p. 271). So that ' Both my sons are at home' imports an 
 equation or identification (but identification is not equation) between my 
 sons and two objects which are at home. 
 
 ^ Ibid. p. 244. 5 Ibid. p. 249. * Ibid. p. 250. 
 
Hamilton's 'Discovery' .311 
 
 They follow obediently in the steps of their great master. We 
 owe this doctrine and its prevalence to the precept and authority 
 of Aristotle. He prohibits once and again the annexation of the 
 universal predesignation to the predicate.' * 
 
 § 665. Some logicians at the end of the scholastic period 
 played with quantifying of predicates, and Hamilton allows that 
 the ancients who rejected the idea placed it distinctly before 
 their minds. He himself became convinced of its truth in 1833, 
 and proclaimed it as ' the new doctrine ' which is ' to reconcile 
 the science of Logic with truth and nature '." His followers 
 have hailed it as a 'discovery', which, 'whether competent 
 logicians accept all its details or not, has certainly modified all 
 logical doctrine since its promulgation.* Bentham, however, 
 has also been claimed as its pioneer; and another school of 
 predicate-quantifiers was headed by De Morgan.' 
 
 § 666. To Mill the new Analytic seemed a ' psychological 
 irrelevancy '. Grote is severe on ' these useless ceremonial 
 reforms', 'troublesome and unprofitable.' More recently, Mr. 
 J. N. Keynes, in his Studies and Exercises in Formal Logic 
 (p. 293), writes : — ' It is clear that in the Hamiltonian doctrine 
 there is a want of internal consistency. The doctrine is essen- 
 tially of an unscientific character.' Even more decisive against 
 Hamilton than the opinions of students is the communis sensus 
 of mankind as embodied in the facts of language. He says 
 himself: — 'A logic which cannot be unambiguously expressed in 
 language is no logic at all. Logic, Language and Common 
 
 ^ Op. cit. p. 262. The reference to Aristotle is De Interjir. c. vii and 
 c. X. 
 
 * Ibid. pp. 251, 298. 
 
 ' While Hamilton claimed that his system was that of Aristotle fully 
 developed, De Morgan declared that his had little in common with the 
 old one. He claimed to have 'opened to Logic an indefinite field for 
 improvement'. Hamilton, however, in his Discussions (pp. 707, 708) 
 attacked ' the confident blindness with which a mathematical author can 
 treat a logical subject ', through not considering that ' mathematics are 
 not a road of any kind to Logic ', but are likely to ' ruin the reasoning 
 habits of their votary'. De Morgan, on the other hand, asserted in the 
 Quarterly Review that 'Sir William Hamilton has invented cumular 
 expressions which do not suit the genius of common thought or common 
 language '. His own ' Exemplar system ' (e. g. ' Any one X is any one F' 
 = X is F— there being only one of each) is in turn denounced by 
 Hamilton as satisfying neither sense nor English. 
 
312 Quantification of the Predicate 
 
 Sense are never at variance.'^ He asserts, however, that 'the 
 objection that such quantification would be useless and super- 
 fluous, disorderly, nay confusive, only manifests the limited and 
 one-sided view of the objectors, even though Aristotle be at 
 their head '. 
 
 § 667. Hamilton's co-editor. Professor Veitch, observes : — 
 
 ' The express quantification of the predicate follows as a 
 necessity from the very nature of predication in extension. The 
 predicate in extension indicates a class. Affirmative predication 
 is the reference of the subject to the class. It must have some 
 place in the class — some at least. Why, then, not designate the 
 extent in which I mean the predicate term to be taken ? Again, 
 I may know and mean that the place of the subject in the class 
 is that it occupies the whole of it. I say, all trilateral is 
 triangular — meaning all triangular. Why not, even to avoid 
 ambiguity, express this ? . . . . Hamilton's procedure is in no 
 way a departure from logical method or principle. It is simply 
 a demand that what is understood in thought should not remain 
 implicit or understood, but should be expressly set forth, and 
 that this demand, realized in some propositions, should be 
 applied to all ? ... . The habit of looking explicitly at the 
 quantity of the predicate— considering in all cases exactly what 
 we mean — is of the greatest utility in simplifying our logical 
 statement, in restricting it, guarding it against ambiguity and 
 the possibility of invalid conclusions.' ^ 
 
 § 668. Veitch does not claim that a proposition should contain 
 all that the speaker happens to know about the subject, but only 
 that what is logically implied in the proposition itself should 
 appear on the face of it. ' We must state in language what is 
 efficient in thought.' We must ' enounce as we think '. 
 
 To which the answer is, that the demand is an impossible 
 one. The nature of the proposition, i. e. the form of all thought, 
 forbids it. 
 
 § 669. In the above passage a simpler issue would be presented 
 if the paradoxical claim to be able to say 'All X is all Y' were 
 kept distinct from the claim to be allowed to say 'AH X is some 
 y. For it may be said that the latter, but it cannot be said that 
 the former, statement is implicit in the ordinary A judgement. 
 Let us then defer the more thorny question, and examine first 
 the easier one. 
 
 ^ Discussions, p. 679. 
 
 ' Institutes of Logic, pp. 295, 296, 298, 
 
Ambiguous Use of 'All' 313 
 
 § 670. Now it is true that, as shown above (§ 638), the quanti- 
 fication of the subject of a proposition determines the extent of 
 the predicate term which the predication covers. If seven X's 
 are Y, those seven ^'s are identical with seven Y's, each with 
 each ; and of Y's seven, therefore, are X. If now we use a quanti- 
 fication of which the actual empirical extent is not given, such 
 as all or some, and say that all ^'s, or some ^'s, are Y, we 
 imply that a portion of the Y class is involved in the statement 
 equal to the real extension of the subject, and that, in either 
 case, some Y's at least are X. 
 
 An affirmative proposition about X and Y thus imports that 
 a certain number of -^'s are Y (and the same number, were it 
 ascertained, of Y's are X), and also that to that extent the two 
 spheres of X and Y coincide. 
 
 § 671. But here are two assertions, one about ^s (and by 
 implication Y's) severally, the other about extended wholes. 
 The former necessarily involves the latter, but the latter does 
 not necessarily involve the former. If all men are mortal, this 
 implies that the human class and the mortal class of objects 
 coincide to the extent of the whole of humanity. But if some 
 (a certain number of) ounces are some (a certain number of) 
 pounds, it does not follow that any ounce is a pound. 
 
 § 672. Now the propositions 'All X is some Y' and 'Some A" 
 is some Y' can only be rather awkward English for ' The whole 
 of X, or a portion of X, corresponds to a portion of Y'} They 
 cannot mean grammatically that all X's, or some X's, severally 
 and individually are some Y's, nor do they, as we have just seen, 
 necessarily involve the statement that all X's, or some X's, are 
 Y's at all.^ When Veitch says 'It (the subject) must have 
 some place in the class ' to which it is referred, what does he 
 mean by ' it '■ — the subject as an extensive whole, or each several 
 
 ^ In the trial of Harrison the regicide Chief Justice Yelverton used the 
 phrase — ' You, Mr. Harrison, are not anybody. You know the law.' 
 ' Anybody ' here is d rvx^iv, any ordinary person. 
 
 " Veitch insists on the right to take ' all ' in either a distributive or 
 collective sense. Yes, but it cannot have both senses together. He 
 meets the criticism that ' Every several A is every several £ ', if it has 
 any meaning at all, is two propositions in one by saying that if ' compound 
 propositions ' are to be forbidden, the only admissible form is the Singular 
 Judgement (p. 318). But universal and plural judgements are not 
 composite in any sense which in the least resembles the two-in-one-ness 
 of ' Every A is every B'. 
 
314 Quantification of the Predicate 
 
 member of the subject? The individual units have only one 
 place each in the predicate class. Each is a member of it ; 
 together they are a portion of it. 
 
 § 673. It is possible that some formula might be devised which 
 would combine both statements about the relations of X and Y, 
 The proposed formulas certainly do not do so. Nor can we 
 even admit (what is implied in ' Enounce as you think ') that the 
 extent of the predicate, though logically implied, is actually in 
 the thought. ' The twelve Apostles were inspired ' implies (he 
 existence of twelve (at least) inspired beings or objects. But 
 what is before the mind is merely an intensive attribute, the fact 
 that the Apostles were inspired. 
 
 § 674. So far we have been dealing merely with violence done 
 to grammar. The matter becomes much worse when it is sought 
 to legitimate propositions of the form ' All X is all Y' or ' Some 
 X is all y. These are not contained implicitly in any proposi- 
 tion about X'^ taken severally. ' I may know and mean,' says 
 Veitch, 'that the subject occupies the whole of the class to which 
 it is referred. Why then not express this ? ' Because it can 
 only be known vi materiae} He says, ' I may mean it.' But no 
 proposition about the several ^'s can imply it. ' Enounce as 
 you think' has already become 'Enounce as you know'. It is 
 a fact that equilateral and equiangular triangles are identical. 
 But this does not appear in 'All equilateral triangles are equi- 
 angular'. Further knowledge must be supplied." We might 
 parenthetically insert, ' and they only ' ; but this is to introduce a 
 
 ^ ' It is hardly necessary,' says Hamilton, ' to say anything in confuta- 
 tion of the doctrine that in Reciprocating propositions the predicate is 
 taken in its full extent vi materiae. ... As form is merely the necessity of 
 thought, it is as easy to think two notions as toto-totally coinciding (say 
 triangle and trilateral) as two notions toto-partially and parti-totally 
 coinciding (say triangle and figure) ' {Lectures on Logic, ii. 297). True, 
 But the point is that the reciprocation is not formally implicit in the 
 proposition. Formally, the propositions, 'AH triangles are trilateral,' and 
 ' All triangles are figured ', are exactly alike. That in the former there is 
 equivalence of extent between subject and predicate, and not in the other, 
 is known materially only. 
 
 " Similarly, if spades are trumps the player knows that every trump is 
 a spade. But only because trumps are confined to one suit — a fact which 
 has to be supplied. Conceivably, there might be no such thing in the 
 universe as plurality of causes, and every attribute might be a proprium. 
 Yet this circumstance would still have to be stated. The logical import 
 of a universal proposition would not be affected by it. 
 
Unnatural Formulas 315 
 
 second proposition. If ' All is all ' has any grammatical meaning, 
 it will be only in such a sentence as, ' All the departments of 
 France are all the old provinces ' ; which does not imply that 
 each is each. A statement about aggregates allows us to assert 
 nothing about the individuals which make up the aggregate on 
 either side. 
 
 § 675, This confusion, encouraged by the unchecked use of 
 symbols, and also by the fondness of logicians for illustrations 
 taken from natural kinds, as man, animal, salt, virtue, &c., could 
 hardly, it might seem, have arisen if the double meaning of ' all ' 
 had been borne in mind.^ It ought to be at once dispelled by 
 saying 'All X's', or 'Every X', instead of 'All X', and 'Some 
 ^'s ' instead of ' Some X ', when we are asserting anything 
 about the several X's,. We can say loosely, ' Every X is a kind, 
 or sort, of y ; or, more loosely still, 'is a species of Y.' But we 
 really mean, belongs to a kind, sort, or species of F. 'A lion is 
 a kind of cat' does not mean that each lion is a separate 
 kind. 
 
 § 676. Hamilton, however, aflSrms that 'All man is all risible * 
 has both a collective and distributive meaning, and rashly 
 declares that ' it will not be asserted that any quantification is, 
 per se, necessarily collective or necessarily distributive'.^ 
 'Taken distributively it means. Every several man is every 
 several risible.' Now this seems to mean that the attribute of 
 being every several risible is predicable of every several man- — • 
 an absurd and senseless proposition. But what is meant, doubt- 
 less, is that every man pairs off, and is identical, with a risible, 
 and that there are no risibles left over. Similarly, ' Every X is 
 some Y,' ' Every miller wears a white hat,' must mean, not that 
 every miller is some several wearers of a white hat, but that 
 every miller is identical with a white-hat-wearer, and that 
 (probably) there are not enough millers to go round. 
 
 § 677, In these strained and unnatural formulas — yet far 
 worse are to come — objects are predicated of objects, things of 
 
 ^ Latin has various words for ' all '. Thus, Languet, a social compact , 
 writer, says, ' Magistratus a populo delecti, ut singuli Rege inferiores 
 sunt, ita universi superiores,' 
 
 ' Lectures on Lof^c, ii. 296, 297. Yet he himself (ibid. p. 313) quotes 
 Ridiger, De Sensu Veri ei Falsi (1709), who says : — ' Origo huius erroris 
 neglectus notissimae aequivocationis signorum omnis et quidam esse 
 videtur, qua haec signa vel collective sumi possunt vel distributive.' 
 
3i6 Quantification of the Predicate 
 
 things. We have evidently travelled a long distance from 
 Hamilton's doctrine of predication as notional inclusion to this 
 ultra-Nominalist position. One of the principal results of quan- 
 tifying the predicate is to be ' the revocation of the two Terms 
 of a proposition to their true relation ; a proposition being 
 always an equation of its subject and predicate'.^ Veitch avows 
 that this ' later doctrine ' requires some reconciling with the 
 other, and tries to find it in the idea of part and whole, a. predi- 
 cate notion being recognized intensively as a constituent part of 
 the subject notion, while in extension a 'higher or superior 
 concept' (the predicate) 'stands over' a 'lower or inferior' 
 concept (the subject) in a relation of superordination.^ But sub- 
 ordination and superordination are not equation.' And equation 
 is not identification — ' Every X is every Y'. 
 
 § 678. No room appears to be found in these statements for 
 the usual and natural view of judgement, that the subject is in 
 extension and the predicate is thought intensively — e. g. ' The 
 prince is angry'; 'All our clocks are wrong'; 'Infants grow 
 quickly.' 
 
 § 679. Though in every judgement we think the attributive 'is', 
 while only in a few do we think the quantitative ' equals ', yet 
 undoubtedly there are ways of expressing the circumstance that 
 the spheres of a subject and predicate are co-extensive, that 
 there is a mutual inherence, a reciprocation of attributes. But 
 ' Every X is every Y' (or, ' All X is all Y'), if it were English, 
 which it is not, would be two judgements, not one. The expres- 
 sion, Mill points out, involves a twofold quaesitum, and cannot 
 be contradicted by any single proposition. To reply that ' All 
 X is all y is contradicted by 'All X is not all Y' is no reply at 
 all. For the latter expression may deny the co-extensiveness 
 of X and Y, but does not contradict the possibility of every 
 
 ^ Op. cit. p. 250. Enough has been said elsewhere against the Hobbesian 
 view that ' the predicate is the name of the same thing as the subject '. 
 But though, as Bradley objects {Logic, p. 344), A cannot equal B, A can 
 equal, or be identical with, B C. ' Caesar is sick ' does not identify or 
 equate ' Caesar ' and ' sick ' ; but it does affirm identity between Caesar 
 and a certain sick person or object. 
 
 ^ Ibid. i. 190. 
 
 ° If 'a proposition is always an equation of its subject and predicate', 
 quantity is part of the subject and part of the predicate. For what are 
 equated are not the terms, but the terms as quantified. 
 
A Tzvofold Quaesitum 317 
 
 X being Y, or, if not, of every Y being X. It only refers to X 
 and Y as wholes.^ 
 
 § 680. To say, ' Every X is every Y/ is as though we said, 
 ' Each of ten soldiers is ten wounded men.' No doubt, the 
 several ^'s can be asserted to belong to a specified number of 
 Y's — e. g. ' Every Chinaman belongs to the fourth part of man- 
 kind ' ; ' Six of the diamonds are among the twenty stolen ones' ; 
 ' None of the stolen diamonds is any one of the fifteen in your 
 hand'; 'Some maniacs do, not belong to a particular portion of 
 the lunatic class.' But this is in no sense to equate, or identify, 
 all X's, or some X's, with a quantitatively specified or indicated 
 group or aggregate. ' Every ^ is one often Y's.' But Hamilton 
 leaves out 'one of'.'* 
 
 § 681. He condemns 'the one-sided view that the proposition 
 is not equally composed of the two terms, but is more dependent 
 on the subject than on the predicate.' But such indifference of 
 subject and predicate involves a Leucippian atomism. It makes 
 knowledge to be an identifying of isolated units of fact, each of 
 which is another. It is at variance with the structure of human 
 thought. Yet, if universals are not to be wholly abolished, 'All 
 X's ' means 'If any object whatsoever is X'. 'All ^'s are all 
 Y's ', then, stands for 'siquid est X est siquid est Y'. Now, if 
 meum and tuum between friends are the same, such an expres- 
 sion as ' Whatever is mine is whatever is yours ' might be 
 intelligible. Yet it could only be a compendium irregularly 
 phrased of the two propositions 'Whatever is mine is yours' 
 and ' Whatever is yours is mine '. 
 
 ^ Hamilton is in a position {Discussions, pp. 688, 694) to cite ' a very 
 able logician, Mr. Mansel ', as writing (in the North British Review, vol. xv, 
 p. 116) that, psychologically as well as logically, 'AH A is all B' is 
 a single judgement. ' The true contradictory we take to be " All A is 
 not all B ", which, like the original proposition, may be treated collectively 
 or distributively.' But Veitch {Institutes, p. 316) expounds Hamilton's 
 meaning thus : — ' We can say readily, the whole classman is not identical 
 with the whole class mortal. That is all we need to say in order to deny. 
 We deny the equivalence of the terms as wholes.' 
 
 " De Morgan, on ' the numerically definite proposition ', urges that if 
 the number of X'% is known, and also the number of F's, we may have 
 an affirmative judgement, ' 45 ^'s (or more) are each of them one of 70 
 Y's ' ; and a negative judgement, '45 ^'s (or more) are no one of them 
 to be found among 70 F's.' 
 
 ^ Ibid. ii. 274. , 
 
3i8 Quantification of the Predicate 
 
 § 682. The following are some reciprocating propositions : — * 
 
 The Nile is Egypt and Egypt is the Nile. 
 
 irmTf] TOLVvv f) yvSxrv;, yviocTTrj he rj mcmi St. (Clem. Alex.). 
 
 Snowdrops and February Fairmaids are the same flowers. 
 
 What is real is rational and what is rational is real (Hegel). 
 
 Nought is everything and everything is nought. 
 
 Calculer c'est raisonner, et raisonner c'est calculer (Con- 
 dillac). 
 
 If ye forgive men their trespasses, my heavenly Father will 
 forgive you your trespasses. If ye forgive not men their tres- 
 passes, neither will my heavenly Father forgive you your 
 trespasses. 
 
 The spheres of the true and the beautiful are the same. 
 A phrase like ' Nothing true is new, and nothing new is true' is 
 an E proposition, superfluously converted. 
 
 § 683. It may be granted that, if judgements were equations, 
 all Conversion would be Simple Conversion. On the other 
 hand the New Analytic requires the most wearisome feats of 
 mental gymnastic in other ways. Even the number of preposi- 
 tional forms leaps at once from four to sixteen, as will be seen by 
 combining the possible subjects with the possible predicates ; — 
 
 Aii;^ 
 
 Some X 
 NoX 
 Not all X j 
 
 is 
 
 (all Y 
 
 some Y 
 
 no y 
 I, not all y 
 
 These, however, are reduced to eight by cancelling one of each 
 
 pair of so-called equivalents ; thus — 
 (i) All X is all Y{U) equivalent to No X is not all Y 
 (2)All^issome y(^) „ No X is no y 
 
 (3) All ;f is no y (E) „ No X is some (any) Y 
 
 (4) All X is not all Y „ No Z is all Y 
 
 (5) Some X is all Y(Y) „ Not all X is not all Y 
 
 (6) Some X is some Y{I) „ Not all Z is no y 
 
 (7) Some Z is no Y (O) „ Not all X is some Y 
 
 (8) Some X is not all Y „ Not all X is all Y. 
 
 (U) and (y) are symbols suggested by Archbishop Thomson. 
 
 * Perhaps this very phrase will be claimed as quantifying its predicate. 
 But 'the following' is a concrete aggregate. Substitute 'each of the 
 following ' and ' some ' could no longer stand in the predicate. 
 
' Non-Equation ' 319 
 
 § 684. It will be seen that we can no longer shrink from 
 grappling with the case of Negative Quantifications, which is 
 many times more repelling than that of 'All X is all F' and 
 'Some X is all Y'. In negative judgements the relation 
 between subject and predicate, according to Hamilton, is one 
 of 'non-equation'.^ ' Non-equation ', which he also calls Non- 
 identity or Co-exclusion, should mean that the quantifications 
 are not equal. And yet it appears from the foregoing table 
 that each kind of negative judgement answers to an affirmative 
 one; and the import of every affirmative judgement Hamilton 
 asserts to be an equation. Moreover he describes all conver- 
 sion, negative as well as affirmative, as an ' equi-version ' — 
 dvTufrpo^i; iuriv uroa-rpocfiri Tts. 
 
 § 685. A denial of equation must relate to wholes, and cannot 
 be distributive. It is not the same thing as exclusion. If I 
 deny an equality between seven sous and three francs, I am 
 referring to the totals. But in ' No men are sinless ' or ' Some 
 puppies escape drowning ', the subject is distributively, as well 
 as in the aggregate, excluded from the sphere of the predicate. 
 How now are we to interpret the equivalent of ' All X is all Y', 
 viz. 'No Jf is not all Y'? 'It is not true of any X that it is not 
 all Y' cannot be the meaning intended, though it is the meaning 
 (so far as they have any meaning) of the words. 
 
 § 686. Hamilton surely ought to have said that in negative 
 judgements there is an implicit equation of negated terms, or of 
 a positive and a negative term. Thus, the following identifica- 
 tions of negative sphere are involved in the propositional forms 
 
 given above : — 
 
 (i) Allnon-^ = allnon-F 
 
 (2) Some non-X = all non-V 
 
 (3) Some non-Jf = all Y 
 
 (4) Some non-X = some Y 
 
 (5) All non-.^ = some non-Y 
 
 (6) Some non-X = some Y 
 
 (7) Some X = some non- Y 
 
 (8) Some non-X = some Y, 
 
 On the other hand, ' No X is no Y' has no meaning as an 
 
 equation at all. Distributively, it might be supposed to mean 
 
 that not any X is excluded from the entire sphere of Y, is not 
 
 ^ Lectures on Logic, ii. 257. 
 
320 Quantification of the Predicate 
 
 a F of some sort or other. This is the ordinary A judgement, 
 ' Every X is Y'. The equation is 'All X = some Y', or ' Some 
 non-X = all non-F'. ' No X' cannot mean 'all non-^'. The 
 following from the De Civitate Dei is in the form, ' No non-^ is 
 y — 'ubi non est iustitia, ibi non est respublica'; or this — 'No 
 bishop no king '} 
 
 § 687. It was not till 1840 that Hamilton hesitatingly persuaded 
 himself that Quantification of the predicate might be extended 
 to negative judgements. 
 
 § 688. It is often contended that, say what logicians will 
 against quantification of predicates, they are frequently quanti- 
 fied in common speech and syntax. E. g. — 
 
 Eight stars are all the planets. 
 
 The three boys here are all that robbed the orchard. 
 
 These were certainly some of the rioters. 
 
 ' If All X'ls all Y' {[/) is expressed distributively in the form 'Any 
 X is any V, it surely has for contradictory either ' Any X is not any V 
 (E) or ' Not any X is any Y' (E). But the contradictory of E is /, not U. 
 Or can any other single propositional form be suggested to express ' It is 
 not the case that any X is any Y' ? 
 
 But it is easier to get a meaning of some sort out of a negative judge- 
 ment taken distributively than it will be if we regard it as an equation. 
 What can be the possible sense of saying that ' some X' and ' no Y' are 
 equal? 'No Y' must be supposed unextended. Has 'some X', then, 
 no extension ? 
 
 To give an intelligible sense to 'NoXissome Y', we must take 'some' 
 to mean ' a certain portion of. ' No hypocrite is a conscious deceiver.' 
 ' Democracy is not a stable kind of polity.' ' Some X is not some K' 
 will be illustrated by the proposition, ' Laboured verse is not true poetry.' 
 Hamilton says : — ' In Negative Propositions the logicians say the predi- 
 cate is always distributed — always taken in its full extension. Now this 
 is altogether untenable. For we always can, and frequently do, think the 
 predicate of negative propositions as only partially excluded from the 
 sphere of the subject. ... It cannot be pretended that negation has an 
 exclusive or even greater affinity to universal than to particular quantifica- 
 tion ' (ibid. ii. 273). For the exclusion of the parti-total and parti-partial 
 negative proposition ' no reason beyond the caprice of logicians and the 
 elisions of common language, can be assigned ' (ibid. p. 294). But ' No 
 men are [a certain kind of| animals ' has a distributed predicate directly 
 we replace the words in brackets by the determination which we have in 
 mind, viz. ' irrational '. And every predicate, being a determination of 
 some further unexpressed notion, may be represented by a blank space. 
 ' Ink is not drinkable ' means ' is not a certain kind of liquid ' — viz. a 
 drinkable liquid. Observe the difference between the Hamiltonian ' not 
 some ' and the ordinary English ' not any '. 
 
' Tot Quof ; 'Atone' 321 
 
 Viola disguised as a page tells Duke Orsino : ' I am all the 
 daughters of my father's house, and all the brothers too.' 
 
 Sometimes a numerical equality is asserted by a tot quot, or 
 toties quoHes, as in the Salisbury rhyme beginning — 
 
 As many days as in one year there be, 
 
 So many windows in the church we see. 
 
 As many marble pillars here appear, 
 
 As there are hours throughout the fleeting year, &c. 
 
 It is also pleaded that the predicate is quantified in definitions, 
 and by the definite article, especially in Greek, by the superla- 
 tive degree and in Exclusive and Exceptive propositions, called 
 Exponibles. Thus, ' Brevity is the soul of wit ' ; ' Order is 
 heaven's first law ' ; ^Stop apia-rov ; ' Only the good are happy ' ; 
 'pessimum inimicorum genus laudantes.' 
 
 § 689. But when these cases are examined it is seen that some 
 are equations of totals, some identification of singulars. When 
 we say, ' These are the four possible moves,' we do not mean 
 that this, this, this, and this are severally the four possible 
 moves. The definite article, with or without a superlative — 
 * London is the key to India' ; ' Le style c'est I'homme';^ Wit is 
 'de tous les dons de la nature celui qui est le plus dangereux et 
 le moins utile ' (Selwyn) — affixes a mark of singularity to a class 
 or object. Infinitives in the same way. Sallust says, 'impune 
 quaelibet facere, id est regem esse.' 
 
 § 690. Hamilton, however, especially relies on ' the equipol-> 
 lent forms of Limitation, or Inclusion and Exception,', such as, 
 ' God alone is righteous ' ; ' Man doth not live by bread alone ' ; 
 ' Except One, all have sinned ' ; ' Seul le silence est grand ' ; 
 ' nobilitas sola est atque unica virtus ' ; ' I drink water only ' ; 
 ' My honour is my sole possession' ; 'imperii finis unicus populi 
 utilitas' (Languet); 'horas non nuniero nisi serenas' (a sun-dial). 
 I have dealt with ' only ', ' the only,' ' only the ' and ' alone ' above 
 (§ 619). The last example (' No uhsunny hours do I number ') is 
 simply A — ' All the hours I number are sunny ones '. ' Ce n'est 
 que le premier pas qui coute' = 'Tout ce qui coute est le premier 
 pas' — an identification. 
 
 § 691. While 'not only' marks the predicate of an O judge- 
 ment, ' only ' marks an A predicate. Such a predicate is undis- 
 
 •^ But what Buffon really said in the Discotirs was ' Le style est de 
 I'homme mSme '—other things being ' hors de I'homme '. 
 
 Y 
 
322 Quantification of the Predicate 
 
 tributed. From ' Only healthy men are wanted as emigrants ', 
 then, it does not follow that all healthy men are wanted. 
 
 § 692. In Definitions the subject and predicate are identical 
 both in extension and intension. But this does not appear 
 formally on the face of the definition (see above, § 385), except 
 when the predicate is delimited by ' the ' — e. g. ' Critics are the 
 painters who have failed'; ' Poetry is the counting of syllables' — 
 or by a possessive pronoun ; e. g. ' Thy people shall be my 
 people, and thy gods my gods '. In * Quem nosse vivere ' we 
 have a convertible proposition ; but not in ' laborare est orare '. 
 Keats says, ' Beauty is truth,' but has to add, ' Truth beauty.* 
 The Times is a threepenny daily paper. There happens to be 
 no other. But for this to appear on the face of the proposition 
 we should have to say, 'The Times is the threepenny daily 
 paper.' Some definitions are couched thus : — ' A circle is any 
 figure,' &c. But this means that ' a circle ' is the name given to 
 any figure which, &c. 'Any figure' may be regarded as the 
 true subject. We could not say, 'All circles are any figure,' &c., 
 nor yet 'Any circle is any figure ', &c. — which must mean that 
 there is an identification between any circle we please and any 
 figure which, &c., taken at random (quodvis X est quodvis Y). 
 One might be the size of a sixpence, the other have the sun's 
 diameter. 
 
 § 693. Once more the point is pressed that the predicates of jE 
 and O judgements are undoubtedly quantified to their full extent, 
 while / and E judgements are convertible simply. Even if it 
 be so, it remains true that a distributive quantification is only 
 possible in the subject. E and O declare that the subject is to 
 be found nowhere in the predicate class ; A and / that it is to be 
 found somewhere in that class. ' Some ' is a vague and elastic 
 term. If we insert it in the predicate, its significance will vary 
 not only with every subject but with every predicate. Thus, 
 ' Some roses are (some) red ' may mean, are some red objects, 
 are some red flowers, or are some red roses. In each case 
 ' some ' stands for a different quantification ; in the last it is 
 equivalent to 'all'. In fact, the predicate of an affirmative 
 proposition is necessarily indefinite in extent. In intension, 
 the four forms of judgement may be expressed thus in a single 
 conjunct sentence — 'All, or some, X's, have, or lack, the 
 characteristic of Y-ness '. 
 
Disappearance of Subject and Predicate 323 
 
 § 694. To conclude this tedious but necessary discussion. 
 The absence of quantification from the ' traditional ' forms of 
 judgement is not an 'absurd' imitation of 'the aberrations of 
 common language \ nor a mere ' conformity to the precarious 
 ellipses of common speech V but is required by the nature of 
 predication. Hamilton says that the integrate or mathematical 
 whole, as distinct from the universal logical whole, has been 
 contemned by philosophers, since 'all that is out of classification, 
 all that has no reference to genus and species, is out of Logic, 
 indeed out of Philosophy'. Undoubtedly, philosophy deals 
 with the universal and the conceptual, for ever bringing the 
 more particular under the more general. It classifies things 
 according to their qualities, and judges what a thing is rather 
 than the amount of space which its extension occupies in 
 relation to a wider class. It is left to Algebra to draw out the 
 equivalence of sums total. 
 
 § 695. If, therefore, the quantifiers had merely pointed out 
 that every judgement, besides its direct significance, involves 
 implicitly a quantitative identity between aggregates, and had 
 constructed a subsidiary syllogistic scheme based on the quanti- 
 fied predicate, it might have had a limited utility as a byway of 
 thought, or as a school exercise. But quantification of predi- 
 cates can only be made the basis of a universal system of 
 reasoning by falsifying the import of the proposition and by 
 the employment of unnatural propositional forms. Who has 
 more pungently insisted on the danger of corrupting Logic by 
 mathematics than Sir William Hamilton ? 
 
 § 696. The general formula of Judgement, according to De 
 Morgan, would be, 'Every one of a specified ^'s is one or 
 other of b specified Y'%.' When such a proposition is combined 
 syllogistically with another, on the principle of supra-totality, or 
 overlapping middle term, the possible varieties of syllogism will 
 be infinite. Jevons considers A—B to be 'the simple form of 
 all reasoning', the distinction between subject and predicate 
 becoming merely grammatical. If this be so, reasoning becomes, 
 what Condillac and Hobbes asserted it to be, a mere adding 
 and subtracting, and the science of Logic could be written on 
 a half-sheet of note-paper. 
 
 ' Lectures on Logic, ii, 290, 291. 
 y 2 
 
324 Quantification of the Predicate 
 
 § 697. It will be necessary to glance again at Hamilton's 
 doctrine, which, bearing the authority of a great name, has so 
 vexed the logical Israel, when we come to the Syllogism. For 
 it is in the simplifying of syllogistic theory that he places, its 
 chief results. Veitch, contending that Logic must be ' an unex- 
 clusive reflex of thought, and not merely an arbitrary selection 
 of the forms of thinking', reproaches the logicians for their 
 ' contracted views '} Certainly they are content with nineteen 
 legitimate moods out of sixty-four possible ones. Hamilton, 
 however, calculates that a quantified predicate yields 3,072 
 possible moods, of which 480 are legitimate." 
 
 § 698. The levelling atomism which turns all conceptual 
 thought into an identification of equals,' and makes all conver- 
 sion to be simple conversion, appears in Dr. Bosanquet's attack 
 on Plurality of Causes. He writes ; — 
 
 ' It is a corollary from the idea of Grbund that the hypothetical 
 judgement when ideally complete must be a reciprocal judge- 
 ment. " \iA is B it is C" must justify the inference, " If ^ is C 
 it is B!' ... It is obvious that the idea of coherence in a 
 system is reciprocal. A cannot cohere with B unless B coheres 
 with A. If in actual fact this is found not to hold good, and 
 AB is found to involve AC, while AC does not involve ^5, 
 it is plain that what was relevant to ^C was not really AB, but 
 some element ayS within it.' * 
 
 §699. He rejects the 'tempting suggestion' that 'the irrele- 
 vant element is just the element which made AB as distinct 
 from AC, so that by abstracting from it AB is reduced to AC, 
 and the judgement is made a tautology, i.e. destroyed'. A 
 sailor defends his country, shall we say ? So also does a soldier. 
 The irrelevant element in ' sailor ' is that his defence of his 
 country is on the sea. But it is just this which differentiates 
 him as a sailor. Bosanquet, however, maintains that 'a 
 
 ^ Institutes, p. 291. " Lectures on Logic, ii. 356. 
 
 ' In the extreme Nominalism of Antisthenes all distinction between 
 subject and predicate disappeared, the name (sense-impression) simply 
 repeating itself, and even identification becoming a mere tautology. Asser- 
 tion and instruction in such a system there can be none. We can but 
 point aimlessly with the finger and make meaningless sounds. For 
 directly the sounds have a general meaning, the universal reappears. 
 Knowledge is thus impossible. 
 
 ^ Logic, i. 261. 
 
Plurality of Causes- 325 
 
 systematic relation is always within an individual whole'. Sub- 
 ject and predicate are discarded. ' The priority or antecedence 
 of the elements [of the judgement] belongs to the imperfection 
 of knowledge, and not to the relation itself.' 
 § 700. He goes on : — 
 
 'Apart from time and irrelevant elements, I cannot see how 
 the relation of conditioning differs from that of being- con- 
 ditioned. Every B that is conditioned by A is the condition of 
 A being such as to condition B, i. e. of A being what ^ is. . . , 
 In other words, if there is nothing in A beyond what is 
 necessary to B, then B involves A just as much as A involves 
 B. But if ^ contains irrelevant elements, then of course the 
 relation becomes one-sided.' 
 
 § 701. Elsewhere this writer urges that, to purge the judge- 
 ment of irrelevancy, it must pass through scientific induction.^ 
 To roast a logical pig, we may suppose, it is not necessary to 
 burn down one's house, though the Chinese mind was slow 
 to perceive how much was irrelevant in such cookery. 
 
 § 702. Equality between subject and predicate, however, may 
 be restored by noting that the irrelevant part of the cause is 
 reproduced implicitly in the effect. So that, whereas drowning 
 and poisoning both produce death, the one produces death by 
 drowning and the other death by poisoning. The complete 
 judgement will be, ' To be drowned (or poisoned) to death is to 
 be put to death by drowning (or poisoning).' 
 
 § 703. Every effect, in fine, is but the total antecedent. And 
 since neither total consequent nor total antecedent can be de- 
 limited, and the idea of time post or ante must be left out or 
 regarded as common to both, we reach the result that the one 
 and only assertion possible to be made is this, that the universe 
 of things is itself, — a solitary, undifferentiated point. All A is 
 all^. 
 
 § 704. It would seem then that all judgement is an imperfect 
 endeavour towards this propositional simplicity, and that all 
 judgement will be at last swallowed up in pure contemplation — ■ 
 a fixed stare. As men advance in knowledge they will have 
 less to say, and ideas and speech mark the world's nonage ! 
 
 § 705. Logic at any rate belongs to the region of conceptual 
 thinking. The effort to bring experience under this or that 
 
 ' Logic, ii. 88, n. I. 
 
326 Quantification of the Predicate 
 
 notion, to reduce the multiplicity of presented matter to the 
 unity of conceived form, implies that the same consequent may 
 have different grounds. Whence the danger of careless analogy, 
 and of undistributed middle terms, 
 
 § 706. A rumbling noise may be due to distant thunder or a 
 passing train. Both grief and an onion will bring tears to the 
 eyes. Life, says Seneca, has one entrance but many exits. The 
 evidence against a prisoner may be false, yet he be guilty. A 
 judge's reasons may be wrong, yet his decisions right. There 
 are two answers to a quadratic, to y^/tat koI to /x^ y^/^ai 
 Ktt/cov — both bring woe. Bear-baiting would be condemned now 
 because it gives the bear pain. According to Macaulay the 
 Puritans frowned on it because it gave the spectators pleasure. 
 It is related of two very prosperous persons that, being interro- 
 gated as to what they considered to be the cause of their success, 
 one ascribed it to his having answered every letter by return of 
 post, the other to his having never answered any letters at all. 
 There is more than one way of making money — quocumque 
 modo rem} Indeed every common name implies one in many. 
 Every three-sid§d figure is a triangle, whatever the length of 
 the sides. A book is a book, whatever its contents. 
 
 § 707. Because X is Y, then it does not follow that Y is 
 entirely made up of X. And if Y is Z, but no X is Y, it is yet 
 possible that X will be found to be Z in some other way, that is, 
 through some other middle term. A conclusion is more abstract 
 as a proposition than it is as a conclusion ; for it may be reached 
 in various ways. 
 
 We thus come at last to the Syllogism, and the law of its 
 construction. 
 
 ^ It is owing to the logical possibility of plural causes — even when as 
 a contingent fact only one cause is adequate to a certain effect — that 
 judgements are always logically liable to be mistaken. For every judge- 
 ment, as we have seen, is an interpretation (§ 26). I fire ; and, the hare 
 rolling over, 1 say, ' I have shot her.' But some one else may have shot 
 her ; or she may have dropped through fright or heart-disease. At any 
 rate abstract certainty is unattainable. This is so not only in those 
 judgements which are directly about causes. If I say, ' The sky is blue,' 
 or ' It is raining ', the impression on my senses may have been brought 
 about in some other way than I suppose. 
 
CHAPTER XXII 
 
 SYLLOGISM . 
 
 § 708. Although it has been argued above that Concepts 
 and Judgements do not, as such, possess a rational internal 
 character, since whatever is reasoned can only be reasoned 
 through a middle term, and whatever construction has a middle 
 term is a syllogism, it has been necessary to consider Con- 
 ception and Judgement at length. For when we are analysing 
 the pure form of anything it is of no consequence what is the 
 nature of the particular matter of which it is composed. But 
 the materials supplied to the Reason to syllogize with help to 
 determine the form of the Syllogism, which is not pure reasoning 
 — an impossible thing for us — but reason governing the con- 
 nexions of actual human thought. Judgement, as conceptual, 
 possesses a vital structure which enters into the life of 
 Inference. 
 
 § 709. A combination of two concepts or notions gives rise to 
 no ratiocination — e. g. Australian gold and buried gold ; for 
 the implied particular propositions — ' Some gold is Australian ' ; 
 ' Some gold is buried ' — can together yield no conclusion. Nor 
 can a proposition be subsumed under a notion ; for this would 
 make a particular proposition a rule. But a notion can be 
 subsumed under- a universal proposition. E. g. ' All gold is 
 valuable'. Then the idea of a golden egg is the idea of a 
 valuable egg. ' Union (only) is strength,' Then a disunited 
 Christendom is weak, and a weak Christendom is disunited. 
 ' The self-restrained are unimpassioned.' Then the idea of an 
 occasionally passionate man is the idea of one who occasionally 
 loses self-restraint. 
 
 § 710. A notion subsumed under a general proposition is 
 equivalent to the combination of a categorical major with a 
 hypothetical minor premiss.' ' Only the united are strong.' 
 
 ' In Aristotle's Rule of Syllogism, iv &rravn (a-vWoyuriJU^) Set KarriyopLKiv 
 Tivarav opav elvat koLto nadoKov imdpxeiv (An, Pr. i, 24. 41'' 6), KaTrjyopiKov 
 
328 Syllogism 
 
 Then, if Christendom be disunited it is weak. The conclusion 
 is true hypothetically. Of course both premisses may be 
 hypotheses — 'If I lived in London, and London were smokeless, 
 I should live in a smokeless place.' The supposition of S 
 being M and of M always being P is the supposition of S being 
 P. Or the major premiss alone may be hypothetical. ' I live in 
 London. If, then, London were smokeless I should be living 
 in a smokeless place.' This is a combination of fact with idea. 
 
 § 711. Usually in our reasonings both premisses are assertions 
 of fact. But it makes no difference to syllogistic theory whether 
 we deduce a result from supposed or from asserted propositions. 
 In either case the conclusion, as a conclusion, stands or falls 
 with the truth of the premisses. Its truth in fact is conditioned 
 by their truth. Yet the reasoning is unconditional and absolute. 
 ' It undoubtedly follows that, &c.,' so that a conclusion is always 
 stated as inevitable. And it is not a bit more necessitated where 
 the premisses are necessary truths than where they are random 
 guesses. S is necessarily M and M is necessarily P. Then it 
 necessarily follows that S is necessarily P. Aristotle well de- 
 fines Syllogism as Adyos ev & reOivruiv rivmv trepov Ti tSiv KUfiivdiv 
 
 i^ avdyKT]^ (TVfx,jiaivci tS Tavra etvat.^ But, with ontological logicians 
 generally, he regards the highest reasoning as apodeictic? Next 
 to such demonstrative proof he places those statements which 
 
 means affirmative. The other premiss must be a universal. This, the 
 major, premiss was called by the schoolmen propositio or sumptio, and 
 the minor assumptio or subsumptio. Sumption and Subsumption are the 
 expressions brought into vogue by Hamilton. They are also called 
 praemissa continens and praemissa applicativa. 
 
 ^ An. Pr. i. I. 24" 18. 
 
 ^ His crv\\oyt(Tix6s e| {iTToBia-ews aims at demonstrating the truth of the 
 assumption on which some other assertion depends. Sigwart remarks : — 
 ' The Aristotelian doctrine of the Syllogism presupposes established 
 relations amongst concepts. Aristotle himself assumes an objective 
 system of concepts which realizes itself in the material world in such 
 a way that the concept manifests itself everywhere as constituting the 
 essence of things and as the cause of their particular determination. Thus 
 all judgements containing true knowledge are for him the expression of 
 necessary relations, and the function of the syllogism is to reveal the 
 whole force and bearing of each particular concept in our knowledge by 
 combining particular judgements and making them mutually dependent 
 through their conceptual unity. . . .Ordinary logic, on the contrary, is 
 based upon a subjective system of concepts, which is not sought for in 
 the process of knowledge, but is assumed as a preliminary datum.' 
 {Log-ic, i. 349, 350.) 
 
Proposed Formulas 329 
 
 draw out the essential nature of things. From the same extra- 
 logical standpoint Ueberweg observes : — ' Perfect knowledge 
 rests on the coincidence of the ground of knowledge with the 
 real cause. Hence that syllogism is most valuable in which the 
 mediating part (the middle term), which is the ground of the 
 knowledge of the truth of the conclusion, also denotes the real 
 cause of its truth.' ^ 
 
 § 712. We can only reply that Logic is not concerned with 
 the valuableness, but only with the validity, of a syllogism, and 
 that it could only aim at ' perfect knowledge ' by investigating 
 not the formal relations but the material content of thought. 
 Directly it asks questions about the data supplied to it, it ceases 
 to be Logic. 
 
 § 713. A conclusion is not a conclusion apart from its pre- 
 misses, the whole constituting inference, which is an indivisible 
 mental act. 'In consciousness,' remarks Hamilton, 'the three 
 notions and their reciprocal relations constitute only one 
 identical and simultaneous cognition.' ^ Inference, however, is 
 not cognitive but ratiocinative. It may be cast in the form of 
 a necessary proposition — ' The case of 5 being M and of M 
 invariably being P is necessarily the case of S being P' — ; but 
 the necessity is given by the reason not by the 'judgement. A 
 complex comparison between three terms compels a rational 
 unification, which is not itself comparison, that is to say, is not 
 a judicial act. As Judgement is the intellective reference, so 
 Inference is the rational reference, of an ideal content to reality. 
 And it is therefore always stated as unquestionable. 
 
 § 714. What is the formula, then, of Syllogism? 
 
 Hamilton adopts the formula, A part of the part is a part of the 
 whole, as applicable whichever way we read the syllogism — in 
 Extension or in Intension. It certainly will do duty both for 
 class-inclusion (S is part of class M, and class M is part of class 
 P) and for notional inclusion (jP-ness is part of the notion 
 itf-ness, and ilf-ness is part of the notion 5-ness). But we have 
 already had to insist that notional inclusion is peculiar to 
 analytic judgements. 'Has his day' is not part of the notion 
 ' dog \ nor ' is a busy time for grocers ' part of the connotation 
 
 1 Logic, p. 337. ' The ground of Being is the only genuine and com- 
 plete ground of knowledge ' (Bosanquet, Logic, ii. 264). 
 ^ Lectures on Logic, i. 276. 
 
330 " Syllogism 
 
 of 'Christmas', nor 'destructive of civilization' part of the 
 meaning of ' equality '. 
 
 § 715. Mill points this out.' A property of the circle is that 
 its circumference stands to its diameter in the approximate ratio 
 of 3-14159 to I. Now even those who regard a notion as a 
 fixed, normal content, universally accepted, will hardly affirm 
 that this ratio is in the mind of the ordinary person who talks 
 about a circle and whose eye can at once detect when the moon 
 is not quite full. But Mill's criticism of Hamilton's formula 
 overshoots the mark. Hamilton's instance of syllogistic inclu- 
 sion or comprehension is this — Man comprehends responsible 
 agent, and responsible agent comprehends /ree agent. Therefore 
 Man comprehends free agent. But, Mill objects, if the last 
 notion is part of the middle notion, and that is part of the first 
 notion, how is not free agent at once recognized as part of the 
 notion Man, since the notions, by supposition, are in the mind ? 
 What need of a middle notion at all? If the meaning of Man 
 has been partly forgotten, or is indistinct, it is to that extent not 
 possessed by the mind, and, not being there, cannot be proved to 
 be there by ratiocination. 
 
 § 716. But the whole meaning of analytic or explicatory 
 judgement is that it brings to light and to conscious recognition 
 what was before only implicit in a notion. And Mill's criticism 
 extends equally to all inclusive aspects of judgement, whether 
 inclusion of a subject in a class or inclusion of a predicate 
 among attributes. If we know that S is included in class M 
 and class M is included in class P, we infer that class 5 is 
 included in class P. Again, if P-ness is included among the attri- 
 butes of objects that are M, and M-ness is included among the 
 attributes of objects that are 5, we infer that P-ness is included 
 among the attributes of objects that are 5. But, Mill would 
 say, why pass through M at all ? In other words, if I know 
 that a penny is circular, and know also that the length of the 
 perimeter of a circle is to that of its diameter as 3-14159 is to 
 I, then, since these items of knowledge are, by supposition, in 
 my mind, I know that those are the measurements of a penny 
 without my mind passing through the intermediate idea of 
 circular. 
 
 § 717. This is, of course, the old fallacious charge against 
 
 ' On Hamilton, c. xix. 
 

 c 
 
 
 
 r^ 
 
 
 
 
 
 'A Mark of a Mark' 331 
 
 the Syllogism that it involves a petitio principii, to which charge 
 we shall have to return later. In asserting M to he P 
 (major premiss) we have already, it is said, asserted 5, which 
 is known to be part of M (minor premiss), to be P (conclusion). 
 The wider knowledge includes the narrower. Must, then, 
 major and minor premisses be always apprehended simul- 
 taneously ? I see in the papers that the Belle Amelie has gone 
 down with all hands. I learn six months after that my friend 
 was on board. According to Mill I knew he was drowned 
 directly I heard of the crew's fate. There are major premisses 
 as old as Time still waiting for their minors. There are facts 
 of experience for which no law has yet been discovered ; and 
 what is progress in reflective knowledge (eTriyvajo-ts) but the 
 fuller realization of what is implied in some old conception ? 
 The school of Mill writes about our ideas as 
 though they lay dissected under glass cases, and 
 about our acquaintance with facts as though we 
 knew everything not discursively but simul- 
 taneously and equally. Inference becomes 
 simple inspection, as in a visualized notation, without the eye 
 having to travel from space to space. 
 
 § 718. The formula for Syllogism preferred by Mill — Nota 
 nofae est nota ret ipsius — is open to exactly the same criticism 
 that he directs against A part of the part is a part of the whole. 
 It is exposed to the further objection that it cannot stand for 
 Extension as well as Intension. A graver fault in this formula 
 is that it is dangerously ambiguous. For the mark of anything 
 must mean an indication by which we can know the presence 
 or existence of that thing. But the predicate of a proposition, 
 even of a universal one, is no sure indication of the presence 
 of the subject. All pennies are circular coins ; but circularity 
 in a coin is no conclusive indication or token of it being a penny. 
 Being worth, nominally, ^^ of a £ would be ; but that is because 
 we get there a convertible proposition, since no other coin is of 
 that exact value. The formula, nota notae est nota ret ipsius, 
 then, only serves for a limited number of propositions. It 
 might perhaps be said, ' Happiness is a mark of contentment, 
 and contentment is a mark of humility ; therefore happiness 
 is a mark of humility ' — though even this will not bear much 
 scrutiny. 
 
332 Syllogism 
 
 § 719. It is difficult to translate the formula into the terms 
 of Mill's explanation. He says, 'It means that two things 
 which constantly co-exist with the same third thing constantly 
 co-exist with one another.' ' What is meant by A constantly 
 co-existing with B ? That where the one is found the other 
 is also found ? But this is a double proposition (see above, 
 § 674). It either means, then, that where A is found B is 
 also found, or that where B is found A is also found. FalstafF 
 says, 'You cannot separate age and covetousness ' — not that 
 the covetous are always old, but the old are always covetous. 
 But how is the syllogism to proceed? No further statement 
 about the old will allow us to infer anything universally about 
 the covetous, nor will any further statement having ' covetous '' 
 as predicate enable us to infer anything at all about the old. 
 Where then is the constant co-existence between two things 
 which constantly co-exist with a third ? 
 
 § 720. Again, Mill's canon makes no provision for syllogisms 
 with a particular minor premiss. Nor yet for syllogisms with 
 a negative premiss. Hutcheson's formula, adopted by many 
 modern writers, ' Things which agree with the same third agree 
 among themselves,' is, as a rule for affirmative inferences, aa 
 faulty as Mill's. But negative syllogisms in the Second Figure 
 find a rough formula in the following : — ' Things whereof the one 
 agrees, the other does not agree, with one and the same third, 
 these things do not agree among themselves.' Yet though the one 
 is not the other, they may agree in certain respects, A coster- 
 monger sells apples, and a newsvendor does not ; but both (as 
 the names imply) sell something. Probably by ' agree' is meant 
 coincidence in extension. This assumes an equational Logic. 
 
 § 721. Hamilton's notional inclusion, or exclusion, it should be 
 added, equally leaves no room for particular inferences. For 
 though a notion can be partly included in another notion, as 
 ' four-footed ' and ' two-footed ' share the characteristic of having 
 feet, yet this does not allow us to say that some bipeds are 
 quadrupeds. For the rest, his formula seems as weak as that 
 of his eminent critic. 'Reasoning,' he says, 'is an act of 
 mediate comparison or Judgement ; for to reason is to recog- 
 nize that two notions stand to each other in the relation of 
 a whole and its parts, through a recognition that those notions 
 ^ On Hamilton, p. 442. 
 
Conditions of Valid Inference 333 
 
 stand severally in the same relation to a third.' ' It is only in 
 one mood of Figure III {Daraptt) that this happens; and then 
 the conclusion is a particular one, and is not concerned with 
 any relation of whole and parts. 
 
 Conditions of Valid Inference. 
 
 § 722. Inference is, broadly, the bringing of a case under a 
 rule, or else the denial that a' rule applies to a certain case. 
 
 No conclusion, accordingly, can be drawn from a pair of pre- 
 misses which are mutually inconsistent ('No ^ is ^'; 'Some 
 -B's are A ') or mutually unrelated ('^ is 5 ' ; ' C is £» '). They 
 will be unrelated (i) if neither premiss be universal ; (ii) if both 
 be negative ; (iii) if there be no middle term ; (iv) if the middle 
 term be not taken once at least in its full extension ; (v) if there 
 be more than three terms.^ 
 
 § 723. Caution (i), against two particular premisses, insists 
 that ' once at least in every inference you must show your 
 hand and develop your universal in terms of its positive con- 
 tent '.' There must be a rule of some kind. Seeming exceptions 
 are when a mark of occasionalness attaches to the predicate — e. g. 
 'The wisest sometimes make mistakes'. Compare *A friend 
 loveth at all times ', and contrast ' Windsor Castle is frequently 
 the residence of the Sovereign ' with ' Castles are frequently 
 ruinous'. The two propositions 'John is sometimes merry' 
 and 'John is often in great pain' will yield the conclusion (in 
 Darapti) that there is one instance at least of a person who 
 often suffers great pain being sometimes merry. 
 
 This syllogism, however, has two singular premisses, and 
 
 ^ Lectures on Logic, i. 274. 
 
 ^ The principal syllogistic rules are contained in the following lines : — 
 Distribuas medium ; nee quartus terminus adsit ; 
 Utraque nee praemissa negans, nee partkularis. 
 Seetetur partem conclusio deteriorem, 
 Et non distribuat, nisi quum praemissa, negetve. 
 What is meant by the conclusion ' following the worse part ' is that if 
 either premiss be negative it must be negative, and if either be particular, 
 particular. The Port Royal Logic has the following : — ^ 
 
 Ant semel aut iterum medius generaliter esto. 
 Utraque si praemissa neget, nihil inde sequetur. 
 Ambae affirmantes nequeunt generare negantem, 
 Nil sequitur geminis ex particularibus unquam. 
 ' Bosanquet, Logic, ii. ill. 
 
334 Syllogism 
 
 this is another seeming exception to the caution that one must 
 be universal. But a proper name or designation of a definite 
 object or aggregate ranks for syllogistic purposes as a universal, 
 the minor term being identified with it. E. g. ' This rose 
 takes the prize. It is the one you gave me '. There is a 
 well-known story of Keate at Eton getting two lists of names 
 mixed, and flogging his Confirmation class. Sometimes the 
 minor term is not identified with a singular middle, but really 
 subsumed. E. g. ' Vandyck always painted nobly. This is one 
 of Vandyck's works. Then it is painted nobly.* ' Edward is 
 always late. Then he will be late to-day.' ' Ecclesia non sitit 
 sanguinem. The bishop, then, will intercede for him.' 
 
 § 724. The rule against two negatives is a caution against 
 disconnexion. Yet if I want to find that S is P, and know 
 that no M is P, it will encourage me to remember that no 5 
 is M. For if any S were M, to that extent S could not possibly 
 be P. An adverse chance is thus struck out. Dr. Bosanquet, 
 to show that an inference may be obtained from two negative 
 premisses, gives this illustration — 'Light is not matter; light 
 does not gravitate. Whence we infer that something which 
 is not matter does not gravitate '. But he admits that either one 
 premiss has become affirmative (' Light is not-matter '), or there 
 is a quaternio terminorum. 
 
 § 725. The rule against a syllogism having more than three 
 terms is the one which seems to be more often violated in daily 
 discourse than any other. See above, Introduction, § 13. What 
 is more common than this kind of argument — ' The clock struck 
 eleven just now. I promised not to be late. You and I, then, 
 must say farewell ' ? The reduction of the facts of actual speech 
 to syllogistic form is practical Logic. No doubt the steps to be 
 supplied in the process may be numerous) and ' It strikes eleven ; 
 I must be off ' may grow into a chain of syllogisms. It is the 
 commonest thing for an argument to seem to be without a middle 
 term. 
 
 § 726. Pairs of premisses in neither of which the middle 
 term is distributed are often employed as suggesting material for 
 thought, chiefly in the Second Figure. 'Are they Hebrews ? So 
 am I.' Because kings work hard and cobblers work hard we 
 cannot conclude that kings are cobblers or cobblers kings. But 
 it is instructive to know that both classes work hard, or live by 
 
Undistributed Middle 335 
 
 food and drink, or are mortal, or the like. If I am reminded 
 that a philosopher is an animal and a rat is an animal, it comes 
 home to me that they share a common animal nature. Shake- 
 speare says 
 
 The lunatic, the lover and the poet 
 Are of imagination all compact — 
 
 which is more than a compendium of three propositions — 
 
 The lunatic is of imagination all compact. 
 The lover „ „ „ 
 
 The poet „ „ „ 
 
 It is not like — 
 
 Great praise the Duke of Marlborough won, 
 And our good prince Eugene. 
 
 The argument may be stated formally in an intensive form in 
 Figure III 
 
 ^-ness is an attribute of P 
 
 M-ness is an attribute of 5. 
 Then one attribute at least of 5 is an attribute of P. 
 
 § 727. Undistributed Middle is a besetting fallacy, as in the 
 play — ' Have you a strawberry-mark on your left arm ? No ! 
 Then you are my long-lost brother ! * The paralogism here 
 (which may also be considered as two negative premisses) is so 
 obvious that every one laughs. But if the argument had been 
 Yes ! instead of No ! the conclusion would have been, in strict 
 logic, just as inadmissible. It assumes — as, indeed, arguments 
 with seemingly undistributed middle always really do — a con- 
 vertible premiss — ' My brother, and he only, has a strawberry 
 mark on his left arm. You have one. Then you are he.' So 
 in the Comedy of Errors — ' My husband is of such a form. You 
 are of such a form.* There are no exact replicas in human 
 nature. Or if the mark were extremely rare, the inference 
 ef ciKorajj' would be proportionately strong. Similarly, if almost 
 every one possessed such a mark, the absence of it would be 
 reasonable proof of identity. 
 
 § 728. Certain principles about Conclusions will be obtained 
 by a little thought. Thus, a conclusion cannot be affirmative if 
 either premiss has been negative, or negative if both have 
 been affirmative, or universal if either premiss has been 
 particular. 
 
336 Syllogism 
 
 § 729. A distributed term is a term taken as to its entire 
 extension. Let it now be noticed that 
 
 In A the subject is, the predicate is not, distributed, 
 
 In O the subject is not, the predicate is, distributed. 
 
 In E both are distributed, 
 
 In / neither is distributed, 
 (the contradictories herein being doubly contrasted). 
 
 Then, remembering the rule against two negative, or two 
 particular, premisses, we observe that 
 
 If the premisses contain one distributed term between them, 
 they must be AI (lA) ; from which the conclusion must be /. 
 
 If two between them, they must be A A, with conclusion A or I; 
 or else^O (0^4) or EI (IE); the conclusion from which mustbeO. 
 
 If three between them, they must be AE (EA), and yield an 
 £ or an O conclusion. 
 
 § 730. We notice, then, that the premisses together have always 
 at least one more distributed term than the conclusion. Which is 
 also obvious from the fact that neither major nor minor term can 
 be distributed in the conclusion unless it has been distributed in 
 the premisses — else we should be arguing from part to whole — 
 and that the middle term, which has at least one distributed 
 term, has dropped out. 
 
 If a term has been distributed in the premisses it may always be 
 distributed in the conclusion. For whatever has been said about it 
 in its entire extension is entitled to a place in the inference drawn.' 
 
 § 731. The attempt to distribute a term in the conclusion 
 which has not been distributed in the premiss in which it 
 occurred is called Illicit Process, either of the Major or of the 
 Minor. The latter is the more venial error ; for it only draws 
 a universal in lieu of a particular conclusion (' Sylvia is both kind 
 and fair ; then beauty always dwells with kindness '). But the 
 former draws a conclusion where none is admissible. E.g. 
 ' Tables are articles of furniture ; chairs are not tables ; then 
 chairs are not articles of furniture '. 
 
 § 732. By the help of one or two of the foregoing rules, we 
 are able to demonstrate that a true conclusion may be drawn 
 from false premisses. 
 
 § 733- For that falsity in both premisses does not necessarily 
 
 ^ Bramantip (All P is M, all M is S, therefore some S is P) really 
 concludes universally about P rather than particularly about S, 
 
True Conclusions from False Premisses 337 
 
 involve falsity in the conclusion may be shown as follows : — 
 (i) If both premisses be afBrmative, the denial of them will give 
 two negative premisses, from which nothing whatever can be 
 inferred. (2) If one premiss be affirmative and one negative, 
 denial gives us a negative and an affirmative premiss. In either 
 case the conclusion is negative. But one negative cannot con- 
 tradict another negative. Example — Oysters are nightingales. 
 Nightingales do not live in the woods. Then oysters do not 
 live in the woods. 
 
 § 734. To prove the same thing where only one premiss is 
 false is less easy. Example — Three is four. Four is a number. 
 Then three is a number. But by inspection of the moods of 
 Figures I and II, shortly to be explained, we shall see that, if 
 either premiss be false, no conclusion whatever can be drawn. 
 And the same is found to be the case with most of the moods of 
 Figures III and IV. In the others, negation of either premiss 
 merely opposes ' Some S is P ' to ' Some S is not P '. But this 
 is no contradiction. The foregoing exercise may be recom- 
 mended to the student.^ 
 
 § 735. If, then, a conclusion is correctly drawn and true, the 
 premisses may either or both be false. 
 
 If it is correctly drawn and untrue, one or both of the pre- 
 misses must be false. 
 t 
 
 If it is incorrectly drawn, whether it be true or untrue, nothing 
 whatever can be said about the premisses. 
 
 If both premisses be true, a conclusion correctly drawn must 
 be true. 
 
 If either or both premisses be false, a conclusion correctly 
 drawn mayor may not be true.^ 
 
 ' Mr. St George Stock kindly supplies me with the following suggested 
 proof : — 
 
 In a universal mood (concluding in A or £), if the contradictory 
 of either premiss be substituted for it, it can be shown that no conclusion 
 follows. Therefore a universal conclusion cannot be thus destroyed. 
 In a particular mood (concluding in / or O), if the contradictory of either 
 premiss be substituted for it, it can be shown that the conclusion of the 
 new syllogism must be particular. But one particular conclusion cannot 
 contradict another particular conclusion. 
 
 * See above, §§ 6, 31. Aristotle observes : e^ aXriBav fih ovv a'lK eo-Ti 
 ■^fvSos iruWoyiiTCUTBai,, €K ■\frevBSiv 8' eaTLv oKriBes, n\i)V ov'-Siori dXX' on 
 {An. Pr. ii. 2, S3''7). The conclusion is true in fact, but not by virtue of the 
 premisses. From falsity truth may follow, but from truth truth only. 
 
 z 
 
338 Syllogism 
 
 § 736. The truth of a Consequent does not necessarily involve 
 the truth of the Antecedent, nor the falsity of an Antecedent the 
 falsity of the Consequent. Unless the antecedent is a conditio 
 sine qua nan. But a conclusion can always be arrived at in 
 more ways than one. If it is false, says Aristotle, the grounds 
 on which it rests must necessarily be false, in whole or part; 
 but if true, it does not follow that they are in every, or even in 
 any, part true.^ 
 
 * iavepov oTt h/ fiev y ro (TV^Trepacriui ^evSis, avdyKr], i^ Zv 6 \6yos, ijrev&rj 
 fivai ri Tvavra t) tvia, orav fi' aKii]6es, ovK. dvdyKrj dXrides eivai ovrf tl ovtc TTavra 
 {Aft. Pr. ii. 4, 57''36). 
 
CHAPTER XXIII 
 ■ MOOD AND FIGURE 
 
 § 737- We now proceed to consider what variations of mode 
 or construction valid syllogistic inference can assume. 
 
 The arrangement of syllogisms according to the quantity and 
 quality of the propositions of which they are composed is called 
 Mood; while their arrangement according to the position in the 
 premisses of the ground, or middle term, is called Figure. 
 Figure, the skeleton of Syllogism, is really prior to Mood, which 
 clothes it. 
 
 § 738. Logicians usually set about the ascertainment of the valid 
 Moods by finding what combinations are possible,- and striking 
 cut those which transgress any of the rules of Syllogism. 
 Thus — 
 
 The possible combinations of A, I, E and O in the three 
 judgements of syllogism are 4 x 4 x 4=64. Of these only eleven 
 are found not to offend, viz. AAA, AAI, AEE, [AEO], All, 
 AOO, EAE, EAO, EIO, lAI, OAO. [AEO] will be found 
 always to conclude weakly in O when it might conclude in E. 
 
 The illegitimate Moods are as follows •.—Excluded for two 
 negative premisses — EEA, EEE, EEI, EEO, EOA, EOE, EOI, 
 EOO, OEA, OEE, OEI, OEO, OOA, OOE, OOI,'000. 
 
 Excluded for two particular premisses — 1 1 A, HE, III, IIO, 
 lOA, lOE, lOI, 100, OIA, OIE, Oil, 010. 
 
 Excluded for an affirmative conclusion after a negative premiss — 
 AEA, AEI, AOA, AOI, EAA, EAI, EIA, EII, lEA, lEI, 
 OAA, OAI. 
 
 Excluded for a negative conclusion from two affirmative pre- 
 misses— KAS., AAO, AIO, lAO. 
 
 Excluded for a particular premiss followed by a universal con- 
 clusion— KIK, AIE, AOE, EIE, lAA, lAE, lEE, OAE, 
 
 Illicit process of the major — lEO. 
 
 Of course, some of these are condemned on more grounds 
 than one. 
 
 z 2 
 
340 Mood and Figure 
 
 § 739. But further, in each of the above combinations the 
 Middle Term may have one of four possible positions relatively 
 to the extremes. It may be (i) subject of major and predicate 
 of minor premiss ; (2) predicate of both premisses ; (3) subject 
 of both premisses; or (4) predicate of major and subject of 
 minor premiss. These are the four Figures or schemata. 
 
 §740. There are not, however, 11x4 valid constructions. 
 A mood which will stand in one figure may be invalid in another. 
 There survive, if five moods with weak conclusions are admitted, 
 six valid moods in each of the four figures. If the weak 
 moods be struck out there remain nineteen possible con- 
 structions, viz. : — • 
 
 In Figure I (SM, MP, SP) 
 
 AAA (bArbArA) 
 All [dArll) 
 EAE [cElArEnf) 
 EIO fJErlO). 
 In Figure II (SM, PM, SP) 
 
 EAE {cEsArE) 
 EIO (fEstInO) 
 AEE (cAmEstrEs) 
 AOO {bArOcO). 
 In Figure III (MS, MP, SP) 
 
 AAI (dArApiI) 
 
 All (dAtlsI) 
 
 lAI (dlsAmls) 
 
 EAO (fElAptOn) 
 
 EIO [fErlsOn) 
 
 OAO {bOcArdO). 
 
 In Figure IV (MS, PM, SP) 
 
 AAI (brAmAntlp) 
 lAI [dlmArls) 
 AEE [cAmEnEs) 
 EAO {fEsApO) 
 EIO (frEsIsOn). 
 The Moods with weakened conclusions are — 
 Fig. I AAI [bArbArl), EAO (cElArOnf} 
 Fig. II EAO (cEsArO), AEO (cAmEsirOs 
 Fig. IV AEO (cAmEnOs). 
 
Valid and Invalid Constructions 341 
 
 The four first are sometimes called Strengthened Syllogisms 
 because they assume more in the premisses than is necessary 
 for proof of the conclusion, regarded as a probandum. But 
 Darapti, Bramantip and Fesapo also do this. 
 
 The names in brackets will be explained below (§§ 764 seq.). 
 
 § 741. But the same number of figured Moods is obtainable 
 in a more satisfactory and scientific way by an a priori considera- 
 tion of the nature of Inference.' 
 
 The fundamental basis of Rationality we saw (§§ 75 seq.) to 
 be an assertion of the reality of law and truth. What holds in 
 principle holds in fact. What is true in the abstract is true in the 
 concrete. The rationally and theoretically asserted is, in potentia, 
 asserted of actual things. A truth which is true generaliter is 
 true (apart from counteraction) under any given circumstances, 
 A bishop suffragan and an archbishop are both bishops. A dead 
 coast-guardsman tells no tales because a dead man tells none. 
 Experience consists of universals exhibited in differences, of 
 form clothed with varying matter. The one persists through 
 the many ; the rule pervades every case or manifestation of it." 
 If when a statement had been made it eluded all application, 
 there would be no such thing as coherence and consistency. 
 M is P ; then S, which is a case of IVI, must be P, 
 
 § 742. This is so, whether ' M is P ' (M is always P, Every 
 M is P) implies a principle, a causal connexion, or is a concrete 
 universal proposition arrived at by simple enumeration (' All the 
 Apostles were Israelites ' : contrast ' All the Apostles were in- 
 spired) '. It is true also if M is an individual object — since every 
 object persists through varying circumstances — , or if ' M is P ' 
 
 ' McCosh, on the contrary, inquires : ' Can we determine what is the 
 principle in the mind which regulates reasoning? The answer is that 
 this can be done by carefully observing examples of valid reasoning, by 
 ascertaining what is common to them all, and expressing this in a general 
 formula.' He probably means that we should take illustrations of obviously 
 valid inferences, and analyse them to detect the underlying law. But we 
 cannot be certain that an inference is valid till it has been tested, by that 
 law. McCosh cannot intend that we are to find by experiment whether 
 inferences correspond to facts, and so pronounce them valid. Were it 
 so, ' Logic is Greek verse ; Greek verse is a subject for examination ;. 
 therefore Logic is a subject for examination ' would be good reasoning. 
 
 ' ' Logic is little more than an account of the forms and modes in which, 
 a universal does or does not affect the differences through which it per- 
 sists ' (Bosanquet, Logic, ii. 3). 
 
342 Mood and Figure 
 
 is a mere identification. In this case the inference is called 
 tradndive. In the following — ' Richard 's himself again ; I am 
 Richard; then I am myself again' — 'himself again' must be 
 regarded as conceptual.' 
 
 § 743. That the Law of Rationality is ultimate is seen from 
 this, that each syllogism is itself an application of it, being in 
 fact the minor premiss of a great Syllogism.^ ' This inference 
 is a piece of ratiocination. All ratiocination is governed by the 
 Law of Reason. Then this inference is governed by that Law.' 
 
 § 744. The Canon of Syllogism, then, is this : — Whatever (P) 
 can be affirmed (or denied) of a whole class (M) can be affirmed 
 (or denied) of every member (S) of that class. 
 
 § 745. But persistency has for its other side consistency. 
 Accordingly another way of stating this Canon is that when 
 anything (M) can be affirmed (or denied) of a class (P), but 
 simultaneously cannot be affirmed (or denied) of another object 
 or set of objects (S), the latter cannot be part of the former class. 
 If P is ]M[, anything which is not M cannot be P. 
 
 § 746. In the language of Intension — Whatever (S) has 
 certain attributes (M) has (or has not) the attributes (?) which 
 invariably (or never) accompany them. And whatever (S) has 
 (or has not) certain attributes (M) has not the attributes (P) 
 which they never (or always) accompany. 
 
 M is always (never) P P is always (never) M 
 
 S is M S is never (always) M 
 
 Then S is always (never) P. Then S is never P. 
 
 The Dictum de diverso clearly ranks on a level with the Dictum de 
 omnt et nulla (this expression, however, has regard to Extension). 
 The latter is the principle of the First Figure. The former of the 
 Second. Figure I states extensionally that if a term is included 
 in another term it is included in any term in which that is 
 included. Figure 1 1 states that if one term is included in, and 
 another excluded from, a third term, they are mutually ex- 
 cluded, 
 
 ' A certain Pope desired a divided self-identity at his election. ' Get 
 rid of the Sylvius,' he said, ' and keep the Pius.' 
 
 ^ Bosanquet condemns this as ' subsumption under the principle of 
 Subsumption ' {Logic, ii. 61). But Reison is none the less imperative for 
 being an enormous petitio principii. Every question must ultimately be 
 begged. 
 
A Twofold Norm of Reasoning 343 
 
 Figure I. Figure II. 
 
 All birds have .wings All swans are graceful 
 
 A swan is a bird A pelican is not graceful 
 
 Then a swan has wings. Then a pelican is not a swan. 
 
 No swans are green No swans are green 
 
 This bird is a swan This bird is green 
 
 Then this bird is not green. Then this bird is not a swan. 
 
 The Second Figure has as much right to be called 'perfect' 
 
 and ' primary ' as the First. They have an equal status. 
 
 The major premiss in Figure I may be affirmative or negative, 
 but the minor premiss must be affirmative. In Figure II one 
 premiss must be affirmative and the other negative — it does not 
 matter which. 
 
 § 747. In both Figures the major premiss must be universal ; 
 the minor may be either universal or particular. The quantity 
 of the minor will always be reproduced in the conclusion. In 
 Figure I the quality of the major will always be echoed in the 
 conclusion; but moods in Figure II are bound to conclude 
 negatively 
 
 § 748. Representing P and not-P alike by 11, and ' Every S ' 
 and ' Some S's ' alike by 2, the norm of all inference in Figure I 
 
 will be — 
 
 Every M is n 
 
 Sis M 
 
 Then S is n. 
 Or, representing the judgement about M as J, we get 
 ■ MJ 
 
 Sis M 
 
 Then S J. 
 Again, if /a be a common symbol for M and not-M, the norm in 
 Figure II will be 
 
 Every P is /a 
 
 S is not /A 
 
 Then S is not P. 
 
 § 749. Kant expresses the principle of Syllogism thus — ' What 
 
 stands under the condition of a rule stands under the rule '.* 
 
 The corollary of which is that what does not stand under the 
 
 rule does not stand under the condition of the rule. We cannot 
 
 > Logik, § 57. 
 
344 Mood and Figure 
 
 say that because anything does not stand under the condition of 
 a rule it necessarily stands outside the rule ; nor yet that every- 
 thing which stands under a rule stands under the condition of it.^ 
 The former caution forbids a negative minor premiss in 
 Figure I ; and the lattfer prevents any mood in Figure II (in 
 which the middle term is always a predicate) from having two 
 premisses of like quality. The following Syllogism has given 
 trouble to logicians. 'A good pastor is prepared to give his life 
 for his sheep. Few pastors of our day are prepared to do 
 this. Then few pastors of our day are good pastors.' If 'few' 
 meant 'a few' the minor premiss, like the major, would be 
 affirmative, and the middle term undistributed. But 'few' 
 means ' not many ', and the minor premiss is negative. 
 
 Posit the condition, and the conditioned follows. This is 
 Figure I. Sublate the conditioned, and the condition falls to 
 the ground. This is Figure II. If X is Y, then so far as X is 
 found (universal or particular minor premiss) Y is found ; and 
 so far as Y is not found X is not found. 
 
 § 750. We shall find that the existence of this twofold, instead 
 of single, norm or type of Inference greatly simplifies reduction. 
 A complementary relation of equality between the two aspects 
 of Syllogism runs all through. They are not, however, dis- 
 tinguishable as Affirmative and Negative, but rather as Ponent 
 and Tollent Moods. We proceed to state them — 
 
 Figure I. Figure II. 
 
 Barbara. Camestres. 
 
 Every M is P Every P is M 
 
 Every S is M No S is M 
 
 .-. Every S is P. .-. No S is P. 
 
 Darit. Baroco. 
 
 Every M is P Every S is M 
 
 Some S's are M Some S's are not M 
 
 .•. Some S's are P. .*. Some S's are not P. 
 
 Celarent. Cesare. 
 
 No M is P No P is M 
 
 Every S is M Every S is M 
 
 ,-. No S is P. .-. No S is P. 
 
 "Orav duo '^-)(rj ovTca Trpos aXKrfKa SiO'Te daripov Svtos i^ avayKTjs elvai BarspoVf 
 TovTov fir) ovTos jiiv ovdc ddrepov coral, ovtos &' ovk avdyKrj ehai Bdrepov 
 (Aristotle, An. Pr. ii. 4, S7*i). 
 
Double Aspect of Syllogism 
 
 345 
 
 Ferio. 
 No M is P 
 Some S's are M 
 , Some S's are not P. 
 
 Festino. 
 No P is M 
 Some S's are M 
 .•. Some S's are not P. 
 
 § 751. We next consider whether there are any arguments 
 which, though differently expressed, are easily convertible into 
 any of the above. We notice, then, that, since ' Some S's are 
 M ' is the converse both of ' Every M is S ' and of ' Some M's 
 are S ', these propositions may take its place wherever it occurs, 
 viz. in Darii, Ferio and Festino. We also notice that ' No S is 
 M ' in Camestres may be replaced by ' No M is S ', Were we 
 to make a similar change in the major premisses of Celarent and 
 Ferio, respectively, we should merely get Cesare and Festino 
 again, and vice versa. We have then seven new Moods, four 
 ponenf and three tollent : — 
 
 Figure III. Figure IV. 
 
 Camenes. 
 Every P is M 
 No M is S 
 .'. No S is P. 
 Darapti. 
 Every M is P 
 Every M is S 
 .". Some S's are P. 
 Datisi. 
 Every M is P 
 Some M's are S 
 .: Some S's are P. 
 Felapton. 
 No M is P 
 Every M is S 
 .'. Some S's are not P. 
 Ferison. 
 No M is P 
 Some M's are S 
 .'. Some S's are not P. 
 
 Fesapo. 
 No P is M 
 Every M is S 
 , Some S's are not P. 
 Fresison. 
 No P is M 
 Some M's are S 
 . Some S's are not P. 
 
 The new minor premisses in the above are in italics. 
 
 § 752. These are the fifteen Direct Moods. There are, how- 
 ever, certain Indirect Moods, in which the major premiss is 
 
346 Mood and Figure 
 
 seemingly particular. But in truth the conclusion is about P 
 rather than about S, a conclusion about S being obtained from 
 it by conversion. In the above list of Moods the following have 
 a convertible conclusion — Barbara, Darii, Datisi, Darapti, 
 Celarent, Cesare, Camestres, Camenes. But it is only the first 
 three affirmative ones which yield a new mood. Darapti remains 
 Darapti, Celarent becomes Camenes and Cesare Camestres. The 
 conclusion of Barbara converts per accidens, and is weakened 
 in conversion. The other two convert simply. We thus get — 
 Indirect Moods (premisses transposed) : — 
 
 Figure III. 
 Disamis [Datisi). 
 Some M's are P 
 Every M is S 
 .*. Some S's are P (converted from Some P's are S). 
 Figure IV. 
 Bramantip {Barbara). 
 Every P is M 
 Every M is S 
 .•- Some S's are P (converted from Every P is S). 
 Dimaris {Darii). 
 Some P's are M 
 Every M is S 
 .•. Some S's are P (converted from Some P's are S). 
 
 § 753- There is yet another possible way of obtaining Indirect 
 moods, viz. by getting a conclusion about not-P and then con- 
 verting and obverting it. Only one new Mood, however, is 
 obtainable in this way, viz. 
 
 Figure III. 
 Bocardo {Datisi). 
 Some M's are not P (are not-P) 
 Every M is S 
 .'. Some S's are not P (obverted from Some S's are not-P, 
 which is converted from Some not- P's are S). 
 Or else Bocardo may be regarded as simply Disamis with 
 not-P instead of P as major term. It may be questioned whether 
 such indirect Moods are admissible. They represent perfectly 
 cogent arguments ; and we are entitled to ask, From what 
 affirmations involving S, P and M can a vaHd conclusion be 
 
Reduction Simplified 347 
 
 drawn ? On the other hand, it may seem better to regard the 
 four Indirect Moods merely as alternative forms of Direct 
 Moods. Bramanttp might be called Barbarap, Dimaris Dariis, 
 and Disamis Datisis, 
 
 § 754. The above account of the nineteen figured Moods is 
 offered to the reader as more scientific, and far simpler, than 
 the traditional system based on the sole supremacy of the First 
 Figure. Apart from the Indirect Moods, the only manipulation 
 required for reduction is conversion of the minor premiss of 
 seven moods. Camestres and Camenes become direct moods, 
 Fesapo and Fresison in Figure IV are seen to be natural argu- 
 ments, and there is not the slightest trouble about Baroco. In 
 any other plan O premisses have no legitimate place. 
 
 Nevertheless the familiar names of the Moods all imply 
 a process of reduction to Figure I as the pure type of Syllogism. 
 And the principle that a statement, affirmative or negative, made 
 about a class generally is true of whatever may be found to be 
 a member of that class, is so simple and all-sufficing that it is 
 desirable to consider how the nineteen Moods can be obtained 
 by a ponent system on the basis of the First Figure only. 
 
 § 755- We have already seen that conversion of the minor 
 premiss per accidens enables a mood Darapti to be reduced to 
 Darii and a mood of the form Felapton to Ferio respectively ; 
 while two constructions, Datisi and Ferison, by simple conver- 
 sion of the minor premiss, also become Darii and Ferio. 
 
 As regards the major premisses of Figure I, no proposition 
 will convert to A; but E converts simply. Accordingly two 
 moods in Figure II, Cesare and Festino, become by conversion 
 of their major premisses Celarent and Ferio respectively. 
 
 Next, we try what conversion of both premisses will effect. 
 It gives us two moods in Figure IV, either of which reduces to 
 Ferio — 
 
 Fesapo. 
 
 NoPisM(=No Mis P) 
 
 Every M is S (=Some S's are M) 
 .*. Some S''s are not P. 
 
 Fresison. 
 
 No PisM(=NoMisP) 
 
 Some M's are S (=Some S's are M) 
 .". Some S's are not P. 
 
348 Mood and Figure 
 
 § 756. We next discover five Moods which yield a conclusion 
 not directly but indirectly, by conversion of the direct con- 
 clusion. The premisses of these, therefore, will need trans- 
 position, if they are to be exhibited normally. For Bramantip, 
 Dimaris and Camenes nothing more is wanted. They are merely 
 Barbara, Darii and Celarent with converted conclusions. But a 
 fourth converts to iPam by further converting its major premiss — 
 
 Disamis. 
 Some S's are P=Some P's are M ) 
 Every M is S ) transpose. 
 
 .•. Some S's are P (converted from Some P's are S). 
 Disamis is merely Datisi, in the same Figure III, with converted 
 conclusion. A fifth indirect mood converts to Celarent by con- 
 verting its minor premiss — 
 
 Cantestres. 
 Every P is M ) ^ 
 
 NoSisM = NoMisSr'"^"^P°^^- 
 .-. No S is P (converted from No P is S). 
 Camestres is merely Cesare in the same Figure II with con- 
 verted conclusion. 
 
 § 757. There remain two Moods from which the disguise is 
 removed by means of ' negative conception '. One, in the 
 Second Figure, requires both premisses to be obverted, and the 
 major then to be converted, when it is seen in that form to be 
 
 the same as Ferio — 
 
 Baroco. 
 
 Every P is M --= No P is not-M = No not-M is P 
 Some S's are not M = Some S's are not-M 
 .•. Some S's are not P. 
 The other, in Figure III, is an indirect mood, requiring the 
 premisses to be transposed, and the original major, but real 
 minor, to be obverted and then converted. Finally, the conclu- 
 sion has to be converted and then obverted. It then appears as 
 
 Darii. 
 
 Bocardo. 
 
 Some M's are not P = Some M's are not-P = 
 Some not-P's are M 1 transpose. 
 
 Every M is S / 
 
 .-. Some not-P's are S = Some S's are not-P = Some S's are 
 not P. 
 
' Clumsy ' Reductions to First Figure 349 
 
 If Felapion were treated (which is unnecessary) in a similar 
 manner, Bocardo would stand to it in the same symmetrical 
 relation in which Baroco stands to Camestres} 
 
 § 758. It must be admitted that such reductions to a single norm 
 of Syllogism appear clumsy and awkward, and give colour to 
 the charge against ' the logicians ' of seeking a false simplicity 
 by the torturing of arguments into unnatural shapes. De Morgan 
 affirms that ' Baroco and Bocardo do not admit of resolution to 
 the first figure by any fair use of the phrase ; but the logicians 
 were determined they should do so '.* Minto says : — ' It may 
 be conceded that the Aristotelian processes are artificial stages, 
 courses that thought does not take naturally, but into which it 
 has to be forced for a purpose." Yet thought does take all 
 these forms. Our only question at this moment is whether it 
 is natural to reduce them all to the type of Figure I. When 
 clothed with matter, the clumsiest reductions will often appear 
 natural and easy. Thus Bocardo — 
 
 Some beautiful things are not wholesome = Some unwhole- 
 some things are beautiful. 
 
 Every beautiful thing is pleasant. 
 
 Then some pleasant things are not wholesome (Some unwhole- 
 some things are pleasant). 
 
 Again, Baroco — 
 
 All who are able to enter the cavalry are well-to-do- 
 Some men of ancient birth are not well-to-do. 
 
 It follows that some men of ancient birth are unable to enter 
 the cavalry. 
 But it is almost as simple to say in Ferio — 
 
 None but well-to-do men (no not-well-to-do men) can enter the 
 cavalry. Some men of ancient birth are not-well-to-do (far- 
 from-well-to-do). Therefore, &c. 
 
 ^ Camestres and Camenes may also be reduced to Celarent by obversion 
 (or permutation), and will then appear as direct Moods. Camestres goes 
 with Baroco, except that the minor premiss is universal. In Camenes, 
 the minor premiss has to be converted and then obverted, the major 
 obverted and then converted : — 
 
 Every P is M = No P is not-M = No not-M is P 
 No M is S= No S is M = Every S is not-M 
 Then, No S is P. 
 " p. 132. = Logic, p. 39. 
 
350 Mood and Figure 
 
 § 759. The expansion of ' Some X's are Y ' into ' Some X's are 
 not not-Y ' is quite natural in such a phrase as * Some afflicted- 
 people are happy ' — ' are not unhappy '. ' Every one is glad ' 
 and ' No one is otherwise than glad ' are equally plain. It may 
 even be less natural to say ' Every X is Y ' than ' No not-Y is X '. 
 ' All wise persons think so ' is more pointed in the form—' No 
 one who does not think so is wise ' ; and ' No tree that does not 
 bear fruit has stones flung at it' conveys the intended moral 
 better, perhaps, than ' Every tree that has stones flung at it is 
 a fruit-bearing one'. Instead of saying ' omne ens est corporale ', 
 Tertullian more clearly observes, — ' nihil est incorporale nisi 
 quod non est ' (i. e. nullum non-non-ens est non-corporale — No 
 not-non-X is non-Y = Every X is Y). Again, Juvenal's line, 
 ' nee pueri credunt nisi qui nondum aere lavantur,' is at once 
 intelligible. Yet when represented symbolically — No not-non- 
 YX's are Z — it seems roundabout and strained. The Port 
 Royalists, however, point out that it is less natural to say, ' No 
 one who is to be believed is a liar,' than ' No liar is to be be- 
 lieved '. And, again, there is considerable risk, when obverting, 
 of confusion between contrary and contradictory. We have 
 no logical right to assume that 'is not happy' means 'is 
 unhappy '. 
 
 § 760. It cannot on the whole be said that reduction of all 
 arguments to a single type is as natural or simple as reduction 
 to two equal types has been shown to be. 
 
 § 761. Yet Thomson's ridicule of such a reduction from 
 Figure III to Figure I as this is surely undeserved.^ 
 
 Darapti. Darii. 
 
 Aristides was just Aristides was just 
 
 Aristides was a pagan. Some pagan was Aristides. 
 Therefore Some pagan was just. 
 
 For ' some ' write ' a certain ', and the reduction is natural, 
 and also gives an instructive conclusion. If I wished to show 
 that a pagan can be just, and were casting about for an example, 
 my thought would take this shape. The conclusion is that a 
 case has occurred of a pagan being just. 
 
 § 762. The object of Reduction is the exhibition of an argu- 
 
 ' Laws of Thought, p. 329. 
 
Mnemonics 351 
 
 ment in a clearer light — Seiktikios, to use Aristotle's word — by 
 bringing to view the rational principle which governs it. 
 
 § 763. We can now look at the mnemonic names by which 
 the Moods are usually distinguished, as a guide for reducing to 
 the First Figure. They are an-anged in Latin hexameters. This 
 ingenious aid to the memory is ascribed to Pope John XXI 
 (Petrus Hispanus, 1226-77).' Negative moods are placed next 
 to affirmative ; though it has seemed to me above to be more 
 instructive to put each mood with a particular minor premiss 
 next to the corresponding universal mood. The lines are 
 these — 
 
 Barbara, Celarent, Darii, Ferioque, prions. 
 
 Cesare, Camestres, Festino, Baroco, secundae. 
 
 Tertia Darapti, Disamis, Datisi, Felapton, 
 
 Bocardo, Ferison habet. Quarta insuper addit 
 
 Bramantip, Camenes, Dimaris, Fesapo, Fresison. 
 
 § 764. The vowels A, E, I and O are the propositional symbols. 
 The initial letters indicate the mood in Figure I to which any 
 mood is to be reduced. The consonants s, p, m and c are also 
 significant. Thus, s means that the proposition (if a premiss) 
 represented by the vowel after which 5 is placed must be con- 
 verted simpUciter ; while p shows that it is to be converted per 
 accidens, or by limitation (Every X is Y ; Some Y's are X). When, 
 however, s or p occurs at the end of a word, it is the new conclu- 
 sion which has to be converted, not the original one. For what 
 we do in reducing a mood to a type is to show that its premisses 
 can be changed into the premisses of that type, the conclusion 
 from which involves the conclusion of the reduced mood. When 
 m occurs in a name, it indicates that the premisses must first 
 
 ' About the same time Nicephorus Blemmydes made an '^mrofiri 
 XoytK^y, and in the margin of the MS. are written, probably by a later 
 hand, certain Greek voces memoriales in imitation of Barbara Celarent. 
 (See Ueberweg's History of Philosophy, i. 404.) Lines closely resembling 
 those of the Spanish pontiff are traced to William of Shyrewode, chan- 
 cellor of Lincoln, c. 1249, in which, however, the five Moods of the Fourth 
 Figure are given as indirect Moods of the First. The final syllables of the 
 first two lines are metri causa only, and Shyrwode indicates reduction per 
 impossibile by b and r in the same word. The lines are these : — 
 
 Barbara, Celarent, Darii, Ferio, BaraJip-ton, 
 Celantes, Dabitis, Fapesmo, Frisesom-orum. — 
 Cesare, Campestres, Festino, Baroco, — Darapti, 
 Felapton, Disamis, Datisi, Bocardo, Ferison. 
 
352 Mood and Figure 
 
 be transposed [niutare). The letter c will be explained in the 
 next section. 
 
 Example — Disamis (Fig. Ill) to Darii. 
 
 Some M's are P, converted simply = Some P's \ 
 
 are M \ transpose. 
 
 Every M is S i 
 
 Then, Some S's are P, converted simply from Some P's are M. 
 E. g. — ' Some tigers are man-eaters ; all tigers are large cats ; 
 then some large cats are man-eaters ' becomes — ' All tigers are 
 large cats ; some man-eating animals are tigers ; therefore some 
 man-eating animals are large cats (= Some large cats eat men).' 
 Again, Fesapo (Fig. IV) to Ferio. 
 
 No P is M, converted simply = No M is P. 
 
 Every M is S, converted per accidens = Some S's are M. 
 
 Then, Some S's are not P. 
 
 § 765. All other reduction is direct and ostensive. But Baroco 
 and Bocardo can only be reduced to the First Figure indirectly, 
 viz. by reduction, if the conclusion be denied, to an absurdity — 
 redudio per impossibile — unless we employ the method already 
 indicated of Reduction by Obversion and Conversion. The 
 letter c (sometimes written k) indicates that the contradictory of 
 the questioned conclusion is to be substituted for the premiss 
 after which c is placed. This is in both cases O. 
 
 Combining the new premiss, then, with the other one, we pro- 
 ceed in Figure I to draw a new conclusion. As this will be found to 
 contradict the displaced premiss, which is confessedly true, the 
 premiss substituted for it must be false. For it cannot be the 
 other premiss which is false, since this was one of our original 
 data. Therefore (since a false conclusion cannot be drawn from 
 two true premisses) the falsity must lie in the substituted pre- 
 miss. In other words, the original conclusion, of which it is the 
 contradictory, must be true. Thus — 
 
 Baroco. 
 
 Every P is M 
 Some S's are not M 
 Then, Some S's are not P. 
 Suppose this conclusion false. Then it must be true that 
 Every S is P. Combine this proposition with the original major 
 
Redudio ad Absurdum 353 
 
 so as to form a syllogism in the admittedly perfect Figure I. 
 The new syllogism will be — 
 
 {Barbara). 
 Every P is M 
 Every S is P 
 Then, Every S is M. 
 
 But it was conceded that Some S's are not M (the old minor 
 premiss). The new conclusion, then, is false. And if so, one at 
 least of the premisses on which it is grounded must be false (see 
 above, § 735). It cannot be the major — Every P is M. Then it 
 must be the other — Every S is P. But if this is false, its contra- 
 dictory, our original, conclusion, Some S's are not P, must be 
 true. 
 
 Again, Bocardo. 
 
 Some M's are not P 
 
 Every M is S 
 
 Then, Some S's are not P. 
 
 Suppose this untrue. Then it must be true that Every S is P. 
 Substitute this for the old major premiss — 
 
 {Barbara). 
 Every S is P 
 Every M is S 
 Then, Every M is P. 
 But it was agreed that some M's are not P. The new conclu- 
 sion then is false, and it must be untrue that Every S is P. 
 
 § 766. Baroco and Bocardo, it must be said, are the worst 
 illustrations possible of the method of redudio ad absurdum. 
 For indirect proof of these two moods could not be obtained 
 if it were the O premiss which was left in and the other taken 
 out. For O cannot stand as a premiss in the First Figure. 
 Baroco would become by 'internal reduction' Bocardo and 
 Bocardo Baroco, and so there would be no reduction to Figure I. 
 Yet it should be observed that these moods are not really them- 
 selves reduced to Figure I, so as to exhibit the rationality of 
 their construction in the form Barbara, but are only proved by 
 means of Barbara. The Port Royal Logic complains of Euclid's 
 excessive use of redudio ad absurdum (Pt. iv. ch. x). Such 
 proof may convince the mind, but does not enlighten it 
 § 767. The principle of dedudio ad (or redudio per) impossibile 
 
 A a 
 
354 Mood and Figure 
 
 is capable of universal application; and by this method a mood 
 in any Figure can be reduced to a mood or moods in some other 
 Figure, supposed admittedly valid. To show this, except in an 
 Appendix,^ would be tedious, but two examples are offered — 
 
 Darii. Camestres. 
 
 Every Y is Z Every Y is Z 
 
 Some X's are Y x,^^^ No X is Z 
 .-. Some X's are Z ^/\No X is Y. 
 
 Celarent. Disamis. 
 
 No Y is Z\ /Some X's are Z 
 Every X is Y yC Every X is Y 
 .-. No X is z/ \Some Y's are Z. 
 
 § 768. As regards Banco and Bocardo, the difiSculty about 
 ostensive reduction of these two moods to Figure I is that 
 in Baroco — the middle term being undistributed in the major 
 premiss — it is not at first clear where the rule hes ; while in 
 Bocardo— six\c& ' Some M is not P ' will not convert as 'Some P 
 is not M ' — we are at a loss for a subsumption under the rule, 
 which must be looked for in the minor premiss. 
 
 § 769. We have seen by what rules every one of the nine- 
 teen Moods may be reduced to the First Figure, based on the 
 Principle of Identity. The possibility of such reduction may 
 seem to establish the pre-eminence of that Figure. But it is 
 equally possible to reduce all the Moods to the type of the 
 Second Figure, based on the Principle of Contradiction. 
 
 It has been shown above (§ 751) that Camenes, Fesapo and 
 Fresison (Fig. IV) reduce to this type by conversion of the 
 minor premiss. 
 
 The other negative direct Moods are, in Figure I, Celarent and 
 Ferio, which reduce to Cesare and Festino respectively by simple 
 conversion of the major premiss; and, in Figure III, Felapton 
 and Ferison, which reduce to Festino by conversion of both 
 premisses. 
 
 § 770. It may be thought that considerable violence will have 
 to be offered to the Moods in which both premisses are affirma- 
 tive to bring them into line with those which express repugnance. 
 But the direct Moods in Figure I require no change beyond 
 
 ' See Appendix E. 
 
Reduction to Figure II 355 
 
 conversion by negation' (obvefsion — conversion) in the major 
 premiss. The conclusion must be obverted. Thus^ 
 Barbara becomes Cesare. 
 Every M is P=No not-P is M 
 Every S is M 
 .-. Every S is P (No S is not-P).: 
 Example : — 
 
 Those who have suffered are sympathetic =The unsympathetic 
 have not suffered. 
 
 Every woman has suffered. 
 
 Then [non ignara malt) every woman is sympathetic (No 
 woman is unsympathetic). 
 
 Z>ar?i' similarly reduces to Festino. Jn Figure III the direct 
 affirmative Moods, besides conversion by negation in the major, 
 require conversion of the minor, premiss. Thus — 
 Darapti becomes Festino. 
 Every M is P = No not-P is M 
 Every M is S = Some S's are M 
 .*. Some S is P (Some S's are not not-P). 
 Datisi reduces to Festino in the same way. 
 
 § 771. There remain the indirect Moods, Disamis, Bocardo, 
 Bramantip and Dimaris. In these the premisses must be trans- 
 posed. Then Bocardo becomes Festino by obversion followed 
 by conversion in both premisses, while the conclusion is reached 
 by obversion, followed by conversion, followed by obversion 
 again — this threefold process is called contraposition ^ — , of the 
 conclusion oi Festino. Thus — 
 
 _ f Some M's are not P = Some not-P's are M 
 
 ranspose | ^^^^ M is S = No not-S is M 
 
 .•. Some S's are not P (Some not-P's are not not-S, 
 = Some not-P's are S, = Some S's are not-P, 
 = Some S's are not P). 
 
 * This name (applied also to conversion — obversion) seems less suitable 
 in dealing with negative propositions. 
 
 " In Contraposition the terms are transposed and their quality changed, 
 that of the proposition itself being unchanged. Thus, ' Every X is Y ' 
 becomes by contraposition ' Every not-Y is not-X '. ' No X is Y ' 
 becomes ' Some not-Y is not not-X '. ' Some X is not Y ' becomes 
 ' Some not-Y is not not-X '. Particular affirmative propositions do not 
 admit of contraposition. Conversion — obversion— conversion (Keynes's 
 ' Inversion ') is only possible with E judgements. 
 
 A a 2 
 
356 Mood and Figure 
 
 Example : — 
 Some good men are not wise = Some unwise men are good. 
 Every good man is well-intentioned = No one who is not well- 
 intentioned is good. 
 Then, Some who are well-intentioned are not wise (reached thus 
 —Some unwise men are not otherwise than well-intentioned = 
 Some unwise men are well-intentioned = Some well-intentioned 
 men are unwise = Some well-intentioned men are not wise). 
 There is nothing very far-fetched in this. Disamis also be- 
 comes Festino in the same way, except that the apparent major 
 premiss merely wants converting. 
 
 The two Fourth Figure Moods, Bramantip and Dimaris, 
 reduce to Figure II by conversion by negation in the apparent 
 minor premiss. The conclusion is reached in either case by 
 obversion followed by conversion. Thus — 
 
 Bramantip. 
 
 ~ f Every P is M 
 
 iranspose | ^^^^^ M is S = No not-S is M 
 
 .•. Some S's are P (No P is not-S = Every P is S, 
 converts /er accidens to Some S's are P). 
 
 Dimaris. 
 
 ( Some P's are M 
 Iranspose ^ ^^^^^ M is S = No not-S is M 
 
 .•. Some S's are P (Some P's are not not-S = Some 
 P's are S = Some S's are P). 
 
 These reducts are Cesare and Festino respectively. But it 
 must be observed as regards all the affirmative Moods reduced 
 to Figure II that the negative conclusion is directly about the 
 relations, not of S and P, but of S and not-P or of P and not-S. 
 Bramantip in fact can be reduced to Camestres without trans- 
 position of premisses, the conclusion being No not-S is P, = No 
 P is not-S, = Every P is S, which converts p.a. to Some S's 
 are P. 
 
 § 772. Enough has been said to show that there are in Logic, 
 as in England, two primacies rather than one, and that the 
 First Figure has only a precedence of honour over the Second. 
 Given a rule, then wherever the condition is fulfilled the rule 
 applies, and wherever the rule does not apply the condition is 
 not fulfilled. Repugnans notae est repugnans rei ipsi. 
 
Cross-Reduction 357 
 
 § 773. It is possible, indeed, to reduce all the Moods of the 
 First or Second Figure except Barbara to Moods of the Third 
 or Fourth Figure. Thus Darii by a trifling change can be 
 exhibited as Z)«/«s« (Fig. Ill), and, by transposition of premisses, 
 as Diniaris (Fig. IV). Feria easily glides into Fresison (Fig. 
 IV). Celarent can be reduced to Camenes (Fig. IV), Again, of 
 Moods in the Second Figure, Camestres and Cesare will reduce 
 to Camenes. Festino reduces by conversion of one premiss to 
 Fresison (Fig. IV), and of both to Ferison (Fig. III). Baroco, 
 made amenable by obversion, can be exhibited in the construc- 
 tion Fresison. Finally, four Moods of Figure IV can be reduced 
 to Figure III, viz. Bramantip and Dimaris, if the premisses be 
 transposed, to Datisi, Fesapo to Felapton and (less easily) to 
 Daraptif and Fresison to Ferison and (with some pressure) to 
 Disamis or Bocardo. But Camenes, having a universal conclu- 
 sion, refuses to be so treated. Reduction from one imperfect 
 Figure to another is called by Stock Transverse or Cross-reduc- 
 tion. Neither the Third nor the Fourth Figure can be regarded 
 as a type or .norm. 
 
 § 774. The expressions Major, Minor and Middle have 
 reference originally to the First Figure. The Major Term (ro 
 fji£i^ov) and the Minor Term {to eXarrov) are 
 so called because in Barbara — leaving identi- 
 fications on one side— the one has a larger 
 and the other a smaller extension. The 
 minor term is there ' wholly in ' the middle, 
 and the middle 'wholly in' the major. 
 Such, Aristotle says, necessarily constitutes 
 a perfect corrationalizing {avXkoyt<j[j.6%) of the 
 extremes..' 
 
 But there is no other Mood in Figure I in which we can tell 
 whether major or minor term has the larger extension. E and O 
 are exclusive. I merely affirms that the two spheres partly 
 
 ' "Orav Spoi rpels ovtcos ep^owrt Trpos aW^Xour more tov e(TXaTov iv oka uvai 
 TBI liAcm Koi TOV fU(rov iv oka ra Trpoirm fj elvai fj fifj eivai, avdyKr) tS>v axpav ilvat 
 cruXXoyicr/iov TfKeiov (An. Pr. i. 4. 25''32). e(TxaTov and irpSirov seem to refer 
 to the order of the premisses in the usual Greek form — ' P is preicdated 
 of M, M of S '. KOTrj-yopslrai Kara should be the form for judgement in 
 intension, eV Ska ia-n for judgement in .extension. But Aristotle uses the 
 two expressions in the same sense (An. Pr. i. I, § 8). 
 
358 Mood ani Figure 
 
 coincide. When the syllogism is expressed in intension, the 
 major term ol Barbara will be the least (see below, p. 571). 
 
 § 775' The Major Premiss is, that which contains the Major 
 Term; the Minor Premiss is that in which the Minor Term 
 occurs. In speaking of the Indirect Moods, however, I have 
 spoken of the ' apparent ' major. For these moods are really 
 inverted. The true major premiss in thought must be that which 
 states the rule or principle. So in common speech — " I deny 
 your major " — referring to some general assertion under which 
 a case is to be brought. 
 
 § 776. The Middle Term was partly so called from its position 
 in the First Figure, as enunciated by the Greeks, SM, MP; 
 therefore SP. Aristotle, however, also calls it by this name 
 because it ' is both in another and another in it '?■ But this is 
 only true of Barbara. The expression ' middle term,' however, 
 has a significance which is not merely technical, nor confined to 
 a single type of reasoning. For all argumentation is essentially 
 mediate ; and we can never judge P of S without an intermediary 
 ground. 
 
 § 777- The honour traditionally paid to the First Figure was 
 connected with the conception, already several times mentioned, 
 of a fixed subordination of concepts, each having a natural 
 predicate in the concept just above it. 'The first figure,' says 
 Dr. Wallace, ' as corresponding more than other figures with 
 the natural order of phenomena, because its middle term really 
 lies between the two extremes, is regarded by Aristotle as the 
 typical form of syllogistic reasoning, and as therefore pre- 
 eminently cogent and conclusive.' ' The Second Figure gives 
 only negative conclusions, the Third only particular. The 
 First alone, in Barbara, enables universal affirmative inferences 
 to be drawn, and so is regarded as the scientific figure.' To 
 reduce a mood to it is to show that the conclusion holds if the 
 premisses are stated in the construction of Figure I. 
 
 § 778. Something further should be said about certain special 
 features of the Four Figures. 
 
 ^ KaXoi hi \ik<jov o nai airo iv aXXo) Kai aXXo iv Tovra iariv, o Ka\ rrj BiaH 
 ylvirai fjAaov {An. Pr. i. 4. 25''3S). 
 
 ' Outlines, p. 39. 
 
 * To )x.\v ovv KaTafjyaTiKOP to Kad6\ov bia tou irpaTov tr^rjfiaTOS SeUvvrai /iovov, 
 Kai iia TOVTOV fiovaxo>s {An. Pr. i. 26. 42*32). 
 
Figure I 359 
 
 Figure I. 
 
 Whatever is predicated of a term distributed affirmatively or 
 negatively may be predicated likewise of everything contained 
 under it. Aristotle's short Canon is this — • Whatever is stated 
 of the predicate will be stated also of the subject'. What is in 
 the contained is in the containing. This formula of Buffier's 
 will cover the intensive as well as the extensive aspects of syllo- 
 gism, and give a particular as well as a universal conclusion. 
 
 This Figure exhibits the bringing of case under rule. But 
 such subsumption cannot take place unless what is said about 
 the middle term, whether affirmatively or negatively; be said 
 about the whole of it. The major premiss, then, must be A or E. 
 And subsumption must be an assertion, not a denial. Otherwise 
 We get irrelevance and disconnexion. Accordingly the minor 
 premiss, whether universal or particular, must be affirmative — 
 that is, either A or I. In this Figure, then, there can be no 
 place for O premisses. 
 
 § 779. Whatever be the quality of the major premiss will be 
 the quality of the conclusion. And whatever be the quantity of 
 the minor premiss will be the quantity of the conclusion. But 
 the latter rule requires to be guarded. The quantity of the con- 
 clusion is thought as a minimum, even when stated in the minor 
 premiss as a maximum. Thus — 'All kings eat ; only one man in 
 England is a king ' — we do not conclude that only one man in 
 England eats, but that one man at least does so. Again, ' Few 
 Chinamen are Christians. All Christians are bipeds ' ; then a 
 few [at least), not. few, Chinamen are bipeds. 
 
 Of course, such conclusions are absurdly inadequate, the fact 
 being that quantification expressed with a limitation — 'only 
 sometimes', 'just fourteen,' 'less than half,' 'scarcely a tenth' — 
 is of the nature of an O judgement — a minus quantification — 
 and has its natural place as the negative premiss of an argument 
 in Figure II. Thus — 
 
 All who are in earnest signed the paper. 
 
 Only a few (or, not more than nine) signed the paper. 
 
 Then only a few (or, not more than nine) are in earnest. 
 
 § 780. The quantity of the minor premiss in Figure I might 
 be filled up with any number. 'Those who were there had 
 a happy day. Seven were there. Then seven (at least) had 
 a happy day.' But the specified figure cannot be zero. For 
 
360 Mood and Figure 
 
 nought is in itself a limitation ; and ' none at least ' in a conclu- 
 sion would be meaningless. 
 
 The exception to the above is when the major premiss is 
 understood as a convertible proposition. In that case the limi- 
 tation reappears in the conclusion. Thus — 'All who signed 
 the paper are in earnest ' probably implies that all who are in 
 earnest signed the paper. ' Only nine signed it. Then only 
 nine are in earnest.' But this, we have seen, is really an argu- 
 ment in Figure II. 
 
 Figure II. 
 
 § 781. ' So far as an attribute is affirmed of one class and denied 
 of another, those two classes exclude one another.' What is not in 
 the containing is not in the contained [Camestres, Baroco). What is 
 in the not-containing is not in the non-contained {Cesare, Festino). 
 
 In this Figure the middle term is taken twice as attribute, once 
 affirmatively and once negatively. 
 
 Francis Quarles thus quotes St. Ambrose {De Virg. lib. iii)— 
 ' Christ is not in the market nor in the streets. For Christ is 
 peace, in the market is strife ; Christ is justice, in the market 
 is iniquity ; Christ is a labourer, in the market is idleness ; 
 Christ is charity, in the market is slander ; Christ is faith, in 
 the market is fraud.' 
 
 § 782. If Figure I answers to the ratio essendt, Figure II sets 
 forth the ratio cognoscendi in its negative and only cogent form, 
 of denial that a mark is present in a particular case. 
 
 This is the figure of Comparison. Agreement (unless our 
 premiss states a proprium) proves nothing ; only disagreement. 
 A gentleman acts considerately. 
 X does not act considerately. 
 It follows that X is not a gentleman. 
 A fuller form of the argument is this : 
 Every A is both B and C ; 
 
 D is B but not C {or, is C but not B). 
 Then D is not A. 
 
 Example (see Leviticus xi) — 
 
 A clean beast is one which chews the cud and divides the hoof. 
 
 The camel cheweth the cud but divideth not the hoof; he is 
 unclean unto you. 
 
 The swine, though he divide the hoof, yet he cheweth not 
 the cud ; he is unclean unto you. 
 
Figures II and III 361 
 
 Minto well calls this the figure of Negative Diagnosis.^ 
 A physician concludes from the absence of a symptom. This 
 patient is not suffering from scarlet fever, for he has no sore 
 throat. The Second Figure, then, is the basis of Induction, and 
 is the form taken by the Method of Exclusions. Two affirmative 
 premisses, the agreement of two objects in some characteristic, 
 will help but little towards an Induction. Nevertheless, such a con- 
 struction is often adopted to show that two objects — they cannot 
 be regarded as subject and predicate — have something in com- 
 mon ; as when the unwieldy knight writes to Mistress Page : — 
 
 'You are not young, — no more am I — go to, then, there's 
 sympathy. You are merry ; so am I — ha ! ha ! then, there 's 
 more sympathy. You love sack, and so do I— would you desire 
 better sympathy ? ' We say epigrammatically of two people who 
 commit the same fault, ' It is six of one and half a dozen of the 
 other' (C'est bonnet blanc et blanc bonnet). See also Eccles. iii. 19. 
 
 But when Bertalda is known to be the fisherman's daughter by 
 the marks on her left instep and shoulders, or Ulysses is recog- 
 nized by the nurse by the scar from the boar's tusk, the major 
 premiss is really, ' Only she (or he) could be so marked.' 
 
 Figure III. 
 
 § 783. In this Figure two statements are made about the same 
 subject. If any subject is said to have two attributes (A is both B 
 and C), those attributes are thereby seen to be at least sometimes 
 found in combination. ' Grote was a banker — Grote was a man 
 of letters. Then a banker may be a man of letters.' Or if it has 
 one attribute and lacks another (A is C but not B), the former attri^ 
 bute is seen not necessarily to carry with it the latter. ' Two 
 terms which contain a common 
 part partly agree ; or, if the one 
 contain a part which the other 
 does not, they partly differ.' But in 
 this formula ' contain a part ' must 
 be understood in extension ; and 
 ' agree ' and ' differ ' must mean 
 coincide and the reverse in sphere. 
 
 Or thus — ' If two classes contain the same thing — the one 
 wholly, the other wholly or in part, then they partially coincide '. 
 
 ' Logic, p. 200. 
 
^2 Mood and Figure 
 
 But for this formula to cover negative moods, it must be possible 
 for one of the containing classes to be negative. 
 
 § 784. In this Figure theminor premiss must always be affirma- 
 tive, and the conclusion particular. An argument in Figure III 
 may seem to have two negative premisses — M is not P, M is 
 not S. But the conclusion here is about not-S — Some not-S is 
 not P. As regards the particular conclusion Sigwart observes : — 
 
 ' The particular judgements of fig. 3 differ essentially from 
 those of figs. I and 2. In the latter the term which is particular 
 stands from the first 'as subject, and the fact that it is particular 
 is unimportant, may indeed be due merely to the verbal expres- 
 sion ; the subjects of the minor premiss and of the conclusion 
 are the same. But in the third figure the particular term is 
 subject only in the conclusion, and possesses therefore all the 
 indefiniteness of the particular. It is equivalent to a mere 
 judgement of possibility ; and in the third figure there can be 
 no such thing as a necessary consequence in the ordinary 
 sense.' ' 
 
 § 785. The conclusion, in other words, is essentially, and not 
 accidentally, particular. The two predicates, we judge, are not 
 necessarily incompatible, or are not necessarily connected". S may 
 be P. S is not obliged to be P. So that Datisi is not, except 
 in form, a subordinate mood to Darapti, nor Ferison to Felapton, 
 in the same way that Darii in Figure I stands under Barbara 
 and Ferio under Celarent. For the subsumption can never be 
 universal, the A minor premiss of Z>ara/ifo' having to be converted 
 to I before case can be brought under rule. 
 
 § 786. Not concluding universally, the Third Figure is com- 
 monly employed to establish an objection to a too sweeping 
 statement. A is confronted with O and E with I. Thus, if it be 
 asserted that no good man ever practises deception, it might be 
 replied {Darapti) that all anglers practise deception, and that 
 anglers are invariably good men. An unqualified statement can 
 be upset by a single instantia. The argument from Analogy is 
 often of this kind ; and accordingly the principle underlying 
 Figure III is called the Dictum de Exemplo. ' So-and-so of our 
 College won the Newdigate, and also took a First Class in 
 Mathematics. This shows that mathematicians sometimes are 
 poets.' 
 
 § 787. Identifying judgements with a singular subject are 
 
 ' Logic, i. 35S. 
 
Figure IV 363 
 
 usually in this Figitre. Thus — ' Wellington was the victor at 
 Waterloo. Wellington was our greatest commander. It follows 
 that it was our greatest commander who was the victor at 
 Waterloo.' 
 
 Figure IV. 
 
 § 788. ' If any class is wholly or partly contained in another 
 class which is wholly contained in a third class, some of the 
 members of this last class have the characteristics of the first 
 class.' But this formula needs some restatement for the nega- 
 tive moods. This much derided schema is required for logical 
 symmetry, since Figures are distinguished by the position of the 
 middle term ; and we have not yet considered the case of 
 premisses which have the middle term as predicate of the major 
 and subject of the minor. The more or less of utility possessed 
 by any arrangement of terms is not the question. Logic is not 
 a mere Art. We have to inquire what forms of argument have 
 rational cogency. Moreover, in view of the endless variations 
 of shape which thought actually takes, the charge of uselessness 
 should not be too quickly accepted. It all depends on what point, 
 we are interested in establishing. The following, for instance, 
 is in Camenes — 
 
 The man wanted by the police is a criminal ; no criminal lives 
 in our court ; 
 
 It follows that no one who lives in our court is the man wanted 
 by the police. 
 And this is in Bramantip — 
 
 Swordsmanship is a noble accomplishment. 
 
 All noble accomplishments ought to be practised by you. 
 
 Then one of the things you ought to practise is swordsmanship. 
 Or the question may arise, how to get at a secret. The following 
 is Fesapo — 
 
 Philip never exceeds ; 
 But in vino Veritas ; 
 Then one way of getting at the truth is not to be hoped for 
 from Philip. 
 
 Bain, speaking of an indirect Mood, Disamis, in Figure III, 
 gives as example — 
 
 Some men are kings; 
 
 All -men are fallible beings; 
 
 Then some fallible beings are kings. 
 
3^4 Mood and Figure 
 
 Substitute for ' kings ' ' invested with Divine authority ', and the 
 argument will be a usual and instructive one. A similar argu- 
 ment in Dimaris (Fig. IV) is equally to the point — 
 
 Some persons invested with authority are parents. 
 
 All parents are fallible. 
 
 Then some fallible persons are invested with authority. 
 This answers a question which has often been debated. 
 
 Another example of Dimaris might be this — 
 
 Men of genius sometimes commit crime. 
 
 Those who commit crime find their way to prison. 
 
 Then some who find their way to prison are men of genius. 
 In Figure I the mind would be directed to the question, What 
 happens to men of genius? In Figure IV, the question is rather, 
 What kinds of men get into prison ? If one went through the 
 cells, whom would one find there ? 
 
 § 789. The Fourth Figure is not mentioned by Aristotle, who, 
 attending only to the possible combinations of premisses, without 
 reference to the conclusion, regarded the Middle Term as occupy- 
 ing one of three positions. It might stand (i) above both 
 premisses, i. e. be predicate of both ; (2) below both premisses, 
 i. e. be subject of both ; or (3) between the premisses, i. e. be 
 subject of one and predicate of the other.' 
 
 § 790. When we think, however, of the premisses in connexion 
 with the conclusion to be drawn from them, it cannot be left 
 undetermined which is the major (i. e. contains the major term,, 
 or predicate of the conclusion), and which is the minor (i. e. con- 
 tains the subject of the conclusion). Or, if we have the premisses 
 and the conclusion is not yet drawn, then, according as the 
 middle term is predicate of the one premiss or of the other, the 
 conclusion can be drawn in two different ways. The arrange- 
 ment is not ' fortuitous and arbitrary ', as Veitch ^ maintains. 
 
 § 791. McCosh states an objection to the Fourth Figure thus — 
 
 'In the minor premiss S, the predicate, is more extensive 
 than M, the subject ; and in the major premiss M, the predicate, 
 is more extensive than P. But in the conclusion we find S, the 
 
 ' These are not the precise expressions of Aristotle, who says of 
 
 Figure II : riBeTai to fieaov e^a> fjiev Tav aKpa>v, wpSiToi> 8e rfj 6e<Tei (Aft. Pf- 
 i. Si § l), and of Figure III : Tiderai to fiea-ov e^a fiiv tS>v aKpav, ((rxatov Si 
 TTj 6ia-fi {An. Pr. i. 6, § i). 
 ^ Institutes, p. 396. 
 
Figure IV 365 
 
 ■more extensive, the subject, and P, the less extensive, the predi- 
 cate, which is not agreeable to spontaneous thought, and should 
 not have a place in reflective thought.' ^ 
 
 If the conclusion were about all S's this would be a valid 
 objection. But it is about some S's. The extension, then, of S 
 and P in the conclusion cannot be compared. The only mood 
 in Figure IV with a universal conclusion is Camenes, which is 
 negative. It might as well be objected to Darapti that its middle 
 is less extensive than its minor term, or against Camestres and 
 Baroco that their major is less extensive than their middle term. 
 
 §792. Hamilton derides this Figure as a hybrid. Its premisses 
 are in Intension, its conclusion in Extension. He should have 
 said that, while the minor term is in the premiss intensive but in 
 the conclusion extensive, it is just the opposite with the major 
 term. 
 
 But this indictment is really directed against all Indirect Moods, 
 and holds good, not only against Bramantip and Dimaris, but 
 against Disamis and Bocardo also. 
 
 § 793. It is the rugged anfractuosities of Bramantip which 
 excite so much wrath against the Fourth Figure generally. 
 That luckless mood seems to combine all syllogistic weaknesses, 
 as Barbara all syllogistic virtues. Bramantip is dSitix-Barbara, 
 Barbara topsy-turvy. 
 
 Camenes, however, we have seen to be a perfectly respectable 
 Mood, on the lines of Figure II. If reduced, it is true, to the 
 First Figure, it must be regarded as an indirect Mood. On the 
 other hand, this cannot be alleged against Fesapo and Fresison. 
 No transposition of premisses is possible in dealing with these 
 two.^ Yet scarcely a logician but has thrown a stone at them 
 as at the others, on the alleged ground of their being merely 
 moods of Figure I in the disguise of a transposed arrangement. 
 Thus Bain says : — 
 
 ' The modes of the Fourth Figure are, with the appearance of 
 great inversion, mere varieties of the primary Figure. The trans- 
 position of the order of the premisses is the most insignificant of 
 all the alterations made on a syllogism. It signifies nothing to 
 the reasoning in what order the premisses are stated.' ' 
 
 ^ Laws of Discursive Thought, pp. 133, 134. 
 
 ^ They would be indirect Moods if reduced to AEO and lEO in 
 Figure I ; but those syllogisms are invalid. 
 ' Logic, Pt. I, p. 145. 
 
366 Mood and Figure 
 
 And meanwhile Disamis and Bocardo, which are really guilty 
 in this matter, are allowed to pass unreproved. If Fesapo and 
 Fresison are indeed First Figure moods upside-down, where is 
 the tell-tale s or p after their last syllable ? ' Bocardo, it is true, 
 is without such a mark. But logicians have given it a treatment 
 all to itself. 
 
 § 794. It must be repeated that the real gravamen is not against 
 the Fourth Figure in itself, but against the Indirect or Inverted 
 Moods in the two last Figures — Disamis, Bocardo, Bramantip 
 and Dimasis. 
 
 § 795. Kant attacked the distinction of Figures. But that 
 distinction exists in the structure of human thought. Reason on 
 the other hand is one. Logic exhibits the unity of Reason in the 
 diversity of Thought — it cannot be said that there is no unity 
 to be exhibited. Each Figure has its own use. Yet we have 
 shown that not all are normal ; but that the last two Figures are 
 subordinate to, and resoluble into, the two first. 
 
 ' Bain says that Fesapo and Fresison ' present both premisses con- 
 verted ; and the first of the two is superfluous, even as a form ' (loc^ cit.). 
 But why more superfluous than Darapti, which yields the same conclusion 
 as Datisi or Disamis ? 
 
CHAPTER XXIV 
 MOOD AND FIGURE (continued) 
 
 § 796. The two syllogistic types may be represented in this 
 categorical form— ^ 
 
 Ponenf. Tollent. 
 
 FisZ FisZ 
 
 X is y Z is not Z 
 
 .-.X is Z. .-. X is not Y. 
 
 Or in semi-conjunctive form thus — 
 
 \iX\%Y,XisZ liX\.%Y,X\%Z 
 
 X\&Y Z is not Z 
 
 .-. ^isZ. .-. ;? isnot y. 
 
 If the conditio^ is fulfilled the rule applies. If the rule does 
 not apply, the condition is not fulfilled. 
 
 § 797. The following Conspectus of figured forms of argument 
 is based on this double principle. But it has to make room for 
 the partial fulfilment of the condition and the partial non-applica- 
 tion of the rule (Particular Judgements) ; and also for a negative 
 equally with a positive rule. 
 
 Direct Moods (15). 
 
 I (Figs. I and III),— Condition fulfilled (carrying with it the 
 assertion 6f the rule's application). 
 
 y Positive rule 
 
 Universally 
 (entire affir- 
 mation of the 
 antecedent) 
 
 (Fig. I) Barbara, Yh,Z, X is Y; .: X is Z. 
 
 Negative rule 
 (Fig. I) Celarent, Y is not Z, X is Y; .: ,X^is 
 ^ not Z. 
 
368 
 
 Mood and Figure 
 
 (minor pr. converted s). 
 
 antecedent) 
 
 /Positive rule 
 
 (Fig. I) Darii, Fis Z, Some X is Y; .-. Some 
 
 X is Z. 
 
 (Fig. Ill) Darapti, Y is Z, Y is X; .: Some 
 
 XisZ 
 
 (minor pr. converted p). 
 
 I (Fig. Ill) Datisi, Y is Z, Some Y is Z; .-. 
 
 Ti ^- 1 1 I Some X is Z 
 Particularly ^^.^^ 
 
 (partial affir- / 
 
 mationoftheX ,, . , 
 Negative rule 
 
 (Fig. I) Ferio, Y is not Z, Some ^ is F; .-. 
 
 Some X is not Z. 
 
 (Fig. Ill) Felapton, Y is not Z, F is X; .: 
 
 Some X is not Z 
 
 (minor pr. converted p). ' 
 
 (Fig. Ill) Ferison, Y is not Z, Some F is Z; 
 
 I .-. Some X is not Z 
 
 V (minor pr. converted s). 
 
 II (Figs. II and IV). — Rule not applying (carrying with it 
 the non-fulfilment of the condition). 
 
 / (Fig. II) Cesare, Z is not Y, X is F; .•. X is 
 not Z. 
 (Fig. II) Camestres, ZisY, X is not F; .-. X 
 is not Z. 
 
 Universally 
 (entire denial of ■ 
 the consequent) 
 
 (Fig. IV) Camenes, Z is F, Fis not X; .: X 
 is not Z 
 
 (minor pr. converted s). 
 
 Particularly 
 (partial denial 
 of the conse' 
 
 : 
 
 / (Fig. II) Festino, Z is not F, Some X is F; .'. 
 
 Some X is not Z. 
 (Fig. II) Baroco, Z is F, Some X is not F; 
 
 .-. Some X is not Z. 
 (Fig. IV) Fesa/io, X is not F, Fis Z; .-. Some 
 
 quent) 
 
 X is not Z 
 
 (minor pr. converted p). 
 (Fig. IV) Fresison, Z is not F, Some F is X, 
 .". Some X is not Z 
 
 (minor pr. converted s). 
 Fxcept for a missing mood just before Camenes there is an exact 
 parallelism in the above scheme. 
 
Condition and Rule 369 
 
 § 798. In the four Indirect Moods, including Bocardo, the 
 condition must be regarded as fulfilled, carrying with it a posi- 
 tive rule. Bocardo concludes, however, directly about not-P. 
 
 Condition fulfilled : — 
 Universally — (Fig. IV) Bramantip, Z is Y, Y \% X; :. (Z is X) 
 Some Xis Z 
 
 (conclusion conv. p). 
 
 I (Fig. IV) Dtmaris, Some ZisY, Yis X ; .: (Some 
 Z is X) Some ^ is Z 
 
 (conclusion conv. s). 
 (Fig. Ill) Disamis, Some YisZ, Yis X; .: (Some 
 Particularly ■/ ^ is ^ Some X is Z. 
 
 (major pr, conv. s, and conclusion conv. s). 
 (Fig. Ill) Bocardo, Some Y is not Z, Y is X; 
 
 .•. (Some not-Z is X) Some X is not Z 
 (obvert and convert major pr., convert and obvert 
 conclusion). 
 The direct conclusions are the ones in brackets. 
 § 799. Once more. If the First Figure be taken as the syllo- 
 gistic type, then, since the major premiss in this figure must be 
 universal and have a distributed middle term, the possible major 
 premisses are: — 
 
 Every M is P 
 No ikf is P 
 No P is M. 
 
 And since the minor premiss must be affirmative, it may take 
 one of these four shapes^- 
 
 Every S is M 
 Every M is S 
 Some 5's are M 
 Some M's are S. 
 Combining, we get twelve direct Moods. Five others reduce 
 to this type by transposition of premisses, viz. Camestres, 
 Disamis, Bramantip, Dimaris and Camenes. There remain 
 Baroco and Bocardo. The former, a direct Mood, gives a 
 conclusion in Ferio through not-ilf — 
 
 Every PisM = No P is not-ilf = No not-M is P 
 
 Some S's are not M = Some 5's are no\.-M. 
 
 :. Some 5's are not P — 
 Bb 
 
370 Mood and Figure 
 
 and the latter, an indirect Mood, concludes in Darii about not-P— 
 Some M's are not P = Some M's are not-P = Some not-P's 
 
 are M 
 Every M is S 
 .'. Some not-P's are 5 = Some 5's are not-P — Some 5's are 
 
 not P. 
 
 § 800. It should be noticed that some judgement about non-P 
 is involved in the conclusion of every Mood, if it is A, E or 0. 
 ' Every S is P' implies that No non-P'sare S; 'No S isP' that 
 Some non-P's are S ; and the same judgement is involved in 
 ' Some S's are not P '. Thus from an argument in Ferio — 
 No arguments based on an undistributed middle term are 
 
 legitimate ; 
 Some arguments often advanced are so based ; 
 Then, some arguments often advanced are not legitimate — 
 
 we get the judgement, ' Some illegitimate arguments are often 
 advanced.' 
 § 801. Some judgement about non-S is involved in every A 
 
 or E conclusion, viz. a particular negative judgement in A, and 
 
 a particular affirmative judgement in E. Thus in Barbara — 
 
 Every S is P. Everything that is knowledge is known to me. 
 
 = No S is non-P. Nothing that is knowledge is unknown to me. 
 
 = No non-P is 5. Nothing unknown to me is knowledge. 
 
 = Every non-P is non-5. All I do not know is not knowledge. 
 
 = Some non-5's are non-P. Some things which are not know- 
 ledge are unknown to me. . 
 
 Celarent, Cesare, Camestres and Camenes, on the other hand, 
 
 enable us to infer that Some non-S's are P. 
 
 Nothing whatever can be inferred universally about non-S; 
 
 nor yet about non-P, except the absence of 5. 
 
 A universal negative conclusion about non-S is never involved 
 
 in any judgement about 5. We cannot infer that none but the 
 
 brave (no non-brave) deserve the fair from any pair of premisses 
 
 which have ' the brave ' for minor term. 
 
 § 802. Inasmuch as every negative proposition can be made 
 an affirmative one by attaching the negation to the predicate, it 
 may be inquired how far the abolition of quality would simplify 
 syllogism. 
 
 
Negative and Privative Conception 371 
 
 Figure I. 
 
 (Celarent) becomes {Barbara) 
 
 No M is P Every M is not-P 
 
 Every S is M Every S is M 
 
 No S is P Every S is not-P. 
 
 [Ferio) becomes [Darii) 
 
 No M is P Every M is not-P 
 
 Some 5's are M Some S's are M 
 
 Some S's are not P Some 5's are not-P. 
 
 Figure II. 
 [Cesare) becomes {Barbara) 
 
 No P is M Every M is not-P 
 
 Every S is M Every S is M 
 
 No S is P Every S is not-P. 
 
 {Camestres) becomes by transp. {Barbara) 
 Every Pis M Every M is not-S 
 
 NoSisM ' Every P is M 
 
 No S is P Every P is not-S 
 
 (= No S is P). 
 
 {Festino) becomes {Darii) 
 
 No P is M Every M is not-P 
 
 Some S's are M Some S's are M 
 
 Some S's are not P Some S's are not-P. 
 
 {Baroco) becomes {Darii ) 
 
 Every P is M Every not-M is not-P 
 
 Some S's are not M Some S's are noi-M 
 
 Some S's are not P Some S's are not-P. 
 
 Figure III. 
 {Felapton) becomes {Darii) 
 
 No iJ/ is P Every M is not-P 
 
 Every M is S Some S's are M 
 
 Some S's are not P Some S's are not-P. 
 
 {Bocardo) becomes by transp. {Darii) 
 Some M's are not P Every Mis S 
 
 Every M is S Some not-P's are M 
 
 Some S's are not P Some not-P's are S 
 
 (= Some S's are not-P). 
 B b 2 
 
372 Mood and Figure 
 
 {Ferison) becomes {Darii ) 
 
 No 71/ is P Every M is not-P 
 
 Some M's are 5 Some 5's are M 
 
 Some S's are not P Some S's are not-P. 
 
 Figure IV. 
 {Camenes) becomes (Barbara) 
 
 Every P is M Every not-M is not-P 
 
 No ilf is S Every S is noi-M 
 
 No 5 is P Every S is not-P. 
 
 aliter per transpositionem 
 Every P is M Every M is not-5 
 
 No J/ is S Every P is M 
 
 No S is P Every P is not-5 
 
 (= Every S is notP). 
 {Fesapo) becomes (Darii) 
 
 No P is M Every M is not-P 
 
 Every M is S Some 5's are M 
 
 Some S's are not P Some S's are not-P. 
 
 (Fresison) becomes (Darii) 
 
 No P is ilf Every M is not-P 
 
 Some M's are S Some S's are M 
 
 Some S's are not P Some S's are not-P. 
 
 § 803. We see then that Celarent, Cesare, Camestres and 
 Camenes may be exhibited as Barbara, and the other eight 
 negative moods as Darii. Such abolition of prepositional 
 quality, however, is not in every case obvious and natural. 
 For the mind may perhaps pass instantaneously from 'No 
 shallow natures are patient' to 'All shallow natures are im- 
 patient '. But there is not an immediately obvious equivalence 
 between this syllogism (Camenes) — 
 
 Every disciplined nature is patient. 
 No patient nature is complaining, 
 .'. No complaining nature is disciplined, 
 and this (Barbara) — 
 Every impatient nature is undisciplined, 
 Every complaining nature is impatient, 
 .'. Every complaining nature is undisciplined. 
 § 804. Moreover, as we have more than once noticed (§ 158), 
 negative conception only in a certain ' universe of discourse ' be- 
 
Suggested Simplifications 373 
 
 comes privative and implies a positive idea. If a line is not 
 straiglit it must be curved or crooked, and if we say that an action 
 is not kind it is probably unkind (though even this does not 
 follow, for most actions are neither, yet that would usually be 
 our meaning). But we cannot say that because ink-pots are not 
 successful novelists, they are therefore unsuccessful novelists. 
 Arguments are in practice seldom framed except as under- 
 standing a positive idea by a negated term. But logically it is 
 different. And therefore, although negative moods may all be 
 exhibited easily in an affirmative form, the idea of negation 
 cannot be abolished, not-X meaning a thing which is not X. 
 § 805. It has already been noticed that, when the mark of 
 negation is attached to the predicate, every negative mood in 
 whatever figure appears as Barbara or Darii. But Fesapo may 
 also be exhibited as Darapti (Every M is not-P, Every M is S, 
 .•. Some S's are not-P), and Fresisori as Datisi. Fdapton glides 
 easily into Darapti in the same figure (Every M is not-P, Every 
 M is S, .•. Some .5's are not-P), Ferison into Datisi, Bocardo into 
 Disamis. In Figure II, Fesfino can be exhibited as Datisi in 
 the Third Figure or as Dimqris in the Fourth ; Baroco also as 
 Datisi or as Dimaris. Ferio in Figure I can be shown as Datisi 
 or as Dimaris. But the four moods with universal conclusion, 
 Celarent, Cesare, Camestt^es a,nd Camenesy cannot be exhibited 
 except in Barbara. 
 
 § 806. The following simplification of Syllogism is here 
 suggested, by which also quality is got rid of. Negative pro- 
 positions have a distributed predicate. If, now, all distributed 
 terms are indicated by a capital letter, and undistributed terms 
 by a small one, mere juxtaposition of subject and predicate will 
 suffice for any kind of proposition. A will be Sp. I will be sp. E 
 will be shown as SP and O as sP. The relation of the middle 
 term to the extremes will accordingly be fourfold in the minor 
 {Sm, sm, SM, sM), and fourfold in the major {Mp, mp, MP, mP). 
 The moods which, on thebasis of 'Figure I, conclude about S 
 directly will then appear thus : — 
 
 Figure I. 
 {Barbara) (Darii) (Celarent) (Ferio) 
 Mp Mp MP MP 
 
 Sm sm Sm. sm 
 
 Sp sp SP sP. 
 
374 
 
 Mood and Figure 
 
 
 Figure II. 
 
 {Cesar e) 
 
 (Festind) (Baroco) 
 
 PM 
 
 PM Pm 
 
 Sm 
 
 sm sM 
 
 SP 
 
 sP sP. 
 
 
 Figure III. 
 
 [Darapti) [Datisi) (Felapton) [Ferison) 
 
 Mp 
 
 Mp MP MP 
 
 Ms 
 
 MS Ms ms 
 
 sp 
 
 sp sP sP. 
 
 
 Figure IV. 
 
 (Fesapo) 
 
 (Fresison) 
 
 PM 
 
 PM 
 
 Ms 
 
 ms 
 
 sP 
 
 sP. 
 
 § 807. It will be observed that the conclusion is obtained at 
 once by merely dropping out the middle term.' The subsumption 
 is also obvious, or easily distinguished, except in Baroco, where 
 the middle term is undistributed in the major premiss — Pm, 
 We have seen above that if we reduce to Figure I this is here 
 not the true middle term, and that an inference can only be 
 drawn by an obversive process — Not-lfP, s not-m, sP. Noi-M 
 (not-m) might be replaced by M' (m'). Baroco will then be 
 
 M'P 
 
 sm' 
 
 sP. 
 The predicate of Bocardo must be treated in the same way 
 to yield an inference. But, this being an indirect Mood, the 
 premisses have also to be transposed. 
 
 Ms /\/i'w 
 
 sP p's = sp' = sP. 
 
 § 808. As regards those other moods, besides Bocardo, in 
 
 which, on the basis of Figure I, we conclude about 5 indirectly 
 
 —the premisses being transposed and the conclusion converted 
 
 —we shall find that, except the intractable and incorrigible 
 
 ' This is something like the rule set forth by Ploucquet (1763), who 
 based his Calculus on it, — 'Deleatur in praemissis medius; id quod 
 restat indicat conclusionem ' (criticized by Hamilton, Lectures on Logic, 
 ii. 316). 
 
Suggested Simplifications 
 
 375 
 
 Bramantip, the conclusion of them also is found by merely 
 dropping out the middle term. But the subsumption appears 
 as reversed (owing to the transposition of the premisses) ; and it 
 is only because the indirect conclusion shown by Bramantip 
 (Some S's are P) has been converted ' by limitation ' from the 
 direct conclusion (Every P is S) that it differs from Camestres, 
 Disamts, Dimaris and Camenes, in which the conclusion has 
 been converted simpliciter. In the case of Bocardo, as we have 
 just seen, the distributed term P of a negative proposition is 
 changed to an undistributed term p'a of an affirmative proposition. 
 
 Figure II. 
 {(^amestres) 
 
 Pm 
 
 SM 
 
 PS = SP. 
 (But Camestres may also be exhibited with a direct conclusion 
 like Baroco 
 
 M'P 
 
 Sm' 
 
 SP.) 
 
 Figure III. 
 
 {Disamts) 
 
 
 (Bocardo) 
 
 mp 
 
 
 mP-. 
 
 =.■ mp' — p'm 
 
 Ms 
 
 
 Ms 
 
 
 ps = sp 
 
 Figure IV. 
 
 p's = 
 
 ■■ sp' = sP. 
 
 (Bramantip) 
 
 (Dimarts) 
 
 
 (Camenes) 
 
 Pm 
 
 pm 
 
 
 Pm 
 
 Ms 
 
 Ms 
 
 
 MS 
 
 Ps = sp 
 
 ps — sp 
 
 
 PS = SP. 
 
 De Morgan (p. 333) quotes Ploucquet's notation — 
 Pm \ „ 
 
 i. e. quoddam s non est P (Baroco)— where > is the sign of 
 negation. Some of the S's are not any M's, are not those M's 
 which make up all the P's, are not therefore any P's. ' This 
 demand for identical substitutes requires both kinds of quantity 
 for every predicate.' 
 
376 Mood and Figure 
 
 § 809. It is difficult to improve on Pope John's time-honoured 
 mnemonics for reduction to the First Figure. They fail, how- 
 ever, to appeal to the ear, and the significant consonants are not 
 at once distinguishable from those — e. g. in Barbara, Celarent, 
 Bramantip, Fresison — which are without meaning. The conso- 
 nants used meirely for euphony might be one only, say /, which 
 might always be placed after the true major premiss or rule, 
 so that if it occurred after the second syllable of any mood 
 we should notice at once that the Mood is indirect and the 
 premisses must be transposed. Further, that the ear may 
 assist the memory, let the true major premiss always be long and 
 the other premiss short. Then Bdlad would supersede Barbara, 
 Celde Celarent, Bddlip Bramantip, and so forth. 
 
 § 810. Camestres and Camenes, however, as shown above, should 
 not indicate transposed premisses and an indirect conclusion, 
 nor should Baroco and Bocardo be reduced by the ad absurdum 
 method. In these four moods we have to change affirmative into 
 negative propositions and vice versa, by obversion. 
 
 Then Camestres (Every P is M, No 5 is M, .: No 5 is P) 
 becomes No not-M is P, Every S is not-M, .: No S is P 
 (= Celarent). Baroco in the same way takes the form. No not-M 
 isP, Some S is not-lf, .•. Some S is not P {— Ferio). 
 
 Bocardo must have its premisses transposed. But it need not be 
 reduced ad impossibile. Some M is not P, Every M is S, .'. Some 
 S is not P, becomes, Every M is S, Some not-P is M, .: Some 
 not-P is S = Some S is not-P = Some S is not P (= Darii). 
 
 Camenes (Every P is M, No M is .S, .*. No S is P) becomes, 
 No not-M is P, Every S is not-M, No S is P (= Celarent). 
 
 § 811. Now change in the quality of a proposition (obversion) 
 may be denoted by the letter b put after the syllable. This 
 followed by conversion (conversion by negation) may be denoted 
 by n. Conversion followed by obversion may have m for symbol. 
 
 The letter s will still signify simple conversion and p conver- 
 sion per accidens. The initial letters indicate the mood in 
 Figure I, to which any mood is to be reduced. It seems better 
 to juxtapose moods according to the quantity of the minor pre- 
 miss than according to the quality of the major. Then, 
 
 I. Hosce modos dat prima figura — 
 
 BalaS, Dalii ; Celae, Felio, 
 (^Barbara) [Darii) [Celarent) [Ferio) 
 
Suggested Simplifications 377 
 
 2. Quattuor hos appone secundae — 
 
 Celsae, Felsio; Calnebe, Dalnobo. 
 {Cesare) {Festino) (Camestres) (Baroco) 
 
 3. Exhibet has sex tertiaformas — 
 
 Daiapi, Dalisi; Felapo, Feliso 
 {Darapti) (Datisi) (Felapton) (Ferisoii) 
 
 deinde Disalis, et adde D6nal5m ■ 
 (pisamis) (Bocardo) 
 
 4. Quinque vices habet ultimus ordo — 
 
 Has tres : Calneme, FelsSpo, FelsisS 
 {Camenes) i^Fesapd) {Fresison) 
 
 Quarta Baalip ; quinta Dialis 
 {firamantip) (Dimaris) 
 
 § 812. I am unable to agree with Professor Veitch when he 
 says : ' The usual logical tests of the major and minor terms in 
 a reasoning are obviously of a wholly superficial nature. The 
 main one is really the relative local position of the terms.' ^ But 
 the difference between subject and predicate in the conclusion 
 is much more than a question of local position. No doubt 
 Hamilton's Unfigured Syllogism, based on an equational theory 
 of judgement, destroys the distinction, and in the Syllogism of 
 Comprehension Hamilton's claim for the minor term and pre- 
 miss to be the major can be admitted. But, from whichever 
 end we start, the difference between major and minor is not 
 superficial or accidental, but essential. Veitch himself speaks 
 of ' the essential mental relations of Containing and Contained '? 
 It is true that in the Second and Third Figures S and P have 
 not M, the 'middle' term, between them, that some moods 
 require a transposed statement, and that one, Darapti, admits 
 of either premiss being the rule. But that is far removed from 
 the assertion that 'there is formally or logically no major or 
 minor term or premiss in the second or third figures'.' Veitch 
 says : — 
 
 § 813. ' In the Second Figure the middle term is the predicate 
 of both premisses — 
 
 C\%M, 
 T isM. 
 
 ' Institutes of Logic, p. 383. ^ Ibid. p. 406. 
 
 ^ Ibid. p. 383. 
 
378 Mood and Figure 
 
 The form thus merely tells us that each extreme is contained 
 under the middle, but it says nothing of the relation of the one 
 extreme to the other. There is no subordination of greatest or 
 least.' ^ 
 
 He appears to overlook the circumstance that in this figure 
 one premiss is negative and the other affirmative, and that in 
 none of the moods can there be any doubt which is logically the 
 major premiss or rule, and which the minor premiss or sub- 
 sumption. But the Professor slips from Figured to Unfigured 
 Syllogism and back again. He expands C is Af, r is M, thus : — 
 (Some) C is (some) M 
 (Some) r is (all) M 
 .'. (Some) C is (some) r 
 or, (Some) V is (some) C — 
 and remarks : ' Now it is obvious that we are very near the 
 abolition of Figure altogether. We may now reason that, as 
 C is M and T is Jf , C is r or r is C ^ Thus to mix up two 
 questions is intolerable. To be sure, Quantification of the Pre- 
 dicate, if admitted, leads to a great many consequences and 
 obliterates many logical distinctions. But the point we are 
 immediately concerned with relates to ordinary syllogistic 
 reasoning, and to the allegation that the distinction there be- 
 tween major and minor is merely superficial and local. 
 
 § 814. Of course the mere order in which the premisses are 
 stated is quite immaterial, and implies at most a slight shifting 
 of the point of view, or it may be the succession in which the 
 facts become known and the judgements present themselves. 
 From Aristotle to Boethius logicians preferred to state the 
 minor premiss, or fact, first, and the major premiss, or principle, 
 second', thus giving the 'middle' term a local as well as a 
 rational mediation. S is M, M is always, or never, P 
 
 § 815, It has been said that there are many good maxims in 
 
 ' Op. cit. p. 409. " Ibid. pp. 409, 410. 
 
 ' This order seems to reconcile logic and grammar best. For we must 
 regard the element in the grammatical sentence on which emphasis is 
 placed as the true logical predicate. But if the major premiss is stated 
 before the minor, the stress of the voice falls on the subject in both. 
 ' The e/desi must work. /oAn is the eldest. Then John must work.' 
 John here is the real quaesitum. In the reverse order, we are asking 
 what John is to do. 'John is the eldest. The eldest must work. Then 
 John must work.' 
 
Order of Parts in a Syllogism 379 
 
 the world. The difficulty is to apply them. Here the major pre- 
 miss presents itself earlier than the minor. On the other hand, 
 every unrelated and unexplained experience is waiting for its 
 major premiss. 
 
 § 816. The position of the Conclusion has a different signifi- 
 cance. When we- argue synthetically we put the conclusion 
 last. In an analytic argument the conclusion — here more 
 properly called the propositum, quaesitum or thesis — is followed 
 by the reasoning on which it rests.' Of the latter kind were 
 most of the formal disputations of the schools. Should the 
 thesis be propounded as a question, it may be repeated as con- 
 clusion. 'Is5P?' ' Yes, for S is M and M is always P. So 
 that SisP: 
 
 § 817. According to Dr. Max Miiller the logicians of India 
 employ a five-membered syllogism : — 
 
 (i) Assertion. This mountain is on fire. 
 
 (2) Reason. Because it smokes. 
 
 (3) General proposition. Now no smoke is without fire. 
 
 (4) Assumption. And we agreed that this mountain smokes. 
 
 (5) Condttsion. Therefore it is on fire.'' 
 
 When a propositum is followed by its premisses, the minor is 
 usually stated first : — 
 
 This is a volcano. 
 
 Because it smokes. 
 
 And there is no smoke without fire. 
 But in the example of Indian logic just given the minor is 
 repeated, or resumed, after the major premiss. 
 
 § 818. When the major premiss precedes the minor, the mind 
 is looking for subjects of propositions ; when the minor precedes, 
 it is looking for predicates. 5 is P, for M is P, and 5 is M. 
 Again, 5 is P, for 5 is M, and M is P. ' It is he is the coward, 
 for those who run away from danger are cowards, and he ran 
 away.' Or again, ' He is a coward, for he ran away, and those 
 who run away are cowards.' ' This is the volcano. For where 
 there is smoke there is fire. And this mountain smokes.' Or, 
 
 ' ' It is not the case that a conclusion ceases to be an inference the 
 moment that it becomes familiar, i. e. that it ceases to be a discovery. 
 On the contrary, discovery without proof is tonjecture. . . . Novelty' or 
 discovery is an accident of inference' (Bosanquet, Logic, ii. 8, g). 
 
 " Quoted in Appendix to Thomson's Laws of Thought. 
 
380 Mood and Figure 
 
 ' This is a volcano (This mountain is on fire). For it smokes. 
 And where there is smoke there is sure to he_fire.' 
 
 If the conclusion is stated last, there will similarly be a 
 stress on subject or predicate, according as minor or major 
 premiss precedes. 'Where there is smoke there is fire. 
 This mountain smokes. Therefore this mountain is on fire.' 
 That is, the rule applies to the present case. But, 'This 
 mountain smokes. Where there is smoke there is fire. It 
 follows that this mountain is on fire.' That is, we have found 
 a rule to bring this smoking mountain under. This at least 
 is the most natural point of view. A deductive argument begins 
 with the general principle. An inductive inquiry begins with 
 the observed fact. Deductive intellects are always on the alert 
 to conclude something — like the Scotsman who after reading 
 Paradise Lost asked, What does it prove ? 
 
 § 819. The position of the conclusion matters less practically 
 than the order of the premisses, for there can be never any 
 doubt which is the conclusion. It is indeed often enounced 
 between the premisses — M is P, therefore S is P, since S is M. 
 The following, in a very condensed form, is an example of major, 
 conclusion, minor — ' Fire ! Fetch a ladder ! My child is up- 
 stairs '. But this kind of enunciation, or one with minor pre^ 
 miss first and major last, is of course very common. .'Sick 
 people lose their appetite. So he must be ailing, for he eats 
 nothing.' 'He is a liar, and accordingly needs to cultivate his 
 memory ; for liars need good memories.' 
 
 § 820. Hamilton's assault on the common order — major pre- 
 miss, minor premiss, conclusion — as ' unnatural and contorted 
 by hitches and abrupt transitions ' rests on the assumption that 
 the conclusion is always quaesitum. Why should it never be 
 inventum ? Reasoning is not all argumentative and eristic. It 
 more frequently leads us to unexpected applications. ' In the 
 synthetic or common order,' he writes, 'all is pleonastic and 
 anticipative. What is first in reality and interest, and in and 
 for the sake of which the whole reasoning exists, comes last; 
 till the conclusion is given we know not (at least we ought not 
 to know) how the question is answered.' ' ' Question ', however, 
 begs the question. Not that the point is of any importance. 
 We may either regard the enunciation of syllogism as a reasoned 
 ' Lectures on Logic, ii. 400. 
 
Hamiltofis Intensive Syllogism 381 
 
 One analysed into a Many, or as a Many synthesized into a 
 reasoned One. 'How do you prove it?' in the former case. 
 ' What follows ? ' in the latter. A conclusion stands to its pre- 
 misses in syllogism in the relation of predicate to subject. ' All 
 ^-being-M and M-being-i-" is S-being-P.' But judgements have 
 the same logical enunciation whether it were subject or predi- 
 cate that the mind looked for. It may be asked, Who killed 
 Cock Robin ? Or it may be asked, What did the Sparrow do ? 
 In either case the answer is, ' I killed Cock Robin.' Only the 
 emphasis is different. 
 
 § 821. In setting forth his doctrine of the Intensive or Com- 
 prehensive Syllogism, Sir William Hamilton lays it down that, 
 as the counterpart of the Extensive Syllogism, it must necessarily 
 suffer a 'transposition of the order or subordination of the two 
 premisses ', the reciprocal relation of the terms being reversed. 
 That is to say, the term which is usually called the major, as 
 having the larger extension, will now be the minor, as having 
 the less intension. The qualitatively affirmative premiss, usually 
 called the minor, will now be the major premiss or ' sumption ', 
 and the quantitatively definite premiss, usually called the major, 
 will now be the minor, or ' subsumption '. In the Extensive Syl- 
 logism the conclusion must agree in quality with the sumption, 
 and not exceed in quantity the subsumption. In the Intensive 
 Syllogism it must agree in quality with the subsumption and 
 not exceed in quantity the sumption.^ 
 
 § 822. This, however, is only a roundabout way of saying 
 (what Hamilton himself teaches) that the two kinds of Syllogism, 
 in Breadth and Depth, are one and the same thing, regarded in 
 counter-relations and from opposite standpoints. 
 
 Extensive Syllogism. Intensive Syllogism. 
 
 ' Every Fis (or, is not) contained Z-ness is (or, is not) comprised 
 in (class) Z. among the attributes of all 
 
 X is contained in (class) Y. things that are Y. 
 
 Therefore X is (or, is not) con- F-ness is comprised among the 
 tained in (class) Z. attributes of X. 
 
 Therefore Z-ness is (or, is not) 
 comprised among the attri- 
 butes of X. 
 
 ' Op, cit. i. 315 seq. 
 
382 Mood and Figure 
 
 In either case what matters is the quality of the relation 
 between Y and Z (the quantity being necessarily universal), and 
 the quantity of the judgement about X (the quality being neces- 
 sarily affirmative). Hamilton, for the intensive syllogism, reverses 
 the order of the premisses, putting the ' extensive ' major, which 
 may be affirmative or negative, second : — 
 
 Prudence comprehends virtue ; 
 
 But virtue does not comprehend blameworthy ; 
 
 Therefore prudence does not comprehend blameworthy. 
 
 § 823. It must be observed in passing that the expressions 
 Sumption and Subsumption, in their reversed application, are 
 most unnatural. The ' sumption ' of Hamilton's intensive syllo- 
 gism may be a particular proposition, the ' subsumption ' a denial 
 of predication, unable therefore to be ' brought under ' a rule. 
 Hamilton says : — ' In the extensive syllogism the subsumption 
 is, and can only be, an affirmative declaration of the application 
 of the sumption as a universal rule. In the intensive syllogism, 
 the subsumption is either an affirmation or a negation of the appli- 
 cation of the sumption as a positive law.'^ It is not easy to see 
 any meaning in this. If we say (intensively). 
 Dullness is an attribute of some books (Hamiltonian sumption); 
 Intolerableness is an attribute of dull things (H. subsumption); 
 Therefore intolerableness is an attribute of some books (i.e. 
 
 Some books are intolerable), 
 a fact is affirmed in the 'sumption' but not a law or rule. 
 Hamilton had just said: 'The condition common to both 
 syllogisms is that the sumption should express a rule. But 
 in the extensive syllogism this law is an universal rule . . . 
 whereas in the intensive syllogism this law is expressed as a 
 position, as a fact; but, as it is not necessarily universal, it 
 admits of limitations or exceptions.'^ It would be better to 
 admit that the expressions ' sumption ' and ' subsumption ' are 
 only applicable to the ordinary order. Hamilton complains 
 elsewhere ^ that ' the whole nomenclature of the syllogistic parts 
 has reference to the one-sided views of the logicians in regard 
 to the process of reasoning '. Here is a piece of reasoning : — 
 ' Four men attacked me. Those who attack me get the worst 
 of it. Therefore these four men got the worst of it.' How can 
 ' Four men attacked me ' be called a ' rule ' or ' positive law ' ? 
 ' Op. cit. p. 317. '^ Ibid. p. 316. ^ Ibid. p. 282. 
 
Reasoning in Comprehension 383 
 
 § 824. Professor Veitch, however, has misgivings about the 
 theory of reasoning in Comprehension. He says — 
 
 ' The defects of the theory come out most markedly in relation 
 to negative conclusions. Here, in fact, it seems to me to break 
 down, when left wholly to itself. The law for affirmatives as 
 given by Hamilton ... is quite valid, and is strictly a reasoning 
 in Comprehension. But take the other half of the rule — that for 
 negatives — " The predicate of the predicate is, with the predicate, 
 denied of the subject ". Thus : — , 
 
 Man does not include in it mineral ; 
 
 Mineral includes in it weight ; 
 
 Therefore man does not include in it weight. 
 This is wholly invalid as a reasoning in Comprehension [or 
 as reasoning at all]. All that is denied is some weight, — the 
 weight that is in mineral. But this is in Extension, and the 
 conclusion is so cloaked as to be deceptive.' ' 
 
 § 825. So far, Veitch's criticism is a mere blunder. He has 
 made the (intensive) major premiss the negative one, instead of 
 the minor. Hamilton's syllogism is : — 
 X comprehends Y, 
 
 Y does not comprehend (i. e. excludes) Z, 
 Therefore X does not comprehend Z. 
 But Veitch states it thus :— 
 
 X does not comprehend Y, 
 y comprehends Z, 
 
 Therefore X does not comprehend Z. 
 Which is, of course, as he says, a fallacious inference.^ 
 
 § 836. On the next page, however, he gets upon the trail of 
 Hamilton's real misconception, viz. his confusion between the 
 attributes of an object and the content of a notion. But, unfortu- 
 nately, he objects to the validity of Hamilton's illustration, when 
 the true objection is to the choice of it. Taking the intensive 
 syllogism. 
 
 Prudence comprehends virtue ; 
 
 But virtue does not comprehend blameworthy ; 
 
 Therefore prudence does not comprehend blameworthy, 
 
 ^ Institutes of Logic, pp. 433, 434. 
 
 '' Though we may contrive syllogisms in which the invalid conclusion 
 comes out true, e. g. — 
 
 Grenadier does not comprehend dwarf; 
 
 Dwarf comprehends very small stature ; 
 
 Then grenadier does not comprehend very small stature. 
 
 For nothing can ' comprehend ' small stature except dwarf. And yet 
 there might be fairy grenadiers. 
 
384 Mood and Figure 
 
 Veitch remarks : — 
 
 ' It seems to me that there is no valid conclusion in the illus- 
 tration given. Virtue is a mark of prudence, i. e. the attribute 
 virtue is an attribute of prudence ; the attribute blameworthy is not 
 an attribute of virtue ; it does not follow from this that the attribute 
 blameworthy is not an attribute of prudence. We might just as 
 well argue that because animal life is an attribute of man, and 
 weight is not an attribute of animal life, that weight is not an 
 attribute of man. What is not simply a mark of the mark is not 
 necessarily not a mark of the thing itself. ... I cannot infer that 
 blameworthy is not imprudence ; but only not in that part of 
 prudence which is convertible with virtue. If I say : — 
 
 Man comprehends animal life ; 
 
 No animal life has weight, 
 I cannot, therefore, say that no man has weight, but only that 
 weight is not in that part of man which is convertible with animal 
 life.'^ 
 
 Hamilton, however, would have insisted, with some reason, 
 that virtue is part of the idea of prudence. And the expression, 
 'Blameworthy is not an attribute of virtue,' should be, 'is 
 excluded by the attributes of virtue.' 
 
 § 827. It would be tedious to examine the conditions which 
 Veitch lays down before reasoning in Comprehension with a 
 negative conclusion can be valid. The confusion really lies in 
 the acceptance of Hamilton's doctrine of conceptual inclusion. 
 The import of ' X is Y' is that F-ness, the being Y, is comprised 
 among the attributes possessed by X, not that it is included in the 
 notion X. 
 
 § 828. These ambiguities would have been detected at once 
 if abstractions like 'Man', 'prudence,' and 'virtue' had been 
 avoided. But Hamilton's doctrine of the import of propositions 
 is radically unsound and confused. 
 
 § 829. The difficulty which is sometimes raised, e. g. by De 
 Morgan, that 'in the affirmative any portion of the intension of 
 the predicate may be affirmed of the subject; in the negative it is 
 not true that any portion of the intension of the predicate may be 
 denied of the subject ', is merely the general doctrine of negation, 
 viz. that an entire concept cannot be negated, so that ' No planet 
 has a circular motion ' denies ' circular ' but not ' motion '. The 
 negated element of the concept is the only part of it which is 
 denied in the conclusion. 
 
 ' Op. cit. pp. 435, 436'. 
 
Attribute 'Involved in' Attribute 385 
 
 § 830. The same addiction to analytic judgements misleads 
 McCosh, who says : — 
 
 'The regulating principle of the Syllogism in Comprehension' 
 will be, " A part of a part of an attribute will be part of the whole 
 attribute." 
 
 ' Free will is an attribute of responsibility. Responsibility is 
 an attribute of man ; . . . Free will is an attribute of man . . . We 
 mean, on the principle that the abstract implies the concrete, 
 that whatever things contain a part must also contain a part of 
 that part, e. g. that men, having the attribute of responsibility, 
 have the attribute of free will involved in that responsibility. 
 We seem thus to be thrown back on extension as the uppermost 
 thought in reasoning.' * 
 
 It is by no means clear what McCosh means by 'part of and 
 'involved in' an attribute. He seems to waver between 'implied 
 in the notion ' and ' necessarily accompanying the attribute ' — an 
 ambiguity which is fostered, as in Hamilton's illustration, by the 
 employment of a middle term like ' responsibility ', which no 
 doubt contains in itself the idea of free will. If a man remarks, 
 'I have been often threatened, but threatened men live long; 
 therefore I hope to see old age,' ought we to say that Having 
 often been threatened is 'part of the attribute self, and long life 
 is 'part of the attribute often threatened'^ McCosh, however, is 
 himself far from satisfied, and sees somewhat confusedly that the 
 middle term in one premiss, viz. where it stands as subject, must 
 be regarded not as attribute but as possessor or possessors of an 
 attribute. He says : — 
 
 § 831. ' In the greater number of propositions the uppermost 
 thought is in comprehension. But it is different when we con- 
 sider judgements so connected as to entitle us to draw a conclu- 
 sion. The uppermost spontaneous thought seems now to be in 
 extension. When we argue that " The Red Indian, having the 
 power of speech, is a human being", we refer, in thought, the 
 Red Indian to a class composed of those who have the power of 
 speech.' " 
 
 Not necessarily in a syllogism any more than in a proposition. 
 Certainly, ' possessor of an attribute ' as the predicate of the 
 one premiss can be thought without any direct reference to others 
 of the same sort ; whereas, as the subject of the other premiss, 
 
 * Laws of Discursive Thought, p. 139, 
 « Ibid. p. 138. 
 
 c c 
 
386 Mood and Figure 
 
 it is necessarily understood in potential universality. S is 
 possessor of attribute Af-ness. A ( = any) possessor of attribute 
 ,ilf-ness is possessor of attribute P-ness. But the essential point 
 is that M as predicate is adjectival, as subject it is substantival. 
 The 'uppermost thought' may be the qualification of the subject 
 rather than the subject itself as object. But when Hamilton 
 speaks of Reasoning in Comprehension he means something 
 more than uppermost thoughts. He means the 'inclusion' of 
 concepts in concepts. He does not mean the attribution of 
 attributes to attributes — a possible but very limited kind of 
 reasoning — e. g. ' Punctuality is the politeness of princes. The 
 virtue I prize most is punctuality ' — where there is, in fact, identi- 
 fication rather than attribution, or rather the attribution of 
 identity with the quality, not the quality itself. What is attributed 
 to punctuality is not politeness (which would require 'is polite'), 
 but intensional equivalence with royal politeness. In ' Stateliness 
 is old-fashioned' an attribute is attributed to an attribute. 
 Hamilton, however, declares that reasoning is a mode of ascer- 
 taining that one notion is part of another. But in synthetic 
 judgements what we affirm is not the inclusion of one notion 
 in another, but the conjunction or coexistence of two attri- 
 butes in the same subject. 
 
CHAPTER XXV 
 UNFIGURED SYLLOGISM 
 
 § 832. A LESS space will suffice for considering the bearing 
 of Hamilton's theory of Extensive Judgement with Quantified 
 Predicate on Inference. 
 
 Propositions becoming equations, and therefore simply 
 convertible, Figure is seen to be unessential. Syllogisms are 
 distinguished from one another, not by the position of the middle 
 term, but only by the quality and quantity of their premisses. 
 In practice the three Figures (Hamilton disallows the Fourth) 
 may have special uses and functions — Figure II, for instance, is 
 suited to deductive reasoning in extension, Figure III to induc- 
 tive reasoning in intension. But Mood alone is the essential 
 thing. 
 
 § 833. The Unfigured Syllogism does not proceed from the 
 more to the less, or from the less to the more, general, but from 
 equal to equal. It is therefore neither deductive nor inductive, 
 but traductive. 
 
 § 834. Hamilton's single Canon of Figured Syllogism is this :— 
 
 ' What worse relation of subject and predicate subsists between 
 either of two terms and a common third term, with which one at 
 least is positively related, that relation subsists between the two 
 terms themselves.' ^ 
 
 § 835. This serves for reasoning in Comprehension as well as 
 in Extension. But the following canon of Unfigured Syllogism 
 adopts the objectionable phrase 'agreement of notions ' : — 
 
 ' In as far as two notions (notions proper or individuals) either 
 both agree, or, one agreeing, the other does not, with a common 
 third notion : in so far these notions do or do not agree with 
 each other.' ^ 
 
 § 836. Upon the abrogation of all the special laws of Syllogism 
 Devey well observes : — 
 
 ' The general rules, and even the special rules of the figures, 
 
 ' Lectures on Logic, ii. 350. '^ Ibid. 
 
 c c 2 
 
388 Unfigured Syllogism 
 
 are in no wise distinct from the canon, but only act as so many 
 cautions, which it is advisable for the reasoner to have before him, 
 in order that he may not violate any of its principles. They 
 might therefore be omitted from the old logic with as much pro- 
 priety as from the system sought to be established, and with, 
 more security against error, since its code of valid syllogisms are 
 much fewer than those arising out of the quantification of the 
 predicate, and consequently afford less ground for the violation 
 of the canon. But in reality they can be spared from neither 
 system, as it is obviously necessary, to secure the understanding 
 from error, that every mode by which a deviation can occur 
 from the principles of right reason should be drawn out distinctly 
 before it.' ' 
 
 § 837. At the same time we need not hesitate to admit that the 
 substitutive inference of an equational Logic is in one sense a 
 simplification — not as philosophy aims at simplicity, but as the 
 inorganic is 'simple'. Subjects and predicates are, as it were, 
 no longer living individualities, but can be transposed and 
 exchanged like pounds of cheese or sugar. Every term as 
 quantified is equal to every other term, and it is of no consequence 
 which comes first or last. But we have already seen (i) that while 
 every proposition involves an equation, or rather an identification, 
 of extensions, its import is much wider, and therefore to regard 
 terms merely in their collective aspect is to confine oneself to a 
 subordinate and unimportant department of reasoned truth. 
 (3) That the only equations thus obtainable from the ordinary 
 forms of judgement 
 
 All = some, 
 
 Some = all, 
 
 Some = some, 
 are three which are obtainable from the propositions A and /, the 
 equation All = all representing no logical proposition except 
 one in which subject and predicate are both singulars or totalities. 
 No doubt there is an existing class of propositions — ' Edward 
 VII is our present King-^our present King is the late Queen's 
 eldest son — therefore ', &c.— but they are identifications simply, 
 and do not follow from any distributive judgement. If 
 'All = all' is to be admitted, why not 'All= twenty', or any 
 algebraic equivalence? (3) Negative propositions cannot be 
 represented equationally, as already shown (§ 684 seq.), except by 
 
 * Logic, p. 119. 
 
Hamiltonian ^Simplification' 389- 
 
 attaching the negative sign to the predicate ; so that ' Some X 
 is not Y' becomes, not ' Some ^ = no Y' (which is meaningless), 
 but 'Some X-= some not-F', and 'No X \& Y' becomes, not 
 ' No X = all Y', nor ' All X = no Y', but ' AllZ = some not- Y'. 
 
 § 838. But if an Unfigured Syllogism would be, so far, 
 a simplification, the great multiplication of moods has just the 
 opposite result, as Hamilton admits : — 
 
 'On the new theory many valid forms of judgement and 
 reasoning, in ordinary use, but which the ancient logic continued 
 to ignore, are now openly recognized as legitimate ; and many 
 relations, which heretofore lay hid, now come forward into the 
 light. On the one hand, therefore, logic certainly becomes more 
 complex. But on the other, this increased complexity proves 
 only to be a higher development. The developed Syllogism is, 
 in effect, recalled from multitude and confusion to order and 
 system.' ^ 
 
 § 839. Hamilton's Prepositional Forms are eight in number ' : — 
 
 1. Toto-total — all is all 
 
 2. Toto-partial — all is some 
 
 3. Parti-total — some is all 
 
 4. Parti-partial — some is some 
 
 5. Parti-partial — some is not some 
 
 6. Parti-total — some is not any 
 
 7. Toto-partial — any is not some 
 
 8. Toto-total — any is not any 
 These eight forms (doubled by conversion) in each of the three 
 
 premisses, and counting three Figures only, will give, according 
 to Hamilton's own computation, 3,072 possible moods; but of 
 these only 160 affirmative and 320 negative moods are legitimate. 
 The number 3,072 is obtained thus, 8x8x8x3x2. Veitch 
 reduces the legitimate moods to 108 ; and, since many of the 
 moods are really the same, he brings down the number to seven 
 affirmative and fourteen negative forms. This is only two more 
 than the traditional logic recognizes ; and, if so, what has become 
 of the 'many valid forms' which Hamilton claims to have 
 recovered from undeserved neglect ? If, on the other hand, the 
 entire 108, or 480, are given a recognized place, syllogistic logic 
 ceases to have any use as an art. Devey remarks : — 
 
 ' Tp scatter the nineteen legitimate forms of inference over 108 
 distinct moods, comprising the conceivable as well as the actual 
 
 ' Lectures on Logic, ii. 252. ^ Ibid. p. 292, 
 
 Affirmative. 
 
 Negative. 
 
390 Unfigured Syllogism 
 
 forms of reasoning, is only breaking down the fence which enables 
 us to hunt a sophism into a corner . . . Even if the new analytic 
 accomplished its object, of enlarging the field of inference, success 
 would be worse than defeat.' ' 
 
 § 840. It should be further observed that in each equation or 
 equivalence, 'some' is an undetermined quantity. This indeii- 
 niteness vitiates any attempt to syllogize by substitution. For 
 instance Barbara — 
 
 All M = some P, 
 All 5 = someil/, 
 .-. All S = some P. 
 But the ' some P' of the conclusion has a narrower extension 
 than the ' some P ' of the major premiss. The same with the 
 other moods of Figure I. In Figure III take Darapti — 
 All M = some P, 
 All M = some S, 
 .: Some 5 = some P. 
 Here Some S and Some P are the same in premisses and 
 conclusion. But in Disamis — 
 
 Some M = some P, 
 All M = some S, 
 .'. Some S = some P — 
 Some P in the conclusion is the same ; but Some 5 is only 
 part of the Some S of the minor premiss. In Datisi it is Some 
 P which has contracted. Felapton (All M — some not-P, All 
 iI/=someS; .*. Some S = some not-P) is like Darapti. But 
 in Bocardo and Ferison the extension of Some S is less in con- 
 clusion than in premiss. 
 
 § 841. An equational theory of Syllogism, then, which fails 
 to specify the quantity in each case of 'some', is at best 
 pseudo-mathematical. 
 
 § 842. It will be noticed that while 'h\\X = some Y' converts 
 to 'Some Y= all X', and 'Some X= some Y' converts to 
 'Some y=some X', the negative universal proposition [E), 
 'All X=some not-Y,' implies that All Y=some not-Z. In 
 this way Cesare (e. g.) is reduced to Celarent: — 
 
 {Cesare) {Celarent) 
 
 All P = some rxot-M. = All M = some not-P. 
 All S = some M. All S = some M. 
 
 .: All S = some not-P. .-. All S = some not-P. 
 
 ' Lo^ic, p. 1 19. 
 
Equational Logic 391 
 
 Baroco assumes the equational form : — 
 All P = some M, 
 Some S = some not-M, 
 .'. Some 5 = some not-P. 
 But ■ All P is Af ' is the proposition, ' No P is not-M,' which 
 is the same as 'No not- J/ is P\ The major premiss, 'All 
 P = some M,' therefore, may be expressed thus, 'AH noi-M = 
 some not-P.' Baroco is thus reduced to Darii. Celarent and 
 Ferio, we must remember, when expressed equationally, are 
 Barbara and Darii. 
 
 § 843. In equational syllogizing there is little fear of illicit 
 process of major or minor term. The errors to guard against 
 are Two negative premisses and Undistributed Middle. Yet 
 the middle term in such syllogizing may seem undistributed (as 
 in Cesare, Ferio, Baroco, &c.) when it is not so in reality. 
 
 § 844. The Hamiltonians, with their erroneous equating of the 
 terms of negative propositions, have neglected the foregoing field 
 of inquiry, and built up instead a perversely ingenious and 
 complicated syllogistic scheme, unintelligible, or at least not 
 likely to repay the trouble of unravelling. 
 
 § 845. It is rightly pointed out, however, by De Morgan, 
 Hamilton, and others that if the Middle Term, instead of being 
 distributed once at least, has a total quantification in both 
 premisses greater than its own full extension, inference based on 
 arithmetical computation is possible in endless forms. There 
 must be overlapping (ultra-totality) of the two extensions of the 
 Middle Term. No syllogism can be formally bad in which this 
 condition is satisfied, and in which one premiss at least is 
 affirmative, whatever the relation of the extremes to each 
 other or to the Middle Term. Hamilton's Canon is framed 
 to cover every legitimate form of quantification. To take an 
 example : — 
 
 Two-thirds oiM is (some) P, 
 Three-fourths of M is (some) 5. 
 
 Therefore some SM (| at most or f at least) is P. Hamilton, 
 indeed, seems to assign too much importance to the condition 
 that the quantification of the Middle Term shall be in one premiss 
 a half of its entire extension, and in the other premiss more than 
 half. He calls these respectively Dimidiate Quantification and 
 
392 Unfigured Syllogism 
 
 Ultra-dimidiate Quantification.^ Why should not the one be 
 
 a quarter and the other more than three-quarters — or any other 
 
 fractional shares together making up more than unity ? 
 
 I ilf is P, 
 
 5 is I Af. 
 
 Then all S at most, or ^ S at least, is P, 
 
 and S = f PM at most or \ PM at least. 
 
 Again — 
 
 f ilf is not P, 
 
 Then all S at most, or ^ S at least, is not P. 
 It should be observed that 'f M is P' expressed algebraically 
 is 'I M = some P', but 'S is \ M' is the equation 'All 5 = iM'. 
 
 That M should be wider in the one premiss than in the other 
 is, of course, not enough. ' Most of my books are bound in calf. 
 Here are a few of my books ' ; — it does not follow that any of 
 them are bound in calf. 
 
 § 846. On the other hand, a probability maybe thus established : 
 ' Nearly all his papers were destroyed. The letter was among 
 his papers. It was probably, therefore, destroyed.' But the 
 probability is affected by material considerations. If a man has 
 burnt nearly all his papers, it does not follow that he has prob- 
 ably burnt his will, or his title-deeds, or a letter to his grandfather 
 from Lord Nelson. Probability, as we have seen, is not expecta- 
 tion founded on partial knowledge, but the measurement of 
 rational ground for expectation. Boole elaborates formulae so 
 as to express the event whose logical probability is sought as a 
 function of the events the probabilities of which are given. 
 Knowledge, as De Morgan says, is treated as a magnitude. We 
 cannot, he contends, invent a case of purely objective probability. 
 It is true that if there are twice as many white balls in a bag as 
 black, white balls will have come out (sooner or later) twice as often 
 as black ones, and if you do not know which balls have come out 
 you have twice as much ground to expect that the next one will 
 be white as you have that it will be black. But the natural laws 
 which determine that this or that ball shall come out are, if we 
 knew them, fixed. 
 
 § 847. It should be observed that, whereas the premisses, 
 ' Most M's are P, every 5 is M,' allow us to conclude nothing 
 
 ^ Lectures on Logic, ii. 351-6. 
 
Algebra applied to Reasoning 393 
 
 certainly, yet from ' Every M is P, Most S's are M ', we are 
 forced to infer that Most S's are P. 
 
 ' Most M's are P ', however, entitles us to say that every M 
 severally is probably P. So that, if every S is M, every S is 
 probably P. The old Chiltern saw, implying that the county 
 is so full of robbers that one lurks in almost every thicket, says : 
 'Beat a bush and it's odds you start a thief.' 
 
 A proposition such as ' Many are called but few chosen ' must 
 not be regarded as partitive but as a compound generalization. 
 ' It is always seen that many ', &c., or ' It is the Divine will 
 that many ', &c. The minor premiss will be, ' This is a case of 
 the implied conditions being satisfied.' Again, ' Most children 
 (i. e. at a treat, or when asked) prefer plum-cake to seed. This 
 is a treat, or we are going to ask the children. Therefore, most 
 of them will choose plum-cake.' 
 
 § 848. The endeavour to represent logical processes by 
 algebraic forms received a great stimulus from Boole's Mathe- 
 matical Analysis of Logic, published in 1847. It was followed by 
 Jevons's Logic of Quality in 1864. Jevons, who speaks of the 
 'newly discovered quantification of the predicate ', while claiming 
 to improve on Boole's system, which is rather numerical than 
 purely logical, describes it as 'perhaps one of the most marvellous 
 and admirable pieces of reasoning ever put together '. It is to 
 De Morgan, however, that he ascribes the 'high honour' of being 
 'probably the first logician who pointed out that syllogistic 
 arguments may exist in which the number of objects forming the 
 several terms of the syllogism may be exactly defined, and that 
 inference is often possible with such premisses when it would 
 not otherwise be valid '. 
 
 § 849. Certainly it is sometimes easier to throw a complex 
 sentence into algebraic form than to express it by a logical 
 formula. For example, Menenius says of Coriolanus (Act V, 
 sc. 4) — ' He wants nothing of a god but eternity and a heaven to 
 throne in.' Sicinius answers : — ' Yes, mercy, if you report him 
 truly.' That is, A god — (eternity -1- a throne in heaven -f mercy) = 
 Coriolanus. 
 
 § 850. We cannot, however, for a moment admit that logic is 
 a branch of mathematics, or that its axioms are ' founded upon 
 and resolvable into the ulterior and more simple ' axioms which 
 underlie the science of numbers. The reasoning process is 
 
394 Unfigured Syllogism 
 
 absolutely prior to all reasoned knowledge. We could not 
 work out the simplest sum or problem if Logic did not lead us 
 by the hand. Nor yet is it possible to admit that Thought is 
 really but adding and subtracting. Boole affirms that 'the 
 ultimate laws of thought forbid, as it should seem, the perfect 
 manifestation of the science of Logic in any other form ' than that 
 of a Calculus. Mathematical language, he maintained, is natur- 
 ally the universal language of thought. Enough has been said 
 above about the view expressed by De Morgan that 'simple 
 identity or non-identity is the ultimate state to which every asser- 
 tion may be reduced '. It is true that every proposition is the 
 statement of identity in difference. One and the same substance 
 underlies the different determinations of subject and predicate. 
 But such identity and such difference are not what the equaters 
 (of whom I would avoid speaking disrespectfully) mean. 'The 
 process of reason,' says Dr. Bradley truly, ' does not consist 
 in substitution,' ^ though in his ardour for logical latitudinarian- 
 ism this writer hastens to add that ' the method of substitution 
 has set itself free from some of the superstitions of the traditional 
 logic. For certain purposes it is far more useful.' ^ 
 
 § 851. If algebraic or geometrical forms are applicable to logical 
 propositions, it can only be on the side of quantity and extension. 
 The circles and other diagrams used to illustrate syllogistic mood 
 and figure are imperfectly applicable to reasoning in intension.' 
 Algebraic expressions again are quantitative. To make x and y 
 the symbols of unknown attributes, and to combine these by + , 
 — , X and -4-, is to confuse quantitative with qualitative rela- 
 tions. Boole, for instance, represents an adjective quaUfying 
 a substantive (' rotten apple ', ' treasure trove ') as x x y. It is, 
 however, ' a fundamental law of thought ' that in Logic xx or x' = 
 X — which is only true in Algebra when a; = oora;=i. A two- 
 footed biped is a biped. A cowardly poltroon is a coward. On 
 this law Boole rests the Principle of Contradiction. For x and 
 
 ' Logic, p. 348. " Ibid. p. 349. 
 
 ^ For though a circle in a circle will stand for the proposition that the 
 attributes of animal are included among attributes of cow, the proposi- 
 tion ' A cow is never a pig ' cannot be represented, when regarded in 
 comprehension, by two exclusive circles, which would mean that none of 
 the attributes of cow are found among the attributes of pig, or vice versa ; 
 whereas cow and pig have many attributes in common, e. g. four-footed- 
 ness. See Appendix. 
 
Algebra applied to Reasoning 395 
 
 non-a; together make up any particular ' universe of discourse' — 
 e. g. brave and cowardly soldiers. The universe of discourse 
 (soldier) may be represented by i. Then x-x? = o. That is, 
 x(i-x) = o. But x-x = non-x (take from the class soldier the 
 brave soldiers and what is left is the class of non-brave soldiers). 
 An X which is non-a: then is nothing. Self-contradictory attri- 
 butes (a cowardly brave soldier) have no existence. And so, 
 remarks Boole in his Laws of Thought, 'What has been commonly 
 regarded as the fundamental axiom of metaphysics is but the 
 consequence of a law of thought mathematical in form.' As 
 though the equation could have moved a step except in reliance 
 on that fundamental axiom ! 
 
 § 852. In the ' demonstration ' just given, x is after all given a 
 meaning in extension, i —a: being the whole class less the x class. 
 What then is the meaning of multiplication oix by x, or oix hyy ? 
 'Good man' has an extension less than that of 'man' or than that 
 of 'good' ; but if x stands for^oorfandj/ for man, the extension of ^ 
 must equal the extensions of x 3.ndy multiplied into one another. 
 Other equational logicians symbolize 'goodman'bya:+jc. Agood 
 man has the qualities both of goodness and of humanity, x+y, 
 then, stands for the entire intension of the term, li x and y 
 were classes, the sum of the extensions of ^oo<^ and of man would 
 again be greater than that of good man. And therefore the 
 logician must rigidly keep to the meaning in comprehension. 
 And yet how can reasoning in comprehension be carried on 
 algebraically ? Are the signs of multiplication and division to be 
 dropped out ? What will be the force of words like all, some, 
 none, except, or of numbers? What will be the meaning of 'All x' 
 or of ' Ten ^s ' ? Directly we make x mean 'whatever is x', and 
 x+y mean 'whatever has the qualities of a;-ness and _y-ness 
 together ', we have got back to classes and to extension. 
 
 In Boole's system, if xyz stands for opaque polished stones, 
 the expression x (i— jv) (i — s) means, 'opaque substances which 
 are not polished and are not stones.' 
 
 ' Either xov y', if ' or ' is not exclusive, is thus represented : — 
 x+y (x+x) — i.e. either x or y ox both. If 'or' is exclusive, 
 thus : — X (i —y) +y {i.—x). 
 
 ' Either x or y or z' in the former case is represented as 
 follows: — x+y (T.—x) + z(i — x)(i—y). In the latter case as 
 follows : — x{i—y){L—z)+y{i—x) {\—z)+z (i—x)(i—y). 
 
39^ Unfigured Syllogism 
 
 ' All men are mortal ', the relationship of species and genus, is 
 symbolized algebraically hy y=vx, v being an indefinite symbol, 
 a class indefinite in every respect but that some of its members 
 are x, and so the differentia of a definition. Men are some kind 
 q/' mortals. ' Stars are either suns or planets ' then becomes : — 
 
 x=v{y (i—x) + z{T-y)] . 
 No y i& X (All ys are non-:«;) becomes : — y = v (i — ^). Some y's 
 are not x is : — vy=v{i —x). 
 
 Syllogistically, if x=vy and y = v's, then, by substitution, 
 X = vv'z. If dwarfs are small men, and men are food-cooking 
 animals, dwarfs are small food-cooking animals. 
 
 The following formula for a division, say of pieces of cloth 
 striped with colours, is not so difficult as it looks at first sight to 
 the non-mathematical reader. Let v stand for white, x for green, 
 v' for black, y for yellow, w for red, s for orange, w' for blue. Then 
 remembering that x—x stands for non-;i;, i— s for non-s, &c., + 
 for or, and seeking x, we have : — 
 
 X = \yv' ww' -f - {vi/ (i — w) (i —w') + ww' (i —v) (i — i)') -1- (i —v) 
 
 (\—w)'\\z-\--{vv' {T.—1i/)-\--l—v] (l— ^). 
 
 This, being interpreted, is: — Pieces of cloth striped with green 
 are either striped with orange or not [i. e. the expression has two 
 members, one consisting of ^;'s, the other of non-^j's (i— s)]. In 
 the former case they are striped with white, black, red, and blue 
 together ; or else with white and black but not with red and 
 blue ; or else with red and blue but not with white and black ; 
 or with orange alone. In the latter case they are striped with 
 Mrhite and black but not with blue, or else with no white stripe 
 at all.> 
 
 Again, if x stands for men, y for heroes, z for practising self- 
 denial, w for practising courage. Then — 
 X (i —zw) = v (i —y) 
 means : — ' No men are heroes but those who unite the practice 
 of self denial to that of courage.' Men who do not practise self- 
 denial and courage together are some non-heroes.^ 
 
 If every ^ is ^ and every non-A is B, then every thing in that 
 universe of discourse is B. Thus : — 
 
 Every AC \s B, every non-.^C is B. Then every C is B. 
 ^ Boole, Laws of Thought (1854), pp. 231 seq. "^ Ibid. p. 64. 
 
Algebra applied to Reasoning 397 
 
 § 853. ' Conversion,' Boole observes, ' is a particular applica- 
 tion of a much more general process in logic which has for its 
 object the determination of any element in any proposition, 
 however complex, as a logical function of the remaining elements.' ^ 
 
 Thus, y = vx, then x =y+ -{i —y). Things that are x's com- 
 prise all things that areji/'s and an indefinite remainder of things 
 that are not ys. Pomegranates are a kind of fruit. Then the 
 c\3,ss fruit comprises all pomegranates and an indefinite number 
 of things that are not pomegranates. 
 
 § 854. Inference, he says, consists in the elimination of those 
 elements in the premisses which we do not wish to appear in the 
 conclusion. What is wanted is a mechanical method of eliminat- 
 ing any number of middle terms by combining equations. Such 
 a method will enable ' the desired relation ' to be obtained, that 
 is ' the full relation which in virtue of the premisses connects any 
 elements selected out of the premisses at will, and which, more- 
 over, expresses that relation in any desired form and order '. 
 
 § 855. We may glance for a moment at some features of 
 Jevons' scheme. He represents by A an intensive quality, by 
 {A) the number of things (extension) possessing that quality. 
 Then if A = B, (A) = (B). ' Sameness of qualities occasions 
 sameness of numbers.' He is taken aback, however, by the 
 impossibility (see above, §§ 684 seq.) of representing a negative 
 proposition in extension as an equation. ' Curiously enough, this 
 does not apply to negative propositions and inequalities.' If 
 B^D (differs from D) it does not follow that (B) -^ (D). Two 
 classes of objects may differ in qualities and yet agree in 
 number. 
 
 Jevons represents non-^ by a, non-B by b. For unexclusive 
 disjunction (either, or) he uses the sign | . Thus 'A is either B 
 or C takes the form — A =B ■[ C=BC \ Be ■[ bC. Such a sentence 
 as this, ' An elector is either an elector for a borough, a county, 
 or a university,' would be stated thus : — 
 A = B\C\D. Then 
 
 {A) = (BCD) + {BCd) + {BcD) + (Bed) + (bCD) + (bCcl) + (beD). 
 That is, 
 All electors are so either for borough, county and university, 
 
 ^ Op. cit. p. 230. 
 
398 Unfigured Syllogism 
 
 or for borough and county but not university, or for borough 
 and university but not county, or for borough but not county 
 or university, &c. 
 
 § 856. The Law of Duahty, as he terms the principle of 
 Excluded Middle, may be symbolized as A = AB \ Ab. And 
 again, A = AC \ Ac. A law may be kind or unkind, logical 
 or illogical. Then 
 
 Laws are either kind and logical, or kind and illogical, or 
 logical and unkind or neither kind nor logical. 
 
 A = ABC I- ABc I AbC \ Abe. 
 And so on with any number of terms. Jevons devised an 
 abacus for working the method mechanically. 
 
 He gives the following problem : — 
 In every 100 ^'s there are 45 B's and 53 C's. Also wherever 
 the attribute B is found the attribute C is found. Required to 
 determine in how many cases C occurs without B, and in how 
 many cases neither B nor C occur. Then 
 
 {A) = 100 (I) 
 
 (^)= 45 (2) 
 
 (Q= 53 (3) 
 
 B =BC 
 
 U.(B)={BC), (4) 
 
 and(5c)=o (5) 
 
 Then by Law of Duality 
 
 {C) = [BC) + {bC) = {,B) + [bQ 
 That is, 53 = 45 + (^Q- 
 
 Then [bC) (i. e. C without B) = 8. 
 Again, 
 
 {A) = (ABC) + (ABc) + {AbC) + (Abe). 
 That is, 100 = 45 + o + 8 + (^6c). 
 
 Then (Abe) (i. e. A without either B or C) = 47. 
 This certainly seems a rather roundabout solution ; for the 
 first quaesitum is obtained at once by subtracting 45 from 53, and 
 the second by subtracting 53 from 100 — since the 53 C's include 
 the 45 ^'s. 
 
 Jevons quotes from De Morgan^ the following argument, 
 
 ' which cannot b§ put into any ordinary form of the syllogism' : — 
 
 ' For every man in the house there is a person who is aged. 
 
 ^ Syllabus of Proposed System of Logic, i860, p. 29. 
 
Algebra applied to Reasoning 399 
 
 Some of the men are not aged. It follows that some persons in 
 the house are not men. How many ? ' 
 
 Let A stand for man ; B for aged person ; w for excess, if 
 any, of aged persons over men ; w' for not-aged men. Then 
 
 {A) = {B)-w (I) 
 
 {Ab) = w' (2) 
 
 By the Law of Duality 
 
 (AB)+{Ab) = (AB) + {aB)-w 
 
 Then {aB) = w + w' (3) 
 
 Adding (ab) to both sides, then, since aB + ab = a, 
 [a) = w+w'+{ab). 
 w and {ab) are unknown quantities, and must be positive, not 
 negative, if anything at all. 
 
 § 857. The following is the formula for Ultra-dimidiate Quan- 
 tification of the Middle Term : — 
 
 Most B's are A's (i) 
 
 Most B's are C's (2) 
 
 Therefore Some C's are ^'s . . . (3) 
 Then 
 
 iAB) = §+w (I) 
 
 {BC) = f+zi/ (3) 
 
 Then 
 
 (AB)+{BQ = B+w+w'. 
 
 Developing the logical terms on either side we get — 
 
 {ABQ + (ABc) + (ABQ + [aBQ = (ABC) + (ABc) + {aBQ+ 
 {aBc) + w + zt/. 
 
 [That is, the B's which are both A and C, and those which 
 are A without being C, added to the B's which are both C and A 
 and those which are C without being A, axe numerically equal to 
 the -B's which are both A and C, and those which are A without 
 being C, added to the B's which are C but not A, and those which 
 are neither C nor A, added to the number of B's which are A 
 in excess of half the B's and the number of B's which are C in 
 excess of half.] 
 
 Then {ABC) = w + w'+{aBc). 
 [That is, the B's which are both A and C (in other words, the 
 number of C's which are A) are equal in number to the B's which 
 are neither A nor C in addition to the ultra-dimidiation in 
 either case. Accordingly, Some C's are A.] 
 
400 Unfigured Syllogism 
 
 § 858. From the ordinary syllogism in Barbara (All ^'s are B, 
 all B's are C, all A's are C), which is represented thus^ 
 
 , "" - „ therefore A = AC, — 
 
 /i = JijD 
 
 we can discover the relative values of B and" of C as well as 
 of^. 
 
 (abC) = {q-{A)-{aBC) 
 Then (C) = {A) + {aBC) + {abC). 
 
 [That is, if A stands for kings, B for humans, C for mortals, 
 the extension of mortal will be all the kings, together with the 
 human mortals who are not kings, and the mortals who are 
 neither kings nor human.] 
 
 And (B) = {ABC) + {aBQ. 
 
 [That is, the extension of human will be all the mortal humans 
 whether royal or not.] 
 
 § 859. Jevons admits that the results can be reached by com- 
 mon sense or ordinary mathematical calculation : — 
 
 ' But what I claim for my logical method and notation is that ' 
 it is in no sense peculiar, but represents truthfully and com- 
 pletely the natural course of intelligent thought ... It is meta- 
 physical speculation which has mystified the subject and rendered 
 [Logic] the laughing-stock of scientific men ... I hold that Logic 
 can only be regenerated by those who will render themselves 
 acquainted with the exact methods of research which lead to 
 undoubted truths in the mathematical and physical sciences. 
 Logic, in short, must be dissociated from metaphysics, with 
 which it has no necessary connexion, and must become an exact 
 science.' 
 
 § 860. He proposes a table setting forth the legitimate varia- 
 tions of the combinations of three terms. A, B and C, with their 
 negatives a, b and c. The possible combinations are eight — 
 ABC, aBC, AbC, ABc, Abe, aBc, abC, and abc. These eight 
 may be varied in 2* possible ways, = 256, of which 63 may be 
 struck out, leaving 193. Jevons says: — 'Such a table enaljles 
 us to learn by mere inspection the laws obeyed by any set of 
 combinations of three things, and is to Logic what a table of 
 factors and prime numbers is to the theory of numbers, or a 
 table of integrals to the higher mathematics.' Beyond three 
 terms the labour would be impossibly great. Four terms (2") 
 
Substitution of Equivalents 401 
 
 gives 65,536 combinations. Five terms 4,294,967,296. Six 
 terms gives eighteen millions of millions of millions.^ 
 
 § 861, An equational theory of reasoning involves the question 
 of Added Determinants. For whatever is done to one side of 
 an equation, whether adding, subtracting, multiplying or dividing, 
 must be done to the other. 5 = sM. But M =a + b. There- 
 fore S = s {a + b). But if s be a relative term (A dwarf is a small 
 man ; Man is an animal ; Therefore a dwarf is a small animal), a 
 fallacy awaits the too mathematical reasoner, the fallacy a dido 
 secundum quid ad dictum simpliciter. 
 
 The following looks like a good equation. It might be held 
 that a person three parts mad was three parts irresponsible. 
 This gives us mad = irresponsible. But also a cup half full is a 
 cup half empty. Then full — empty ! 
 
 § 862. Again, given a syllogism based on substitution of 
 equivalents, the parts of the syllogism can be placed in any 
 order we please. Thus, instead of S = M, M =■ P, therefore 
 S = P,vi& might argue, S = M, S = P, therefore M = P; or, 
 M=P, S = P, therefore S = M. 
 
 § 863. In the ordinary syllogism, on the other hand, we can 
 never by combining the conclusion with one of the premisses 
 deduce the other premiss. This can be shown as follows : — 
 
 (i) The premiss which is retained cannot be a negative or 
 particular proposition, for, if so, the old conclusion was negative 
 or particular (§ 728). As this is now to be combined with the 
 retained premiss, we should have in the new syllogism two nega- 
 tive or two particular premisses, which cannot be allowed (§§ 723, 
 724). The retained premiss, then, is neither E, I nor O, but 
 must be A^ 
 
 (2) The former extreme of the retained premiss is, of course, 
 the new middle term. It must therefore be a distributed term ; 
 for, unless it were so (since neither could it be found distributed in 
 the old conclusion, which is now the new premiss, § 730), we should 
 have in the rievj syllogism an undistributed middle, from which 
 nothing can be deduced. But in an A proposition the distributed 
 term is the subject. Accordingly, since the retained premiss is 
 
 ^ The reader is referred to a Paper prepared by Professor Jevons for 
 the Manchester Literary and Philosophical Society, ' On a General System 
 of Numerically Definite Reasoning,' and to another Paper ' On the 
 Mechanical Performance of Logical Inference' (1870).- 
 
 Dd 
 
402 Unfigured Syllogism 
 
 an A proposition, the old middle term, which is now the extreme 
 of the retained premiss, must be its predicate, and therefore 
 undistributed. But since, as middle term, it must have been 
 distributed once at least in the original syllogism and was not 
 distributed in the retained premiss, it was clearly distributed in 
 the suppressed premiss. Being, however, undistributed, and 
 an extreme, in the retained premiss, the old middle necessarily 
 reappears undistributed in the new conclusion. The new con- 
 clusion then cannot be identical with the suppressed premiss, 
 where it was, as we have seen, distributed. Nor can it be con- 
 verted into the suppressed premiss, for conversion never increases 
 the quantity of a term.' 
 
 § 864. It is plain, then, that there can only be one way of 
 putting together three given propositions so as to frame a valid 
 syllogism. Also that being given three propositions capable of 
 forming a valid syllogism we can always construct it. 
 
 § 865. It follows further that, if from the truth of one premiss 
 and conclusion the truth of the other premiss cannot, as we 
 have seen, be demonstrated, it is possible that this premiss may 
 be false though the conclusion is actually true. People are apt 
 to conclude that an assertion is untrue as soon as they find it to 
 be held on untenable grounds. Practically they may be right ; 
 for the assertor would probably have chosen a better line of 
 argument had it been possible. But it need not be so. It is 
 even more common for premisses to be accepted without exami- 
 nation because they lead to an acceptable conclusion, that is, 
 one assented to as true. As Hamilton says, ' An inference may 
 be subjectively or formally true which is objectively or really 
 false.'" But it may be both subjectively true (i. e. as an 
 inference) and objectively true (i. e. as a proposition) and yet be 
 supported by false arguments.' 
 
 § 866. The possible inter-relations of the extensions of three 
 terms A, B and C; each of which may be in turn major, minor 
 
 ' I have borrowed the foregoing proof, in substance, from Professor 
 W. H. S. Monck's Introduction to Logic, 2nd ed., pp. 201-3. 
 
 ^ Lectures on Metaphysics, ii. 343. 
 
 ' With Mill I wholly fail to understand Hamilton's protest against the 
 ' doctrine prevalent among logicians . . . that it is possible to infer true 
 from false, but not false from true ', and his contention that this doctrine 
 is ' subversive of the distinction of logic as a purely formal science ' 
 {Lectures on Logic, i. 450, 451 ; see Mill on Hamilton, pp. 522 seq.). 
 
Inter-relation of Extensions 
 
 403 
 
 ,or middle, may be stated as follows, the consequences being 
 visible at a glance : — 
 
 (I) Either two extensions, B and C, are together coincident 
 with the third, A— 
 
 either thus {a) or thus (i) 
 
 _A , ^ . A [Darii 
 
 B 
 
 (Ferio 
 \ Felapton 
 ^Fesapo 
 
 B 
 
 B 
 
 C 
 
 C 
 
 Datisi 
 
 Disamis 
 
 Bocardo 
 
 (II) Or both, viz. B and C, are wholly included in the third, 
 A ; in which case either 
 
 (a) C is wholly outside B 
 
 or {fi) C is wholly inside B 
 [or B may be wholly 
 mside C] 
 
 A 
 
 
 A 
 
 
 
 & 
 
 
 (Felapton 
 (Fesapo 
 
 'Barbara 
 Bramantip 
 Darii 
 ■j Darapti 
 Disamis 
 Datisi 
 Dimaris 
 
 or (y) C partly coincides with B 
 
 Darii 
 
 Disamis 
 
 Dimaris 
 
 (III) Or one only, e.g. B, is wholly included in the third, A ; 
 in which case 
 either (a) C is wholly outside A 
 
 (Cesare 
 
 I Q I I Celarent 
 
 ] Camestres 
 \Cantenes 
 
 D d 2 
 
404 
 
 Unfigured Syllogism 
 
 or (/8) C is partly outside A, in which case either (i) it is 
 wholly excluded from B 
 
 ^Ferio 
 c~l -j Felapton 
 \Fesapo 
 
 or (ii) it partly coincides with B 
 
 A 
 
 or (iii) it wholly includes B 
 
 A 
 
 
 El 
 
 c 
 
 
 
 (Darii 
 Disamis 
 Datisi 
 Dimaris 
 Baroco 
 
 \Bocardo 
 
 Darii 
 
 Darapti 
 
 Dimaris 
 
 (these diagrams under (III) will be reversed if it be C which is 
 included in A) 
 
 (IV) Or neither B nor C is wholly included in ^ ; in which 
 case either (a) both are wholly outside A 
 
 m 
 
 zn 
 
 no syllogism possible, every- 
 thing being negative. 
 
 or (y8) one, e.g. B, is wholly outside A, while C partly 
 coincides with A 
 
 
 
 A 
 
 
 
 B 
 
 
 
 
 
 C 
 
 
 
 
 
 
 \Ferio 
 [Festino 
 
 or (y) both B and C partly coincide with A ; in which case, 
 either (i) they partly coincide with each other 
 
 no universal, and there- 
 fore no syllogism. 
 
 
 
 A 
 
 
 B 
 
 
 
 
 1 
 
 C 
 
 
 
 
 
 
 
 
 
Inter-relation of Extensions 
 
 or (ii) the one includes the; other 
 
 'Darii 
 
 Disamis 
 
 Datisi 
 
 ^Dimaris 
 
 iBaroco 
 
 \Bocardo 
 
 or (iii) they do not coincide at all 
 
 405 
 
 
 A 
 
 
 
 
 
 
 
 B 
 
 C 
 
 
 A 
 
 
 
 B 
 
 ' 
 
 
 C 
 
 ■ 
 
 - 
 
 
 
 
 'Ferio 
 Festino 
 Ferison 
 Fresison 
 
 These diagrams exhaust,, I think, the possible relations of 
 three extensions — omitting, however, the cases of all three coin- 
 ciding, or of any two exactly coinciding. Coincidence cannot 
 be expressed save by quantifying the predicate — All B is all C. 
 A disjunctive judgement, A is either B or C, may be shown as 
 (I) (a) or (I) {b) above, or thus — 
 
 or thus — 
 
 
 
 c 
 
 
 
 
 ° 1 
 
 
 '^ 1 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 ' 1 
 
 
 ^ 1 
 
 
 
 In the first and fourth of these B and C are mutually exclusive. 
 § 867. Various methods of notation have been proposed for 
 visualizing the extension of the nineteen syllogistic Moods. The 
 following linear scheme, based on the idea of subsumption, the 
 falling of the extension of one term under that of another, is 
 here suggested as the simplest. Lines protracted on the opposite 
 
4o6 
 
 Unfigured Syllogism 
 
 side, be it to right or left, of the vertical line represent exten- 
 sions which do not fall under those on the other side. 'Some' 
 requires a possible protraction of the same line, indicated thus — 
 S', M' or P'. Non-protraction indicates a negative extension 
 Thus in Celarent, All M is non-P, in Ferio, Some 5 (at least) is 
 non-P. Notice that the line S' is not necessarily in the same 
 place as P. 
 
 Figure I. 
 
 In this figure ^is in the middle place. 
 
 Allil/isP 
 All S is If 
 
 Barbara 
 
 Darii 
 
 Celarent 
 
 Ferio 
 
 
 M 
 
 
 8 
 P 
 
 
 M 
 
 s- 
 
 S 
 
 
 P 
 
 M 
 
 
 S 
 
 P 
 
 M 
 
 
 S 
 
 s' 
 
 Alii/ is P 
 Some Sis M 
 Some S is P. 
 
 No JJ/is P 
 All SisM 
 No 5 is P. 
 
 No if is P 
 Some S is if 
 Some S is not P. 
 
 Figure II. 
 
 Here M is at the top, and both the other extensions fall 
 (positively or negatively) under it. 
 
 jM 
 
 No P is M 
 All S is if 
 No 5 is P. 
 
 
 P 
 
 
 
 P 
 
 s 
 
 
 M 
 
 Festino 
 
 
 
 S' 
 
 S 
 
 
 s 
 
 M 
 
 Camestres 
 
 P 
 
 
 No P is if 
 Some S is if 
 Some 5 is not P. 
 
 All P is M 
 No 5 is i/ 
 No 5 is P. 
 
Syllogistic Notation 
 
 M 
 
 407 
 
 Baroco 
 
 S' 
 
 All PisM 
 Some 5 is not M 
 Some S is not P. 
 
 Neither Camestres nor Baroco needs in this notation any 
 transposing of premisses. 
 
 Figure III. 
 
 Here M is at the bottom, and falls (positively or negatively) 
 under the extensions both of P and of S. 
 
 P 
 
 All if is P 
 
 — ^ All MisS 
 
 M Some 5 is P- 
 
 Darapti 
 
 S' 
 
 Datisi ' 
 
 M' 
 
 'AViMisP 
 Some Mis S 
 Some S is P. 
 
 Disamis 
 
 s 
 
 S 
 
 M 
 
 M 
 
 
 
 Some M is P 
 All MisS 
 Some S is P. 
 
 Felapton 
 
 Ferison 
 
 
 P 
 
 s 
 
 S' 
 
 M 
 
 
 
 
 
 P 
 
 s 
 
 S' 
 
 M 
 
 
 No Jf is P 
 All if is S 
 Some 5 is not P. 
 
 NoMisP 
 Some M is S 
 Some 5 is not P. 
 
 
 P 
 
 
 S 
 
 M 
 
 M 
 
 
 
 Some M is not P 
 All MisS 
 Some 5 is not P. 
 
4o8 
 
 Unfigured Syllogism 
 
 Figure IV. 
 
 In this figure M is in the middle place. But S appears 
 above P. 
 
 Bramantip 
 
 ^ All Pis if 
 All MisS 
 Some S is P 
 (All P is S). 
 
 Ditnaris 
 
 M 
 
 . Some Pis M 
 AWMisS 
 Some S is P 
 (Some P is S). 
 
 Camenes 
 
 M 
 
 All PisM 
 NoMisS 
 No S is P 
 (No P is 5). 
 
 Fesapo 
 
 S' 
 
 s 
 
 
 M 
 
 p 
 
 
 No P is il/ 
 All if is S 
 Some 5 is not P. 
 
 Fresison 
 
 S' 
 
 s 
 
 
 M M' 
 
 p 
 
 
 No Pis J/ 
 Some M isS 
 Some S is not P. 
 
 The diagram of each Mood should be compared with that of 
 the Mood or Moods to which it can be reduced, e. g. Fesapo is 
 Ferio upside down. 
 
Syllogt'stt'c Notation 
 
 409 
 
 § 868. A Sorites, or chain of arguments, is thus represented in 
 Figure I : — 
 
 Affirmative. Negative. 
 
 
 B 
 
 
 c 
 
 
 D 
 
 
 E 
 
 
 F 
 
 ' 
 
 G 
 
 
 H 
 
 
 1 
 
 
 K 
 
 l; 
 
 L 
 
 
 A 
 
 B 
 
 
 C 
 
 
 D 
 
 
 £ 
 
 
 F 
 
 
 C 
 
 
 H 
 
 
 1 
 
 
 K 
 
 
 L 
 
 L' 
 
 r 
 
 All Z. is ^ 
 or Some L is A. 
 
 No Z, is ^ 
 or Some L is not A. 
 
 § 869. 'The chief end of any adequate system of notation,' 
 remarks Devey, 'is to present to the eye, by a species of 
 symbolical language, all the intricate relations which subsist 
 between terms in a syllogism, so that no point may be overlooked 
 which has any bearing on the conclusion, and the inference be 
 viewed in all the various shapes which the premisses allow it to 
 assume.' ' 
 
 ^ Logic, p. 126. 
 
CHAPTER XXVI 
 
 ELLIPTICAL REASONINGS 
 
 § 870. The Sorites is a compendious polysyllogism, usually 
 in the First Figure, which if stated argumentatively must be 
 broken up into a series or concatenation of syllogisms, the con- 
 clusion of each prosyllogism being the minor premiss of the 
 proximate episyllogism. Thus — 
 
 Minor Major Conclusion 
 
 A is B B is C A is C 
 A is C C is D A is D 
 
 A is n D is E A is E 
 
 A ■ rp j E is F j A is F 
 "^ ^^ ^ 1 £• is not Z' t ^ is not F 
 In the Sorites the conclusions are omitted until the last one is 
 reached. A is B, B is C, C is D, D is E, E is F (or E is not 
 F). Therefore A is /'(or A is not F). 
 
 § 871. The following poetical Sorites is by Sir Thomas Wyatt 
 (1503-44)— 
 
 The longer life the more offence, 
 The more offence the greater paine, 
 The greater paine the lesse defence, 
 The lesse defence the lesser gaine; 
 The loss of gaine long yll doth trye. 
 Wherefore come death and let mee dye. 
 
 The shorter life, less count I finde, 
 The lesse account the sooner made, 
 The account soon made, the merier minde. 
 The merier mynd doth thought evade. 
 Short life in truth this thing doth trye. 
 Wherefore come death and let mee dye. 
 
 Come gentle Death, the ebbe of care. 
 The ebbe of care the flood of life, 
 The flood of life the joyfull fare. 
 The joyfull fare the end of strife. 
 The end of strife that thing wish I ; 
 Wherefore come death and let mee dye. 
 
Sorites 
 
 411 
 
 § 872. When represented by a notation, whether of subordinate 
 lines or of circles one within another, though there appears to be 
 nothing compendious in the argument, the eye at once sees that A 
 is F, or not F. Yet it is too much to say with Hamilton that 
 'the relation is equally cogent and equally manifest between 
 a whole and a remote, and a whole and a proximate part '.^ In 
 a notation A is ascertained to be F, not through the mediation 
 of B, C, &c., but at a glance. But in strictness the eye should 
 be allowed to see only two lines or circles at a time. 
 
 § 873. Aristotle does not speak of the Sorites ; but the principle 
 of it is contained in the Aristotelian rule, praedicatum praedicati 
 est praedicatum subiecti, which is really the dictum de omni et 
 nulla. "Whatever is affirmed or denied of an entire class may 
 be affirmed or denied of whatever is contained in that class. 
 The affirmation of the ground involves that of every consequence 
 of its consequence, till the first ground is connected with the last 
 consequence. 
 
 § 874. It will be observed that, since every unexpressed con- 
 clusion has to serve as a minor premiss, all (in a scheme based 
 on the First Figure) must be affirmative ; also that the last datum 
 before the conclusion may be negative. Thus — 
 
 A' 
 
 D_ 
 
 C 
 
 Some A is B, All B is C, All C is D, All DisE; then Some 
 A (at least) is E. A particular proposition after the first would 
 invalidate the reasoning. Again — 
 
 B 
 
 Lectures on Logic, i. 371. 
 
412 Elliptical Reasonings 
 
 All y4 is 5, All 5 is C, All C is A NoZ>is£; then No ^ is £. 
 A negative proposition before the last would make the chain 
 invalid. Thus — 
 
 E 
 
 E' 
 
 D 
 
 
 C 
 
 
 
 B 
 
 
 A 
 
 All A is B, No B is C, All C is D, All D is E. Evidently it does 
 not follow that any A is, or is not, E. A particular negative 
 conclusion is obtained thus — 
 
 E 
 
 
 
 D 
 
 
 C 
 
 A' 
 
 B 
 A 
 
 Some A is B, All B is C, All C is Z>, No Z) is £■ ; then Some 
 A (at least) is not E. 
 
 § 875. If, instead of the last step being No E is F, we end thus, 
 No F is E, the final syllogism of the Sorites appears in the 
 Second Figure as Cesare or Festino. We might end. No E is G, 
 
 F 
 
 
 
 E 
 
 
 D 
 
 
 C 
 
 K 
 
 B 
 A 
 
 All F is G, which would give Camestres or Baroco. But this 
 running to and fro between the terms would be destructive of 
 the chain. It is really destroyed also by a final syllogism being 
 obtained in the Third. Figure ; which may be done if at the 
 
Sorties 413 
 
 lower end of the series ^ to £ we insert, ' A (all or some)^B G.' 
 It follows, all A being E, that some G is jE (Darapti or Datisi). 
 Mill remarks that this kind of Sorites 'all logicians have 
 admitted '} But it is really a combination of two lines of argu- 
 ment, and not an orderly concatenation. 
 
 I— 
 
 E 
 
 
 D 
 
 
 C 
 
 
 B 
 
 G 
 
 G 
 
 Some A is E, All A is G, will also give Some G is E (Disamis). 
 No A is F, All A is G, gives Some G is not F {Felapton). 
 No A is F, Some A is G, gives Some G is not F {Ferison). 
 Some A is not F, All ^ is G, gives Some G is not F {Bocardo). 
 
 § 876. Mill rightly rejects Hamilton's paradigms in which all 
 the steps are in the Second or in the Third Figure, ' No B is A, 
 No C is A, No D is A, No E is A, All /'is ^ ; therefore No B or 
 C or Z? or £■ is F.' Or again, 'A is 5, ,<4 is C, ^ is D, A is ^"^ 
 ,^ is i^; therefore some B and C and Z) and £ are F.' There 
 is here only one middle term, rather than a successive chain of 
 middle terms. ' Neither of these is a Sorites at all. It is not 
 a chain argument. It does not ascend to a conclusion by a 
 series of steps, each introducing a new premise. It does not 
 deduce one conclusion from a succession of premises, all 
 necessary to its establishment: It draws as many different con- 
 clusions as there are syllogisms, each syllogism depending only 
 on the two premises of one syllogism. . . . [Each] would be 
 proved, though all the other premises of the pretended Sorites 
 were rejected."" Yet Hamilton complains that 'all logicians 
 have overlooked the Sorites of Second and Third Figures '.* 
 Elsewhere he says, 'The Sorites is capable of all the four 
 schematic accidents by a little contortion ; but this at best con- 
 stitutes only a logical curiosity.' * 
 
 § 877. It is of no consequence from which end the Sorites 
 starts. The difference between saying, ' A is B, B is C, C is D, 
 
 ' Ok Hamilton, p. 530. ' Ibid. p. 531. 
 
 ' Lectures on Logic, ii. 395. * Ibid. i. 448. 
 
414 Elliptical Reasonings 
 
 D is E ; therefore A is E' (Progressive Sorites), and saying, 
 ' D is E, Cis D, B is C, A is B ; therefore Ais E' (Regressive 
 Sorites) is merely the difference between stating minor premiss be- 
 fore major, in Barbara, or major premiss before minor. That in 
 the former order the predicate of each proposition is the subject 
 of the next, and in the latter order the subject of each proposition 
 is the predicate of the next, constitutes no difference, except in 
 the point of view. But Hamilton elevates a mere variation in 
 the order of argument into a vital difference between two forms 
 of reasoning, that in ' the quantity of extension ' and that in ' the 
 quantity of comprehension'. Strangely enough (he says) the 
 sequacious logicians, who usually so blindly ignore the latter 
 kind of reasoning, have here fallen into the opposite error. And 
 ' what renders it still more wonderful that the logicians did not 
 evolve the competency of [the Sorites] in either quantity, and 
 thus obtain a key to the opening up of the whole mystery of 
 syllogistic reasoning, is this — that it is now above two centuries 
 since the Inverse or Regressive Sorites in comprehension was 
 discovered and signalized by Rodolphus Goclenius, a celebrated 
 philosopher of Marburg. This Sorites has from him obtained 
 the name of Goclenian.' ' 
 
 § 878. I confess to having completely failed to understand 
 which Sorites Sir William Hamilton means by the one in exten- 
 sion and which by the one in comprehension. He gives the 
 following from Seneca, which follows the order of the ' common ' 
 Sorites, Ais B, B is C, &c. — 
 
 'He who is prudent is temperate, 
 He who is temperate is constant. 
 He who is constant is unperturbed. 
 He who is unperturbed is without sorrow. 
 He who is without sorrow is happy; 
 Therefore the prudent man is happy' — 
 
 and goes on : — 
 
 ' In this Sorites everything glides easily and smoothly from 
 the whole to the parts of comprehension. But though the 
 process will be rather more by hitches, the descent under exten- 
 sion will, if not quite so pleasant, be equally rapid and certain. 
 
 He who is without sorrow is happy, 
 
 He who is unperturbed is without sorrow, 
 
 ^ Op. citv i. 383. 
 
Sorites 415 
 
 He who is constant is unperturbed, 
 He who is temperate is constant, 
 He who is prudent is temperate. 
 Therefore the prudent man is happy.' 
 
 Why the former is more in comprehension and less in extension 
 than the latter it is impossible to understand. ' In the Progres- 
 sive Sorites of comprehension,' he says, 'and in the Regressive 
 Sorites of extension, the middle terms are the predicates of the 
 prior premises, and the subjects of the posterior; the middle 
 term is here in position intermediate between the extremes.'' 
 How is this exemplified in the above regressive Sorites, which, 
 he declares, is a 'descent in extension'? It is the opposite, 
 we are told, in 'the Progressive Sorites of extension and the 
 Regressive Sorites of comprehension '. Hamilton gives as an 
 example of the latter— 
 
 'An animal is a substance, 
 A quadruped is an animal, 
 A horse is a quadruped, 
 Bucephalus is a horse. 
 Therefore Bucephalus is a substance.'^ 
 
 Of the former, the same propositions in the same order, but 
 differently explicated. The explication of Regressive Compre- 
 hensive is — 
 
 The notion animal comprehends the notion substance; 
 The notion quadruped comprehends the notion animal, &c. 
 
 Of the Progressive Extensive — 
 
 The notion animal is contained under the notion substance ; 
 
 The notion quadruped is contained under, &c. 
 
 Progressive Extensive and Regressive Extensive are explicated 
 alike, but in inverse order, and Progressive Comprehensive 
 and Regressive Comprehensive also. 
 
 § 879. According to Hamilton, a proposition is in extension or 
 in intension, not as it is worded but according as we * explicate ' 
 its meaning to be either ' Notion X is contained under notion Y', 
 or ' Notion X comprehends the notion Y'. So elsewhere, ' The 
 term Caius contains in it the term Man.' ' I submit once more, 
 however, that X is not as a notion but as a class contained under 
 
 * Op. cit. i. 379. 
 
 ^ So also Veitch, Institutes, p. 446. ° Op. cit. i. 296. 
 
4i6 Elliptical Reasonings 
 
 Y, and that Y is comprehended not in the notion, or term, X 
 but among the attributes possessed by the class X. If we wish 
 to state a proposition in extension, we must say, '^is a YJ belongs 
 to the class Y.' If in intension, we must say, 'X has the attribute 
 F-ness.' Or otherwise — 'The class F includes Z'' (extension). 
 'The attribute Y-ness belongs to X' (intension). In such an 
 example as Hamilton gives, the notion temperate maybe compre- 
 hended in the notion prudent. But can we say that the notion 
 tiresome is comprehended in the notion boy ? ' Bucephalus is 
 a horse' Hamilton explicates thus — 'The representation Buce- 
 phalus comprehends the notion horse' (comprehensive); 'is 
 contained under the notion horse ' (extensive). 
 
 § 880. A Sorites in comprehension will either be progressive — 
 A has the attribute 5-ness, B (i. e. whatever has the attribute 
 jB-ness) has the attribute C-ness, &c. — or regressive : — ^-ness 
 is an attribute of D (things which have the attribute Z>-ness), 
 Z)-ness is an attribute of C, &c. 
 
 § 881. A Sorites may be cast in hypothetical form : — If A is, 
 B\&] if -B is, C is, &c. ; therefore if A is, E is. This is logically 
 equivalent to All A is B, All B is C, &c. Or more fully— If ^ 
 is B, C is D; if C is D, E is F; if E is F, G is H. Therefore 
 if A is B, G is H. Regressively these will become — E is if Z) 
 is ; Z) is if C is, 8z:c. Ag3.in, G is H ii E is F ; EisFifCisD,&c. 
 
 To posit now that E is F will not carry with it the conse- 
 quence that G is H, unless all the other suppositions are true 
 also. But if we deny that G is H, all the prior propositions fall 
 to the ground, as propositions, though not, of course, as conse- 
 quences. 
 
 To prove G to be i/ we should have to say, ' GisH ifE is F; 
 now E is F, because C is D; and C is Z> because A is B.' Or, 
 in casting about for some firm foundation for the statement that 
 G is H, we say, ' GisHif E is F; and E is Fit C is D; and C 
 is D if A is B. But A is B; therefore G is H.' Such a regres- 
 sive argument is employed when we are seeking for a proof; 
 the progressive order when we are examining consequences. 
 The way, then, in which Hamilton states the regressive Hypo- 
 thetical Sorites is not quite natural : — 
 
 If Harpagon be discontented he is unhappy; 
 If intent on gain he is discontented ; 
 If avaricious he is intent on gain ; 
 
Sorites 
 
 417 
 
 Now Harpagon is avaricious. 
 Therefore he is unhappy.' 
 \t would be more natural to say : — 
 
 Harpagon is unhappy if he be discontented. 
 He is discontented if intent on gain, &c. 
 This illustration takes the following form, progressively — • 
 If ^ is 5 it is C. 
 UA is C it is Z). 
 If A isZJitisZ:— 
 {'A is C, 'A is D,' corresponding to middle terms) ; and regres- 
 sively) — 
 
 A is £ if it is Z). 
 A is n if it is C. 
 A is C if it is 5. 
 
 The modus ponens is — A is B ; therefore it is C and D and E. 
 And B is C, and C is D, and D is E. 
 
 The modus tollens — A is not E ; therefore it is neither D nor 
 C nor B. Yet D is E, and C is D, and B is C. 
 
 § 882. A Disjunctive Sorites takes the following form : 
 A is either B or C. 
 
 B is either D or E. 
 
 D is either H or /. 
 £ is either K or Z. 
 
 C is either 7^ or G. 
 
 F is either ilf or N. 
 G is either O or P. 
 
 ' Lectures on Logic, i. 372. 
 E e 
 
4i8 
 
 Elliptical Reasonings 
 
 Therefore A is either H or I ox K or Lor M or N or ox P. 
 A 
 
 -a 
 
 X 
 
 £ 
 
 K ; L 
 
 a. 
 O 
 
 z 
 2 
 
 I K 
 
 L M NO 
 
 If now we posit, A is B, it follows that A is either H ox I ox 
 K or Z. If ^ is C, it is either 71/ or iV or O or P. 
 
 But if A is none of these, then it is neither A nor B. 
 
 § 883. Sorites, the piler-up, is a name given to the chain-argu- 
 ment by transference. Both are rather compendious than elliptical 
 arguments, the conclusion being held in reserve and gathering 
 force at each step. We must go on to consider arguments 
 which are really elliptical, that is where some element of the 
 syllogism is understood but altogether omitted. 
 
 § 884. An argument with either of the premisses, or the con- 
 clusion, suppressed is usually called an Enthymeme, which is 
 explained as the holding back something in the mind. Mansel 
 points out that ivBvit.y]\ija. cannot mean this, but seems rather to 
 mean a thought suggested.^ He shows that Aristotle's Enthy- 
 meme is not an argument with any part suppressed, but an 
 inconclusive syllogism in which an inference is rather suggested 
 than proved. Aristotle defines it as <ruXXo7io-/x,os ef eiKoTiov 17 
 tnj/ietW. The eiKos is a probability. ' She to her father lied ; 
 why not to thee ? * 
 
 Most men who envy, hate ; 
 This man envies ; 
 
 Therefore this man (probably) hates. 
 I do not know why Mansel says that 'the reasoning is logically 
 faulty', the middle term being undistributed. It follows abso- 
 lutely that there is a probability that 'This man hates', for 
 
 ' Aldrich, App. F. 
 
Enthymeme 419 
 
 ' Most men who envy hate ' implies that every man who envies 
 is probably a hater, 
 
 § 885. The etKos need not necessarily be the major premiss. 
 
 All fierce creatures are dangerous, 
 
 Most caged creatures are fierce ; 
 
 Therefore this caged creature is probably dangerous. 
 
 (It would be best not to go too near.) 
 
 § 886. The a-qfieiov or Indication is usually the minor premiss 
 of a halting syllogism in Figure II. 
 
 Those who take scarlet fever have sore throats, 
 
 This child has a sore throat; 
 
 Therefore, probably, it has taken scarlet fever. 
 
 'Perhaps' is all that the premisses strictly allow. The sore 
 throat is an indication suggesting fever only. We recognize the 
 old defect of the ratio cognoscendi. Sore throat may be a mark 
 or sign, but it is not an infallible sign, of the malady ; for you 
 may have sore throat without having scarlet fever. The middle 
 term is undistributed. 
 
 Again — 
 
 How know you I am in love ? By these marks, &c. 
 
 (Two Gentlemen.) 
 But here the marks are propria and TeK/iiJpia. 
 
 § 887. In Figure II there is an illicit process of the minor 
 term, if we go beyond a peradventure. 
 
 Every intelligent man is a whig (or tory). 
 
 .X" is a whig (or tory). He is sure then to be an intelligent 
 man. If what is meant in the major is that a man proves his 
 intelligence by being a whig (or tory), the inference is valid. 
 But formally it is fallacious. 
 
 Yet we frequently argue in this way, and, if we have observed 
 a good many instances of two attributes being combined in one 
 subject, we are often safe in doing so. The one attribute is a ' 
 probable indication of the other's presence. 
 
 § 888. In the First Figure there cannot be anything short of 
 proof, unless for the particular conclusion of Darii or Ferio we 
 substitute a universal, which would be mere guessing. ' Some 
 5's at least are P ; therefore all probably are.' But we often 
 
 E e 2 
 
420 Elliptical Reasonings 
 
 frame a formally invalid mood with a negative minor premiss, 
 and jump to a conclusion. E. g. — 
 
 The brave are modest. 
 William is not brave. 
 
 Probably therefore he is not modest. His not being brave 
 suggests it, is an indication of it. 
 
 So much in these and similar reasonings depends on material 
 considerations. The inferences we draw from moment to 
 moment are nearly all of this kind, probability being the very 
 guide of life. We must be always adventuring something. Our 
 logic is correct enough, but our premisses seldom warrant a 
 universal. Yet there is more than one Perhaps which not to 
 put to the touch would be cowardice and treason. 
 
 § 889. Our present subject, however, is not reasoning about 
 probabilities, but reasoning not fully expressed in words. As 
 the two things have no kind of connexion, it would be better to 
 discard the name Enthymeme, however time-honoured, to repre- 
 sent the latter, and to call this simply the Elliptical Argument. 
 
 As Hamilton says : 'A syllogism is considered by the logician 
 not in relation to its expression (ov wpos tov e^u Xoyov), but ex- 
 clusively as a mental process (dAXct Trpos tov iv ry ij/vxy Xoyov).' ^ 
 
 § 890. For rhetorical reasons, however, and for brevity, man- 
 kind seldom states its syllogisms in full. Brevity is especially 
 the soul of epigram. Sometimes one premiss is omitted, some- 
 times there is scarcely a rag of either ; sometimes the conclusion 
 is left unexpressed. We say : ' I leave you to draw your own 
 conclusions.' Occasionally all that is expressed of a syllogism 
 is one premiss. Constantly we leap over several intermediate 
 steps. There are several syllogisms, e. g., contained in ' The 
 kitten can get through that hole, since the cat did '. 
 
 § 891. American humour often consists in an extreme abbrevia- 
 tion of the argument, ' The youth looked down the muzzle to 
 see if the gun were loaded. The coroner's jury decided that 
 it was.' The President of a South American republic remarked 
 that the lack of interest taken in public affairs was the country's 
 
 ' Lectures on Logic, iii. 388. He is quoting Aristotle, An. Post. i. 10, 7. 
 Veitch (p. 447) cites a remark of Duncan's : — ' Dicitur syllogismus imper- 
 fectus non respectu mentis sed probationis. Nam in mente proponentis 
 integer esse potest et solidus syllogismus, etsi proferatur truncatus.' 
 
An Un-expressed Premiss 421 
 
 curse. He had not been shot at for at least a fortnight.^ Or 
 the humour may be unconscious — ' Go and see what Baby is 
 doing, and tell him not to '. The omitted premiss is often a sly 
 insinuation, as when in the play some one says: ' It is of no use 
 crying over spilt milk. It only makes it more watery.' Or the 
 philosopher's, ' Be serious. Here comes a fool.' The jest is 
 spoilt by supplying the missing step or steps. A rhetorical 
 statement also gains in impressiveness by assuming that the 
 omitted premiss is so certain and familiar that it needs no stati 
 ing. ' Confide ; scias te Caesarem vehere ' (to the sbipman in 
 the storm). It is related of Sir Thomas Brisbane, when serving 
 under Abercromby in the West Indies, that on his way to capture 
 a fort he was met by a brother officer who said it could not 
 possibly be taken. ' It can,' he replied, ' I have the order in 
 my pocket.' Phocion, being told that men praised him, asked, 
 ' Have I, then, done anything wrong ? ' 
 
 § 892. The following are examples of a conclusion followed 
 by a single premiss : — 
 
 Deus patiens, quia aeternus. 
 
 Death cannot be an evil, being universal (Goethe). 
 
 I could not love thee, dear, so much. 
 
 Loved I not honour more. 
 The reasoning here is pointedly compressed. But we can 
 easily supply the missing premiss when, in Beaumont and 
 Fletcher's play, Valentinian says : ' Justice shall never hear you. 
 I am justice.' 
 
 This child can't be ' right '. It never does anything wrong. 
 
 Carlyle says of Sansculottism : It too came from God ; for has 
 it not been ? 
 
 Mass, thou lov'st plums well that would venture so. 
 
 (Henry VI, Part II.) 
 
 Let us not meet her. Why ? They say she 's mad. 
 
 [Coriolafius.) 
 
 These hands do lack nobility, that they strike, &c. 
 
 (Antony and Chop.) 
 
 He is in love. He brushes his hat. (Much Ado.) 
 
 Pardon it, as you are a gentleman. (Hamlet.) 
 
 ^ Diary of Sir Mountstuart Grant-Duff. In the republic of Colombia, 
 up to 1903, there have been fifty-fovir insurrections in forty-seven years. 
 
422 Elliptical Reasonings 
 
 Forbear to judge; for we are sinners all. [Henry VI.) 
 
 Sell when you can. You are not for all markets. 
 
 {As You Like It.) 
 
 Why dost thou wrong her, that did ne'er wrong thee? 
 
 [Taming of the Shrew.) 
 
 Why 'knaves'? Are they not all Athenians? 
 
 [Timon of Athens) 
 ' Stop thief!' gives conclusion followed by ground. It is quite 
 ratiocinative. Thieves ought to be stopped. This man is a thief. 
 Therefore I call to you to stop him. 
 
 § 893. Some other curtailed reasonings, in which the conclu- 
 sion comes last, are as follows : — 
 
 Cogito, ergo sum. (Descartes.) 
 
 He bears the third part of the world. The third part of the 
 world, then, is drunk. [Antony and Cleop.) 
 
 She is a woman, therefore may be won. 
 
 [Titus Andronicus.) 
 
 Because thou art virtuous, shall there be no more cakes and 
 ale ? [Twelfth Night.) 
 
 There 's blood upon thy face ! 'Tis Banquo's then. 
 
 [Macbeth.) 
 
 The north wind doth blow, and we shall have snow. 
 
 It is my son's coat. An evil beast hath devoured him. 
 
 The children are so quiet they must be in some mischief. 
 
 It is too good to be true (i. e. It, being so good, is not true). 
 Very often indeed the missing parts of the syllogism are filled 
 up by action. A man says, ' Honesty should be rewarded,' and 
 proffers money. To the first settlers in New England the follow- 
 ing Sorites, with the final steps and conclusion left to be under- 
 stood, is attributed : — 
 
 'Resolved (i) That the earth is the Lord's and the fulness 
 thereof. (2) That what is the Lord's is His Saints'. (3) That 
 we are His Saints.' Ending with the attempt to exterminate 
 the Indians.' 
 
 Similarly a whole train of reasoning may be suggested by one 
 imperative, as Cherchez la femme, the ' la ' implying a premiss 
 too well established to need expressing in full. 
 
 First they fell upon their knees ; 
 And then upon the aJDorigines. 
 
Example 423 
 
 An action may take the place of a premiss, as in the argu- 
 mentum ad baculum. 
 
 § 894. When a general assertion is couched in a conditional 
 form, with a suggestion of the absurdity of the consequent, it is 
 unnecessary to fill up the syllogism. Thus Falstaff protests : — 
 ' If I fought not with fifty of them, I am a bunch of radish. If 
 there were not two or three and fifty upon poor old Jack, then 
 am I no two-legged creature.' These are arguments in Camestres 
 and Cesare respectively. 
 
 § 895. The place of the major premiss is sometimes taken by 
 a maxim or proverb. / Rome was not built in a day. You must 
 have patience.' ' If gold rust, what shall iron do ? You must 
 therefore set a good example to your flock.' 
 
 § 896. Similar to this is the Example. ' Had Zimri peace 
 who slew his master?' 
 
 A man might read Wordsworth's Ode to Duty, or the life of 
 a saint, and saying, ' Here lies my duty,' do it. This would be 
 major, minor, and conclusion. 
 
 John Ball's text to the insurgents at Blackheath — 
 When Adam dalf and Eve span. 
 Who was thanne a gentilman? — 
 was itself a compressed syllogism, and the inference, ' There 
 were neither villeins nor gentlefolks in those days,' served as 
 premiss to the preacher's conclusion, ' Good people, things will 
 never go well in England till goods be all in common,' and that 
 as premiss to seizing clubs and billhooks. 
 
 § 897. To build up and complete an imperfect argument, we 
 may start — 
 
 (i) From one term only, S, M or P. 
 (a) S. What are we to say about it and on what ground ? 
 
 That S is P, as being M. 
 (J3) M. What results from it ? S being P results, since S 
 
 is M. 
 (y) P. Of whom or what can we say this, and why ? Of 
 
 5, which is M. 
 
 (3) Given two terms only — 
 (a) S is P. On what ground ? On the ground of being 
 
 M. It is M and M is P. 
 {/3) S is M. What follows ? That it is P, M being P. 
 
424 Elliptical Reasonings 
 
 {y)MisP. How do you apply this? To the case of 5, 
 since S is an M. 
 
 (3) Given the minor premiss — 
 
 If every S is M, 
 Then every S is P, since every M is P (Barbara). 
 Or, no 5 is P, since no Af is P (Celarent). 
 Or, no S is P, since no Pis, M (Cesare). 
 
 If some 5's are M, then 
 Some S's are P, since every M is, P (Darii). 
 Some 5's are not P, since no M is P {Ferio). 
 Some S's are not P, since no P is M (Festino). 
 
 UnoSis M, then 
 No S is P, for every P is M (Camesires). 
 
 If some 5's are not M, then 
 Some 5's are not P, since every M is P (Baroco). 
 
 If every M is 5, then 
 Some S's are P, since every M is P {Darapti). 
 Some S's are P, since some M's are P (Disamis), 
 No S is P, since no M is P [Felapton). 
 Some S's are not P, since some M's are not P [Bocardo). 
 Some S's are P, since every Pis M (Bramantip). 
 Some S's are P, since some P's are M [Dimaris). 
 Some S's are not P, since no Pis M (Fesapo). 
 
 If some M's are S, then 
 Some S's are P, since every M is P {Datisi). 
 Some S's are not P, since no ilf is P (Ferison). 
 Some S's are nofP, since no P is M (Fresison)'. 
 
 If no M is 5, then 
 No 5 is P, since every Pis M (Camenes). 
 
 If some M's are not 5, — no syllogism. 
 
 Or if the major premiss only is given, we shall find that — 
 Every M is P suggests Barbara, Darii, Darapti, Datisi. 
 Some M's are P „ Disamis. 
 
 No M is P „. Celarent, Ferio, Felapton, Ferison. 
 
 Some M's are not P „ Bocardo. 
 
 Every P is M „ Camesires, Baroco, Bramantip, 
 
 Camenes. 
 Some P's are M „ Dimaris. 
 
Syllogism in One Proposition 425 
 
 No P is M suggests Cesare, Festino, Fesapo, Fresison. 
 
 Some jP's are not M „ no syllogism. 
 
 § 898. From one premiss and conclusion the other premiss 
 can always be supplied, although, as we have seen, it cannot be 
 proved from the former premiss and conclusion regarded as 
 propositions. But if we say. It follows from P not being M that 
 no 5 is P, we are able to supply the understood premiss, Every 
 5 is M. Being given that every S is M and 5 is P, we cannot 
 prove that every M is P; but if every 5 is M we can show that 
 ' Every M is P' is the only possible premiss which will yield the 
 conclusion Every S is P. Indeed in the case of this conclusion 
 (but not of any other), since only Barbara concludes in A, we 
 can reconstruct the skeleton of both premisses from the con- 
 clusion alone. 
 
 § 899. A syllogism, with major premiss understood, is fre- 
 quently expressed in a single sentence. 
 
 Physician, heal thyself. 
 
 She, being mortal, of that boy did die. 
 
 (Midsummer N. D.) 
 
 ABdvarov 6pyr]v fxir] <j>v\wm, Ovryros tov. 
 
 Now a participial clause may be represented by an adjective, 
 either qualifying, as 
 
 All inspired writings are to be received ; 
 or descriptive, as 
 
 All the inspired Scriptures are to be received. 
 The former means, 'All writings if inspired,' the latter means, 'All 
 Scriptures because inspired.' The proposition, 'All the Scriptures 
 of the New Testament are to be received' does not explicitly state 
 its own ground, unless the idea of authority is meant to be con- 
 veyed by 'New Testament'. But 'AH inspired writings' does. 
 It is the difference between an observed fact and a general law ; 
 between ' A postboy never dies ', and ' The King never dies ', 
 or between 'Black swans are uncommon', and 'Angry swans 
 are dangerous'. 
 
 § 900. Whereas, however, a descriptive adjective or participial 
 clause is really a minor premiss — 'The Scriptures are- to be 
 received because they are inspired '. ' Because thou art mortal, 
 thou must not nurse undying resentment' — this is not the case 
 with a qualifying adjective or clause, 'Pead men tell no tale^ ', 
 
426 Elliptical Reasonings 
 
 i. e. ' Men, if they are dead, t6ll no tales ' is a simple proposition. 
 It is true it implies 'because they are dead '. But, if we are to 
 construct a syllogism out of this, it cannot take the form — 
 Things that are dead tell no tales. 
 Men are things that are dead. 
 Therefore men tell no tales — 
 but only, 
 
 Things that are dead tell no tales. 
 Dead men are dead things. Therefore, &c. 
 Such a syllogism would be less unnatural if, instead of ' A dead 
 man tells no tales ', we said, ' A dead accomplice.' It would 
 then be — 
 
 Dead men tell no tales. 
 A dead accomplice fulfils the condition. 
 Therefore he will tell no tales. 
 The proposition then will be in the form, ' If any 5 is Af it 
 is P' (understood, 'since il/ is P'). If any coastguardsman be 
 dead he will tell no tales (since the dead tell no tales). Every 
 MS is P. 
 
 But where M is assumed true of S, the form of the proposition 
 is, ' The MS, or this MS, is P.' More fully, ' S, being M (i. e. 
 because it is M) is P.' 
 
 § 901. The syllogism resting on a double hypothesis cannot be 
 expressed in a simple proposition, 'li S is M and if M is P, 
 S is P' could only become, 'Every PMS is P.' It is good 
 reasoning to argue, ' If life be short, and if what is short be 
 precarious, life is precarious.' But we could not express this as, 
 ' Precarious short life is precarious,' nor can the premisses, ' If 
 a man is mad and if all the mad are dangerous,' be expressed 
 by ' A dangerous madman ', which implies two particular pro- 
 positions, ' Some men are mad ' ; and ' Some of the mad are 
 dangerous '. 
 
 The difficulty of expressing an entire syllogism in a simple, 
 uncomplex, proposition, will appear from the circumstance 
 that the ground, or major premiss, must be universally taken. 
 We cannot say, ' If any S is M and if any M is P, that S will 
 be P' ; but only, ' If any S is M and if every M is P, that 5 will 
 be P.' The formula then will not be, 'Every MS is P,' but 
 ' Every MS (M being P) is P'. M being P, whatever 5's are 
 M are 5's that are P, S may be universal or particular. 
 
Syllogism in One Proposition 427 
 
 § 902. The formula for the First Figure then will be this, com- 
 prising all four moods — 
 
 Given that.il/ is P (or not P), Every MS is P [or not P). 
 
 For the Second Figure — 
 
 (i) Given that M excludes P (no P is M), No MS can be P. 
 
 (ii) Given that M includes P (Every P is Tif), No noxi-MS is P, 
 
 For the Third Figure — 
 
 Given that M is P (or not P), then 
 
 Whatever S any M is is P, or is not P. 
 
 But to express this as ' Every MS is P (or not P) ' is to con- 
 fuse the Third with the First Figure. It includes the case of 
 all 5's being M. This may be materially true, but cannot be 
 formally implied in the premiss, ' Every M is S,' apart from 
 Hamiltonian theories of quantified predicate. 
 
 Disamis and Bocardo, having a particular major premiss, 
 permit of no direct attribution of P to S,^ and cannot be 
 recognized here. Nor yet Diman's in Fig. IV. 
 
 For the Fourth Figure — 
 
 (i) Given that M includes P (all P is M), then whatever S any 
 M, is includes P. It may be some 5's, if every M is S (Bra- 
 mantip), or none, if no Af is S {Camenes). 
 
 (ii) Given that M excludes P (no P is M), then whatever 5 any 
 M is is not P [Fesapo, Fresison). 
 
 § 903- Or the Mood formulas may be more generally expressed 
 thus :— 
 
 Figure I. 
 
 Barbara. When S must be something which must be P, S 
 must be P. 
 
 Darii. When S may be something which must be P, 5 may 
 be P. 
 
 Celarent. When 5 must be something which cannot be P, S 
 cannot be P. 
 
 Ferio. When S may be something which cannot be P, S 
 need not be P. 
 
 ^ Why not, I have been asked, if Disamis be expressed thus— Given 
 that some M is P, then, some 5's being all the M's, some of them must 
 be /" ? Bocardo likewise. But this is equational reasoning, which does 
 not run in the ordinary grooves. ' Some 5's ' and ' all the M^s, ' are 
 totals. 
 
428 Elliptical Reasonings 
 
 Figure II. 
 
 Cesare. When S must be something which P cannot be, 5* 
 cannot be P. 
 
 Festino. When S may be something which P cannot be, 5 
 need not be P. 
 
 Camestres. When S cannot be something which P must be, 
 S cannot be P. 
 
 Baroco. When S need not be something which P must be, 
 5 need not be P. 
 
 Figure III. 
 
 Darapti. When something which must be P must also be S, 
 S may be P. 
 
 Datisi. When something which must be P may also be S, 
 S may be P. 
 
 Disamis. When something which may be P must also be 5, 
 vS may be P. 
 
 Felapton. When something which cannot be P must also be 
 5, 5 need not be P. 
 
 Ferison. When something which cannot be P may also be S, 
 5 need not be P. 
 
 Bocardo. When something which need not be P must also 
 be S, S need not be P, 
 
 Figure IV. 
 
 Bramantip. When something which P must be must be S, 
 S may be P. 
 
 Dimaris. When something which P may be must be S, S 
 may be P. 
 
 Camenes. When something which P must be cannot be S, 
 S cannot be P. 
 
 Fesapo. When something which P cannot be must be S, 
 S need not be P. 
 
 Fresison. When something which P cannot be may be S, 
 S need not be P. 
 
 For ' must be ' we might say ' is always '. For ' may be ' 'is 
 sometimes '. For ' cannot be ' 'is never *. For ' need not be * 'is 
 not always '. 
 
 § 904. Or, more generally still, the formulas might be phrased 
 
Reconstruction of Parts 429 
 
 thus : — ' When anything must be something which must be some 
 third thing, the first thing is always this third thing.' And so 
 forth. 
 
 § 905. If in the above the indifference of the quantity of the 
 minor premiss (which reappears, whatever it is, in the conclu- 
 sion) seems to be obscured, a general formula for Barbara-Darii, 
 &c., would be — ' If any 5's are M when M is always P, all such 
 S's are P '. Substituting not-P for P, the same formula serves 
 for Celarent-Ferio. 
 
 § 906. The ground of a proposition frequently unites subject 
 and predicate in a less direct way than in the simple proposition, 
 'MS is P: (If any S is M it is for that reason P.) Instead of 
 being a qualifying adjective or participial clause, it may be a 
 clause absolute or conditional, containing two terms. If ^ is B, 
 C is D. That is C (A being B) is Z*. ' When thieves fall out 
 honest men come by their own,' ' Te duce, milites vincunt.' 
 
 § 907. That is, C, under the condition (not of being M but) of 
 M's actuality, is P. ' C (A being B) is D,' may be taken to mean 
 ' C {C being A and B being D) is D '. Yet we cannot identify 
 honest men with rogues or fall out with come by their own. The 
 condition here should be regarded as a single term — ' MC is D '. 
 With protasis ' If ^ is B', the apodosis and its syllogistic 
 implication will be — 
 
 ■ g I C is ZJ, implying that ^^ J- C is ^, and All B is D. 
 
 3. No C is D, implying that All C is. A and no 5 is Z? (or 
 else that No C is S and All D is A). 
 
 4. Some C is not D, implying that Some C is ^ and no B 
 is D (or else that Some C is not B and All D is A). 
 
 With protasis, ' If Some A\s, B' then — 
 
 5. Some C is Z> will imply that All A\%C and All B is D. 
 
 6. Some C is not D will imply that All ^ is C and no B isD 
 (not that No ^ is C and All B is D). 
 
 With protasis, 'UNoA is B,' then— 
 
 7. All ] r- n Ml • 1 *i, ^ All 1 C is ^ and All not-B 
 ' „ I C is Z?, will imply that c, > . „, .„ ^. „^ 
 
 8. Some/ ^ -^ Some J isZ>(=Allnot-Z>is5). 
 
 9. No C is D, will imply that All 1 C is ^, and No not-B is 
 10. Some C is not Z) „ Some; D{=:AU. D is B), 
 
 With protasis, 'If some A is not B,' then — 
 
430 Elliptical Reasonings 
 
 11. Some CisD will imply that All A is C and All noi-B is D 
 (=A11 not-D is B). 
 
 12. Some C is not D will imply that All ^ is C and No not-5 
 is D (=A11 Z> is ^). 
 
 § 908. "When either premiss indicates, not hypothetically but 
 categorically, the ground of its assertion, exhibiting in an abbre- 
 viated form the way in which it has been arrived at, the syllogism 
 is called an Epicheirema. Or both premisses may do this. 
 As Hamilton says, 'There is little or nothing requisite to be 
 stated in this variety of complex syllogism, as it is manifestly 
 nothing more than a regular episyllogism with an abbreviated 
 prosyllogism interwoven.' * 
 Bis A. 
 C, being D (i. e. because it is D, not, if it is D), is B. 
 
 Therefore C is .^4. 
 All vice is odious. 
 
 But avarice is a vice, for it is enslaving. 
 Therefore avarice is odious.'' 
 But the auxiliary reason may be attached to either major or 
 minor premiss, or both. More fully — 
 
 M is P, for it (M) is D. 
 SisM for it (S) is G. 
 Therefore S is P. 
 The reason thus rendered for the premiss is merely paren- 
 thetical, and does not affect the syllogism. It is explicative, not 
 conditional. 
 
 The reason may be simply an assertive adjective, epithet, or 
 participle, as 
 
 The winner will get the prize. 
 Lucky William is sure to win. 
 Therefore William is sure to get the prize. 
 
 ' Lectures on Logic, i. 365. 
 
 ° The illustration given by Veitch {Institutes of Logic, p. 444) — 
 ' It is permissible to take the life of a man who lays an ambush for the 
 purpose of taking yours. 
 
 ' Milo, therefore, was justified in killing Clodius, for Clodius had laid an 
 ambush against Milo's life ' — 
 
 is not an Epicheirema as it stands, but merely major premiss, conclu- 
 sion, minor premiss. It should be expressed thus — 
 
 Whoever kills a waylayer is justified. ^ 
 
 Milo killed a waylayer, for he killed Clodius. 
 Therefore Milo was justified. 
 
Epicheirema 431 
 
 Ships which cannot pass the bar must wait outside. 
 
 The enormous (or heavily-laden) troopships cannot pass it. 
 
 It follows that the troopships must wait outside. 
 
 ' Lucky ' means because he is lucky. ' Enormous ' or ' heavily- 
 laden ' in the same way alleges an assumed fact as the reason. 
 But if ' the heavily-laden troopships ' meant those troopships 
 which are heavily laden (implying that some are and some are 
 not), the reason would no longer be stated assertorily but hypo- 
 thetically, and there would be no epicheirema. The minor 
 term in the conclusion could not be simply ' the troopships ', but 
 must be 'the heavily-laden troopships'. It is the difference 
 between *A soft answer turneth away wrath' and 'Her soft 
 answers turn away wrath ' — , an answer ^soft, and her answer 
 because soft. Thus there is nothing recondite about epicheire- 
 matic arguments. 
 
CHAPTER XXVII 
 CONDITIONAL REASONING 
 
 § 909. The connexion of subjects has now brought us back to 
 Conditional Reasoning, the simplest form of which is — 
 If^isFitisZ. 
 X is Y. Therefore X is Z. 
 
 Conditional arguments are subdivided into (i) conjunctive, or 
 simply hypothetical, (ii) disjunctive, (iii) dilemmatic. In defer- 
 ence to Sir William Hamilton's great learning Conditional is 
 here regarded as genus and Hypothetical as species. But, as 
 he notes, conditionalis is the usual Latin translation of viroOeTiKoi,^ 
 and the point is not a material one. 
 
 A syllogism is called Conditional not because the conclusion, 
 like all conclusions, is conditionally true, but because the major 
 premiss or sumption is explicated in the form of a conditional 
 statement, while the minor premiss takes the form of an assertion 
 that the condition is realized. 
 
 § 9ic>-. It is plain that such a syllogism does not differ in 
 principle from the ordinary categorical syllogism of the form — 
 Every MS is P (= If any S is Af it is P). 
 This (5) is an MS (=this is a case of 5 being M). 
 Therefore this (5) is P- 
 
 Hard words break no bones. This (word) is a hard word. 
 Therefore it breaks no bones. 
 
 § 911. The 'conditional' syllogism, however, is ordinarily one 
 in which the sumption cannot be expressed in the form, ' Every 
 MS is P,' owing to 5 being an individual object or concrete 
 class, and in which the subsumption, instead of bringing under 
 MS as middle terra some as yet unspecified minor term X 
 (' Every X is MS', or ' Some X's are MS '), asserts that 5, the 
 concrete S, is M. 
 
 § 912. So that the conditional syllogism which seems at the 
 
 ' Lectures on Logic, i. 236. 
 
How Many Terms? 433 
 
 first glance to have five terms — liA isB,CisD; such and such 
 is a case of A being B ; then such and such is a case of C being 
 Z>— might in a sense be said to have only two, the minor term 
 being represented by Tki^, or the idea of assertion. 
 If S be il/ it is P. 
 
 5 is M. Therefore 5 is P. 
 If MS then P (MS involves P). 
 
 The case of MS is a real one. 
 
 Therefore P. 
 If the grass is wet it will give you damp feet. 
 The grass is wet. Therefore, &c. 
 'If the grass is wet' here means, 'If the lawn, or some speci- 
 fied piece of grass, is now, or at some particular time, wet.' But 
 were we to say, ' If the grass is wet it is easier to cut,' the proposi- 
 tion would be more general. It could be expressed thus, ' Wet 
 grass is easier to cut.' But not the former proposition. Yet in 
 both propositions there is condition and conditioned. Only, 
 whereas the abstract principle may be expressed in full conditional 
 form, the concrete connexion must be so expressed. 
 
 § 913. It is surely in quite another sense, then, that Bosanquet 
 remarks: 'The Universal Judgement, when pushed to the ex- 
 treme point of abstraction, becomes the Hypothetical Judge- 
 ment.' ^ He contrasts the abstract, as ' the thought of an ideally 
 isolated attribute ', with ' the thought of a self-dependent and 
 self-related individual '. 
 
 The abstract ' does not refer to a concrete subject, . . . and 
 consequently we do not consider whether its subject is given in 
 actuality or not, for it is essentially the judgement of necessity 
 or relativity in which the subject is taken, not given, and taken 
 not for its own sake but for the sake of that which is to follow 
 from it '. 
 
 But it is precisely the concrete: and actually-given about which 
 no general statement can be framed except in explicit hypothetical- 
 form. ' If John is hungry he must have his supper ' can only be 
 expressed by protasis and apodosis. ' Hungry John must have 
 his supper' would mean 'because he is hungry'. 'A hungry 
 John ', &c. would be a more abstract proposition than was in- 
 tended. On the other hand Bosanquet admits that between the 
 hypothetical judgement and the abstract statement of a rule 
 
 ^ Logic, i. 249. 
 
 Ff 
 
434 Conditional Reasoning 
 
 the difference is ' grammatical rather than logical *, The hypo- 
 thetical judgement ' is found whenever we frame assertions about 
 an abstract content ', and can then ' be expressed without a con- 
 ditional sentence at all '.' As he says : — ' All hypothetical judge- 
 ment rests on a categorical basis. That is to say, all relativity 
 rests on an absolute datum, and all necessity on fact.'^ The 
 consequence in a conditional proposition has necessarily a uni- 
 versal character. In 'Were the whole realm of nature mine", 
 &c., or ' If they were all one member, where were the body ? ', 
 the universality does not lie in ' whole ' or ' all ', but in the 'if 
 followed by the assertion of consecution. And an arithmetical 
 problem of the form, ' If five men worked a piece of ground 
 in fifteen days, and each day had ten working hours, then,' &c., 
 is just as universal as the above, and a necessary judgement as 
 well. Apart from any sign of conjunction, ' The whole realm of 
 nature is mine* is a concrete proposition. To become general 
 it requires an if or suppose, the grammatical indications of 
 consecution. Or, ' The case of all the sea being ink would be 
 (or is) the case of our having nothing to quench thirst.' 
 
 § 914. The major premiss of the Conditional Syllogism 
 being thus a supposition, usually, about a concrete individual 
 or aggregate, the minor premiss, or subsumption, is necessarily 
 an assertion that the supposition is realized. The true subject, 
 or minor term, is actual Reality. ' If this rope is frayed it is 
 dangerous. It is frayed.' Reality is actually qualified in the 
 supposed way. But to ' Frayed ropes (i. e. If ropes are frayed 
 they) are dangerous ' we cannot put the minor premiss, ' It is 
 so. They are frayed.' But we must say, ' It is so in this case, 
 or in such and such a case ' — introducing a new minor term. 
 
 § 915. Hamilton" adopts the following paragraphs from 
 Krug's Logik: — 
 
 ' This consequence [if is — then is) is the copula in hypo- 
 thetical propositions; for through it the concepts are brought 
 together, so as to make up, in consciousness, but a single 
 act of thought; consequently, in it lies that synthesis, that 
 connexion, which constitutes the hypothetical judgement. Al- 
 though, therefore, an hypothetical judgement may appear 
 double, and may be cut into two different judgements, it is 
 nevertheless not a composite judgement. For it is realized 
 through a simple act of thought, in which tf and then, the 
 
 ' Z.O£u, i. p. 252, ^ Ibid. p. 256. ^ Lectures on Logic, i. 238, 239. 
 
Abstract and Concrete 435 
 
 antecedent and Consequent, are thought at once, and as in- 
 separable. The proposition. If B is, then A is, is tantamount 
 to the proposition A is through B. But this is as simple an 
 act as if we categorically judged B is A, that is B is under 
 A. Of these two, neither the one — If the sun shines, nor the 
 other — then it is day, if thought apart from the other, will 
 constitute a judgement, but only the two in conjunction. But 
 if we think — The sun shines, and it is day, each by itself, 
 then the whole connexion between the two thoughts is abolished, 
 and we have nothing more than two isolated categorical 
 judgements. The relatives if and then, in which the logical 
 synthesis lies, constitute thus an act one and indivisible.' 
 
 § 916. What follows, however, confuses the ontological 
 standpoint with the logical : — 
 
 ' For the same reason an Hypothetical judgement cannot be 
 converted into a Categorical. For the thought, A is through B, 
 is wholly different from the thought A is in B. The judgement 
 — If God is righteous, then will the wicked be punished, and the 
 judgement — A righteous God punishes the wicked, are very 
 different, although the matter of thought is the same. In the 
 former judgement, the . punishment of the wicked is viewed as 
 a consequent of the righteousness of God; whereas the latter 
 considers it as an attribute of a righteous God. But as the 
 consequent is regarded as something dependent from, — the 
 attribute, on the contrary, as something inhering in, — it is from 
 two wholly different points of view that the two judgements are 
 formed. The hypothetical judgement, therefore, A is through B, 
 is essentially different from the categorical judgement, A is in 
 B ; and the two judgements are regulated by different funda- 
 mental laws. For the Categorical judgement, as expressive of 
 the relation of subject and attribute, is determined by the laws 
 of Identity and Contradiction ; the Hypothetical, as expressive 
 of the relation of Reason and Consequent, is regulated by the 
 principle of that name.' 
 
 § 917. This distinction between consequence and attribution 
 is wholly extra-logical. 'Rainy weather will be bad for the 
 review.' ' If the weather is rainy it will be bad weather for the 
 review,' Are these two propositions governed 'by different 
 fundamental laws ' ? Possibly, however, Krug distinguishes 
 between If God is righteous then will the wicked be punished and 
 If God is righteous, then will He punish the wicked, intending 
 the latter proposition not as a general statement but as applying 
 to certain specified wicked people. The difference in this cas^ 
 will be the one between ' Rainy weather is bad for regattas ' and 
 
 F f 2 
 
436 Conditional' Reasoning 
 
 ' Rainy weather will be bad for our regatta.' Looking to the 
 expression, it is the difference between ' If ^ is B, it is C and 
 ' If A is B, Cis D '. Excessive rain is damaging to the crops. 
 If rain is excessive, the crops are damaged, or, our crops will be 
 damaged. Logically, however, the proposition, ' BA is DC,' 
 means, If A is B, C is Z>, the distinction between subject and 
 attribute on the one hand and reason and consequent on the 
 other being immaterial to the logician, and superficial even for 
 the metaphysician.' 
 
 § 918. Bosanquet says that Conditional reasoning is usually 
 stated in one of three forms in ' the traditional logic ' — If A is, 
 B is.— If ^ is B, then C is Z».— If ^ is B, it is C. 'The third 
 is the form which guides us to the true import of the judgement,' 
 although the second is most commonly in use, ' conformably to 
 the habitual irrelevancy of popular thought.' ' If .^ is jB, C is D,' 
 is 'a broken-backed sequence in which no point of unity is 
 formally recognized between the antecedent and the consequent'; 
 though, he allows, when significant words are substituted for 
 letters the unity would generally be obvious — ' but in such 
 a case the expression is not essentially distinguishable from the 
 third form.' ^ But " where no rational nexus is traceable, but 
 only a coincidence in fact, however general, we cannot admit 
 that the essentials of hypothetical judgement are present '.^ It 
 is surely impossible to assert one phenomenon to be invariably 
 and necessarily coincident with another without implying some 
 abstract relation of cause, whether understood or not. Most 
 weather maxims are of this kind. Even superstitions like a 
 harelip meaning luck, or a magpie portending a marriage, are 
 referred to some real though unknown cause. ' With that 
 forehead he is sure to be hanged ' cannot be distinguished from 
 
 ' Veitch observes that the nexus between antecedent and consequent 
 may be a relation either (l) of whole and part, or (2) of cause and effect, 
 or (3) of sign and thing signified, or (4) of genus and species, or (5) of 
 mark of a mark. ' But the connexion is only of one kind for the logician. 
 It is given as that of condition and conditioned, determining and deter- 
 mined. The formula really is: Think this and you must think that' 
 {Institutes, p. 502). A proposition like Horace's, ' non, si male nunc, et 
 olim Sic erit,' denies the connexion, the universal. It is analogous to 
 'neque semper arcum Tendit Apollo'. Antecedence, of course, is 
 understood in a logical, not a temporal or spatial, sense. 
 
 * Logic, p. 251. 3 Ibid. p. 254. 
 
Antecedent and Consequent 437 
 
 'With that mole on his neck he is sure to be drowned ', though 
 in the one case the connexion is less mysterious than in the 
 other. No doubt we sometimes, half in jest, speak of two 
 phenomena as inseparable where no causal connexion is really 
 believed in. ' I never meet B, but I hear afterwards of a death 
 in his family.' ' When I sit in this chair I always win.' But 
 even if this be stated as a mere coincidence, all that is required 
 logically to make a proposition conditional is an affirmation of 
 antecedence and consequence. There need not indeed be any- 
 thing general about the form of the proposition. ' If he said 
 that, he said something unusually foolish^ He did say it. 
 Then,' &c. ' Suppose I miss the 9.40 train I shall come by 
 the 1 1.5. You are sure to miss it. Then \ am sure to come 
 by the 11.5.' 
 
 There is, of course, a relation of cause and effect between 
 missing the one train and coming by the other. But it is, no 
 doubt, judgements of this kind to which Bosanquet too hastily 
 refuses the name of hypothetical. 
 
 § 919. The conjunctive particle may be when or where. ' Ubi 
 desinit medicus incipit Dominus-.' But the logical nexus is the 
 same. ' When in doubt trump about.' But in ' When all is so 
 doubtful I can take no step ' the conjunction is causal. ' Better a 
 dinner of herbs wkere love is than a stalled ox and hatred there- 
 with.' Where is less local here than in ' Where the bee sucks there 
 suck I ', or in ' ubi episcopus, ibi ecclesia ', or in ' Whither thou 
 goest I will go '. From different points of view these conjunctions 
 express the universality of the coexistence of two states or 
 events — either an empirical universality or one abstract and 
 general. But> remarks Sigwart, ' we cannot state that two 
 events will happen together in the future, nor that they will 
 always and unconditionally take place together, unless there is 
 some necessary connexion between them. To this extent, 
 therefore, the meaning- of what was originally no more than 
 a temporal particle {when) comes to include this necessary 
 connexion, and thus to serve as the conditional conjunction in 
 the hypothetical judgement. Where in its general significance 
 passes through the same process.' ^ 
 
 * Antecedent and consequent are frequently merely coupled 
 together by and. ' Spare the rod and spoil the child^' 'Ask no 
 
 * Logic, i. 218. 
 
438 Conditional Reasoning 
 
 questions and you will hear no lies.' Or merely juxtaposed. 
 ' Love me, love my dog.' ' Aide-toi, Dieu t'aidera.' ' Fay bien. 
 Grains rien.' In ' Seek and ye shall find ', ' Give him an inch and 
 he will take an ell,' ' crede et manducasti,' and similar sentences, 
 the protasis is an imperative and the apodosis a judgement about 
 what will result if the command is obeyed. So, ' accedat verbum 
 et fit elementum.' But there might be an imperative in the 
 apodosis alone ; as ' si vis pacem para bellum ', Gnomic 
 wisdom, of course, aims at extreme brevity. ' Down corn, up 
 horn ' means that what is bad for arable is often good for pasture. 
 ' Festina lente' may be expanded into ' If you go slowly you are 
 more likely to get ahead quickly '. 
 
 As for 'If ^ is ^, C is Z)' being a 'broken-backed sequence', 
 this is merely to say that the sequence is synthetic and not 
 analytic — a consequence, as Mansel says (Prolegomena Logica, 
 pp. 213, 214), necessitated by laws other than those of thought. 
 Any synthetic abstract judgement whatever might similarly be 
 called broken-backed, as asserting a material rather than a 
 conceptual consequence. 
 
 § 920. Boole holds that ' If ^ is B, C is D' implies time, and 
 is not ' All cases of A being B are cases of C being D '. His 
 ' I ' then, or Unity, in what he calls secondary propositions, 
 stands not for the universe of events but for 'the eternity in 
 whose successive moments they are evolved'. The idea of 
 space, as though identity meant coextensiveness, is not neces- 
 sary either for secondary or for primary propositions. The 
 laws of combination of the literal symbols are in both cases, he 
 says, the same, the only difference being one of interpretation.^ 
 
 § 921. The logician, however, can leave such metaphysical or 
 grammatical questions on one side. He is not concerned with 
 the form of hypothesis and thesis, asking only whether there is 
 an assertion of antecedence and consequence. Whether the 
 connexion be one of inherence of quality in substance, or of 
 effect produced by a cause, or of simple coexistence and co- 
 incidence, does not affect the logical character of a conditional 
 proposition, which depends not on substantive equivalence or 
 temporal and spatial coincidence but on conjunctive assertion. 
 And 'all categorical judgements which are unconditionally 
 universal are exactly equivalent in meaning to hypothetical 
 ' Op. cit. p. 176. 
 
Law of Reason and Consequent 439 
 
 judgements '} Moreover, since ' all ' is ambiguous, and may 
 introduce either a judgement which is empirically universal, or 
 one which is unconditionally universal, general statements are 
 more adequately expressed in the hypothetical form. Even an 
 empirical universal may be stated in hypothetical form. ' All 
 the Apostles except Iscariot were Galileans " (a fact), or ' were 
 inspired ' (causal relation). If any one was of the number of 
 the Apostles — Judas Iscariot apart — he was a Galilean, or was 
 inspired. The question, e. g., might arise about St. James the 
 Just. 'All the summer months here are free from frost.' If any 
 month is a summer month it is- free from frost. But there 
 might be uncertainty as to whether May and September were 
 included. 
 
 § 922. Hamilton himself observes : — 
 
 ' In point of fact, logically or formally, the Jaw of Identity, 
 and the law of Reason and Consequent in its affirmative form, 
 are at bottom the same ; the law of Identity constitutes only the 
 law of Reason and Consequent— the two relatives being con- 
 ceived simultaneously, that is, as subject and predicate ; the law 
 of Reason and Consequent constitutes only the law of Identity, 
 the two relatives being conceived in sequence, that is, as ante- 
 cedent and consequent. And as the law of Reason and Conse- 
 quent, in its positive form, is only that of Identity in movement ; 
 so, in its negative form, it is. only that of Contradiction in 
 movement.*^^ 
 
 § 923. Again :— 
 
 'Inasipuch as a notion is thought, it is thought either as 
 existing or as. non-existing, and it cannot be thought as existing 
 unless it be thought to exist in this or that mode of being, which, 
 consequently, affords it a ground, condition, or reason of exis- 
 tence. This is merely the law of Reason and Consequent ;; and 
 the hypothetical is only the limitation of a supposed notion to 
 a certain mode of being, by which, if posited, its existence is 
 affirmed; if sublated, its existence is denied.'^ 
 
 § 924. Either, however, the last words are a slip,. — for the 
 sublation of the antecedent is not the denial of the consequent, — 
 or Hamilton is here assuming his doctrine of equational predica- 
 tion. An equation, however, cannot be represented as a relation 
 of Reason and Consequent. It is true that a condition may be a 
 
 ' Sigwart, i. p. 224. " Lectures on Logic, i. 354. 
 
 ' Ibid. ii. p. 377. 
 
44° Conditional Reasoning 
 
 conditio sine qua non} Only MA is B can C be D. But then, 
 strictly taken, this fails to assert that, if A is B, C always is D. 
 The proposition is rather, ' Every DC is BA ' (Every case of C 
 being D involves the case, supposition, or condition, of A being 
 B), than 'Every 5^ is DC. ' Only if ' is the force of si in 
 Horace's — 
 
 Si pugnat extricata densis 
 Cerva plagis, erit ille fortis 
 Qui perfidis se credidit hostibus (iii. 5). 
 
 Also of sentences such as ' When rivers run upward to their 
 fount, then will I forget thee '. 
 
 § 925. Elsewhere Hamilton explicitly applies his equational 
 doctrine to hypothetical propositions. He says : — 
 
 'The interdependent propositions are erroneously called 
 Antecedent and Consequent. Either is antecedent, either is 
 consequent, as we choose to make them. Neither is absolutely 
 so. This error arose from not expressing overtly the quantity 
 of the subject of the second proposition.' " 
 
 § 926. His general Canon for Hypotheticals is this : — 
 
 ' Two or more propositions thought as indetermined in quality, 
 but as in quality mutually dependent, the determination of quality 
 in the one infers a determination of the corresponding quality in 
 the other.' ' 
 
 § 927. The ancient logicians, including Aristotle, were content 
 
 ^ ' The requisite or condition is that without which the phenomenon 
 never is ; the cause, on the other hand, is that through which it always 
 is' (Esser, quoted by Hamilton, ii. 159). Sigwart urges that the ordinary 
 sense of condition is necessary condition. 'The view that the hypo- 
 thetical judgement states the consequent as necessary consequence of the 
 antecedent seems contrary to the way in which logic and grammar 
 generally speak of the antecedent as presupposition or condition of the 
 consequent. For if we understand condition in its ordinary sense as 
 meaning the conditio sine qua non, as that which must be realized before 
 something else happens or is valid, then it seems to imply that the 
 negation of the antecedent involves that of the consequent, and that 
 the consequent ceases to be valid when the antecedent is not true. But 
 this is just what necessary consequence does not involve. The con- 
 sequence may be there even when the ground is wanting, unless indeed 
 it is the sole ground, and all agree that the invalidity of the antecedent 
 does not involve that of the consequent' (Logic, i. 383, 384). There is 
 certainly some ambiguity about the words condition and presupposition, 
 which does not attach to antecedent. Yet a supposition must be a, pre- 
 supposition, and ' granted that ' is conditional. 
 
 " Op. cit. ii. 375. 3 Ibid. p. 374. 
 
Hypotheses 441 
 
 to set forth the law of Reason and Consequent without recog- 
 nizing Hypothetical Syllogisms as a separate class.* Such forms 
 are more necessary to some languages than others, the distinction 
 being one of syntax rather than of philosophy. From a psycho- 
 logical point of view these forms, Hamilton remarks, 
 
 'are not argumentations, but preparations (explications) for 
 argumentation. They do not settle the quaesitum, they only put 
 the question in the state required for the syllogistic process . . . 
 E. g. let the problem be. Does animal exist ? This question is 
 thus hypothetically prepared — If man is, animal is. But [as is 
 conceded] man is; therefore animal is.' ^ 
 
 § 928. In other words, we look about for some possible ground 
 or cause for a phenomenon Y, of whose reality we are uncertain. 
 We observe that -X" is such aground or cause. If ^, then y. X 
 will involve Y. But is JT a vera causa ? Has it reality ? The 
 minor premiss asserts that it has. Then Y has reality. Or 
 regarded from the other end — What is the outcome, the con- 
 sequence, of the existing situation ? If the existing situation 
 were X the consequence would be Y. But it is X. Then 
 expect Y. 
 
 § 929. Sigwart observes : — 
 
 ' Reflexion concerning the value and significance of hypotheses 
 is always necessary where we cannot form a definite judgement, 
 but must endeavour to arrive at truth by way of a preliminary 
 experiment. Thus hypothetical and disjunctive judgements 
 rank with the negation, which, like them, is a. judgement concern- 
 ing a tentative judgement. They both apply to that stage of 
 thought which lies between the question and decision.' * 
 
 Again : — 
 
 'The consequent is not to be stated till the antecedent has 
 been confirmed. A conditional proposition is therefore an 
 expression of uncertainty with reference to both antecedent and 
 
 ^ ' The omission of hypothetical syllogisms has frequently been blamed 
 as a defect in Aristotle's Organon ; and his French translator takes some 
 fruitless pains to strain his text, in order to make out that he does in fact 
 treat of them. . . . Aristotle understood the limits of logic better than his 
 critics ; and his translator had better have allowed the omission as a merit 
 than have attempted to deny it as a fault ' (Mansel, Prolegomena Logica, 
 p. 215, and Aldrich, p. 235). On the meaning of cruXXo-yto-^ioj e^ \mo6eiT€a>s 
 in Aristotle see Mansel's Aldrich, Note I. Aristotle opposes Hypo- 
 thetical not to Categorical but to Ostensive (Sciktikos). 
 
 2 Op. cit. ii. 376, 377. = Logic, i. 219. 
 
442 Conditional Reasoning 
 
 consequent. Both are problematically stated, or, as we should 
 say, express mere hypotheses. So far as concerns the two 
 propositions themselves, therefore, there seems to be no judge- 
 ment at all in the proper sense, no utterance, that is, which is 
 stated as true and necessary. And this view is confirmed by 
 the fact that conditional propositions are sometimes stated with 
 the avowed consciousness of the falsity of both antecedent and 
 consequent (si tacuisses, philosophus mansisses)} Nevertheless 
 such a combination of propositions does contain a statement 
 which is a judgement in the proper sense of the word, and this 
 the Stoics were the first to recognize definitely. Such a com- 
 bination tells us that antecedent and consequent are related to 
 each . other as ground and consequence, that to accept the 
 antecedent makes it necessary to accept the consequent. It is 
 this relation of necessary consequence which is the true predicate 
 of the hypothetical judgement.* ''■ 
 
 § 930. In the fully deployed hypothetical judgement the terms 
 of the major premiss are the constituent propositions. ' BA is 
 always DC is explicated in the form, ' The supposition of ^ being 
 B is always the supposition of C being D.' Yet this can be 
 stated in the form — C, when A is B, is always D. The conclusion 
 moreover is, C is Z*. It might seem, therefore, that Cand D are 
 minor and major terms respectively, the middle term being the 
 proposition, A is B. And yet that involves the anomaly that 
 the minor term is found in the major premiss. The seeming 
 difficulty really lies in the subsumption. It is this and not the 
 major premiss which differentiates the ' hypothetical ' form of 
 syllogism from the ' categorical '. The former is really a cate- 
 gorical syllogism in the form, not ' M is P, S is M, S is P ', but — 
 
 Every MS is a P5 (= If any S is ilf that S is P). 
 
 But Every S is an MS ; or. This S is an MS (This is a case 
 of MS). In the above syllogism, C is an (A is B) C. 
 
 Therefore Every 5 is a PS; or, This 5 is a PS (This is 
 a case of PS). 
 
 In such a syllogism the minor term S appears in the major 
 
 ^ The falsity of the consequent, carrying with it the falsity of the 
 antecedent, is suggested by the pluperfect subjunctive (Greek av with 
 indicative). ' If it was an adversary that had done this thing I could have 
 borne it ' — implying that it could not be borne, and therefore it was not 
 an enemy that did it. ' I will not come ( Y) unless (or until) you write 
 (X) ' is of the form, ' If not X then not K' ' I shall not write ' affirms the 
 antecedent, involving the affirmation of the consequent, 'I will not come.' 
 
 " Op. cit. p. 220. 
 
Where is the Middle Term? 443 
 
 premiss, but not as the ground of the predicate P, which is M ; 
 or rather, 5 when qualified as M is the ground of 5 being 
 qualified as P. 
 
 Again — 
 
 Every BA is DC ( = If in any case A is B, in that case C is 
 D). But every A is a BA (= In all cases ^ is^), or, This^^ is 
 a BA ( = In this case A is B). Then every, or this, A is DC 
 ( = In all cases, or in this case, the phenomenon A is attended 
 by the phenomenon of C being D). A, B, C and D are not 
 really a quatemio terminorum. 
 
 Should the hypothesis take the common form, ' If (in this case) 
 A'\s,B then (in this case) C is D,' this should still be represented 
 categorically by the general principle, Every BA is DC — that is. 
 All supposition of BA involves DC. If A isB means. If A prove 
 to be B. The thesis also is still ' This A i^ BA ' — this is so ; it is 
 as you suppose ; the case taken is real. 
 
 § 931. Inference in the hypothetical syllogism is, like all 
 inference, mediate — from 'This diamond, if real, is valuable' 
 we can neither infer that it is real nor that it is valuable ' — but 
 
 ' Veitch thinks that Hamilton's 'final view' (i.e. after 1850) about 
 Conditional Reasoning is that ' there is no reaching a conclusion through 
 a middle term. There is thus no mediate inference, or reasoning 
 syllogistically. The so-called major premiss is not properly a major 
 premiss. There is but one premiss, and all that it does is to state 
 a relation or dependence between the judgements or propositions. You 
 have but to apply the rule of the Condition and Conditioned. We do 
 not need to go beyond the given relation or dependence ; we do not need 
 another term or proposition, in addition. We have only to apply the 
 rule of inference to what we have — in a word, the inference is immediate. 
 And it belongs to what may be called Explicative Inference ' (Institutes, 
 p. 498). Indeed, a darkening of counsel ! How can an assertion of 
 actuality be immediately diawn from a conditional assertion, from an 
 assertion about a relation, terms of fact from terms of concept — ' C is Z? 
 because A\%B' from ' C is D if A is 5 ' ; ' This is Y' from ' Every X is 
 Y' ? Veitch well remarks that ' Hamilton cannot be said to have reached 
 a conclusion wholly definite, clear, or satisfactory' (ibid. p. 368}. 
 ' Explication of what is conditional can only state the condition in a 
 particular form' (ibid. p. 499). On the other hand, ' If with an optative 
 or pluperfect indicative usually expresses something more than a doubt. 
 ' If he were wise he would go ' — ' If he had been wise he would have 
 gone.' We can infer that he is not going or has not gone from the 
 implied assertion of his unwisdom. 'Perierat totum quod Deus 
 fecerat nisi misericordia subvenisset,' ' Werena my heart licht I wad 
 dee.' 
 
444 Conditional Reasoning 
 
 the mediation instead of being simply M, i. e. if anything is M, is 
 MS, i. e. ifanySisM.i 
 
 § 932. The Law of Persistency governs the illative process. 
 Given the abstract principle that MS is PS, or that BA is DC, 
 then it holds in this concrete case of S being M, or of A being B. 
 
 ^ It must be confessed that there is some array of authority for the 
 view that conditional inference is immediate — Boole (who says that 
 the hypothetical syllogism need contain no more than two terms), 
 De Morgan, Bain, and others. Such a view, however, is based upon 'if 
 concessive ( = even if), not 'if conditional. ^ If h.\s temper is hot it 
 soon subsides.' In thought, though not in form, the condition is conceded 
 as true. The sentence is equivalent to — ' His hot temper soon subsides ' 
 — i.e. 'his temper, though hot,' 'his temper (which I grant is hot),' 
 a concrete not an abstract judgement. The condition then might be 
 omitted, and we might assert at once, ' His temper soon subsides.' But 
 then there is no inference here at all, whether mediate or ' immediate '. 
 Bain, in fact, says 'There is no inference in this case. Accepting "A is 
 B " we accept " C is Z) " ; this is another expression for the same fact.' 
 But ' accepting ' here should mean ' because we accept ', not ' if we 
 accept '. He goes on, however, — ' " If the weather continues fine we shall 
 go into the country" is transformable into the equivalent form, "The 
 weather continues fine, and we shall go into the country " ' {Logic, i. 1 17). 
 This I do not follow. The late Professor Croom Robertson {Mind, 
 ii. 264, ' The Logic of "If" ') quotes a passage from Clarissa Harlowe, 
 where Morden says : ' Had you heard me out, Mr. Lovelace, you would 
 have found that my y^ was an y^ of inference rather than of doubt.' I prefer 
 to say ' an if of concession '. All conditional statements suggest an 
 inference. Concessive ' if is seen in such phrases as — ' Si la foi est 
 immobile, la science ne Test pas '.(D'Hulst) ; ' If I am not an Apostle unto 
 others, yet doubtless I am to you ' ; ' Gin a body meet a body, need 
 a body cry?' ('If = 'given that', = here 'granted that'.) The 
 apodosis is usually negative — ' It does not follow that '. ' Non, si Opi- 
 mium defendisti, idcirco te isti bonum civem putabunt ' (Cicero. This is 
 really an O proposition). Again, ' si omnes, ego non.' 'If is not always 
 expressed ; e. g. ' merses profundo,pulchrior evenit.' The conjunctive mood 
 sometimes imports a condition — ' unum cognoris, omnes noris ' (Ter.) ; 
 ' Use every man after his desert and who would scape whipping ? ' — 
 sometimes a concession — ' naturam expellas furca tamen usque recurret ' ; 
 ' Be thou as chaste as ice, as pure as snow, thou shalt not escape 
 calumny ' ; ' Come what come may, Time and the hour run through the 
 roughest day.' Cf. the French soit. For the double sense of ' if (cac) see 
 I Cor. xiii. 1-3, ' If I speak with the tongues of men and of angels,' &c. 
 Sometimes conditional ' if implies an a fortiori argument — ' If gold rust, 
 what then shall iron do ? ' The protasis is sometimes put interrogatively 
 — ' negat quis ? nego. Ait ? aio ' (Ter.). In ' si vis amari, ama ' (Seneca) 
 the apodosis ' ama ' seems to be the condition, viz. of being loved. But it 
 cannot be the condition of ' si vis amari '. In full, ' Whatever desire you 
 have to be loved carries with it the duty of loving.' 
 
Modus Ponens and Modus Tollens 445 
 
 Granted the general supposition that when 5 is ^ it is P, or 
 that when AisB CisD, then that applies to the case before us, 
 in which 5 is M, or A is B. 
 
 § 933. Similarly the sublation of the predicate, or consequent, 
 involves the denial of the subject, or antecedent. 
 
 If S is iJ/ it is P. It is not P. Then it is not M. 
 
 If AisB,C is D. C is not D. Then A is not B. 
 Such denial of the consequent is styled the Modus tollens, as 
 the affirmation of the antecedent is named the Modus ponens. 
 
 § 934. It makes no difference whether antecedent and con- 
 sequent are, as propositions, affirmative or negative. The 
 consecution, the inter-dependence, is always asserted. So that 
 the following are varieties of the Modus ponens : — 
 
 (i) If A IS B,C is D. A is B. Then C is D. 
 
 {2) If ^ is not B, CisD. A is not B. Then C is D. 
 
 (3) UA is B, C is not Z>. A is B. Then C is not D. 
 
 {4) If ^ is not B, C is not D. A is not B. Then C is not £>. 
 
 The above t'n mode toUente will be as follows : — 
 
 (1) If AisB, C is D. C is not D. Then A is not B. 
 
 (2) If A is not B, CisD. C is not D. Then A is B. 
 
 (3) If A is B,C is not D. C is D. Then A is not 5. 
 
 (4) If ^ is not B, C is not D. C is D. Then .<4 is B. 
 Such a proposition as, e. g., (4) would stand categorically as 
 'Every non-^^ is a non-DC. 
 
 Lord Falkland said : ' When it is not necessary to change, it 
 is necessary not to change.' The symbolic form of this pro- 
 position would be, Every non-BA is a B non-A. If change is 
 not necessary, not-to-change is necessary. ' Ce qui ne vaut pas 
 la peine d'etre dit on le chante ' (the Opera). This is ' Every 
 non-BA is C 
 
 § 935- ■A- negative antecedent or consequent (If A is untrue 
 B is untrue) must not be confused with the negation of ante- 
 cedent or consequent. If we say, ' When ^ is .S C is not D. 
 But C is not D,' we have affirmed, not denied the consequent, 
 and having done so we can neither infer that ^ is .S nor that it is 
 not B. To deny the consequent we must say, C is D. As 
 Sigwart says : — 
 
 ' Passing to hypothetical judgements concerning negations, we 
 find that the form, ' If .^ is. Vis not,' represents the negation of 
 
446 Conditional Reasoning 
 
 a proposition as the necessary consequence of an affirmation,' 
 thus affirming that the hypotheses X and Y are incompatible. 
 The relation is always mutual. If the negation of F necessarily 
 follows from the affirmation of X, then (according to the law of 
 ground and consequence) the negation of X follows necessarily 
 from the affirmation (i. e. the denial of the negation) of Y. To 
 such a hypothetical judgement there corresponds the categorical 
 judgement which is universal and negative. The proposition 
 ' No right-angled triangle is equilateral ' makes the same state- 
 ment as the proposition ' If a triangle is right-angled, it is not 
 equilateral ; the negation of the predicate equilateral is stated as 
 the necessary consequence of the determination right-angled.' ' 
 
 § 936. But it must be by a confusion of thought that Sigwart 
 maintains that ' No right-angled triangle is equilateral ' is nega- 
 tive, while ' If a triangle is right-angled it is not equilateral' is 
 affirmative. In the latter, he seems to say, we affirm a nega- 
 tive proposition as a necessary consequence. Surely in every 
 proposition, affirmative or negative, we affirm the predicate as 
 a necessary consequence of the subject. (I assume that, in the 
 illustration given, the material or mathematical necessity of the 
 consequence, as a ' synthetic judgement a priori', may be left out 
 of account : we are only dealing with formal and logical rela- 
 tions.) Of course all predication is, in a sense, an affirmation. 
 But in denial we affirm an incompatibility. To use Sigwart's 
 words, ' The determinations contained in the thought of X neces- 
 sitate the negation of Y.' ' This,' he adds, ' which is the meaning 
 of a universal negation, the hypothetical judgement expresses 
 by affirmation of this necessity.'^ But why does it do this 
 more than a categorical negation ? ' No X is Y' is the same 
 statement logically as 'Every X is not-Y', which, in full hypo- 
 thetical explication, becomes, ' If anything is X it is not Y.' In 
 such a proposition the antecedent and consequent are not X and 
 y (the being X and the being Y), but X and not- Y (the being 
 X and the not being Y). 
 
 § 937. A hypothetical judgement is not more a negative judge- 
 ment if it is phrased, ' No case of A being 5 is a case of C being 
 
 ^ Logic, i. 226. 
 
 * Veitch says : ' In the Hypothetical Syllogism the major or Sumption 
 is always definite in quantity and affirmative in quality ; the Subsumption 
 may vary in these respects. ... It should be explained that affirmative 
 [here] means simply the assertion of dependence between antecedent and 
 consequent ' {Institutes, pp. 493, 494). 
 
Particular Conditional Judgements 447 
 
 D,' than if it is phrased, 'li A'ls B, then C is not D.' We call 
 the latter a negative proposition because we assert the incom- 
 patibility of C and D in the case of A being B. 
 
 § 938. A categorical universal judgement is denied by a 
 particular judgement, and vice versa. It is the same with hypo- 
 theticals. Thus we deny — 
 
 {A) li A is B C is always D, by (O), Sometimes if -4 is 5 
 C is not D. 
 
 {I) U A is B C is sometimes D, by {E), U A is B C is 
 never D. 
 
 {£) U A is B C is never D, by (I), U A is B C is some- 
 times D. 
 
 . (O) If ^ is 5 sometimes C is not Z>, by {A), If ^ is 5, C is 
 always D. 
 
 § 939. A hypothetical judgement, in other words, like a cate- 
 gorical, is contradicted by denying the consequence, the necessity 
 of the connexion. ' If ^ is B, C isD' is not contradicted by ' If 
 A is B, C is not D ' (this is its contrary), but by ' When A is 
 B C need not be D '. Similarly, to deny the consequent is not 
 to deny the consequence. ' C is not D ' does not deny that, if A 
 were B, C would be D.. 
 
 § 940. A hypothetical judgement can be particular in exactly 
 the same way as a categorical. The connexion between ante- 
 cedent and consequent is affirmed or denied not as objectively 
 necessary or invariable, but as possible or occasional. Some 
 Cs, when A is B, are D, or are not D. Regarded, however, 
 subjectively and logically, the particularity is not a modification 
 of the consequence (which answers to the categorical copula),, 
 but is part of the consequent." A being B it follows that C is 
 
 ' ' The true character of hypothetical reasoning is lost sight of in the 
 examples commonly selected by logicians, which have for their subject 
 a proper name, and indicate, not a general relation of reason and con- 
 sequent between two notions, but certain accidental circumstances in the 
 history of an individual. The adoption of this type has led to the logical 
 anomaly that the propositions of a hypothetical syllogism are generally 
 stated without any designate quantity' (Mansel, Proleg. Logical, p. 216). 
 We have seen, however, that an abstract proposition about a concrete 
 existence requires to be stated in hypothetical form. A relation between 
 two individual facts, moreover, leading to a singular conclusion, may be 
 asserted or denied as occasional. ' If John is the driver I feel safe. John 
 is usually the driver. I therefore usually feel safe.' Or again, ' If John 
 drives, an accident is possible (accidents sometimes occur). John is now 
 
448 Conditional Reasoning 
 
 sometimes D. Deny the consequent — It is untrue that C is. 
 sometimes D; it is never D — and the supposition necessarily' 
 falls to the ground — A is not B. Affirm this supposition — A 
 is B, — and the consequent is necessarily true, viz. that C is 
 sometimes D. The consequence is peremptory, though the 
 consequent be in itself, as a proposition, uncertain or particular, 
 § 941. The positing of the antecedent is called by the Schoolmen 
 the return (17 eTravoSos) upon the prior. The sublation (dratpeo-ts) 
 of the consequent is called the return upon the posterior."^ 
 
 § 942. But the positing or sublation contained in the minor 
 premiss may be itself conditional. We saw this in treating 
 of Sorites. F\s, if E is. E isif D is. Z> is if C is. Cis if ^ is. 
 B is if A is. Now to assert that A is is to assert that F is. 
 And to deny that F is is to deny that A is. 
 
 A hypothetical major premiss, then, ' If A is B, C is D,' may 
 have for subsumption, not the flat assertion that A is B or that 
 C is not D, but the hypothetical assertion that A is B if E is F, 
 or that C is not D if G is H. Conclusion — If E is F, C is D. 
 IfGisH.A is not 5. 
 
 It is the difference between— 
 
 Every MS is a PS. 
 
 This S is an MS (or. Every 5 is an MS). 
 
 Therefore This 5 (or. Every S) is a PS. 
 and — 
 
 Every MS is a PS (If any 5 is M, it is P). 
 
 Every XS is an MS (If any S is Z, it is M). 
 
 Therefore Every XS is a PS. 
 or (in Fig. II), with the same major premiss — 
 
 No XS is a PS (If 5 is X, it is not P). 
 
 Therefore No XS is an MS. 
 
 driving. Therefore an accident is possible (may occur).' Or the par- 
 ticularity may be in the condition. ' If John sometimes has an accident, 
 he is an unsafe driver. He does sometimes have an accident. There- 
 fore, &c.' This is in Barbara. The following also is in Barbara not Darii, 
 since the particularity is in the term rather than in the subsumption or the 
 sumption. ' If some kings are unwise, monarchy is not a good institution. 
 Some kings are unwise. Therefore, &c.' 
 
 ' 1As.iX)S\i.(m., Lectures on Logic, W.yyi. We must beware how we carry on 
 a limitation from the minor premiss into the conclusion. Thus — ' If A 
 is B, C is D. It is barely (or scarcely) possible that A is B. Then it is 
 barely (or scarcely) possible that C is Z>.' A fallacy. Limitation is of the 
 nature of negation. We have not posited but sublated the antecedent. 
 
Mood and Figure 
 
 449 
 
 If A is true, B is true. But B is untrue if C is true. 
 Therefore if C is true A is untrue, and if A is true C is untrue 
 {Camestres and Cesare). That is, if two hypotheses have con- 
 tradictory consequences, the truth of either involves the untruth 
 of the other. 
 
 § 943. In Figure I then the explicated form will be — 
 
 Barbara. 
 If A is B.CisD 
 If EisF,AisB 
 Then if E is F, C is D. 
 
 Celarenf. 
 UA isB, CisnotZ) 
 UE\sF,A isB 
 Then if E is F, C is not D. 
 
 Darii. 
 IfAisB, CisD 
 U E is F, A sometimes is B 
 Then if E is F, C sometimes 
 
 isD. 
 
 Ferio. 
 If AisB, C is not D 
 If E is F, A sometimes is B 
 Then if E is F, C sometimes 
 
 is not D. 
 
 Note, that 'lfEisF,A sometimes isB' is equivalent to ' Some- 
 times, if ^ is F, A is B' — some cases ofE being i^are cases of 
 A being B. Therefore some cases ofE being F are cases of C 
 being D, or not being D. 
 
 Figure II. 
 
 Cesare. 
 
 If A isB, CisnotZ) 
 
 If £ is is CisZ» 
 
 Then if E is F, A is not B 
 (the suppositions are incom- 
 patible). 
 
 Camestres. 
 If AisB, CisD 
 If E is F, C is not D 
 Then if E is F, A is not B. 
 
 Festino. 
 If A isB, CisnotZ* 
 If jE is Z", C sometimes is D 
 Then if E is F, A sometimes 
 is not B. 
 
 Baroco. 
 If A isB, Cis D 
 IfE is F, C sometimes is not D 
 Then if E is F, A sometimes 
 is not B. 
 
 Darapti. 
 If A is 5, C is Z> 
 If ^ is B, EisF 
 Then if E is F, C sometimes 
 isD. 
 
 Figure III. 
 
 Datisi. 
 If A isB, CisD 
 If A is B, E sometimes is F 
 Then if E is F, C sometimes 
 isZ>., 
 
 Gg 
 
450 Conditional Reasoning 
 
 Disamis. 
 If A'\^ B,C sometimes is D 
 If A isB, EisF 
 Then if E is F, C sometimes is D. 
 
 (This seems plainer than the reasoning in Datisi. But in reality 
 it is an indirect conclusion, obtained by simple conversion from 
 the direct conclusion, If C is D, E sometimes is F.) 
 
 Felapton. Ferison. 
 
 If A is B, C is not D If A is B,C is not D 
 
 If A is B, E is F If A is B, E sometimes is F 
 
 Then if E is F, C sometimes Then if E is F, C sometimes 
 
 (at least) is not D. is not D. 
 
 Bocardo. 
 If A is B, C sometimes is not D 
 If A is B,E is F 
 Then if Eis F, C sometimes is not D. 
 
 (This again seems plainer than Ferison ; yet it yields only an 
 indirect conclusion converted from ' If C is not D, E sometimes 
 is F'.) 
 
 Figure IV. 
 Bramantip. Dimaris. 
 
 If A is B, C is D If A is B, C sometimes is D 
 
 If C is D, EisF If C is D, E is F 
 
 Then if E is F, A sometimes Then if E is F, A sometimes 
 is B. is B. 
 
 Camenes. 
 If A is B,C is D 
 If Cis D, E is not F 
 Then if E is F, A is not B. 
 
 Fesapo. Fresison. 
 
 If ^ is 5, Cis not Z» If ^ is 5, C is not Z> 
 
 If C is D, E is F If C is D, E sometimes is F 
 
 Then if E is F, A sometimes is Then if E is F, A sometimes 
 
 not B. is not B. 
 
 § 944. It will be observed, however, that while in Figure I 
 there is a conditional positing (in whole or part) of the ante- 
 cedent contained in the major premiss, and in Figure II there 
 is a conditional sublation (in whole or part) of the consequent 
 
Hypotheticals — how Converted? 451 
 
 contained in the major premiss, in Figure III, on the other 
 Jiand, where the middle term (' \i A is B ') is the antecedent 
 condition of both premisses, there is not, as the Figure stands, 
 either position of antecedent or sublation of consequent. The 
 Moods must be reduced to one of the two former Figures before 
 either can appear. Darapit and Datisi, Felapton and Ferison must 
 convert the minor premiss — 
 
 UA isB, C is Z> (or not Zl) 
 
 If E is F, A is sometimes B 
 
 Then if E is F, C is sometimes D (or not D), {Darii, 
 Ferio) ; 
 
 while Disamis must transpose its premisses and convert the 
 original major — 
 
 If ^ is B,EisF 
 If C is Z>, ^ is sometimes B 
 Then if C is D, E is sometimes F. {Darii.) 
 § 945. In the Fourth Figure Bramantip, Dimaris and Camenes 
 need only to have their premisses transposed for the conditional 
 positing of the antecedent {E is F) to appear. In Fesapo and 
 Fresison, however, when the premisses are transposed, there 
 appears only sublation of the antecedent, which affords no 
 inference. We must not then transpose the premisses, but 
 rather convert the minor, when we obtain a sublation of the 
 consequent — 
 
 If ^ is B, Cis not Z> 
 HE is F, C sometimes is D 
 Then if Eis F, A sometimes is not B. (Festino.) 
 § 946. The above hypothetical Forms are well worth study. 
 The illative process in them is not so obvious as in the ordinary 
 categorical syllogisms. But they make it even more clear that 
 the two former Figures are greatly superior to the two latter. 
 Figure I exhibiting the result of affirming the antecedent. 
 Figure II that of denying the consequent. Grant the cause, 
 the effect must follow. Deny the effect, the cause disappears. 
 The formula 'As ^ is .6 is' is a misleading substitute for 'If 
 ^ is 5 is'; for 5 may exist without A, but A cannot exist 
 without B. 
 
 § 947. A word should be added about the conjunction ^with 
 the adversative force referred to above, of although or even if, 
 
 Gg2 
 
452 Conditional Reasoning 
 
 implying a rule or natural expectation to the contrary. ' If 
 I should die with Thee I will not deny Thee.' ' Were there 
 neither heaven nor hell, yet sin should be my hell and holiness 
 my heaven ' (Divine Breathings). Similarly concessive while 
 (Latin ut), &c,^ The sublation of the consequent, in such a 
 sentence, does not negate the antecedent in the sense of taking 
 from it but rather of adding to it. The case of St. Peter denying 
 his Master would be a sign not of his not dying with Him, but 
 of his having to suffer some greater extremity. So, categorically, 
 'Even a savage has virtues.' 'Even a worm will turn.' A being 
 without virtues must be more inhuman than a savage. A creature , 
 that will not turn must be more spiritless than a worm — must be 
 beyond the limit. ' Up to a certain limit at least ' is the sense 
 of Even. 
 
 ^ In Suetonius' phrase, 'Oderint dum metuant,' however, the gram- 
 matical apodosis ' oderint ' is really the concession in thought — ' However 
 much they may hate, I do not care, on condition that they fear '. 
 
CHAPTER XXVIII 
 
 DISJUNCTIVE. REASONING 
 
 § 948. So fax: we have considered the principle of hypothetical 
 judgement generally. It involves a conjunctive synthesis. The 
 Disjunctive Judgement is a particular case, or aspect, of hypo- 
 thetical statement. Instead of If— then, it is marked by 
 Either — or. 
 
 Either ^ is or S is. 
 
 Either A is B or it is C. 
 
 Either ^ is 5 or C is D. 
 Either — or means, If not one then the other. It is thus seemingly 
 a duplex judgement. Allnon-XisY,a.ndiAllnon-YisX. Whether 
 the import is also exclusive—^// X is non- Y and All Y is non-X 
 — will be considered below ; e. g. whether ' She will weep or she 
 will die ' formally and necessarily means that if she weeps she 
 will not die. 
 
 § 949. A disjunctive judgement can take the following leading 
 forms : — 
 
 (i) A is either B or C Either ^ is S or C is D. He is 
 either a knave or a fooL Either you said it or I am dreaming. 
 (All non-X is Zand all non- F is X.) 
 
 (2) A is either B or not C. Either A is B or C is not D. 
 He was either impudent or not soben. Either the train is late 
 or my watch is not correct. (All non-X is non-Y, and All Y{all 
 not non-Y) is X.\ 
 
 (3) A is either not B or not C. Either A is not 5 or C is 
 not D. Either you do not understand, or you are not telling 
 the truth. Either the train is not punctual or my watch is not 
 correct. (All X (not non-X) is non-Y, and all Y (not non-Y) is 
 non-X.) 
 
 (4) Either .^ or 5 is C. Either author or printer made a slip. 
 In practice this commonly means that the choice is confined 
 to A and B exclusively, so that if ^ is C nothing else is C ; and 
 
454 Disjunctive Reasoning 
 
 the same with B. (4) is in that case not distinguishable from ' C 
 is either A or B'. It must be either Aor B that is C. Whoever 
 made a slip (the slip) was either author or printer. Any 
 not-author-made slip was a printer-made slip, and vice versa. 
 It is clearly meant that no one else could have had a hand 
 in the mistake. The proposition is convertible. But ' Either 
 James or Edward tells lies' does not mean that no one else 
 tells lies. What it means is that every supposition of the one 
 not telling lies includes and involves the certainty of the other 
 telling them. So that ' Every non-XZ is YZ ' ought not to be 
 understood to mean that L, M ox N cannot be Z, so long as 
 the extension of L, M ov N coincides with that of .X^ or V or 
 with part of either. All telling lies under the supposition 
 of James not telling them includes their being told by Edward, 
 and vice versa. 
 
 (5) Similarly with, Either ^ or 5 is not C. Either prosecutor 
 or defendant is not telling the truth. And 
 
 (6) Either ^ is C or ^ is not C. Either the man is guilty or 
 the witness is not to be believed. 
 
 But the best general type for Disjunctive Judgement is — 
 Either A is B or C is D.^ 
 
 § 950. Either — or is contradicted by Neither — nor. But ' All 
 A's are either B or C is contradicted, not by 'All A's are 
 neither B nor C, but by 'Some A's are neither B nor C (If 
 the disjunction is understood exclusively, ' It must be either one 
 or the other ' is contradicted by ' It is both one and the other'. 
 'You can either eat your cake or have it' by 'I can eat my 
 cake and have it'.) The contradiction of '^ is always either 
 B or not C might be phrased, 'Sometimes ^ is C without 
 being B' ; or, ' Sometimes A is not B and yet is C 'A is either 
 not B or not C ' is countered by the allegation, ' A is both B 
 and C ' Either A is not B, or C is not D', is contradicted by 
 ' Sometimes A is B and C is also D '. ' Either ^ or 5 is not C 
 is contradicted by ' Both A and B may be C. 
 
 ^ For, as the letters stand for any terms, this does not exclude the 
 possible identity of any pair of them ; nor does it exclude any term from 
 being negative. 
 
 (i) Either ^ is 5 or C is D. 
 
 (2) Either ^ is 5 or C is B. 
 
 (3) Either A is B or A is D. 
 
 (4) Either ^ is 5 or C is A. 
 
Exclusive Alternatives 
 {Disiunctio ambigui.) 
 
 455 
 
 Y X 
 
 Y X 
 
 denied by 
 
 In Extension Z=YZ + XZ, YZ= non-XZ, XZ= non-FZ. This 
 is denied by ' Some non-FZ is not XZ.' 
 
 § 951- But the question arises whether ' Z is either V or ^' 
 is exclusive as well as alternative, in which case this proposition 
 contains prima facie four judgements : — 
 
 (i) If Z is not y it is Jf = All not-YZ is XZ. 
 
 (2) If Z is not X it is Y= All noi-XZ is YZ. 
 
 (3) If Z is Z it is not Y= No XZ is YZ. 
 
 (4) If Z is Fit is not Z= No FZ is XZ. 
 
 The two latter, however, are clearly one and the same judge- 
 ment, and the two former will also be found to be identical. One 
 member in each case is the converse by contraposition of the 
 other. So that the question is whether the Disjunctive Judge- 
 ment comprises, or can comprise, a double assertion, that This 
 is one thing or the other, alterutrum, and cannot be both. I say 
 that Z, or any particular Z, is found either in the X class or 
 
 (5) Either ^ is 5 or ^ is D. 
 Now if we ring the changes on (i) by making some or all of the terms 
 negative, we get — 
 
 (i) Either no\.-A is ^ or C is D. 
 (ii) Either A is not -5 or C is D. 
 (iii) Either A is B 01 not-C is Z>. 
 (iv) Either A is B or C is not-Z*. 
 (v) Either not-^ is not-B or C is. D. 
 (vi) Either not-^ is B or not-C is £>. 
 (vii) Either not-^ is ^ or C is not-i?. 
 (viii) Either A is not--S or not-C is Z>. 
 (ix) Either A is not-^ or C is not-D. 
 (x) Either ^ is ^ or not-C is not-X*. 
 (xi) Either not-^ is B or not-C is D. 
 (xii) Either A is not-^ or not-C is not-Z>. 
 (xiii) Either not-A is B or not-C is not-Z>. 
 (xiv) Either not-^ is not-^ or C is not-i3. 
 (xv) Either not-A is not-^ or not-C is not-i?. 
 Thus there are fifteen variations to be had from (i) alone. The total 
 number then will be 15 x 5 = 75. I owe this note to Mr, Stock. 
 
456 Disjunctive Reasoning 
 
 in the Y class. If these classes overlapped it might be found 
 in both. But do I say further that they do not overlap ? 
 
 If I do, then in •^ Orjpiov^ Oeo?, then, are involved four judge- 
 ments — (l) O-qpiov, ov Otos apa : (3) Oeos, ov Orjpiov apa : (3) ov OrjpCov, 
 
 Oeos apa : (4) Seos, ov Otjpiov apa. But if the alternatives are not ex- 
 clusive, the two former must be struck out. Now (i) and (2) are 
 rationally one judgement — as No JST is Y and No F is ^ are 
 rationally one judgement (or All X is non-F and All Y is non-Z) 
 — and (3) and (4) are also interchangeable statements — as All 
 non-JT is Y and All non-Y is X are equivalents. Mill finds 
 unnecessary fault with Hamilton here :^ 
 
 ' Much as he had thought on the subject, the simple idea 
 never seems to have occurred to him that every disjunctive 
 judgement is compounded of two or more hypothetical ones. 
 " Either A is B, or C is Z> " means If A is not B,Cis D; and if 
 C is not D, A is B. This is obvious enough to most people ; but 
 if Sir W. Hamilton had thought of it, he probably would have 
 denied it; its admission would not have been in keeping with 
 the disposition he shows, in so many places, to consider as 
 one judgement all that it is possible to assert in one formula.' ^ 
 
 §952. But Mill further complains that Sir William 'takes 
 for granted through the whole of his exposition that when we 
 say A is either B or C we imply that it cannot be both '.^ In 
 adopting the exclusive view of disjunction — expressio unius est 
 exclusio alterius — Hamilton doubtless does hold that a single 
 formula implies a single judgement; for while that view, as 
 we have seen, implies the duplex judgement, ' All non-X is Y' 
 and 'All X is non-F', Hamilton would no doubt consider this 
 a single judgement expressed by his formula, 'Allnon-Xis all 
 Y' — which implies, of course, that All non-F is all X. Mill, 
 I conceive, is wrong in objecting to the doctrine that a single 
 formula expresses a single judgement. The true objection to 
 the formula 'All non-Xis all Y' (in other words, to the exclusive 
 view of Disjunction) is, as Mill elsewhere lucidly insists, that it 
 is only admissible as a formula, and can only represent a single 
 judgement, when the terms are taken as totalities. If 'All ^ 
 is all B' is to be taken distributively, it is, as we have seen 
 under Quantification of the Predicate, a clumsy and logically 
 inadmissible complex of the two judgements, ' Every A 15 B' 
 and ' Every ^ is ^ '. ' All non-^ is all B ' is similarly an 
 ^ On Hamilton, p. 530. '^ Ibid. p. 528. 
 
Disjunction of Uncertainty 457 
 
 objectionable expression of the two judgements, ' Every non--<4 
 is B ' and ' Every B is non-^ '. The former, which is disjunc- 
 tive, does not formally involve the latter. 
 
 We have therefore to distinguish between two kinds of Dis- 
 junction. Speaking of the total extension of Z as a class, we 
 may say that it is divided into the extensions or classes^ and Y. 
 To express this in the formula, ' Z is either X or Y,' is per- 
 missible. The whole class of Z's which are not X's is identical 
 with the whole class of Y's ; or (which is the same thing) the 
 whole class of Z's which are not Y's is identical with the whole 
 class of ^'s. All non-ZZ is all YZ. All non-YZ is all XZ, or 
 vice versa. Such disjunction is Division of a Concept, accord- 
 ing to its Extension. The genus is composed of its co-ordinate 
 species, which together exhaust it. 
 
 § 953- But it is different when we speak of Every several 
 Z — Z distributively — or of This or That Z. This is no longer 
 Division but Determination. ' Bankrupts are either unfortunate 
 or dishonest' is a divisive judgement. It divides the class 
 Bankrupt under those two heads. Some are one some the other 
 (partim . . . partim). If the meaning is that the number of bank- 
 rupts who are not unfortunate is identical with the number who 
 are dishonest, and vice versa, this is a single judgement about 
 aggregates. But if we judge of any individual bankrupt that he 
 is either unfortunate or dishonest, the suggestion that he is not 
 both constitutes a further judgement. We saw this in treating 
 of Definition. ' Every X is a non- YZ ' may be intended to suggest 
 that every non- YZ is an XZ. If we understand that X is being 
 defined, we take the words in that sense. But they do not 
 formally convey it, and the identification of the extensions of 
 subject and predicate is in truth a separate judgement. It is 
 equally correct to say that a savage is a human being who is 
 not civilized, and that he is a human being who does not live in 
 Belgravia. But the one is a definition, the other is not. Many 
 people who do not live in Belgravia are not savages. 
 
 
 z 
 
 X 
 
 Y 
 
 Definition v V — ^ '^ a non- YZ. 
 
458 
 
 Disjunctive Reasoning 
 
 2 
 
 Description 
 
 X 
 
 Y 
 
 W 
 
 -^is a non- yZ. 
 
 § 954. Disiundio ambigui. This brings us to the Disjunction 
 of Uncertainty. 'Every Z is either ^ or Y', means that each 
 several Z will be found in the one class or the other. The ^'s 
 are together made up of those two classes. But in saying of 
 each several Z, ' This Z is either ^ or Y,' we usually mean 
 that we do not know to which class he belongs. Sailors are 
 either in the King's service or the mercantile marine. They 
 are, as a class, in both. But ' This sailor is either in the Navy 
 or merchant service ' implies what has been called a disjunction 
 of ignorance, or of doubt. So also in placing a class of things 
 under a higher class, ' Sea anemones are either animal or 
 vegetable.' ' Whales are either viviparous or oviparous.' ' Free 
 libraries are either useful or mischievous.' ' Planets either shine 
 by their own light or are lighted by the sun.' 
 
 Of the same nature is the disjunction referred to a point of 
 time. Distinguish ' He is always either reading or writing ' 
 from ' He is now either reading or writing ' ; and ' The signal 
 is always either at safety or at danger ' from ' The signal is at 
 this moment either at safety or at danger.' ^ 
 
 § 955. The members of a Disjunction are, of course, reci- 
 procally exclusive — i. e. ' Either A ox B' means not only ' All 
 not-^ is B ', but ' No ^ is .S (All A is uot-B) '—when the choice 
 
 ^ Sigwart observes : ' Trendelenburg's doctrine that the disjunctive 
 judgment is a statement of the extension of the subject concept applies 
 only to those disjunctive judgments which are based upon a division of 
 the subject concept. It is not applicable when the disjunction refers to 
 changeable states' {Logic, i. 231 n.). This is an unnecessary distinction. 
 The disjunction of uncertainty must be preceded by, and based upon, 
 a divisive judgement in all cases. A doubt whether the water in the jug 
 is at this moment hot, cold or tepid, is based upon a division of water 
 temperature into those three states. It is objected to me that ' A pig is 
 either asleep or eating ' is of different calibre from ' A triangle is either 
 equilateral, isosceles or scalene '. The latter exhausts the extension of 
 'triangle'. Does the former exhaust the extension of 'pig'? I reply 
 that it exhausts the extension of the state of a pig. The distinction does 
 not go deeper than the distinction between ' The church is always open ' 
 and ' Churches are always interesting '. 
 
Disjunction of Contradictions 459 
 
 is between contradictories, i. e. when B = not-^. Every several 
 Z is either X or non-X. Such a disjunction of contradiction is 
 not empirical, but is necessitated by the Principle of Excluded 
 Middle. It is true even if no Z at all is X, The caution, how- 
 ever, must here be repeated against confusing negative with 
 privative conception. Of all armchairs it may be predicated 
 that either they are happy or they are not happy. But we 
 cannot divide armchairs into happy and unhappy. We have no 
 right, then, to divide Z into XY and non-^y, unless all Z's are 
 Y, nor into X non-Y, and non-X non-F, unless no Z's are Y. 
 
 Lord, it belongs not to my care 
 Whether I die or live. 
 
 The possible contingencies (Z) are either dying (X) or not dying 
 (non-^. If both alternatives are apart from care (non- Y), then 
 whatever may befall me belongs not to my care (no Z is Y). 
 
 § 956. The empirical Disjunction may have many members. 
 A is either B or C or D or E, &c. But we could not say, A is 
 either B or not-^, or C, or D, &c. Rather, A is either B or 
 not-B ; in which latter case it is either C or D or E, &c. (or C 
 and not-C, and so forth). 
 
 § 957- Why so many logicians have regarded the terms of the 
 empirical disjunction as always reciprocally exclusive ^ is perhaps 
 that in the illustrations chosen by them there is a material 
 or quasi-formal incompatibility. Cicero says : ' Graeci dicunt 
 omnes aut Graecos aut barbaros esse.' Even in the famous 
 dilemma about the Son of Man, 'aut Deusaut non bonus homo,' 
 what is insisted on is not that He cannot have been both 
 
 ^ Mansel dissents emphatically from this opinion. ' But let us grant for 
 a moment the opposite view, and allow that the proposition, " All C is 
 either A or B" implies, as a condition of its truth, " No C can be both." 
 Thus viewed, it is in reality a complex proposition, containing two 
 distinct assertions, each of which may be the ground of two distinct 
 processes of reasoning, governed by two opposite laws. Surely it is 
 essential to all clear thinking that the two should be separated from each 
 other, and not confotmded under one form by assuming the Law of 
 Excluded Middle to be, what it is not, a complex of those of Identity and 
 Contradiction' {Proleg. Logica, p. 221). 
 
 Caesar Borgia having adopted the motto 'aut Caesar aut nihil', this 
 gave rise to the following epigrams : — 
 
 (i) Borgia Caesar erat factis et nomine Caesar. 
 
 Aut nihil aut Caesar, dixit. Utrumque fuit. 
 (2) Aut nihil aut Caesar vult dici Borgia. Quidni? 
 Cum simul et Caesar possit et esse nihil. 
 
460 Disjunctive Reasoning 
 
 (unspeakably impossible though it be), but that if He was 
 not the one He was the other. This is so, again, in the ■ 
 case of a signal being at danger or at safety. Equally, dead and 
 alive, free and under compulsion, are contradictories (within the 
 sphere to which they belong) as well as contraries. The same 
 thing applies to the lines quoted by Hamilton ' from Purchot, 
 beginning — 
 
 Falleris aut fallor ; fallor; non falleris ergo. 
 We cannot (in a supposed case) both be wrong. I am wrong. 
 Then you are not wrong. Or again, 'This is either true or 
 false.' Even when he takes a proposition with three disjunct 
 members, Hamilton selects three which are severally exclusive 
 as well as together exhaustive. E. g. — 
 
 The ancients were in genius either superior to the moderns, 
 or inferior, or equal. 
 
 Now the ancients were superior. 
 
 Therefore, they were neither inferior nor equal.^ 
 This throws no light on the question whether we ought to argue — 
 
 A is either 5 or C or D. 
 
 A is B. Then it is neither C nor D. 
 For we do not know whether B excludes C and D. If, 
 being told that some one was born either in 1850, 1851 or 1852, 
 I find he was born in 1851, and thereupon deny that he was 
 born in 1850 or 1852, I can do this, not from the form of the 
 Disjunction, but from knowing that birth only takes place once 
 — a good instance of the material nature of the modus ponendo 
 tollens. Mill, on the other hand, insists that if we say that to 
 make an entirely unselfish use of despotic power a man must 
 be either a saint or a philosopher, we do not necessarily mean 
 that the same person cannot be both saint and philosopher.' In 
 religion, on the other hand, a definite side must be chosen. 
 ' He that is not with Me is against Me.' But the knowledge 
 that alternatives are mutually exclusive is always extra-logical. 
 
 § 958. The Disjunctive Syllogism has a disjunctive proposition 
 for major premiss. It is only, in fact, one form of the Hypo- 
 thetical Syllogism. ' She must weep or she will die ' is equivalent 
 to ' If she does not weep she will die '. The modus ponens of 
 the latter — ' She does not weep ; then she will die ' — is the modus 
 
 ^ Lectures on Logic, i. 327. '^ Ibid. p. 33P. 
 
 ' On Hofnilton, p. 529. 
 
Tollendo Ponens and Ponendo Tollens 461 
 
 toUendo ponens of the former. The modus tollens of the ordinary 
 hypothetical syllogism — ' She will not die ; it follows that she 
 weeps' — is again the modus tollendo ponens of the Disjunctive form, 
 but it is now the alternative (' she will die ') which is sublated. 
 
 § 959- To what, then, does the modus ponendo tollens of the 
 Disjunctive syllogism correspond in the ordinary Hypothetical 
 form ? It has no valid place there, and least of all in those cases 
 where antecedent and consequent are convertible. In con- 
 junctive reasoning ponendo ponimus, not tolltmus ; and positing 
 the consequent, where not convertible with the antecedent, has 
 no result. The modus ponendo tollens has only a formal place in 
 contradictory disjunction, and only a material place where there 
 is a material incompatibility. The disjunction, ' A is either B 
 or not-B,' expressed conjunctively, becomes, 'li A is not B it is 
 Tiot-B.' (No not-BA is B.) He is either awake or asleep (dis- 
 junctive). If he is not awake he is asleep (conjunctive). Now 
 in the latter or hypothetical form, by affirming that he is asleep 
 we should not logically be affirming that he is not awake, unless 
 asleep and not awake be given first as equivalent. 
 
 § 960. Indeed, what Hamilton says about Hypothetical reason- 
 ing being not mediate but immediate is true of Contradictory 
 Disjunction, though of this only. In other words, there is no 
 reasoning at all. To take the old example — 
 
 Sempronius is either honest or dishonest. 
 
 Affirmative, or Modus ponendo Negative, or Modus tollendo 
 
 tollens. ponens. 
 
 Now Sempronius is honest. Now Semprenius is not honest. 
 
 Therefore he is not dishonest. Therefore he is dishonest. 
 
 There is here no mediation, and therefore no inference. The 
 conclusion follows from the soi-disant minor premiss, not by the 
 help of the major premiss, but on the strength of the Principle 
 of Contradiction in the Affirmative mode, of the Principle of 
 Excluded Middle in the Negative mode. The major premiss — 
 apart from any question about 'is not honest' meaning 'is 
 dishonest ' — might be altogether omitted. There may be more 
 appearance of subsumption when the major premiss is universal 
 and the minor singular or particular : — 
 
 Every A either is B or is not B. 
 
 This A is B. Therefore it is not woi-B. 
 
462 Disjunctive Reasoning 
 
 But here too the major premiss is wholly superfluous. More- 
 over it does not express a real hypothesis, or connect a real 
 antecedent and consequent, but is a mere truism, a mere case 
 of the fundamental Law of Reason which is the true major 
 premiss of the reasoning.^ 
 
 Ponendo tollens. Tollendo ponens. 
 
 Nothing can be something and Everything is everything or 
 
 also its contradictory. else its contradictory. 
 
 A is something (viz. B). A is not a certain thing (viz. B). 
 
 Then A is not that thing's con- Then A is that thing's con- 
 tradictory, viz, not-.S. tradictory, viz. not- A" 
 ^ On the other hand, when the disjunction is not a dichotomy, but of 
 the form, ^A is either B or C,' I fail to understand the meaning of 
 Dr. Bosanquet's assertion that 'the categorical minor adds nothing 
 whatever in the way of content to the disjunctive major premise. It only 
 has meaning as resolving a doubt, or as aflSrming one member of an 
 alternative to be true in a given point of time. ... In the true disjunction, 
 which expresses the organization of a system as such, the reference to an 
 arbitrary condition falls away. . . . We are thus driven to the paradoxical 
 conclusion that the essence of disjunctive argument is included within 
 the disjunctive " major premise " ; in other words that this judgment is 
 in fact not a mere premise but at once a categorical judgment and 
 a complete systematic inference. . . . The disjunction must be taken to 
 correspond not to the major premise of the syllogism but to the whole 
 syllogism' {Logic, ii. 190-92). This is too subtle. I take Dr. Bosanquet 
 to mean something like this. ' Z''s are either X's or F's ' expresses no 
 disjunctive doubt, but simply divides the class of Z'% into two divisions 
 Z = X +Y. It adds nothing in the way of content to this proposition to 
 say that any particular ^ is an ^ (or is a F), for we must be supposed 
 to know this already, just as if we say ' All the months of last year were 
 wet ' we necessarily include March, and do not need to add that March 
 was wet. ' All my sons are in the Army or the Navy ' is stated with the 
 knowledge that James is in the Navy. This, however, looks like the old 
 petiHo principii complaint against the syllogism generally, viz. that the 
 minor premiss is already included in the major {vide infra). To show 
 the real character of a disjunctive syllogism it might be expressed thus : — 
 
 Z'% are either X ox Y (division of class). 
 
 Then this Z is either ^ or K (doubt about individual member). 
 
 It is not X (minor premiss). 
 
 Then it must be Y. 
 In a disjunctive proposition, ' Either A \% B or C 'm D' (or, 'A is either 
 B or C \ or, 'Either A or 5 is C), it is immaterial which member 
 we regard as antecedent and which as consequent. ' Time must friend 
 or end' {Troilus and Cressidd). All n.orv-BA is DC is equivalent to All 
 non-Z'C is BA. A minor premiss, then, of negative form may stand either 
 as a negation of the consequent (Figure II in categorical reasoning) or as 
 affirmation of the antecedent (Figure I). It may be of any quantity. 
 
Conjunctive Judgements 463 
 
 § 961. The simplest form of the Conjunctive Judgementwe 
 saw to be 'li A is, then B is '. Of the Disjunctive Judgement 
 the two simplest forms are, ' A is either Bor C and ' Either A or 
 B is C We can further combine conjunction and disjunction 
 in the same judgement. The most elementary forms are, ' If A 
 is, then either B or C\s' ; and, ' If either Aor B is, then C is.' 
 The judgement is conditional, but either antecedent or consequent 
 is disjunctive. 
 
 More fully.' If ^ is S then either C is Z? or J? is F. 
 
 Or, Whether A is 5 or C is D, then in either case E is F. 
 Now positing the condition, the consequent follows. A is. 
 Then either 5 or C is, A is B; then either C is D, or E is F. 
 Again, Either A or B is. Then C is. Either A is B or C is D 
 Then E is F.^ 
 
 Or, denying the Consequent, the Antecedent is destroyed. 
 Neither B nor C is. Then A is not. Neither Cis Z* nor E is F. 
 Then A is not B. Again, C is not. Then neither A nor B is. 
 E is not F. Then neither ^ is ^B nor C is D. 
 
 § 962. Such a Syllogism does not vary from the ordinary 
 Conjunctive Syllogism in principle, the only difference being 
 that either in Antecedent or Consequent a disjunctive judgement 
 takes the place of a simple judgement. Or the disjunction may 
 occur in both Antecedent and Consequent. If either ^ is or 5 
 is, then either C is or Z) is. If A is either B or C, it is either D 
 or E. If either A is B or C is D, then either £ is Z' or G is H. 
 Of course there may be as many members in a disjunction as we 
 please. If ^4 is 5 or C is Z) or £ is F, then either Gis H or I 
 is K or L is M. Examples — 
 
 § 963. A. Simple. 
 
 I. (i) Constructive. 
 
 If he said this he was either mad or wicked. 
 
 He did say it {modus ponens). 
 
 Then he was either mad or wicked. 
 
 The conclusion will be of the same quantity as the minor premiss, but 
 of the opposite quality. 
 
 ^ Hamilton observes that 'every syllogism that has a disjunctives 
 sumption is not, on that account, necessarily a disjunctive syllogism'. 
 The syllogism, ' B is either C ox D; but ^ is ^ ; then A is either C or D,' 
 is exactly analogous to the syllogism, ' B \s C; Ais B ; then ^ is C 
 (Lectures on Logic, i. 328). But this merely means that the principle 
 of all syllogism is the same. 
 
464 Disjunctive Reasoning 
 
 (ii) Destructive. 
 He was neither mad nor wicked {modus tollens). 
 Then he did not say it. 
 
 II. (i) Constructive. 
 
 Whether among friends, or by myself, I am at ease; 
 You know that I am either among friends or by myself {modus 
 ponens). 
 
 Therefore you may be sure I am at ease. 
 
 (ii) Destructive. 
 I am not at ease {modus tollens). 
 This shows you that I am neither among friends nor by myself 
 
 B. Double. 
 
 III. (i) Constructive. 
 
 If he either was married or lived in that parish, you will 
 either find his name in the church registers or will hear of him 
 by inquiry. 
 
 He certainly either was married or lived there {modus 
 ponens). 
 
 Then either his name will be in the registers or else you will 
 learn of him by inquiry. 
 
 (ii) Destructive. 
 
 His name is not in the registers and I can learn nothing by 
 inquiry {modus tollens). 
 
 Then he neither was married nor lived there. 
 
 § 964. We can express ' If either A is jB or C is D, in both 
 cases E is F' by a double proposition — ' If ^ is B, E is F, and 
 also if C is D, E is F'. But we cannot express ' If ^ is B, either 
 C is D or E is F' by the two propositions 'U A is B, C is D ', 
 and also 'Ii A is B, E is F'. 
 
 The double disjunction, as above (III) is not a very usual or 
 natural form — ' If either ^ is ^ or C is D, then either E is For 
 G is H'. If the meaning is that ' E is F' is the consequent of 
 A being B, and ' G is H' is the consequent of C being D, we 
 should express it thus — ' If AisB, E is F, and if Cis D, G is H '. 
 
 The minor premiss and conclusion, however, will always 
 be,- 
 
 But either A is B or C is D. 
 Then either £ is i^ or G is H. 
 
Dilemma 465 
 
 or else {modus toNens) — 
 
 But neither E is F nor G is H. 
 Then neither A isB nor C is D. 
 
 § 965. Whately gives this illustration : — 
 
 If the world existed from eternity there would be records 
 prior to the Mosaic. And if it were produced by chance, it 
 would not bear marks of design. 
 
 But there are no pre-Mosaic records, and the world does bear 
 marks of design {modus tollens). Therefore it neither existed 
 from eternity, nof is the wotk of chancie. 
 
 § 966. The Dilemma is a syllogism with a Complex conjunc- 
 tive major premiss and a disjunctive minor prertiissi Its 
 simplest form is, constructively — 
 
 UA is B it IS C] and HA is D it is C, 
 
 But A is either B or D (disjunctive affirmation), 
 
 .•. A is in either case C, 
 
 or destructively : — 
 
 li A is B it is C; and if .<4 is Z?it is E. 
 
 But either A is not C or it is not E (disjunctive denial). 
 
 Then either A is not B or it is not D. 
 
 The following is a Constructive Dilemma — 
 
 Whether we live we live unto the Lord, and whether we die 
 we die unto the Lord. 
 [But we must either live or die.] 
 Whether we live, therefore, or die we are the Lord's. 
 
 The following, from Whately*s Logic, is a Destructive 
 Dilemma — 
 
 ' If this man were wise he would not speak irreverently of the 
 Scripture in jest ; and if he were good he would not do it in 
 earnest. 
 
 But he does it either in jest or earnest. 
 
 Then he is either not wise or not good. 
 It should be observed that the affirmative form of the Minor 
 Premiss does not make or prevent this from being a Destructive 
 Dilemma, The two consequents are negative, and so are sub- 
 lated by an affirmative. 
 
 § 967. When the antecedent is a disjunction of contradictory 
 
 Hh 
 
466 Disjunctive Reasoning 
 
 alternatives ' the major premiss may be expressed in either of two 
 ways : — ' Whether A is B or is not B, C is D' and, ' If ^ is 
 B, C is D, and if A is not B, C is D.' Marcus Aurelius 
 writes : — ' It were well to die if there be gods, and sad to live if 
 there be none.' But contradictory disjunction can have no 
 place in the consequent. ' If A is B then either C is D or is 
 not Z*' is a superfluous and useless proposition, for C must 
 either be or not be D independently of A being B or of any 
 other condition, in virtue of the principle of Excluded Middle. 
 Such a consequent could not be sublated. It should be noticed 
 also that 'If either' introducing an antecedent should rather be 
 ' Either if, which can be expressed as ' Whether '. A disjunctive 
 antecedent does not usually contain a disjunction of ignorance — '■ 
 ' If it be the case that either A is 5 or C is D, then in that case,' 
 &c. — , but means in either (both) of two possible cases, so that 
 either (both) can be transferred to the vinculum, so as to introduce 
 the consequent. 'If ^ is £ or if C is D, in either case it is true 
 that E is F.' This will appear more clearly in the case of con- 
 tradictory disjunction, 'If either ^ is ^ or ^ is not B' is 
 meaningless. A is necessarily either B or not B, and no ' if is 
 needed. 
 
 § 968. The argument, ' If ^4 is true B is true ; ii A is untrue 
 C is true — therefore either i? or C is true,' may be expressed 
 thus in Barbara — 
 
 If 5 is untrue A is untrue. 
 
 li Ais untrue C is true. 
 
 Then, if B is untrue C is true. 
 
 And similarly, if C is untrue B is true. By a strange slip 
 Sigwart adds, 'That is, the consequence of an affirmation and 
 the consequence of its denial are mutually exclusive ' (i. 329 n.). 
 § 969. McCosh " gives the two following examples : 
 
 If a man can help a thing he should not fret about it. If he 
 cannot help a thing he should not fret about it. 
 
 ^ ' Heads I win ; tails you lose ' is a mere trick of speech, suggesting to 
 the mind that ' I win ' and ' you lose ' are contradictory consequents, 
 instead of being one and the same. Heads and tails are, in speaking of 
 a coin, contradictories. The proposition is of the form, ' Whether A is 
 or is not B, in either case C is D.' It is like ' Tide life, tide death, I come 
 without delay' {Midsummer Nighfs Dream), or, 'Will you, nill you, &c.' 
 — though, to be sure, between willing and nilling comes indifference. 
 
 ^ Laws of Discursive Thought, p. 150. 
 
Dilemma 467 
 
 But he can either help it or not help it. 
 Therefore he should not fret about it. 
 
 If that narrative be true you must believe it. 
 
 If it be false you must disbelieve it. 
 
 But it must either be true or false. 
 
 Therefore you must either believe it or not believe it. 
 
 The second example, however, is only in form a dilemma. It 
 has a contradictory disjunction in consequent as well as in 
 antecedent. The reasoning proceeds smoothly. But it guides 
 us to a conclusion which is self-evident quite independently of 
 the premisses. We might as well argue: 'You must either 
 believe or disbelieve it. Therefore jt is either true or untrue.* 
 ■ I assume that tnte and untrue, believe and disbelieve are intended 
 here as contradictories, though, strictly speaking, as McCosh 
 points out, a narrative may be partly true and partly false, and 
 belief may be partial or entire. Dilemmas are frequently falla- 
 cious by assuming that no third supposition is possible. Such a 
 fallacy of false assumption, however, is material, not formal. 
 
 § 970. The following is a good Dilemma — ' Neither if we eat 
 are we the better ; neither if we eat not are we the worse '. As 
 we must either eat or eat not, it follows that we shall be either 
 none the better or none the worse. These, observe, are not 
 contradictories. It is possible to be both none the better and 
 none the worse. Between better and worse is a third possi: 
 bility, neither one nor the other. And this is what St. Paul 
 means. Whether we eat or eat not is indifferent. 
 
 § 971. The Apostle frequently uses the dilemma — e. g. just 
 before — 'He that eateth eateth unto the Lord, for he giveth God 
 thanks ; and he that eateth not, unto the Lord he eateth not, and 
 giveth God thanks.' Again — 'Some preach Christ even of 
 envy and strife, and some also of good will. . . . What then ? 
 Only that every way, whether in pretence or in truth, Christ 
 is preached.' 
 
 § 972. Archbishop Whately remarks that many arguments 
 which are commonly called dilemmas 'hardly differ from 
 simple conditional Syllogisms.' In fact, a dilemma is often 
 sufficiently expressed by a single proposition — e.g. 'It is 
 cheap, whichever way you look at it.' 
 
 § 973- The distinction between the Double Destructive Con- 
 junctive Syllogism {'li A is B, E is F ; and if C is D, G is H. 
 
 H h 2 
 
468 Disjunctive Reasoning 
 
 But neither E is F nor G is H. Therefore neither A Is B nor 
 C is Z) ' ) and the Destructive Dilemma is plain, if we notice that 
 neither . . . nor is two denials (so that we might equally well 
 have said, ' E is not F; therefore A is not B) and G is not H; 
 therefore C is not D ' ), whereas either ... or is not two affir- 
 mations, but only one. We could not replace ' Either A is B, 
 or C is D; therefore either £ is i^ or G is H' hy 'A is B, 
 therefore E is F; and C is D, therefore Gis H'. 
 
 § 974. The word Dilemma merely means a double lemma or 
 sumption. If .^4 is 5 it is either C ot D. '\i Ais B it is either 
 Cor Dot E' would be a Trilemma.* ' If .<4 is 5 it is either CorD 
 or E or F' would be a Tetralemma — contradicted by ' If .4 is S it 
 is neither C nor D nor E nor F'. And so forth. But the expres- 
 sion commonly conveys the idea of controversial argument, in 
 which you say to an opponent, ' It must be either one or the 
 other. Take your choice. In either case the consequence will 
 be unpalatable to you.' The dilemma is regarded as a parti- 
 cularly triumphant method of reasoning. The antagonist if not 
 impaled on one horn will be gored by the other. On the other 
 hand it is liable to prove a dangerous weapon to the user. The 
 horn on which the antagonist is not transfixed may transfix 
 himself. This has already been briefly pointed out (§ 168). 
 
 § 975- The method of rebutting a dilemma is usually this. It 
 has been argued that if Aeschines joined in the public rejoicings 
 he was inconsistent; if he did not join he was unpatriotic. 
 Therefore he must have been either inconsistent or unpatriotic. 
 Or, contrariwise, if AeschineS was consistent he refused to join 
 in the rejoicings ; if he was patriotic he did join in them. But 
 either he joined or refused to join. It follows that he was either 
 not consistent or not patriotic. 
 
 To which it might be replied : If Aeschines joined in the 
 rejoicings he was not unpatriotic. If he did not join he was 
 not inconsistent. Either then he is clear of the charge of 
 unpatriotic, or of that of inconsistent, conduct. Or contrari- 
 wise, if Aeschines was unpatriotic he refused to join ; if he was 
 inconsistent he did join. But he cannot both have joined and 
 
 ^ If ^ is 5 it is either C or Z? or E. But it is not C and not D. Then 
 it must be E. So the Wykehamist is given his choice — Aut'disce, aut 
 discede. Manet sors tertia — caedi. 
 
Dilemma; how Rebutted? 469 
 
 not- joined. Therefore either he wa,s not unpatriotic or not 
 inconsistent. 
 
 (0, 
 
 Dilemma. Rebutter^ 
 
 iUAisBitisC ( If A is not B it is not C 
 
 (UAisBitisC (If 
 
 I If A is not B it is D t If 
 
 ■ A is B it is, not D 
 A is either B or not B -4 is either not B or jB 
 
 Then A is either C or D,. Then •<4. is either not C or 
 
 not D, 
 
 (ii). , 
 flf ^ is not C it is not ^6 If ^4 is, C (not not-C) it is B 
 
 I If ^ is not ZJ it is jB \fA is Z» (not not-Z>) it is not B 
 
 A is either not not-5 or not A is either not B or not xvoi-B 
 
 B {modus toHens) 
 Then A is either not not-C Then A is either not C or not 
 
 or not not-Z) D. 
 
 i. e. A is either C or 2?. 
 
 § 976. On the other hand this, rebutter has. a grave weakness. 
 The rebutting syllogism is formally valjd, but the conclusion 
 which it establishes contradicts that of the original argument in 
 appearance only. Its assumptions also halt. We cannot say 
 in (i) that, because if A is B it is C, if A is not B it is not C ; or, 
 because if A is not B it is D, if A is B it is. not D. Sublation 
 of antecedent does not involve sublation of consequent. The 
 rebutter of (ii), has the same defect. Nevertheless in practice it 
 often happens that, if BA involve C, non-BA will involve non-C, 
 and the above dilemma about Aeschines is met quite legitimately. 
 Controversialists are often prudent in getting the other side to 
 open fire first.. To accept and rebut a dilemma is rhetorically 
 effective. The wound received is forgotten in the counter- 
 thrust. A point admittedly scored by the adversary is shown 
 to lead to a consequence which- he does not hke. He cannot 
 have it both ways. In arguing about ecclesiastical revenues it 
 has often been- alleged, that they were given only half voluntarily 
 for securing private masses for departed souls. The defender 
 affects to grant this, and adds, 'Then they were not, as you say 
 at other times, given, to the nation for public purposes.' But 
 to estabhsh this, without agreeing to the other proposition the 
 defender has to find arguments elsewhere. Otherwise he only 
 proves inconsistency in. the assailant. 
 
470 Disjunctive Reasoning 
 
 § 977- The dilemma between Protagoras and Euathlus may 
 find a place here. The former undertook to teach the latter 
 the art of pleading, and payment was to be by results. When 
 Euathlus won his first cause he was to pay Protagoras an 
 honorarium. It happened, however, that he disliked the dusty 
 atmosphere of the law, and cheated Protagoras of his fee by 
 refusing to become a pleader. Whereupon Protagoras sued 
 him, considering that should the Court award the money to 
 himself it would be his ; while even if the Court gave a verdict 
 for Euathlus he would still have the money, which Euathlus 
 would then be bound to pay to him in virtue of the agreement. 
 He triumphantly told Euathlus that he would have to pay in 
 either case. But Euathlus said. No. If I win this cause, 
 the judges will have decided that I need not pay the money. 
 If I lose it I shall have no obligation under our agreement 
 to pay. 
 
 The weakness of Euathlus' defence seems to be that the loss 
 of his cause did not place him under an obligation not to pay ; 
 and the Court would then have decided that he must pay. On 
 the other hand, if he won it, it is true that the verdict was that 
 nothing had occurred up to that moment to oblige him to pay; 
 but the reasons for the verdict were presumably negative. His 
 winning his cause was subsequent to those reasons, and though 
 involved in the verdict being given was not prior to the verdict. 
 We shall probably consider that, whichever way the Court 
 decided, Euathlus was bound to pay, but that the verdict on 
 the issue before the judges should have been in his favour. 
 Protagoras could only sue him for declining to be a pleader, 
 not for refusing to pay the money. But was there evidence 
 that he had agreed to become a pleader? 
 
 Very similar is Chfysippus' cross-dilemma of the Crocodile 
 and the abstracted Infant, which is too familiar to be given here. 
 
 § 978. The dilemmatic, or hypothetico-disjunctive, judgement, 
 as Hamilton remarks, 'cannot be analysed into an hypothetical 
 and a disjunctive judgement. It constitutes as indivisible a unity 
 of thought as either of these.' ' ' If ^ is either Y or Z it is ^ ' 
 is the simplest form of the dilemmatic, as ' Xis either F or Z ' 
 is of the disjunctive judgement. The latter ' is realized by one 
 simple energy of thought, in which the two relatives, — the either 
 ' Lectures on Logic, i. 242. 
 
A Judgement about Judgements 471 
 
 and the or, — are thought together as inseparable, and as binding 
 up the opposing predicates into a single sphere.' ^ 
 
 § 979. In what has been said above about Conditional Judge- 
 ments I have refused to admit the logical distinction between 
 Reason and Consequent, on the one hand; and any other form 
 of general predication On the other ; or between the hypothetical 
 proposition as a judgement about judgements and the categorical 
 abstract proposition as a judgement about objects — the difference 
 being one of syntax and grammatical convenience and not of 
 logic. 'It is one thing,* remarks Professor Veitch, however, ' to 
 say. Lying is dishonourable ^ it is quite another to say, If this man 
 lies, he dishonours himself. In the former case we affirm an 
 attribute of a subject ; in the latter we do not properly affirm, 
 but state a supposition or sequence following the realization of 
 a definite hypothesis."' I have shown that the only difference 
 between such an hypothetical judgement (' If this man lies he 
 acts dishonourably') and a categorical judgement ('Lying is 
 dishonourable ' = If men lie they act dishonourably) is that 
 the hypothesis is about an actual existence — 'this man' — and 
 ' If this ^ is 5 it is C* therefore cannot grammatically be thrown 
 into the form, 'All BA's are C But an hypothesis about 
 a concrete individual or an immediate case is nevertheless just 
 as abstract as any other.' 'If you stole the cup I must punish 
 you. I find you did steal it {mssertio conditionis). I must 
 
 ' Krug, quoted by Hamilton (op. cit. i. 241). He adds : ' In consequence 
 of this, a disjunctive proposition cannot be converted- into a categorical. 
 For in a categorical judgement a single predicate is simply affirmed or 
 denied of a subject ; whereas in a disjunctive judgement there is neither 
 afifirmation nor negation, but the opposition of certain attributes in 
 relation to a certain subject constitutes the thought. . . . The disjunctive 
 judgement is one essentially different from the categorical' {Logik, 
 pp. 170, 171). But a disjunction is merely a categorical proposition with 
 a negatively determined subject. ' Every X is either Y or Z' may, as we 
 have seen, be written ' Every non- YX is ZX ', which is the same judge- 
 ment, realized by the same energy of thought, as ' Every non-ZX is YX '. 
 ' Victory or Westminster Abbey ' means ' If we do not gain the victory, 
 at least we shall have a grave among heroes ' — which is the categorical 
 judgement — ' Failure to conquer involves at least a hero's grave.' 
 
 " Institutes of Logic, p. 271. 
 
 ' Mansel asserts that ' the only hypothetical judgement which can be 
 employed as the real major premise of a syllogism may be expressed in 
 the form, " If any A is B, it is C," where A, B, and C represent concepts 
 or general notions' (Prol. Logica, p. 218). I cannot follow this usually 
 
472 Disjunctive Reasoning 
 
 therefore punish you (assertio conditionati).' There is no logical 
 difference between such a major premiss and one like ' Godliness 
 with contentment is great gain '. ' You take my life when you 
 do take my name ' is as abstract as ' Thieves never prosper ' or 
 ' Diamond cut diamond '. 
 
 Frequently a proposition is explicated not only in h3rpothetical 
 form but in conditional grammatical mood in order to suggest 
 non-fulfilment of the condition; as in Pascal's apophthegm — 
 ' If all men knew what is said behind their backs there would 
 not be two friends in the world'. The assunied existence of 
 friendship {sumptio dati) proves that me^ do not know what 
 is said of them. Cf, ' si amitti beata vita potest, beata esse non 
 potest' (Cic). Or in th§ fourth Qeorgic — 'ignoscenda quidem 
 scirent si ignoscere Manes ', They never forgive, it is implied, 
 and therefore Qrpheus' madness in looking back at Eurydice 
 was unforgivable — where sublation of the antecedent involves, 
 for once, denial of the consequent, the reasoning being of the 
 form, ' If any ^ is ^ this A is B- No A is B, Then this A is 
 not.' Usually, as we have seen, when the verb is in the con- 
 ditional pluperfect, it is suggested that sublation of the antecedent 
 involves denial of the consequent — ' If ^ had been B, C would 
 have been D '. In other words, the condition is here a conditio 
 sine qua non. 
 
 § 980. Every BA. is C = Every BA because it i^ 5 is C = 
 Every A y^ it is 5 is C = If it is true that if a thing is A it is B, 
 in that case it is C. Similarly, Every BA is DC = If it is true 
 
 lucid writer's distinction between the two meanings of ' If Caius is free 
 from business he is writing poetry', which means either, generally, 
 'Whenever Caius is disengaged he writes poetry,' or, specially, ' If he is 
 now disengaged he is writing poetry.' The former, he says, yields a 
 conclusion ex hypothesi. In the latter case the inference is made not 
 from the hypothesis but materially from some circumstance known to the 
 reasoner, but not appeariiig in the proposition. ' Any one being asked, 
 "Why do you infer that Caius, being now disengaged, is writing poetry?" 
 would reply, " Because he told me he should do so," or something of the 
 kind' {Proleg. Logica, p. 217 n.). But what did he tell him? That he 
 would be writing poetry at a certain hour ? No ; but that if he were at 
 some particular moment found disengaged, it might be presumed that he 
 was writing poetry. The two meanings of the original proposition are 
 both abstract. But the former means, 'All the cases of Caius being 
 disengaged are cases,' &c. ; the latter means, ' All the present possibilities, 
 or contingencies^ &c. 
 
A Judgement about Judgements 473 
 
 that if a thing is A it is B, in that case it is true that if a thing 
 is C it is D. An abstract categorical proposition is then seen 
 to be an hypothesis about an hypothesis. It is a problematic 
 synthesis. The supposition that the supposition of ^ involves 
 the assertion of B involves the assertion that the supposition 
 of C involves the assertion of D. Thus, ' 111 weeds grow apace.' 
 The supposition of anything which is a weed being an ill one 
 involves the assertion that whatever growth it has is a quick 
 growth. 'Evil communications corrupt good manners.' The 
 supposition of any communications that exist being evil ones 
 involves the assertion that any good manners that exist will be 
 corrupted. In sublating the consequent (predicate), however, 
 we must not say ' does not involve ' but ' excludes '. The sup- 
 position of the supposition of C excluding the assertion of D 
 involves the assertion that the supposition of A excludes the 
 assertion of B. 
 
 § 981. Mansel rightly says : — * The distinction so much insisted 
 on by the Kantians of the problematical character of the two 
 members of an hypothetical judgment is, like the whole Kantian 
 doctrine of modality, of no consequence in formal Logic. All 
 formal thinking is, as regards the material character of its 
 objects, problematical only.' ^ Sigwart observes : — ' The neces- 
 sity of each particular phenomenon is never more than a 
 conditioned necessity, an avdyKt) cf vTro6i<xeu>^. When some- 
 thing is said to be necessary, it is not the cause, but the fact 
 that it results from the causes present, which is called necessary."' 
 
 ' Proleg. Logica, p. 214, and Al^rich, p. 234, ^ Logic, p. 200. 
 
CHAPTER XXIX 
 
 ATTACKS ON THE SYLLOGISM 
 
 § 982. To the reader of the foregoing pages it may now be 
 left to say whether Syllogistic Reasoning can be superseded, or 
 admit a rival. A modern school of writers, however, who are 
 metaphysicians rather than logicians, have challenged the 
 Syllogism's indefeasible claim by what is very like a reckless 
 and unscientific appeal to a common jury, relying upon the 
 complexity and subtlety of thought and language — to which 
 ' traditional ' logicians have certainly paid too little attention — 
 for a triumphant disproof of the syllogistic laws. In England 
 the leaders of this destructive and sans-culottist school have been 
 Dr. Bosanquet and Dr. Bradley. The former says — 
 
 ' There is no such thing as an antecedent scheme prescribing, 
 so to speak, a set of schedules in one or other of which every 
 argument can be written out merely by filling in the blanks. 
 The form of knowledge is an active and constructive principle, 
 to the workings of which no abstract type, antecedently applied, 
 can be adequate. Logic is incapable of prescribing beforehand 
 the type of relations which an inferential totality may impose 
 upon its parts.' 
 
 He speaks of 
 ' the difficulty of moulding the vital and constructive action of 
 thought into shapes prescribed by an artificial scheme which 
 does not precisely correspond to any single type of intellectual 
 action. The violent transformations by which formal logic attains 
 this end are not perhaps an undesirable scholastic exercise ; 
 for they unquestionably drag into light, though only as a meagre 
 and skeleton framework, a certain ultimate community and type 
 in all inferential operations.' ^ 
 
 But he will only hesitatingly allow us to say that ' in the common 
 nature of thought a system of conditions can be discovered 
 which in one way or another is conformed to by every act of 
 inference '.^ 
 
 § 983. Inasmuch as the end and aim of Logic is to detect the 
 
 ^ Logic, ii. 197, 198. ^ Ibid. p. 199. 
 
Majors and Minors 475 
 
 unity of reasoning, that which gives to one and all inferdnces 
 their validity and compulsiveness, the assertion that no abstract 
 and universal type can be found is an assertion that Logic is 
 a failure, that there is no One in the Many, and that the form 
 of Reason varies with its matter. Nevertheless ' a certain 
 ultimate community and type ' is conceded. But it is disparaged 
 as a meagre and skeleton framework — as though form could be 
 anything else. It is a 'system of conditions', which, however, 
 are only approximately laws. Every inference must have three 
 terms and no more, and two premisses possessing an identical 
 term in common, which must be universal, ' for a universal is 
 that which without prejudice to its identity persists through, or 
 contains in itself, different relations.' Yet there is ' no justifica- 
 tion for the traditional pre-eminence assigned to one premiss 
 as the " major " '. Such a pre-eminence is bound up with ' the 
 vicious quantitative form of the universal, and carries with it 
 the petitio principii which has been irresistibly demonstrated to 
 be present in the traditional syllogism '. Further, there is ' no 
 justification for the distinction between universal and particular 
 premisses '. Both must really be universal (apparently as both 
 sides of an equation are totals), and, ' if negation implies signifi- 
 cant denial only, both may be negative.' * All M is non-P, all 
 M is non-5. Non-S (the absence of S) and non-P (the absence 
 of P) are therefore sometimes found in combination. This is, 
 I imagine. Dr. Bosanquet's meaning. Bare denial, he says, is no 
 judgement, and therefore both premisses are thought as positive. 
 § 984. The old logicians certainly employed a narrow range 
 of illustration, and regarded reasoning too exclusively in its 
 aspect of subordinating one class to another class, species to 
 genus. The objection to the premiss which states the rule 
 being called the ' major ' is, however, trivial. The criticism of 
 'AH ^ is 5' as a vicious formula of universality, inasmuch as 
 it ' excludes such vital and genuine processes as, e. g., modal 
 conversion,' has been shown above to be ill-founded. Generally, 
 Dr. Bosanquet contends, ' The traditional syllogism is a hybrid 
 between analogical inference and inference or induction by 
 complete enumeration.' He says it excludes calculation and 
 geometrical construction, and has no place for Induction, for 
 Analogy, or for philosophical subsumption. In short, it 'fails 
 ^ Logic, ii, 202. 
 
476 Attacks on the Syllogism 
 
 to recognize the synthetic activity of thought '. For example, 
 having asserted that ' the mind is a unity of determinate and not 
 exclusive parts ', we could not, he says, go on to say, ' A feeling 
 is the mind, and therefore A feeling is a unity,' &c. We could 
 only say that a feeling is a factor or element in such a unity. 
 
 § 985. Thought undoubtedly is manifold. But Reason is 
 one. The whole object of Logic is, after analysing the synthetic 
 activity of thought, to exhibit the single ' form ' underlying its 
 rational connexions. What are we offered instead of the 
 ' traditional syllogism ' of subsumption under rule ? ' Syllogisni 
 is a subsumptive reasoned judgement, depending upon the unity 
 of differences within an individual subject, and making the 
 intelligible ground of this unity explicit in various degrees." 
 This, if I understand it aright, seems to be only the ' traditional ' 
 idea of inference in a more abstruse form, with a leaning however 
 to the Third Figure, and in it to Daraptias the norm of reasoning. 
 A subject combines in itself two distinct characteristics, which 
 are therefore shown to have a possibility of combination, so far 
 as their union has an intelligible ground in the subject or middle 
 term. In another place the same talented writer observes : ' If 
 the present reaction against formal logic should end in establish- 
 ing a more vital conception of universality than that which sets 
 it down to mere abstraction, a fundamental reform will have 
 been made in philosophic first principles.' ^ 
 
 § 986, Turning to Dr. Bradley, we have an indictment of the 
 Syllogism which would be more appropriately called scolding. 
 We are witnessing, it seems, 'the dying effort of a hard-run and 
 wellnigh spent chimera ' which has deluded mankind for some 
 two thousand years. The time has come when such truth as it 
 contained should be disengaged from it and be able to stand by 
 itself. 
 
 ' We cannot for ever with eyes fast closed swallow down the 
 mass of orthodox rubbish in which that truth has wrapped itself 
 up.' 'The first to go must be the major premise. . . . An effete 
 superstition is doomed. Begotten by an old metaphysical 
 blunder, nourished by a senseless choice of examples, fostered 
 by the stupid conservatism of logicians, and protected by the 
 impotence of younger rivals, this chimera has had a good deal 
 more than its day. Really dead long since, I can hardly believe 
 that it stands out for more than decent burial. . . . The major 
 
 ' Logic, ii. 203. ^ Ibid. i. 63. 
 
'Synthetic Activity of Thought^ 477 
 
 premise is a delusion, and the syllogism itself, like the major 
 premise, is a mere superstition. ... It professes to be the 
 model of reasoning, and there are reasonings which cannot by 
 any fair means be conformed to it.' 
 
 § 987. The axiom of inclusion within class extension, Dr. 
 Bradley continues, gives no new information and involves 
 fetitio principii. It is therefore vicious. The axiom too of Kant 
 — * What stands under the condition of a rule stands under the 
 rule ' — applies only to the category of subject and attribute, and 
 fails whenever you pass beyond. Even in that category it is 
 a mistake, as the Third Figure shows, to insist on the necessity 
 of a major premiss. 
 
 § 988. The following * palpable inferences ' are adduced as 
 indefensible on the principles of the ordinary Syllogism : — 
 
 (i) A is to the right of B, B is to the right of C, therefore A 
 is to the right of C. (ii) A is due north of B, B due west of C, 
 therefore A is north-west of C. (iii) A is equal to (greater or 
 less than) B, B is equal to (greater or less than) C, therefore A 
 is equal to (greater or less than) C. (iv) A is in tune with B 
 and B with C, therefore A with C. (v) A is prior to (after, 
 simultaneous with) B, B to C, therefore A to C. (vi) Heat 
 lengthens the pendulum, what lengthens the pendulum makes it 
 go slower, therefore heat makes it go slower, (vii) Charles I 
 was a king ; he was beheaded, and so a king may be beheaded. 
 In (vi) and in (vii). Dr. Bradley observes, ' our old friend the 
 major premise ' is scarcely distinguishable from the minor, (vii) 
 is Darapti, but (vi) is Barbara, and there can be no question 
 which is major premiss and which minor. ' In all the rest he 
 has totally vanished.' ' Logical necessity does not always come 
 from the application of universals to something less universal. 
 But if so there need not be always a major, and the [above] 
 examples put this beyond a doubt.' 
 
 Let me suggest one or two more. A is the friend of 5 ; Bis 
 the friend of C. Then A is the friend of C.—A is thrice as large 
 as 5 ; Bis thrice as large as C. Then A is thrice as large as 
 C—A is B's grandfather ; B is C's grandfather. Then A is 
 C's grandfather. — A is next to B; B is next to C. Then A is 
 next to C. The reader can compose thousands of such 'palpable 
 inferences ' for himself. 
 § 989. Inasmuch as major premiss is only another name for 
 
478 Attacks on the Syllogism 
 
 the rule or principle on which the conclusion rests, being applied 
 through the minor premiss to some case or other, what we are 
 asked here to admit is that a reasoning can take place without 
 any reason, dispensing with ground, with rule, and with appli-' 
 cation. If the minor premiss applies anything, what is it ? A 
 ground is necessarily a universal. On what ground are we to 
 infer that, when A is to the right of B and B to the right of C, A 
 is to the right of C ? It is easy to ridicule the proposed major 
 premiss, ' Whatever is to the right of a thing which is to the 
 right of some other thing is itself to the right of that other thing,' 
 just as it would be easy to ridicule the imposing and highly 
 complex amplifications of one or two simple axioms in De 
 Moivre's Theorem or one of Euclid's more elaborate con- 
 structions. But we are offered nothing to take its place.^ Dr. 
 Bradley thinks it enough to say: — ' If such reasoning is reason- 
 ing ^ow an axiom, how did people reason before axioms were 
 invented ? ' Which is like asking. How did people count before 
 arithmetic was invented ? or, Who wrote the first book to teach 
 reading? From 'A is like B and B is like C, we cannot, 
 as he himself says, infer certainly a likeness between A and C. 
 Nor, because A is worth five times as much as B, and B five 
 times as much as C, can we infer that A is worth five times as 
 much as C. But why? Because there is no general axiom 
 which would necessitate that inference. 
 § 990. Dr. Bradley says : — 
 
 ' From such premises as " A is to the right of B and B to the 
 right of C" there is and can be no form of reasoning which will 
 give you the conclusion. . . . Where the inference is valid, the 
 special operation by which it is performed falls outside the 
 axiom, and it is impossible therefore that the axiom can supply 
 
 ' ' Bradley confuses two different operations, inference and observation. 
 When there is inference there is a major premiss, which may be un- 
 expressed or cumbrous, but is required for the thought. As Aristotle 
 puts it, the syllogism is directed " not to the outer but to the inner 
 discourse ", or as we should say, not to the expression but to the thought' 
 (Case, Encycl. Britt., tenth edition, Article 'Logic'). Professor Case, 
 however, concedes (contrary to the view taken in this book) that ' there 
 are inferences which are not syllogisms '- He observes in another passage 
 that ' the Logic of the last quarter of the nineteenth century may be said 
 to be animated by a spirit of inquiry marred by a love of paradox and 
 a corresponding hatred of tradition. But we have found, on the whole, 
 that logical tradition rises superior to logical innovation.' 
 
Nihilistic Criticism 479 
 
 any test of validity. . . . The actual operation is not a matter 
 for superior direction ; it is a matter for private inspiration and 
 insight. It is impossible that there should be fixed models 
 for reasoning; you cannot draw out exhaustive schemata of 
 valid inference. There are principles which are tests of the 
 general possibility of making a construction : but of the actual 
 construction there can be no canons. The attempt to manu- 
 facture them would lead to the search for a completed infinity ; 
 for the number of special relations has no end, and the possible 
 connexions in time, space, and degree are indefinite and inex- 
 haustible. To find the canons of valid inference you must first 
 make a list of valid inferences.' 
 
 § 991. This is mere nihilism. Of course Logic cannot supply 
 major premisses. What is meant by 'valid inferences'? Do 
 we measure the relative positions of A, B and C by compass 
 and rule, and find it true that^ is to the right of C? But, then, 
 this is not an inference. The premisses said that A was to the 
 right of C because it was to the right of B. Shall we substitute 
 'proposition' for 'inference'? When A is to the right of B 
 and B to the right of C, measurement or inspection shows us 
 that A is always found to the right of C. That proposition then 
 is valid. But why ' valid ' ? Should we not rather say ' corre- 
 sponds with facts ' ? It is the validity of inference which logic 
 analyses, not the contingent truth of propositions. The logician, 
 Bradley says, is thought to be a spiritual Director who does not 
 supply arguments but tests them. The logician, however, tests 
 them as reasoning, but stripped of everything material, even of 
 language, except as given. He knows nothing about right and 
 left, north and west, about tuning-forks or pendulums. Priority, 
 equality, posteriority, inferiority, belong to the concrete matter 
 of the reasoning. 
 
 § 992. Dr. Bradley confuses Thought with Reason, and 
 because the categories of thinking are many he denies that the 
 form of ratiocination can be one. He draws up a dialectical 
 Declaration of Independence, or rather of Antinomianism. AH 
 inferences are in future to be equal and free, emancipated from 
 rule and domination. He is at once the Robespierre and the 
 Luther of logic. ' The syllogism is effete and its realm is master- 
 less ; and the question for us who aspire to the inheritance is to 
 know in what character we mean to succeed. Do we wish to 
 substitute one despotism for another? Are our principles of 
 inference to be tests and canons ? Most assuredly not.' As 
 
480 Attacks on the Syllogism 
 
 a 'staunch Protestant' he upholds the liberty of private judge- 
 ment, and refuses to submit the validity of an argument to 
 Aristotle or any one else. That one premiss should be called 
 ' greater ' and the other ' less ', in a free country, is a piece of 
 aristocratic pretension which is especially odious. But stay. By 
 stepping down from its high seat and consenting to an equality 
 with, or even inferiority to, the minor premiss, the major premiss 
 may just ' save the syllogism '. ' The one chance there is of pre- 
 serving the syllogism is for us to take our stand upon the third 
 figure. " The attributes of one subject are interrelated " will 
 then become the axiom of inference.' Certainly Figure III is 
 the figure in which it is most difficult to detect the dominate law. 
 Major and minor lie more or less cheek by jowl. The minor's 
 badge of servitude has there almost vanished. It is true that this 
 figure never yields a conclusion which is universally true. But the 
 New Logic has no need of universals or of dominant laws. All 
 judgement will be an equation, an extensional identification, and 
 subordination of concepts will be but a humiliating memory of 
 the past. So Dr. Bradley plants a tree of Liberty on the grave of 
 the Syllogism, and Figure III becomes a kind of sacred Tiers Etat. 
 
 § 993- AH that is needed is a point of connexion between the 
 premisses. Inference is a synthesis, a combination of data, 
 which results in the perception of a new relation within that 
 unity. 'The process is a construction and the result an intui- 
 tion. But this construction must not be arbitrary. There 
 must be " the identity of a common link ". A = B, B = C 
 become a single whole, A = B = C, from which ' we proceed to 
 our conclusion by mere inspection, A = C, " Man is mortal and 
 Caesar is man and therefore Caesar is mortal." There is first 
 a construction as Caesar — man — mortal, and then by inspection 
 we get Caesar — mortal. It is useless to lay down rules for either 
 part of this process. It is the man who perceives the points of 
 union within his premisses — ^who can put (as the saying is) two 
 and two together, — who is able to reason.' 
 
 § 994. It is to achieve this crude and trivial result that Aris- 
 totle is put into the dock, and rated and cross-examined in what 
 I must be pardoned for calling an Old Bailey style of jaunty 
 menace. Certainly the reasoner may expect harder nuts to crack 
 than Caesar — man — mortal. He is warned to secure 'the unity of 
 his construction ', for which ' no models can possibly be invented, 
 
/ / 
 
 Reasoning from Fact to Fact 48L 
 
 And for the process of inspection one wants a good eye; for 
 there are no rules which can tell you what to perceive.' The 
 art of perceiving, however, is entirely outside the province of 
 Logic, The logician does supply models for the reasoning 
 process, and that is all that concerns him. He insists, for 
 instance, that the middle term shall be not merely a point of 
 contaCt,^otherwise 'AisC,BiaC' would yield a conclusion, — 
 but a real keystone to the arch. No inference is warranted by, 
 'A is half of jS, Half of ^ is C Spencer's 'Things related to 
 the same are related to each other ' is therefore an unsatisfactory 
 rule. The ordinary rule against quatemio termmorutn Dr. Bradley 
 repudiates. The limit to the number of terms ' is psychological 
 and is not logical '. Yet 'it is true, no doubt, that in making a con- 
 struction we are forced to establish one link at a time '. Logicians 
 usually call this the Sorites. 
 
 § 995- The endeavour to substitute a rule of thumb for science 
 in reasoning has an earlier champion of another kind in Mill, 
 who pleads that We can and do reason front particular to par- 
 ticular without passing through a universal. It is astonishing 
 that a writer who did so much to place Induction upon its true 
 basis, that of causal connexion, should lead a crusade against 
 major premisses. For what is the statement of a cause but 
 a major premiss ? And what are the Five Canons but highest 
 and most universal axioms ? Mill's own tendencies, no doubt, are 
 nominalistic. He is bent on disparaging universals and deductive 
 inference. But this is to saw off the branch on which he is sitting. 
 
 § 996. According to Mill, then, ' the Syllogism is not the 
 form in which we necessarily reason, but a test of reasoning, 
 a form into which we may translate any reasoning with the 
 effect of exposing all the points at which any unwarranted 
 inference can have got in,' ' It is ' an artificial formula ', not the 
 way in which we do necessarily reason, but a type to which all 
 reasonings ought to be able to conform under pain of being pro- 
 nounced invalid. It is not a ' correct analysis of what the mind 
 actually performs in discovering and proving the larger half of 
 the truths, whether of science or of daily life, which we believe '} 
 On the other hand it is not merely useless and frivolous. One 
 might borrow the language of theologians and say that in Mill's 
 view Syllogism is not of the esse but of the bene esse of Inference. 
 
 ' On Hamilton, pp. 503, 504. " Logic, i. 209. 
 
 I i 
 
482 Attacks on the Syllogism 
 
 § 997- The word ' discovering ' in the foregoing sentence 
 confuses the question at the very outset. But let us leave this 
 till we come to Induction. Mill next says that the doctrine that 
 in every syllogism there is a petitio principii appears to be ' irre- 
 fragable '. For a conclusion can state nothing more than has 
 been already stated in the premisses. Certainly. But it states 
 more than is in either premiss separately (see below, § 10 19), and 
 there is no begging of a question unless the point to be proved 
 be implied in one premiss. Mill, however, immediately slips 
 into the assumption that because a conclusion has been already 
 ' asserted in the premisses ' it has been already asserted in the 
 major premiss — which is like saying that if a man inherited all 
 he possesses from an uncle and a cousin, he inherited it all from 
 the uncle, and also all from the cousin. But to come to closer 
 quarters with Mill's view of the syllogism. The following are 
 the familiar paragraphs : — 
 
 § 998. • Assuming that the proposition, The Duke of Welling- 
 ton is mortal, is immediately an inference from the proposition, 
 All men are mortal, whence do we derive our knowledge of that 
 general truth ? Of course from observation. Now all which 
 man can observe are individual cases. From these all general 
 truths must be drawn, and into these they may be again 
 resolved ; for a general truth is but an aggregate of particular 
 truths ; a comprehensive expression, by which an indefinite 
 number of individuals are affirmed or denied at once. But 
 a general proposition is not merely a compendious form for 
 recording and preserving in the memory a number of particular 
 facts, all of which have been observed. Generalization is not 
 a process of mere naming, it is also a process of inference. 
 From instances which we have observed, we feel warranted in 
 concluding that what we found true in those instances holds in 
 all similar ones, past, present, and future, however numerous 
 they may be. ... 
 
 ' When, therefore, we conclude from the death of John and 
 Thomas, and every other person we ever heard of in whose case 
 the experiment had been fairly tried, that the Duke of Welling- 
 ton is mortal like the rest, we may, indeed, pass through the 
 generalization. All men are mortal, as an intermediate stage; 
 but it is not in the latter half of the process, the descent from all 
 men to the Duke of Wellington, that the inference resides. The 
 inference is finished when we have asserted that all men are 
 mortal. What remains to be performed afterwards is merely 
 deciphering our own notes. 
 
 'Archbishop Whately has contended that syllogizing, or 
 reasoning from generals to particulars, is not, agreeably to the 
 
Mill's View 483 
 
 vulgar idea, a peculiar mode of reasoning, but the philosophical 
 analysis of the mode in which all men reason, and must do so if 
 they reason at all. With the deference due to so high an autho- 
 rity, I ca^nhot help thinking that the vulgar notion is, in this 
 case, the more correct. If froni our experience of John, Thomas, 
 &c., who once were living, but are now dead, we are entitled to 
 conclude that all human beings are mortal, we might surely have 
 concluded at once from those instances that the Duke of Wel- 
 lington is mortal. The mortality of John, Thomas, and others 
 is, after all, the whole evidence we have for the mortality of the 
 Duke of Wellington. Not one iota is added to the proof by 
 interpolating a general proposition. Since the individual cases 
 are all the evidence we can possess, evidence which no logical 
 form into which we choose to throw it can make greater than it 
 is; and since that evidence is either sufficient in itself, or, if 
 insufficient for the one purpose, cannot be sufficient for the 
 other ; I am unable to see why we should be forbidden to take the 
 shortest cut from these sufficient premises to the conclusion, 
 and constrained to travel the " high priori road " by the arbitrary 
 fiat of logicians. I cannot perceive why it should be impossible 
 to journey from pne place to another unless we "march up 
 a hill and then march down again ". It may be the safest road, 
 and there may be a resting-place at the top of the hill, affording 
 a commanding view of the surrounding country ; but, for the mere 
 purpose of arriving at our journey's end, our taking that road is 
 perfectly optional ; it is a question of time, trouble, and danger.' ^ 
 
 § 999. The confusion of thought in this celebrated passage has 
 been so often exposed that I attempt its refutation once more 
 for the sake only of the inexperienced student. We may pass (by 
 a lucky, shot) from particulars to particulars, but we cannot 
 reason directly from particulars to particulars. A reason is 
 essentially a universal — using that expression in its widest sense. 
 There must be some mediation, if there is to be proof. There 
 must be a one in the many when we are arguing from eleven 
 individuals to a twelfth. Mill maintains that from our experience 
 of John, Thomas, and others dying we could 'conclude at once 
 from those instances that the Duke of Wellington is mortal'. 
 On what ground? On the ground that he resembles them? 
 Resembles them in what ? In wearing a cocked hat, in being 
 under a certain height, in being Irish, in having two feet, or in 
 any other such way ? Of course not, but in being a man, or 
 
 "^ Logic, i. 213-15. 
 
 ^ 'Eav Tii KaBokov jitj rf, to fiecrov ovk ecrrai, Shitt' ovS" djro§e(^ij (Ar. An. 
 Post. i. II, 77''7). 
 
 I i 2 
 
484 Attacks on the Syllogism 
 
 a terrestrial living creature, or, if you like, in having a certain 
 physical constitution. As Bosanquet says, ' Particulars must 
 have some element of unity, for inference to take place. From 
 " a, b, c, d are good books " to " e is a good book " no sort of 
 inference holds or is in any way suggested. But from " Ivanhoe, 
 Waverley and Rob Roy are good books " to " Guy Mannering is 
 a good book " there is a self-evident passage by means of the 
 identity of authorship, which is too obvious to be expressed.' If 
 after all we think the Surgeon's Daughter not to be a good book, 
 it is because our induction was rather hastily expressed. The 
 cause of Ivanhoe and the others being good books was not 
 simply that Sir Walter Scott wrote them, but Sir Walter under 
 a certain inspiration or in certain circumstances, which were not 
 always present when he wrote. 
 
 § 1000. The point then in which we consider that (let us say) the 
 present Pope resembles all other beings whom death has over- 
 taken, and which leads us to infer that he too will die, is the ground 
 or reason for that inference. We cannot pass from them to him 
 except through that ground. Our confidence must be based on 
 something. That something, then, in any rational and orderly 
 argument must be explicitly stated. And it must appear twice in 
 the argument. These two appearances are the major and minor 
 premisses. It is not the 'arbitrary fiat of logicians' which 
 requires this. It is because no other method of inference can be 
 conceived or has ever been propounded. Dr. Bradley, as we 
 saw, girds at the necessity for major premisses and at the 
 explicit syllogism — which is like railing at the multiplication 
 table. But he too falls out with Mill, and shows that, if a dog's 
 wagging of its tail is a sign of pleasure, the child who hastily 
 concludes the same of the cat goes on an erroneous analogy. 
 It argues from particular to particular, from fact to fact, but 
 unscientifically. It does indeed mount that hill which Mill 
 considers so superfluous, but it mounts it too hastily, and so 
 descends the other side too precipitately. It is not always wrong 
 to generalize from a single occurrence ; but for most conclusions 
 a patient induction is required. We cannot argue from Mon- 
 mouth to Macedon or from chalk to cheese because they have 
 something in common. As logicians, however, we are not at 
 present concerned with the goodness or badness of our major 
 premisses. They may be the result of an induction which we 
 
Are Universals superfluous? 485 
 
 have framed, or they may have been acquired from others, or 
 obtained in some other way. But all inference is the application 
 of a major premiss to this or that subject. 
 
 § looi. It is this application which the school of Mill deny.^ 
 Their polemic ig really less against major than against minor pre- 
 misses. They admit that a general rule stands in the background 
 of any reasoning, but they say it need not be appealed to ; that 
 the conclusion exists by no grace of that general rule. It is 
 independent of any major premiss. It has been created in the 
 same way in which the universal has been created ; and in 
 inferring from my experience, e. g. of pension,eirs, that they are 
 practically immortal, I, by the same, and not a subsequent, act of 
 thought infer that the poor relation whom? I have just pensioned 
 will live to an enormous age. Or rather, if 'a general truth is 
 but an aggregate of particular truths', the particular inference 
 is really prior to the generalization. A general truth may, Mill 
 says, be 'resolved' into the individual cases of which it is a com- 
 pendious expression. It is 'a contrivance of language which 
 enables us to speak of many as if they were one '. He who 
 admits the major premiss asserts the conclusion. 
 
 'The Duke of Wellington is mortal like the rest.' It is 
 strange that Mill should have ignored the significance of like the 
 rest. The Duke was mortal like the rest because he was like 
 the rest in those attributes of which mortality is the effect. The 
 belief that mortality is the effect of those attributes (major pre- 
 ,miss), and that the Duke possessed them (minor), necessarily 
 preceded the conclusion that he was mortal. ' The inference,' 
 writes Mill, 'is, finished when we have asserted that all men are 
 mortal.' Why, then, preface the particular conclusion with 
 a therefore ? The Disciples who believed that St. John would 
 not die were conscious, not merely that in this he would be 
 
 ' ' Mr-. Mill's defence of the Syllogism in fact amounts to an abandon- 
 ment of all formal reasoning. All reasoning, he tells us, is really from 
 particulars to particulars. But, in that case, all inference must depend 
 upon the matter, and cannot be reduced to any general type. If, for 
 example,, I couplude that a man now living is mortal, solely from the 
 premises, "A, B, apd C, who. are dead, were mortal, and this man 
 resembles th,em in, certain other attributes of humanity," I may, by an 
 argument of precisely the same form, prove any given man to be six feet 
 high, because A, ^, and C, whom he resembles in the common attributes 
 of humanity, were all of that stature' (Hansel's Aldrich, p. 201). 
 
486 Attacks on the Syllogism 
 
 unlike others whom they had known to pass out of life, but that 
 his case would be an exception to a rule embracing mankind 
 generally. 
 
 § I0O2. The demonstration of the properties of a circle re- 
 presented by a diagram is, Mill maintains, only true of that 
 particular circle ABC. Yet he goes on : — 
 
 ' One instance only is demonstrated. But the process by 
 which this is done is a process whicH, when we consider its 
 nature, we perceive might be exactly copied in an indefinite 
 number of other instances ; in every instance which conforms 
 to. certain conditions. ... If we can prove an individual con- 
 clusion by assuming an individual fact, then, in whatever case 
 we are warranted in making an exactly similar assumption, we 
 may draw an exactly similar conclusion. . . . The proof does not 
 rest on the general assumption, but on a similar assumption 
 confined to the particular case: that case, however, being 
 chosen as a specimen or paradigm of the whole class of cases 
 included in the theorem, there can be no ground for making 
 the assumption in that case which does not exist in every other ; 
 and to deny the assumption as a general truth is to deny the 
 right of maldng it in the particular instance.*^ 
 
 It is exactly this possibility of standing as a representative 
 type of all instances that conform to the same conditions which 
 constitutes abstract thought. We argue, as Bradley says, not 
 from the particularity of the image of a past occurrence but 
 'from the content, the idea which can exist in different times 
 and under diverse conditions '.^ But no. Mill goes on : — 
 
 'All inference is from particulars to particulars. General 
 propositions are merely registers of such inferences already 
 made, and short formulae for making more. The major premise 
 of a syllogism, consequently, is a formula of this description : 
 and the conclusion is not an inference drawn /rom the formula, 
 but an inference drawn according to the formula : the real logical 
 antecedent, or premise, being the particular facts from which 
 the general proposition was collected by induction. These facts 
 may have been forgotten : but a record remains. According to 
 the indication of this record we draw our conclusion : which is, 
 
 ^ Op. cit. p. 220. 
 
 ^ Logic, p. 324. Again, ' You never can say " B follows from A ", " is 
 because of A," " must be, given A," unless A is present in a determinate 
 form. A must be a content without any mixture of sensuous conditioris. 
 It must be ideal, abstract, and so universal. The " because " cannot couple 
 anything but universals ' (p. 220). ' To reason directly from particulars 
 to particulars is wholly impossible ' (p. 322). But Bradley dispenses with 
 the syllogistic bridge. 
 
MinoY Unnecessary if the Major is 487 
 
 to all intents and purposes, a conclusion from the forgotten 
 facts. For this it is necessary that we should read the record 
 correctly : and the rules of the syllogism are a set of precautions 
 to ensure our doing so. They are " a collateral security ".' ' 
 
 § 1003. So that if a schoolboy reads a notice that Trespassers 
 will be prosecuted, and finds himself on the forbidden side of 
 the hedge, the conclusion which he draws, that should the 
 constable or owner appear he will be prosecuted, is not an 
 inference from these considerations but is an inference from 
 the various facts which led to the notice being put up. Or, if 
 he sees a board with 'Dangerous' on it and comes to the 
 conclusion that ht had better not bathe there, this conclusion, 
 according to Mill, is really drawn from the cases of drowning 
 which had taken place at that spot — though he may never have 
 heard of them. It is true that these accidents effectuated the 
 putting up of the board. The Conservancy had them in its 
 mind when it placed it there, and the boy knows vaguely that 
 the Conservancy had . something in its mind. But to say that 
 the boy's conclusion has those fatalities for its premisses is to 
 confuse material conditions with formal. It does n(jt escape 
 Mill that generalization may take the form of a command. 
 
 ' So far as this asserts a fact, namely a volition of the legis- 
 lator, that fact is an individual fact, and the proposition, therefore, 
 is not a general proposition. But the description therein con- 
 tained of the conduct which it is the will of the legislator that 
 his subjects should observe is general . . . The only point to be 
 determined is whether the authority which declared the general 
 proposition intended to include this case in it.' 
 
 We are to ascertain whether the case possesses the marks 
 common to those cases which the legislator certainly had in 
 mind. 'The operation is not a process of inference but a 
 process of interpretation.' Now this is the minor premiss 
 reinstated under the grander name of ' hermeneutics '. I am 
 to take no notice of ' Wait till the train stops ' or ' Beware of 
 the dog' till I am satisfied, not that the warning is a general 
 one, addressed to me as well as others, but that my circum- 
 stances resemble those of various people who have sprained , 
 an ankle or been bitten. But then, being thus satisfied of the 
 resemblance, am I not now a law and a major premiss to myself? 
 
 ^ Op. cit. p. 221. 
 
488 Attacks on the Syllogism 
 
 Resemblance may be material or immaterial. If the former, 
 the recognition of it is eo ipso a general truth. ' Whenever,' 
 writes Mill, 'we can legitimately draw any inference we may 
 legitimately make our inference a general one.' ' The advantage 
 of referring to a parallel case is universally acknowledged.' But 
 real parallelism, being abstracted from the merely contingent 
 features of the two or more cases, itself constitutes a law, a 
 reason, a universal. The consciousness of the parallelism is in- 
 dispensable to any inference. But Mill declares on the contrary 
 that 'the major is no real part of the argument, but an inter- 
 mediate halting-place for the mind, interposed by an artifice 
 of language between the real premises and the conclusion by 
 way of a security '} The ' general proposition is a security for 
 good reasoning, not a condition of all reasoning, and in some 
 cases not even a security '.'' 
 
 § 1004. For our most familiar inferences, he urges, 'are all 
 made before we learn the use of general propositions, and 
 a person of untutored sagacity will skilfully apply his acquired 
 experience to adjacent cases, though he would bungle grievously 
 in fixing, the limits of the appropriate general theorem.' The 
 savage executes unerringly the exact throw which brings down 
 his game. The experienced dyer mixes the ingredients by 
 3 kind of acquired insight, but cannot explain how he does it. 
 The village dame physics a neighbour's child with the camomile 
 which did her Lucy good when her symptonis were the same, 
 Nay, 'we all, where we have no definite maxims to steer by, 
 guide ourselves in the same way.' Even responsible admini- 
 strators have thought it true wisdom to give their decisions 
 boldly without assigning reasons, for, as Lord Mansfield said, 
 the former might be right, but the latter would probably be 
 wrong. 
 
 § 1005. Such a plea for empiricism, based on the limitation of 
 human faculties, assumes that the major premiss in reasoning 
 must be consciously and verbally before the mind if it is in the 
 mind at all. The savage who hurls the boomerang so adroitly 
 ' owes this power to a long series of previous experiments, the 
 results of which he certainly never framed into any verbal 
 |;heorems or rules'. The dyer 'had from the individual cases 
 pf his own experience, established a connexion in his mind 
 ' Op. cit. p. 230. '^ Ibid. p. 236. 
 
Empirical Inductions 489 
 
 between fine effects of colours and tactual perceptions in 
 handling his dyeing materials ', but he ' could not put others 
 in possession of the grounds on which he proceeded from 
 having never generalized them in his own mind, or expressed 
 them in language'. 'Among the higher order of practical 
 intellects there have been many of whom it was remarked 
 how admirably they suited their means to their ends, without 
 being able to give any sufficient reasons for what they did ; and 
 applied, or seemed to apply, recondite principles which they 
 were wholly unable to state.' The old warrior's experience has 
 ' left a number of vivid, unexpressed, ungeneralized analogies 
 in his mind, the most appropriate of which, instantly suggesting 
 itself, determines him to a judicious arrangement". Aubrey 
 cites a saying of Hobbes that he would 'rather use an old 
 tender [attendant] that had many yeares been at sick people's 
 bedsides then the learnedst young unpractised physitian '. 
 
 § 1006. Now this is a question to some extent, no doubt, for 
 the psychologist. He will explain how the human mind can 
 work and arrive at conclusions without being explicitly aware 
 of the grounds and rationale of the conclusions arrived at. By 
 what subtle touches does Experience impress her lessons on 
 the unreflective consciousness ? The boomerang thrower knows 
 nothing about parabolas, nor yet about his own muscles. The 
 delicate touch of the billiard champion is independent, possibly, 
 of any acquaintance with the laws of geometry and of elasticity. 
 And yet, after all, the throw, or the stroke, is governed by 
 universal laws, and it is in obedience, conscious or unconscious, 
 to those laws that the deer is felled or the red ball pocketed. 
 Such examples raise the question of bodily habituation as 
 entering into our knowledge, and large controversies suggest 
 themselves about mental latency, subconscious intelligence, and 
 the subliminal self. But at any rate, however the sleep-walker 
 or the dye-mixer manages to conform his actions to laws, he 
 does conform them. A simple case is that of the admini- 
 strator without legal training, or the chieftain who has never 
 heard of a drill-book arranging his troops after a glance at 
 the ground. The sensible decisions of the one and the shrewd 
 dispositions of the other are the outcome, Mill says, of past 
 experience, not of theoretical maxims. Nevertheless, if they 
 are right they must be right for some reason. T'he result is 
 
490 Attacks on the Syllogism 
 
 in accordance with universal justice or wisdom. The fact that 
 governor and commander arrived at the result which omniscience 
 would have dictated must either have been a mere chance or, 
 if not, proves them to have really apprehended the general 
 truth, however unable they might be to realizfe consciously the 
 principles on which they acted or to put them into words. 
 Perception of the universal in the immediate and individual 
 presentation may be quick and vivid, where nevertheless the 
 reflective ability is confused and slow.' 
 
 § 1007. But the psychological question does not go to the root 
 of the present matter. Suppose that we really could leap imme- 
 diately from particulars to a new particular without any appre- 
 hension of a ground or reason. Suppose by some pre-established 
 harmony our minds were so constituted that one particular 
 truth followed another in them without any, even unconsciously, 
 perceived principle of connexion — for the perception of a prin- 
 ciple is a generalization—, so that, knowing ^ to be .X" and 
 B to be X, we somehow came to know C to be X. Our minds 
 might be transported from truth to truth as the legend afBrms 
 that the angel transported Habakkuk by the hair of his head. 
 The logician, however, will say. All this is nothing to me. I do 
 not wish to know how you came by this conclusion as a pro- 
 position, but how you came by it as a conclusion. With its 
 psychological history, by what cerebral process you reached 
 it, or how you had it revealed to you, I am not concerned. 
 All I ask is on what ground do you now affirm it to be true. How 
 do you justify it rationally? What is your reason for affirming 
 it? But a ground, a rational justification, a logical reason, is 
 necessarily a universal. I cannot argue anything without an 
 argumentum. Even if the reasoner cannot produce his reason, 
 he knows at bottom that it is there. In that expression ' adjacent 
 cases ' lies the whole question. Is the wagging of pussy's tail 
 
 ' That a conclusion about an individual object is essentially general is 
 pointed out by Mill himself when describing the inductive chain of 
 reasoning by which the Moon's distance is ascertained. Not only might 
 a general proposition have been concluded instead of a single fact, but ' in 
 strictness the result of the reasoning is a general proposition ; a theorem 
 respecting the distance, not of the moon in particular, but of any in- 
 accessible object ' {Logic, i. p. 331). In the same way the village wife 
 knows not merely that her Lucy got well after taking camomile, but that the 
 camomile cured her, and perception of cause is perceptioi;i-of a universal. 
 
Case of Infants and of Brutes ' 491 
 
 adjacent to the wagging of Carlo's ? The child who, being 
 apprised of the birth of two baby brothers, asked. Which shall 
 you drown ? supposed that the nativity of boys was adjacent 
 to that of kittens. I knew an analogically minded child who, 
 on emerging from his bath and not being at once dried, was 
 apprehensive of rusting, and many have heard of the schoolboy 
 who, being told that heat expands bodies and cold contracts 
 them, suggested that that might be the explanation of summer 
 days being long and winter days short. ' Parallel cases ', which 
 do not run on all fours but are merely adjacent, are dangerous 
 things. Is the particular case a type, a sample? Inference 
 ascertains the sameness of samenesses ; but are they the same ? 
 Old birds are not caught by chaff, though in Spain and in the 
 Campagna birds are still snared by a fowler carrying a lantern, 
 a cattle-bell, and a small net. The sleepy fowl thinks the steps 
 are those of a wandering cow. 
 
 § 1008. The case of brutes and of babies is naturally relied on 
 by Mill. Both the burnt child fears the fire and also the burnt 
 dog.^ How can an infant generalize? Yet it undoubtedly 
 infers from fact to fact. ' In the same way also brutes reason. 
 There is no ground for attributing to any of the lower animals the 
 use of signs, of such a nature as to render general propositions 
 possible. But those animals profit by experience.' 
 
 § 1009. Bain observes : — 
 
 ' The knowledge that guides the lower animals is unconnected 
 with language. They observe by their senses the things about 
 them and the observations are remembered in sensible forms. 
 The bush that gives shelter, the herbage for food, the animals 
 to be preyed upon, are known and sought after by the sole 
 guidance of sense impressions. 
 
 ' Human beings have numerous experiences of the same kind, 
 involving the order of nature, without being connected with 
 words. The child has a large stock of sense knowledge before 
 it can understand and employ language. The skill of the artisan 
 consists, for the largest part, in associations between sensible 
 appearances and movements ; to the stone-polisher the sight of 
 the surface at once suggests the next blow. 
 
 ' Even in a highly intellectual profession, as the practice of 
 physic, the consummation of skill requires a large sense know- 
 ledge, passing beyond the scope of language. The physician 
 learns from books everything that can be expressed in words ; 
 
 ' Logic, i. 215. 
 
492 Attacks on the Syllogism 
 
 but there are delicate shades of diagnosis that no language can 
 convey, stored up, without verbal expression, in the eye, the 
 ear, and the touch. Such knowledge, however sufficient for the 
 individual, can be only to a very limited degree, and with 
 difficulty, communicated to others. A sense impression, strictly 
 speaking, cannot be directly communicated at all.' ^ 
 
 § loio. The person who has tact, good taste, delicacy of per- 
 ception, natural good manners, could seldom draw up rules for 
 others. 
 
 I might add something which J. P. Richter says, viz. that he 
 had never climbed a steep and difficult staircase of argument 
 without finding a woman at the top of it, who could by no means 
 tell him how she had got there. 
 
 § loii. Certainly more wonderful things are done by unreflec- 
 tive instinct, or rapid insight, a kind of aXoyos ato-^iyo-is, than by 
 ranged and ordered reasoning. No one has ever satisfactorily 
 explained the marvellous homing sagacity of the pigeon or dog, 
 or the unerring sense of direction of the New Zealand bushman," 
 any more than the daring salto mortale, the imaginative leap, of 
 a Kepler or Galileo admits of explanation, or (even to himself) 
 the feats of the calculating boy. Cloten, again, who ' cannot 
 take two from twenty and leave eighteen ', has a cunning whose 
 operation it would be difficult to put into syllogisms. Many 
 intelligences of a low order have a kind of slipshod intuition of 
 
 ' Logic, Pt. I, p. 42. 
 
 ^ The Times correspondent, Mr. Stillman, described in that journal, 
 some years back, his being lost in the forest of the Adirondacks. ' The 
 agitation which supervened in an instant was httle short of insanity.' 
 But instead of racking his brain to recover signs and indications, he says, 
 ' I sat down, covered my eyes, and had still sufficient command of my 
 nerves to wait for will to regain the power over reason ; and when 
 I opened my eyes I had my compass again directly.' (See an article in the 
 Spectator of Sept. 25, 1897, on the Sense of Direction.) Such a power is 
 probably a kind of hyperaesthesia, an extreme sensibility to deviation 
 from a determined line. Most people, after walking or driving through 
 tortuous streets, know which are the cardinal points. It is recorded of 
 Kaspar Hauser that he could not judge distances and saw everything flat. 
 Yet he could distinguish the leaves of trees by their smell. He could not 
 be persuaded that a ball did not roll because it wished to do so, or that 
 his top did not spin of its own accord. He saw no reason why brutes 
 should not behave exactly like human beings, and was seriously annoyed 
 because the cat refused to sit up at table and eat with its paws. As he 
 learned to think like ordinary people the extraordinary acuteness of his 
 senses began to pass away. 
 
The Difficulty Psychological, not Logical 493 
 
 relations and analogies. Lord Melbourne said of a certain 
 measure of reform that all the clever men were for it, and all 
 the fools against it ; and the fools were right ! Hartmann uses 
 the phrase 'unconscious reason'. Hamilton, on the other hand, 
 considers that, unlike digestion, respiration, or circulation of the 
 blood, ' Reason is ipso facto conscious.' 
 
 § 1012. I must repeat, however, that the difficulty is purely 
 a psychological one, with which Logic has nothing to do. It may 
 or may not be true that, as Leibnitz insists, man alone has the 
 power of ratiocinating, and that even man seldom consciously 
 arranges his ideas in regular syllogistic form. But what the 
 logician says is that reasoning or inference can only be rationally 
 exhibited in that form. A baby abstracts a quality. It dimly 
 apprehends it as a cause of some effect — perhaps mistakenly ; 
 but anyhow the perception of causality is a major premiss, and 
 all the elements of mediate reasoning are present. It fears the 
 cat's claws and cries for sweetstufF, reasoning without words, 
 and yet reasoning. But call such mental process, if you will, only 
 association of ideas — though this explains nothing. Be it so that 
 the human infant has not a more direct perception of cause than 
 the bee or the elephant — and at what point the linked association 
 of similars becomes something higher, something more than 
 ' little bells of change ' lightly stirred from one to another, need 
 not be discussed. If men reasoned but as sensitive plants 
 . reason, or even as the veined marble, the dews and frosts, the 
 changing moon or wheeling planet, the omnia opera Domini, are 
 guided from moment to moment by the immanent plan of their 
 being^ — still whatever anything does, be it glacier or fly-catch- 
 ing plant, or pointer,^ or nursery philosopher, or statesman, or 
 
 ' A tree 
 
 That buds and blooms, nor seeks to know 
 The law by which it prospers so. 
 
 ^ The Master of Downing (Dr. Alexander Hill) remarks that ' Dogs can 
 think, for thought is the comparison of present with past sensations, but 
 it is the prerogative of man's reason to argue not from things but from 
 inferences ' (Lecture at the London Institution, Nov. i6, 1903). In a brute's 
 comparison, however, there is no synthesis under a notion. The action 
 of the faculties is reflex only, not intellectual. The sensory impressions 
 are automatically and involuntarily linked together ; whereas thought 
 contains an element of will and attention. The horse which you buy and 
 which you find stops at every public-house has acquired an instinctive 
 
494 Attacks on the Syllogism 
 
 angel, is done,- consciously or unconsciously, in accordance with 
 the law of cause and effect, and if one thing follow rationally 
 from another, if this thing lead rationally to that, the consequence 
 must be in accordance with some law, that is, with some major 
 premiss. 
 
 § 1013. Logic declines to ask how consciousness of, or power 
 to act in accordance with, the law is communicated by the 
 Creator to each of His creatures. That it is communicated is 
 merely to say that nothing happens by chance and without law. 
 The physiological conditions of mental action, again, do not 
 affect the form of Reason. If certain nerves connecting eye 
 with brain were destroyed, a hungry dog with food in front of 
 him would make no effort to obtain it, seeing but not associating 
 this with that. Human beings too may lose the power of sub-, 
 suming presentations under ideas. But none of these considera- 
 tions enters into the province of the logician, who merely says 
 that if a conclusion is drawn it is not a conclusion unless it is the 
 result of a mediated process. We may conceivably get from 
 one fact to another like it, but we can only conclude it by a 
 syllogism.^ The question is not, How do you think this ? but, 
 Why do you think it? Induction seeks the one in the many. 
 Deduction applies the one to the many. We cannot reason 
 from the many to the many except through the one.'' 
 
 habit, and we often remark how wonderfully dumb creatures remember. 
 But memory, in the sense of recollection, implies conceptual intelligence, 
 which brutes certainly do not possess. 
 
 ' ' A conclusion is never a mere perception. It is the result of a process ' 
 (Bradley, Lo^ic, p. 226). ' An inference is nothing but a necessary truth ' 
 (ibid. p. 221). But in Mill's view there is nothing which necessitates. 
 Hume's doctrine of Association ' dissolved knowledge into a chaos of 
 fleeting and unrelated sensations ' (Bosanquet). It was with him a dis- 
 connected manifold. It is difficult, no doubt, to follow abstract reasoning 
 without concrete illustrations. ' Take a case ', we say. But this is because 
 words often fail to convey any clear image to our minds. Only by taking 
 a case' do we perceive the universal in the particular. Spencer, indeed, 
 will not allow that a quality is the same in two objects. It is only like. 
 There is no one in many. What, however, is likeness but the apprehension 
 of one and the same attribute in two or more things ? 
 
 '^ Jevons quotes Sir Walter Raleigh on the dog. ' This creature (saith 
 Chrysippus) is not void of logick. For when, in following any beast, he 
 Cometh to three several ways, he smelleth to the one and then to the 
 second ; and if he find that the beast which he pursueth be not fled one 
 of these two ways, he presently, without smelling any further to it, taketh 
 
Rapidity of Thought 495 
 
 § 1014. It is a commonplace of philosophy that our perceptions 
 only become judgements as inferences. The delicate adjustment 
 of the eye notices the slightest deviation from the perpendicular 
 of a vertical line. But the conscious judgement is mediate, not 
 immediate. If I say, ' This is germander,' it is because I know 
 that the flower of that name is of that shape and hue. A prest- 
 issimo on the pianoforte is performed by a succession of in- 
 ferences. The mind seizes, and works with incredible ra{)idity, 
 on the data which fly by it, and can give very little account of 
 the process at the time or afterwards. In billiards the player 
 thinks sub-mentally, ' This is (approximately) the sort of stroke 
 which effects such or such a result,' though scarcely any colloca- 
 tions of the balls are exactly alike. There could be no illusions 
 of the senses^' cheating the eye with blear illusion ' — apart 
 from inference. The expression would be meaningless unless 
 it implied interpretation. On the other hand, therfe is more 
 intuition, and less syllogizing, in ' Yonder soldier has fallen ', 
 than in ' Yonder soldier is shot '. Inference may occasionally 
 go deliberately counter to the deliverances of sense ; as if I see, 
 or think I see, a pea placed under a thimble I at once infer that 
 it is elsewhere, on the general principle that in the case of 
 a thimble-rigger things are not what they seem. 
 
 § 1015. Is there any major premiss in substitutional inference, 
 the identification or equation of individuals or of aggregates ? 
 Such identification or equation must be looked upon as really 
 a subsumption. We can make a present of the name 'major 
 premiss ' to those who carp at it. All that we have been con- 
 tending is that 5 could not be judged to equal P (as a matter 
 
 the third way. Which, saith the same Philosopher, is as if he reasoned 
 thus : — the Beast must be gone either this, or this, or the other way, but 
 neither this nor this: ergo the third. So away he runneth.' Lord 
 Avebury, on the other hand, considers that brtites are only first-class 
 automata. We refuse to decide. For our purpose it skilleth not. 
 
 In Milton the ' winged hierarch ' Raphael, in conference with Adam, 
 says of the Soul : — 
 
 Reason is her being, 
 Discursive or Intuitive. Discourse 
 Is oftest yours, the latter most is ours. 
 Differing but in degree, of kind the same. 
 
 (P. Z. V. 487-90.) 
 But neither do the mental faculties of angel and archangel concern us as 
 logicians. 
 
496 Attacks on the Syllogism 
 
 not of measurement but of inference) without the mediation 
 of M, which can only mediate if it is (at least once) taken 
 universally. 
 
 § 1016. No doubt numberless examples might be adduced of 
 inferences in which no major premiss, or mediation, is at first 
 visible. For example, being told that there are five balls in four 
 boxes, I infer that one box at least contains at least two balls. 
 Where is the middle term ? In spite of the impatience of those 
 who say that the conclusion is reached by means of ' the syn- 
 thetic activity of thought ' — which is merely an appeal from form 
 to matter — a deeper analysis of what passes in the mind is 
 necessary.^ It is through the material knowledge that five is one 
 more than four, and that balls and boxes are discrete substances 
 (so that a ball could not be partly in one box and partly in 
 another, that the inference is reached. Our syllogism, then, is 
 something like this : — 
 
 When a number of objects are contained in separate recep- 
 tacles, fewer in number than the objects, one at least of the 
 receptacles must contain a plurality of the objects. 
 
 The case of five balls being contained in four boxes is a case 
 of [the middle term]. 
 
 Then it is a case of one at least of the receptacles containing 
 a plurality of balls. 
 
 No doubt, both major and minor premiss admit of explanation 
 by simpler and higher concepts. But the seeming cumbrousness 
 of a process is no presumption against its being a true analysis. 
 Thought is immensely active and employed on the most various 
 materials. It flashes from point to point, seldom conscious of 
 the road it has travelled. It is not strange, then, that to exhibit 
 the rational form underlying a complex thought is often a little 
 difficult. It is unworthy of philosophers to insist on short cuts 
 to truth. The major premiss, says Sigwart, is the statement not^ 
 
 ^ Here are a few reasonings which need analysing : — ' To-day is June 1 7. 
 I need not light the carriage lamps till after nine o'clock.' — ' We just won 
 the last rubber. You owe me sixpence.' — ' Quod tacitum velis nemini 
 dixeris. Why did you speak of your plans before Mr. Pry ? ' — ' Make hay 
 while the sun shines. I will take another.' — ' It never rains but it pours. 
 I had three offers of employment by to-day's post.' Or take the following 
 argument :— ' Christmas Day falls on a Tuesday this time. Then there 
 will be five Sundays in December this year, and also next. No, I forgot 
 that that is a leap year.' 
 
Arithmetical Inferences 497 
 
 of a numerical generality, but of the necessity of connecting the 
 predicate with the subject. Only by proving necessity can the 
 particular data be proof of any particular case.' 
 
 There remain reasonings of the type, ' | of M are P, | of M 
 are 5; therefore Some S's are P.' It is plain that the inference 
 is only possible on the supposition that the relations of the frac- 
 tions f and f to one another and to the whole of which they are 
 parts are a datum. We require to premise that f and § are 
 both greater than f, and further that two fractions of a whole 
 which are both more than the half of it must necessarily overlap. 
 Then, equationally, the portion of P which equals f of M must 
 overlap the portion of S which equals § of M. The young 
 student must beware of thinking that if most of M = ^ P, and 
 most of il/ = f 5, f P = f S; or that, if half of Af = all P and 
 half oiM = all S, any S is necessarily P. 
 
 ^ Logic, i. 361. 
 
 Kk 
 
CHAPTER XXX 
 
 IS SYLLOGISM A PETITIO PRINCIPIIl 
 
 § 1017. Something more must be said about the widely 
 repeated charge against the syllogism oi petitio principii. I have 
 quoted the emphatic assertions of Mill, Bradley, and Bosanquet 
 to that effect. Logicians, remarks the first-named writer, 
 'though unable to dispute it, have usually exhibited a strong 
 disposition to explain it away ; not because they could discover 
 any flaw in the argument itself, but because the contrary opinion 
 seemed to rest on arguments equally indisputable.' The objec- 
 tion is as old as Sextus Empiricus, who argued that the major 
 premiss can only be established by induction, and induction 
 supposes the examination of each individual case. Even authors 
 not of the Empirical school have lent some countenance to this 
 superficial criticism. Hamilton himself, though (following 
 Petrus Hispanus) he observes that it is thoroughly disposed of 
 by the analytical order of the syllogism — when we start from 
 the conclusion, and search for evidence in support of it — has 
 a passage in his Nineteenth Lecture^ about universals which, 
 Grote remarks, ' one might almost imagine to have been written 
 by Mr. Mill.' His expression, 'We can only take out of 
 a general notion what we had previously placed therein,' merely 
 means that definition and deduction cannot lead us to new truths. 
 But it resembles the travesty of the syllogistic process as ' the 
 operation of placing objects in a class and then finding them 
 there '? The question is whether the conclusion is inserted in 
 the major premiss by the minor premiss or (as Mill holds) by 
 the previous induction. Mr. Grundy too remarks : ' It may be 
 conceded that the major premiss virtually contains the con- 
 clusion.' ^ 
 
 § 1018. The proposal to skip the major premiss involves, as 
 
 ^ On Logic, i. p. 380. ' See Mill On Hamilton, p. 504. 
 
 ° Aristotelianism, by Smith and Grundy, p. 120. 
 
Premisses and Conclusion Superfluous 499 
 
 I have pointed out, the abolition of the minor premiss ; for in 
 Mill's view of inference the rule or major premiss needs no 
 explicit application. But why not at the same time abolish the con- 
 clusion also ? If it is already asserted in the major premiss, and 
 is involved in the instances out of which that is built, it is a waste 
 of breath to assert it again. In fact the New Syllogism need have 
 neither major, minor nor conclusion, all that is left being the 
 preliminary inductive scaffolding. And this also, according to 
 Sir William Hamilton, is a ' glaring petitio principii'} It only 
 survives, at most, as a reading-off of shorthand into longhand. 
 But, as Devey asks, ' What help can mood and figure, with the 
 heavy accompaniment of a group of rules and canons which 
 exclusively relate to pure inference, lend to the interpretation of 
 general propositions formed from the results of one's individual 
 experience ? . . . The only things which can be of any service 
 in the interpretation of general propositions are a clear percep- 
 tion combined with a capacious memory; and Dugald Stewart 
 was consequently more consistent when, entertaining the 
 same principles as Mr. Mill, he rejected the syllogistic theory 
 altogether, and resolved all reasoning into intuition and remem- 
 brance.' "^ 
 
 § 1019. That every conclusion from premisses is taken out of 
 the premisses, and is a combination of the two premisses, needs 
 no saying. The act of combining is what we mean by syllogizing 
 (truAAoyt^eor^at). To object to such a mode of proving the conclu- 
 sion that it is a petitio principii would be ridiculous. On that 
 showing all proof is a begging the question, since nothing can 
 be proved except by allegations which together contain it, that 
 is by evidence. An opponent may say, 'I deny both your 
 premisses,' but he cannot say, ' You ought not to ask assent to 
 them, since together they prove your point.' It is just in the 
 together that proof lies (see above, § 997). On the other hand, 
 an opponent may justly object to either premiss separately that 
 it is merely the desired conclusion in another form of words. 
 The charge oi petitio quaesiti, then, can only be advanced against 
 one proposition at a time. In any case it is not a formal, but 
 only a material, fallacy. 
 
 § 1020. Does, then, the major premiss contain the conclusion 
 in such a sense that without the addition of any further material 
 
 ^ Lectures on Logic, ii. 174. ^ Logic, pp. 158, 159. 
 
 K k 2 
 
500 Is Syllogism a Petitio Principii? 
 
 knowledge the latter is seen to be involved in it and can be at 
 once affirmed? If I say, 'AH Members of Parliament have 
 certain privileges,' do I thereby assert that Mr. Wilkins has those 
 
 privileges, or the Earl of ? Surely every one must agree 
 
 that we have first to determine whether Mr. Wilkins has a seat 
 
 in Parliament, and whether the Earl of is a peer of the 
 
 United Kingdom. The conclusion about either having privi- 
 lege of Parliament cannot be formally drawn until the fact ot 
 his being a Member has been asserted in a minor premiss. The 
 hackneyed illustration, ' All men are mortal, therefore Socrates 
 is mortal,' is one to be avoided, because no assertion of Socrates 
 being a man seems needed. (It may be said, perhaps, that from 
 'All Members of Parliament have privileges' we might go 
 straight to the conclusion, 'Then Mr. Wilkins, M.P., has them.' 
 But the parenthetic ' M.P.' here — i. e. 'because he is an M.P.' — 
 is the minor premiss.) On the other hand, I have purposely 
 taken an illustration expressed in extension so as to make no con- 
 cession to the idea that it makes the slightest logical difference 
 whether an abstract universal is expressed in extension or in 
 intension — whether, that is, we say ' All Members of Parliament 
 have', &c., or 'Membership of Parliament involves having'. 
 The former, logically if not grammatically, is just as general 
 a proposition as the latter. 'AH men are mortal' is as 
 abstract as ' The attribute of humanity is accompanied always 
 by the attribute of mortality '. The importance attached by 
 Hamilton and his followers to the distinction was not properly 
 thought out. Imogen, in Cymbeline, says : ' Hardness ever of 
 hardiness is mother ' ; which is as much as to say, ' Those bred 
 in hardship come to be hardy.' 'Men of noble birth should 
 have high ideals ' is equivalent to ' Noblesse oblige '. 
 
 §1021. Mill observes: — 'When you admitted the major 
 premiss you asserted the conclusion. But, says Archbishop 
 Whately, you asserted it by implication merely. This, however, 
 can only mean that you asserted it unconsciously ; that you did 
 not know you were asserting it. But, if so, the difficulty revives 
 in this shape — Ought you not to have known? Were you 
 warranted in asserting the general proposition without having 
 satisfied yourself of the truth of everything which it fairly 
 includes ? ... It is hardly necessary to say that I am not con- 
 tending for any such absurdity as that we actually " ought to have 
 
Rule and Application 501 
 
 known " and considered the case of every individual nian, past, 
 present, and future, before affirming that all men are mortal. . . . 
 I do not say that a person who affirmed, before the Duke of 
 Wellington was born, that all men are mortal, knew that the 
 Duke of Wellington was mortal. But I do say he asserted it.' 
 
 § 1022. It was not asserted implicitly. But 'it is impossible,' 
 says Mill, ' to attach any serious scientific value to such a mere 
 salvo.'' Then it must have been asserted explicitly. How 
 paradoxical such a contention is, is seen directly we leave 
 Socrates and the Iron Duke, and take other illustrations. 
 ' Blessed are the peacemakers. John is blessed.* ' Wednesday 
 is market-day. To-day is market-day.' ' Who drives fat oxen 
 should himself be fat. James should be fat.' ' First come first 
 served. Serve me first.' ' Isosceles triangles have the angle at 
 the base equal. This triangle has the base angles equal.' 
 'A husband should be loved above a brother. Philip should be 
 loved above William.' ' Honesty is the best policy. You are 
 following the best policy.' ' Obsta principiis. I must make 
 a stand now.' 'The slowest horses are to be left behind. 
 Jenny is to be left behind.' 
 
 § 1023. In what conceivable sense these conclusions can be 
 regarded as having been explicitly asserted in the general propo- 
 sitions to which they are annexed I am unable to discover. Is 
 it not obvious that a link is missing ? How do we know formally 
 that John is a peacemaker, that to-day is Wednesday, that James 
 drives fat oxen, that this triangle is isosceles, that Philip is the 
 husband and William the brother, and not the other way, or 
 ascertain without being told any of the other minor premisses 
 which are omitted above? 'Ought you not to have known? 
 Were you warranted in asserting the general proposition without 
 having satisfied yourself of the truth of everything which it 
 fairly includes?' For example, I suppose we must not say 
 ' Whoever gets most marks will win the prize ' until we know 
 for certain that Dobbin will win the prize. Dobbin, of course, as 
 getting most marks. But to add that is to add the minor premiss, 
 which is not wanted if the conclusion has been asserted in the 
 major premiss. 
 § 1024. It cannot be supposed that Mill regarded general 
 
 ' Logic, p. 211. 
 
502 Is Syllogism a Petitio Principii? 
 
 truths as obtained through a 'perfect induction' by simple 
 enumeration without any contradictory instance, for no writer 
 has done more to put the enumerative induction in its proper, 
 and very humble, place. Nor can he merely mean that before 
 making a general assertion we ought to satisfy ourselves that it 
 is not liable to be upset by a contradictory instance, as yet unsus- 
 pected. As soon as we are satisfied of the connexion of cause 
 and effect we proceed to a general statement, and thereafter 
 apply it to any new case which fulfils the conditions. If there 
 was an error in the induction the conclusion may be wrong. 
 But that is very different from the doctrine that the conclusion 
 was actually (not implicitly) asserted in the assertion of the 
 general truth. Abstract is not concrete. We may be sure ot 
 a truth, yet hesitate long as to its application. It is right, as in 
 John Byrom's lines, to wish a blessing on the King and also 
 on the Pretender — but which is King and which Pretender ? ' 
 Shakespeare's burghers of Anglers were similarly perplexed 
 for a minor term. 
 
 § 1025. The Gordian knot waits to be untied till the right 
 person comes. ' Heus ! mensas consumimus' fulfils an old and 
 dark prediction. ' To-day is this Scripture fulfilled in your ears.' 
 Of course futurity makes no difference. A truth is not more 
 general for being about the future. Only in that case the notion 
 that generalizations are summaries of empirical facts is the 
 more paradoxical. ' Whatever thou askest I will give it thee.' 
 If ' the class is nothing but the objects contained in it ', as Mill 
 says, there would be no room for deductive science, and 
 Leverrier would never have conjectured the existence of Nep- 
 tune. If the syllogism is a petitio principii, what room is there 
 for Faith, which is a combination of reliance and venture, cling- 
 ing through good report and ill report to its deductions ? Before 
 I say, ' omne ignotum pro magnifico ', must I first know every- 
 thing that is ignotum ? Or does ' quodcunque evenerit optimum ' 
 imply that I already know everything that has happened or will 
 happen ? Mill's ' You ought to have known ' is certainly very 
 incomprehensible. 
 
 ' God bless the King, God bless the Faith's defender ; 
 
 God bless — no harm in blessing — the Pretender. 
 But which Pretender is and which the King, 
 God bless us all, that's quite another thing. 
 
Simple Enumeration 503 
 
 § 1026. Sigwart well says : — 
 
 ' Thait any idea may be general, i. e. applicable to any number 
 of particular ideas, is involved in its nature as reproducible, and 
 no way depends upon its having been formed from a number of 
 such particular ideas. As soon as it has disengaged itself from 
 the original intuition with its spatial and temporal connexions, 
 and is a mental image which can be freely reproduced, it is 
 capable also of fusing with a number of fresh intuitions or ideas, 
 and of appearing as their Predicate in a judgement.' ' 
 
 § 1027. If any Syllogisms, then, involve a petitio they cannot 
 be those which have a general statement for major premiss, truths 
 which would be true if every individual example were annihi- 
 lated, but only those whose universal major is an inductio com- 
 pleta per enumerationem simpKcem. Such a ' perfect induction ' 
 is not a logical inference but a mere summary, or aggregate, of 
 observations. Every case has been examined. ' Cantico nun- 
 quam utuntur scriptores Novi Testamenti,' says Ewald. King 
 Richard II exclaims — 
 
 Christ in twelve found truth in all but one ; 
 I in twelve thousand none. 
 
 ' Brother, brother, we are both in the wrong.' ' All, all are gone, 
 the old familiar faces.' ' There is not a single misprint in this 
 book.' 'Ilka lassie has hgr laddie.' 'There are no men to 
 conquer in this wood.' ' Every one of my pieces (at chess) has 
 been taken, except the bishops.' 'Never was there Claudius 
 yet but wished the commons ill ' — though for each of these con- 
 crete statements a cause might be suggested. Sir Robert 
 Walpole did not say, ' Every man has his price,' but, ' All these 
 men (his critics) have their price.' The former judgement was 
 regarded by Ruskin as the Free-trade formula. 
 
 § 1028. The charge, however, of petitio principii cannot be 
 brought home even to those syllogisms whose major premiss 
 has been reached by examining each several case. For who 
 has examined the several cases ? Not necessarily the reasoner. 
 To him the major premiss may be a datum supplied from outside 
 his own experience. It is given out, 'All who entered their 
 names have passed.' I entered mine. Then I have passed. 
 This is in my mind a genuine process of illation. I see it stated 
 in the newspaper that all the. members of the Cabinet are 
 
 1 Logic, i. 46. 
 
504 Is Syllogism a Petitio Principii? 
 
 University men. Is Lord in the Cabinet ? (I refer to 
 
 Dod) Yes. Then he was at one of the Universities. All .the 
 men in this room are widowers. Indeed ! I did not know that 
 Mrs. N. was dead. All the present sovereigns of Europe are 
 men of character. Quaere, Is Montenegro in Europe or Central 
 Africa, and has it a sovereign ? 
 
 § 1029. Even when the major premiss has been supplied by 
 the reasoner himself, and he is summarizing facts for no 
 other mind than his own, still it is unlikely that the conclusion 
 has been explicitly stated in the major premiss. To decipher 
 one's own notes or interpret one's own memoranda is actually 
 to infer. If I say, ' Every day since we came home there has 
 been a visitor,' I cannot at once assert that there was a visitor on 
 September 20 without consulting my diary. Did we come home 
 on the i8th or the 21st ? ' They are all dancing so well. Oh, 
 
 there is Mr. , I did not recognize him at first.' ' I liked all 
 
 the masters I was under at school. I forget the name of the 
 German master.' A summary is not a mere compendious 
 enumeration. ' All my brothers are married ' is not merely 
 ' Brother Ned, brother Dick, and brother Henry are married ', 
 but there is the further implication that I have now no unmarried 
 brother. The major premiss might have been so expressed. 
 This is the point of the statement ; and suppose I had so many 
 brothers (or cousins) that I could not in a moment remember 
 their names, even though I had passed through all the list 
 before making the statement, the recollecting of any name would 
 constitute a true logical subsumption. The minor term indeed 
 might actually be mentioned in the major premiss, if it were 
 with a great number of others, and yet the speaker or writer 
 find it necessary to go back to make sure that it was mentioned. 
 The directing special attention to one item or name in a long 
 list is a kind of subsumption. In fact petitio principii is only 
 fallacious relatively to considerations outside the purview of the 
 logician, as such. It is nothing to him by what steps a premiss 
 has been reached. It should be observed that a statement such 
 as this, 'All my brothers, viz. Ned, Dick and Henry, are 
 married,' is really a complex of a major premiss and three 
 minors, enabling three conclusions to be drawn. ' All my 
 brothers are married. Ned is one of my brothers. Therefore 
 &c.' 
 
{Juestion Begged by the Minor 505 
 
 § 1030, There might be a petitio principii in what looks like 
 thq minor premiss, as follows: — 'Few of the crew can swim. 
 William is one of the few.' But in this illustration there is 
 really no minor premiss, for ' one of the few ' means ' one of the 
 few who can swim',' like 'Six have won prizes. You are one 
 of the six '. On the other hand, ' Our six best scholars have 
 won prizes. You are one of the six,' is a true subsumption, if 
 it means, not, You are one of the six who have won a prize, but 
 You are one of our six best scholars. 
 
 § 1031. If the comprehension of judgements be regarded 
 instead of their extension, it would be easy to transfer from the 
 major to the minor premiss the charge of begging the quaesitum. 
 It might be pleaded that we cannot predicate the middle term of 
 the minor unless we know all the characteristics of the latter,' 
 one of which will be the major term. ' Bad poets are insufferable. 
 Bavius is a bad poet ' — but can I, Mill might ask, say this with- 
 out first judging him to be insufferable ? Which is as much as 
 to ask. Can I say that a man has stolen my horse without first 
 judging that he is liable to get five years penal servitude ? 
 
 § 1032. More plausible than any of the objections to the 
 Syllogism hitherto advanced might be a criticism that 
 the middle term is in ordinary speech, more often than not, 
 mixed up grammatically with other elements of the proposition, 
 and yet requires no change of syntax in order that inference 
 shall take place easily and naturally. Thus, 'Little things 
 please little minds. His mind is a little mind. It follows that 
 little things please his mind.* 'A providence watches over 
 fools. He is a fool. Then a providence watches over him.' 
 * Corruptio optimi pessima. This is optimum. Then its corrup- 
 tion is pessima' ' Vae victis. Greece is vanquished. Woe, then, 
 
 ' So- 
 
 Shadows of three dead men 
 
 Walk'd in the walks with me, 
 
 Shadows of three dead men, and thou wast one of the three. 
 Either one of the dead, or one who walked with me. 
 
 ' See Lotze, Logik, and ed., p. 122, and Sigwart, Logic, i. 357-9- 
 We must not confuse the various properties which any nameable thing in 
 fact possesses with the analytical content of the name or concept ; and it 
 maybe said that we cannot but know the latter, for the concept \sour con- 
 cept, whereas the former we may or may not know. But a major premiss 
 is required for realization, as for information. See above, § 529. 
 
5o6 Is Syllogism a Petitio Principii? 
 
 to Greece.' 'In duhiis libertas. This matter is undecided. 
 Then there should be liberty in regard to it.' ' On est punt par 
 ok I'on a pe'che. Her fault was such and such. That, then, was 
 the means of her punishment.' 
 
 § 1033. This is especially the case with propositions which 
 have 'All things' or 'Nothing' for subject, or which are im- 
 personal, or in form imperative. As — ' conanti nihil difficile.' ' All 
 things come to him that waits.' ' To him that hath shall be given.' 
 ' A tout malade il faut un medicin.' ' De gustibus non est dis- 
 putandum.' ' Detur digniori.' ' Experto crede.' Though the 
 subsumption may after all attach itself to the weak grammatical 
 subject; e.g. 'To the pure all things are pure. This thing, 
 then, is pure to a pure person.' ' To him who tries no task 
 (nihil) is difficult. This is a task. Then to him who tries it 
 will not be difficult.' The minor premiss of 'obsta principiis' 
 may be either, 'Here is a beginning. What shall I do to it?' 
 Or, ' I am ready to make a stand. But where ? ' When the 
 grammatical subject is a singular term, it is not usually the true 
 middle. ' God loveth a cheerful giver.' ' Fortes fortuna juvat.' 
 The Americans have a saying, ' You cannot stop half-way down 
 a cataract.' ' England does not love coalitions.' And yet the 
 reasoning might be — ' The country we are speaking of is (re- 
 member) England. In such a country, then, a coalition is sure 
 to fail.' Or, with ' cultores Sui Deus protegit ' as major premiss, 
 the minor might be, not ' This is a worshipper of God ', but ' He 
 whom we are speaking of is God '. Sometimes the middle term 
 might be equally well found in the grammatical subject or object, 
 as, 'finitimus oratori poeta' [Cicero); 'omnia omnium sunt' 
 (Spinoza) ; ' proclivi lectioni praestat ardua.' ' Suum cuique ' 
 might have for minor and conclusion either, '^ is a person. 
 Then let him have his own.' Or ' This is mine. Then meum 
 mihi '. So ' trahit sua quemque voluptas '. Under — 
 
 Every object swells with state ; 
 All is pious, all is great, 
 
 in Handel's Solomon, we must subsume ' So and So is an object '. 
 But to ' No man is a hero to his valet-de-chambre ' it would be 
 unnatural to join, ' A tramp is a man ; therefore a tramp is not 
 a hero to his valet-de-chambre,' though the reasoning is unim- 
 peachable. We want, ' Here are a man (subaudi famous) and 
 his body-servant. The one is not a hero, then, to the other.' 
 
Inference by Substitution 507 
 
 § 1034. It may seem, then, that, instead of Barbara Celarent, 
 we could frame valid syllogisms by merely substituting the 
 minor term for the middle in the major premiss. 
 
 Fata regunt homines ; 
 
 Brutus est homo, 
 
 Ergo, fata regunt Brutum. 
 
 Of that which is good, even in evil things, God is the 
 author (Hooker). 
 
 War is an evil thing. 
 
 Then, Of that which is good in War God is the author. 
 
 § 1035. But what is the justification of such inference ? Is 
 there any rule which we apply ? A rule asserts that a subject 
 possesses such and such attributes, is followed by such and such 
 an effect, exists in such and such a state, or the like. Now the 
 thing predicated of men that they are ruled by destiny may 
 equally well be expressed grammatically by ' fata regunt 
 homines ' as by 'homines a fatis reguntur '. Logically, whether 
 the case be accusative or nominative, a certain subject is said to 
 be affected, or determined, in a particular way. And the same 
 with the other examples. We must get behind the grammar to 
 the logic. 
 
 Of course reasonings like the one just given are not really 
 in the Second Figure. Figure II would require, 'fata regunt 
 homines. Caesar regit homines' — from which nothing would 
 follow strictly. 
 
 § 1036. In such a phrase as ' votis venerabere seris ' the 
 true logical subject is not ' tu ' but ' vota ', ' seris ' being a 
 tertiary predicate. Compare 'inutile ferrum cingitur'. On the 
 other hand, every grammatical categorical sentence, having 
 subject and predicate, constitutes a logical judgement. Thus, 
 ' non haec in foedera veni ' means, ' foedera in quae veni non 
 erant haec' But, taking the sentence as it stands, 'ego' may be 
 regarded as logical as well as grammatical subject (understood), 
 and ' having come into this agreement ' as the logical predicate. 
 
 § 1037. Having vindicated the necessity of major premisses, 
 or universals, we go on to consider how they are obtained. 
 
 The Inductive problem may be stated in various ways (5 = 
 subject, P= predicate, M= middle term), as follows :— 
 
 '*.,. 
 
5o8 Is Syllogism a Petitio Principii? 
 
 1. I (5) have drunk tainted milk {M). What will be the 
 result ? Find a P which can be proved of M (ma. pr.). Then 
 deduce. 
 
 2. I (5) have drunk tainted milk (M). Will typhoid (P) result ? 
 Prove P of M (ma. pr.). Then deduce. 
 
 3. I (S) have typhoid (P). What is the cause {M) ? Find M, 
 and prove both premisses (P of M and M of S). 
 
 4. I (S) have typhoid {P). Is drinking tainted milk (M) the 
 cause ? Prove both premisses [P of M and M of S). 
 
 5. I (S) have typhoid [P). Is the tainted milk I drank {M) the 
 cause? Prove major premiss [P of M). 
 
 6. I (S) have typhoid [P). Drinking tainted milk (M) gives 
 it. Have I drunk any ? Prove minor premiss (M of S). 
 
 7. X, Y and Z (S, S', S") have typhoid (P). What is the 
 cause {M) ? Find M and prove it of X, Y and Z (a succession 
 of minors). 
 
 Deduction. — As many minor terms (S, S', S", S'", &c.) as can 
 be assumed under M, so many conclusions (5 is P, S' is P, &c.) 
 are there. If the major premiss yl/ is Pis a general and abstract 
 principle, the number is ideally unlimited. 
 
 Induction. — Conversely, the major premiss, M is P, is con- 
 stituted of those same propositions, 5 is P,S' is P, S" is P, &c., 
 these together making up M. 
 
 But to rise above enumeraiio simplex and prove a law or causal 
 connexion between M and P, it is not enough to show that 
 S, S', S", &c., being P, are each of them M, and together make 
 up M. We want, 'MS\sP;^q MS is not P- Then M is P.' 
 
CHAPTER XXXI 
 
 UNIVERSALS, HOW OBTAINED? 
 
 § 1038. Tpie Concrete Universal proposition — such as ' All 
 the lights are lit ' ; ' None of the passengers was killed ' ; 
 ' Every question on the paper is beyond my powers ' — was by 
 the original propounder arrived at by simple counting. How 
 is the Abstract Universal proposition reached — that which 
 formulates a law or general principle ? This alone merits the 
 name Universal, for universality and complete enumeration are 
 opposites. ' Every seat is occupied ' is just like ' Glasgow is 
 a large city ', or ' Cain killed Abel '. A general proposition, on 
 the other hand, is extensionally incomplete, unlimited. It implies 
 a pervading rule, applicable to an indefinite number of cases, 
 realized and unrealized. Wherever the cause appears the effect 
 will appear also. An abstract judgement generalizes ; it does 
 not confine itself to the facts it has observed. It is therefore — 
 assuming no counteracting cause — both predictive and retro- 
 dictive — e. g. an astronomical table will foretell eclipses for ages 
 to come and also tell the very moment at which eclipses have 
 occurred in long ages past. Yet a judgement ideally infinite in 
 its application may be, and often is, based upon a single ex- 
 perience. Ab uno disce omnes. The universal is recognized 
 in the particular. And . knowledge is only possible through 
 universals. We are for ever seeking some general law under 
 which to subsume the individual fact. 
 
 § 1039. By what process, then, is the statement of any general 
 principle or law attained ? Is it a formal or a material process ? 
 Given an extension from the known to the unknown, the business 
 of Logic is to justify it formally. What we have to ask is 
 whether the formal justification of this step, which is called 
 Induction, is different from the formal justification of any de- 
 ductive conclusion. Are Induction and Deduction two kinds of 
 reasoning ; or is it not rather out of the question that rational 
 law should be otherwise than one ? 
 
510 Universals, How Obtained? 
 
 § 1040. The One in the Many sought by this or that Induction 
 is not a formal but a material law, just as the conclusion of a 
 syllogism states, qua proposition, a material truth. Nevertheless 
 the connexion between the judgement arrived at and the ground 
 on which we arrive at it is necessarily rational and formal. And 
 Logic is exclusively concerned with what is formal. Were it to 
 concern itself with ' the objects about which thought is con- 
 versant ', its task would be boundless ; for why should it embrace 
 some knowledge and not all? It would be not the' science 
 underlying all sciences, but the universal science, the science of 
 the universe. Logic must deal with all matter or with none. 
 
 § 1041. As Mansel remarks, Logic cannot exhibit a law of 
 external nature. ' Material knowledge arises from the observa- 
 tion of differences : the essential feature of laws of thought 
 must be the abstraction from all differences.' ^ Mill does not, 
 of course, maintain that the logician, as such, investigates the 
 properties of things. But when he affirms that Logic is the art 
 of all Thinking, and that the end of Thinking is the attainment 
 of Truth, he falls into a dangerous ambiguity. Logic, he asserts, 
 is not simply Formal Logic. It has a higher and wider aim 
 than to warn us off from inconsistency. ' The laws or precepts 
 provided for the guidance of thought must surely have for their 
 principal purpose that the products of thinking shall be true.' 
 Does this mean that Logic is to guarantee the materials on 
 which Reason works ? Does it ' guide thought ' in the sense 
 of instructing the intelligence what to observe and how skilfully 
 and accurately to compare ? Is Logic, after all, the Science of 
 Observation and Experience, or of the conditions of Truth? 
 But the conditions of Truth, as distinct from Consistency, are 
 determined by Metaphysics, not by Logic. It is, says Mill, the 
 ' Philosophy of Evidence and of the Investigation of Nature '. 
 Yet he claims that the rules of the Higher Logic, as of the 
 ' narrow ' Logic of Consistency, ' are applicable to thought 
 generally, abstractedly from particular matter.' But then again 
 we are told — ' In no case can thinking be valid unless the 
 concepts, judgements and conclusions resulting from it are 
 conformable to fact '. Therefore we must not merely examine 
 the relations of one part of the train of thought to another, but 
 we must ' ascend to the original sources, the presentations 01 
 ^ Proleg. Logica, p. 176. 
 
Inductive Proof 511 
 
 experience, and examine the train of thought in its relation to 
 these'.' 
 
 § 1042. The word valid in this passage has talcen the place 
 of true. Vahdity is conditional truth. Granted the data, the 
 conclusion if correctly drawn is true. But the investigator of 
 Nature aims not at conditional but at actual truth. He must 
 therefore examine the phenomena. He must interrogate 
 Nature. Only in this way can the bounds of human knowledge 
 be extended and amplified. But then how can Nature be in- 
 terrogated ' abstractedly from particular matter ' ? Rules may 
 be laid down for the investigation of a particular class of pheno- 
 mena, or for the investigation of phenomena generally ; and all 
 rules are abstract relatively to the actions which they prescribe, 
 all method relatively to the knowledge methodized. But it is 
 impossible to draw up rules and principles of observation which 
 shall be purely immaterial. Experimental studies cannot be 
 directed by any science which claims to be wholly formal and 
 abstract. The question is this : — Ought a science which con- 
 cerns itself, however generally, with the contingent Laws of 
 Things to be called by the name of Logic, so long at any rate 
 as that name is given to the science of the principles of valid 
 inference, abstractedly from the materials on which inference is 
 exercised ? It must surely appear unphilosophical to combine, 
 as empirical writers do, between the covers of one book two 
 such diverse kinds of inquiry. 
 
 § 1043. And yet the Inductive process undoubtedly implies 
 inference. And at first sight the process of inference by which 
 we obtain our major premisses, and. that by which we apply 
 major premisses to a variety of cases, must seem to be quite 
 distinct and, in fact, reverse processes. By the one we ascend 
 from the particular to the general ; by the other we descend from 
 the general to the particular. Moreover, by Induction we widen 
 our knowledge and obtain new truth. Deduction, on the other 
 hand, merely makes explicit what before was known implicitly. 
 It can never enlarge experience but only classify and synthesize 
 it. We argue deductively to results, inductively to causes. 
 
 § 1044. For all that, there must be some single element in all 
 reasoning upon which its validity depends. Induction, says 
 Mill tersely, is proof.^ Now, the mental process expressed in 
 1 On Hamilton, p. 471- ^ ^'>^^'^> i- 352- 
 
512 Universals, How Obtained? 
 
 Therefore must be one and the same in all kinds of reasoning. 
 A 'general theory of Evidence' cannot in the last resort be 
 derived from the matter reasoned, the things proved, but only 
 from the constitution of rational thought. What is the principle 
 which permits and compels the mind to conclude one thing from 
 a combination of others ? What is the ultimate formal justifi- 
 cation of any and every argument ? In deductive argument it 
 is that everything persists in its own nature, that a law or 
 principle holds good when applied. M being asserted to be Pi 
 then any case of M, e. g. S, is -P ; and if anything is not P it is 
 not M. Inductive argument has the same justification. There 
 are not two kinds of illative cogency. The legitimacy of proof 
 has but one title. Professor Case, however, complains ^ that 
 ' Such is the passion for one type that from Aristotle's time till 
 now constant attempts have been made to reduce induction to 
 syllogism. . . . Bacon alone was right in altogether opposing 
 them.' 
 
 § 1045. Inductive reasoning is, however, when rigorously 
 analysed, just as syllogistic as Euclid, though not in the way 
 indicated by the old logicians. It is the application of logical 
 law to a particular sphere — that of cause and effect. It tries 
 and rejects hypothesis after hypothesis as inconsistent with the 
 axiom from which it starts, proving or discovering a law, a 
 causal connexion, by successive reductions ad impossibile . It is 
 essentially applicative. But being by its nature pro-syllogistic, 
 that is, undertaking to prove our major premisses for us instead 
 of assuming them as granted, it employs as its own major premiss, 
 ultimate and undemonstrable, the Principle of Causality. Or 
 rather, this principle combined with the complement of it, the 
 Principle of Sufficient Reason. Every cause necessarily has 
 its effects. And every effect necessarily has a cause. A child 
 bursts open its drums and breaks its trumpets to see where the 
 sound comes from, before it has learnt to formulate any general 
 law of acoustics. It is a law that there is a law for everything. 
 
 § 1046. All reasoning presupposes some general proposition 
 as given. Inductive reasoning is the application of one of the 
 most general of all principles, which is assumed as an absolute 
 datum in every investigation, to minor premisses which in the 
 final resort rest upon immediate experience, l/iTretpta, that is on 
 ^ Encycl, Brit., loth ed., art. ' Logic' 
 
Mill's Canons 513 
 
 the direct deliverances of the individual consciousness, eirax^^rat 
 foj l^ovTas aurOrjaiv aSvvaTov. Taking the facts we subsume them 
 under the law respecting laws, and so obtain the law of the facts. 
 
 § 1047. The Canons of Induction as formulated by Mill, im- 
 proving upon Bacon's Tables, are only variations of this highest 
 Premiss as applied to the collated facts of observation or of 
 experiment. The following is Mill's ' Method of Difference ' : — • 
 
 If an instance in which the phenomenon under investigation 
 occurs, and an instance in which it does Hot occur, have every 
 circumstance in common save one, that one occurring only in the 
 former ; the circumstance in which alone the two instances differ 
 is the effect, or the cause, or an indispensable part of the cause, of the 
 phenomenon. 
 
 Let a, b, c, be the combined antecedents of the phenomenon 
 XYZ; b, c, of the phenomenon YZ. What is the cause oi XI 
 By the principle of Sufficient Reason it must haye a cause, and 
 that cause must be found somewhere among its antecedents — 
 using this word in a philosophic sense — a, b or c. 
 
 Now if the cause were b or c, or both combined, X would 
 always be found where ^ or c is found, or b and c together. 
 The Law of Causality is here applied to a particular case. But, 
 as we saw, X is not so found. Therefore neither b nor c is 
 the cause of X. It follows that a is the cause. This is Bacon's 
 method based on Exclusions and on the breaking up of the data 
 natura. It is, of course, the method of the Patagonian child, 
 who ascertains that it is the sun which makes him feel hot by 
 first standing in the sunshine and then in the shadow, and of 
 the infant who ascertains that hunger is relieved by nutriment, 
 through comparing his sensations when he has food and when 
 he has it not. Logically, the method is unexceptionable. What 
 liability to error attends it arises from the practical difficulty of 
 being sure that the instances of the phenomenon under investiga- 
 tion have every circumstance in common save one. Also the 
 cause might be not a separately, but a combined with b or c. 
 The dose which kills a man (combining with his constitution) 
 may cure a rhinoceros. 
 
 § 1048. When a combination of conditions produces a certain 
 effect — e. g. the cavalier and his armoul- together tire the horse 
 by their weight — it is often possible to isolate and subtract from 
 the joint common effect that which each of the antecedents con- 
 
 l1 
 
5T4 Universals, How Obtained? 
 
 tributes to it. We can weigh the armour, and see how much 
 the beast will have to carry without it. The weariness of the 
 horse could be apportioned partly to the rider and partly to his 
 equipment. It is true we could hardly divide a stumble or fall 
 in this way, and the camel's back remains unbroken till the last 
 straw is placed on it. 
 
 Mill calls this way of arriving at a cause- the Method of 
 Residues. 
 
 § 1049. The Method of Concomitant Variations is closely 
 akin to the Method of Difference and the Method of Residues, 
 and yields a perfectly logical inference as to the cause of a 
 phenomenon, always supposing that our observations are correct. 
 If I am more sea-sick when the sea is rough than when it is 
 smooth, I ascribe the sensation of nausea to the motion of the 
 vessel. The increase of the sensation must be due to some 
 added or augmented cause, and, ex hypothesi, the circumstances 
 are the same except as regards the greater roughness of the sea. 
 But I must be sure that the circumstances are the same. Some- 
 thing might depend on my health, or on my diet. 
 
 If a man were to say, ' Directly I married a few grey hairs 
 appeared on my head. After some years of marriage they had 
 much increased, and I find the longer I am married the greyer 
 I get,' the suggestion of a causal connexion would be scarcely 
 scientific. Or rather the lapse of time is here connected causally 
 with the progressive effect, but not necessarily the continuance 
 in a certain state of life. That might be as accidental as living 
 in a certain house would probably be. 
 
 Occasionally the reason for a concomitant variation is obscure. 
 Thus intellectual activity is said to vary with the discovery of 
 gold. 
 
 § 1050. Mill's other two Methods yield a probable conclusion 
 only. The Method or Canon of Agreement says that the sole 
 invariable antecedent of a phenomenon is probably its cause. 
 If a, b, c be followed by X, and a, d, e also be followed by X, 
 a, being the only common circumstance, is very likely, or at any 
 rate possibly, the cause of X. But Plurality of Causes forbids 
 us to say more. X might be due to 6 or c in the one case, and 
 to «^ or « in the other. Because all 5's are P it does not follow 
 that all P'b are 5. We can only go on multiplying instances, 
 thus excluding one hypothesis after another ; and if a is found 
 
Induction is itself Deductive 515 
 
 to be always, in whatever circumstances we verify the sugges- 
 tion, followed by X, we attain to a high probability that it is the 
 cause of X. If a family which moves about a good deal gets 
 into quarrels wherever it goes, we ascribe to it the fault rather 
 than to the neighbours. And yet here, too, we must remember 
 that it takes two to make a quarrel. 
 
 § 1051. The Method of Agreement is reinforced by the Joint 
 Method of Agreement and Difference.* This should rather be 
 called the Double Method of Positive and Negative Agreement. 
 Agreement in the non-possession of a quality is not difference. 
 If wherever the above family resides there is quarrelling, and 
 where it does not reside there is no quarrelling, we are more 
 than ever convinced that it has itself to blame for the want 
 of harmony. Still it may be otherwise. The peace of the 
 places which know not this family may be due to other causes. 
 If in several parishes where it takes up its residence, and in 
 those parishes only in the whole county, there is an outbreak 
 of scarlet fever or of a murrain, this is not enough to prove 
 a connexion of cause and effect. 
 
 § 1052. So far, however, as these two Methods enable inference 
 to take place, that inference, as in the Methods of Difference, 
 Residues and Concomitant Variations, is strictly syllogistic. 
 A law of the highest generality is applied to observed facts, 
 as major premiss to minor terms. That law, however, is not 
 merely itself, like all laws, causal, but is a law about causality. 
 When applied, then, to the observed facts it gives a conclusion 
 which necessarily takes the form of a causal affirmation. In 
 
 ' Mill, who also calls the Method the Indirect Method of Difference, 
 words his Third Canon thus: — ' If two or more instances in which the 
 phenomenon occurs have only one circumstance in common, while two or 
 more instances in which it does not occur have nothing in com.mon 
 save the absence of that circumstance; the circumstance in which alone 
 the two sets of instances differ is the effect, or cause, or an indispensable 
 part of the cause, of the phenomenon.^ The first clause is the Canon of 
 Agreement. The second clause is the same negatively. If it were the 
 Canon of Difference it would run, ' have everything in common save the 
 one circumstance.^ The last part might be worded — ' The circumstance 
 spoken of is the effect, or the cause, &c.' The word ' differ' is unnecessary. 
 Mill's statement errs in two points: (i) The negative instances cannot 
 'have nothing in common save the absence of that circumstance', but 
 must have in common the absence of innumerable circumstances. And 
 (2), the two sets of instances do not differ in one circumstance alone. 
 
 L 1 2 
 
5i6 Universals, How Obtained? 
 
 any ordinary syllogism, on the other hand, the conclusion 
 deduced may be a statement about a particular fact. We see, 
 then, why Induction leads us to general principles, while 
 Deduction conducts us to what is relatively concrete and par- 
 ticular. The conclusion of every syllogism is more concrete 
 than its major premiss. But so are the generalizations obtained 
 by the Inductive methods concrete relatively to the Law of 
 Causality, which is in the highest degree abstract and general. 
 Inductive treatises are really elaborate directions for marshalling 
 the facts of observation and experiment so that each may be 
 subsumed as minor premiss under this great praemissa maxima. 
 
 § 1053. Since M is P and S is M, S is P. But analysing 
 this deductive conclusion I ask, What is the explanation, 
 or cause, of S being PI The answer is that S is M (minor 
 premiss) and that M is P (major premiss). The minor premiss 
 is given as a fact of observation. But how do we know that 
 we must find in M the cause of anything being P ? This is a law 
 or generalization. How is it arrived at ? We have to prove 
 this oi M. M therefore, hitherto suggested as a middle term> 
 must become the minor term of a prosyllogism. Cases of M 
 must be gathered together and examined, in order that we may 
 frame the minor premiss of our prosyllogism. We then take 
 for major premiss the ultimate Law of Causality, in the form 
 (if possible) of the Canon of Difference : — 
 
 ' If an instance in which a phenomenon occurs, and an instance 
 in which it does not occur, have every circumstance in common 
 save one, that one occurring only in the former, this circumstance 
 is the cause of the phenomenon.' 
 
 But in the case of the phenomenon P, M is such a circum- 
 stance. 
 
 Then M is the cause of anything being P. 
 
 § 1054. Thus regarded there is no more an ascent from facts 
 to law in an Inductive argument than there is in any other 
 syllogism. Every syllogism may conclude in a generalization, 
 which however must be narrower than the major premiss. 
 Thus from the law of gravitation we can deduce the general 
 principle that the Earth attracts towards itself all ponderable 
 objects whatsoever. 
 
 § 1055. Every argument is composed of two elements, one 
 given from above, the other won by a nearer experience- 
 
The Great Major Premiss 517 
 
 Meeting they produce a conclusion, in which the law or prin- 
 ciple given is applied to the experience won. If we set to 
 work to prove the law true, we must still appeal to a higher 
 law, which is in the end undemonstrable. There must always 
 be a major premiss given. 
 
 § 1056. From the point of view .of Logic, then, Induction is 
 merely prosyllogizing/ with the Law of Causality for major 
 premiss. The rules for observing and experimenting, that is 
 for arranging and ordering the facts out of which the minor 
 premiss of the prosyllogism is to be constructed, are extra- 
 logical. They belong to the matter, not the form, of reasoning, 
 and constitute a separate subject, which has been admirably 
 expounded by many modern logicians, but should be called 
 Method rather than Logic. 
 
 § 1057. I shoot an arrow into the air. It falls to earth, and 
 I wonder why. What is the reason, the ratio essendil What 
 law should it be brought under ? I consider its properties one 
 by one. Regarded syllogistically, I am starting from the con- 
 clusion ' S\s P' (my arrow falls to the ground), and to find the 
 required M, or middle term, am trying one after another a 
 number of possible minor premisses, having 5 (my arrow) for 
 their subject— 5 '\5 A; S is B; S is.C; and so forth. The 
 arrow is made of wood ; it is feathered ; it is barbed ; it is 
 a yard long ; it is painted green ; it is solid ; it was shot in 
 a certain direction ; it was intended for the heart of a foe ; and 
 so forth. 
 
 The right selection is best arrived at by taking other possible 
 subjects to P, other objects which fall to the ground — an apple, 
 a thunderbolt, a dog, rain — and considering in what respect 
 these all resemble S, my arrow. And if some of them resemble 
 it in more points than one there must be comparison with further 
 instances, until one common property only is left, viz. in this 
 case body. This is the Method of Agreement. Conceivably 
 a comparison with one other case of the phenomenon may 
 suffice to establish an induction good enough to act upon, viz. 
 where the resemblance is in one point only. 
 
 ^ The mediaeval school logician was always prosyllogizing, since in the 
 game of disputation he was called upon usually to prove his premisses. 
 The ground of his major he sought in some more axiomatic truth, 
 finally getting back, if he could, to a text of Scripture or of Aristotle, or to 
 some definition of the Church. 
 
5i8 Universals, How Obtained? 
 
 § 1058. Or we might have proceeded by taking the pro- 
 perties of 5 one by one, and observing whether in other cases 
 that property is followed by the effect, P. A bird, like the 
 arrow, is feathered, but does not for that reason fall to earth. 
 A leaf is green and does. A stone is discharged and does. 
 Then we proceed by elimination and exclusion. 
 
 § 1059. I have purposely taken an illustration — in some 
 respects a poor one — in which the Method of Agreement holds 
 good, for the reason that possible plurality of causes need hardly 
 here be considered. Except a missile hurled by muscular or 
 mechanical force in the direction of the earth, everything falls 
 to the ground through one and the same cause, viz. the earth's 
 attraction. And even the missile falls by the earth's attraction 
 co-operating with the force exerted. 
 
 § 1060. The Method of Difference would not be very easy to 
 apply to this illustration, unless we could conceive an elfin 
 arrow, unearthly and unsubstantial, which should not obey the 
 law of gravitation. (By noticing however that the more solid 
 bodies are the more violently they fall — a lead ball than a pith 
 ball — we may reach our generalization by the Law of Concomi- 
 tant Variations.) Which is the M which explains S being PI 
 We observe something which resembles 5 in every particular 
 but one (which it lacks), and is not P. Then that particular is M. 
 
 § 1061. Logic however, I repeat, contributes nothing to these 
 inductive processes except the syllogistic framework (which, 
 starting from the conclusion, S is P, the investigator is endea- 
 vouring to fill in), and the Law that causes are always followed 
 by their effects. The rest is observation and intelligence. 
 
 Fuller, in impeaching the conduct of John Capon or Salcote, 
 Bishop of Salisbury in Henry VIII's time, and also that of 
 Vesey or Harman, Bishop of Exeter, remarks : — ' It seems as 
 if it were given to binominous bishops to be impairers of the 
 churches.' If the induction were intended seriously and not 
 satirically, it would be a ludicrously unintelligent and careless 
 one. The two prelates must have had some other point of 
 resemblance besides the accident of a double name. But sup- 
 pose both had been guilty of simony, and the phrase had run — 
 ' It seems as if it were given to simoniacal bishops to be 
 impairers of the churches ' — the induction indeed would not be 
 one whit improved logically ; for there must still remain many 
 
aearcn jor ' Forms ' 519 
 
 other points of resemblance; but it would be much more 
 probably correct. Usually it was the married bishops who were 
 accused of rapacious depredations and nepotism. Again there 
 is a droll connexion established in Macaulay's Election Ballad 
 between Roman Catholic Emancipation and the price of 
 firewood — 
 
 A wood merchant told me to-day 
 
 'Tis a wonder how faggots have risen ! 
 
 A child falls into the fallacy of post hoc ergo propter hoc when it 
 supposes that a watch flies open because the owner blows upon 
 it. In seeking for a constant element in the phenomenon it does 
 not disengage it from casual and varying connexions. 
 
 § 1062. With Bacon, followed by Reid and others, Inductive 
 Method is the research for ' Form ', the essence of a thing, 
 Aristotle's to tL ^v eivai. We must analyse concrete phenomena, 
 in which a number of 'forms' are coupled together— formae 
 copulatae— into simple qualities. Finding the form of the 
 ' simple nature ', we are able to reconstruct the phenomenon. 
 Upon the essential qualities depend the derivative qualities. 
 Thus, a triangle, or trilateral, is essentially three-sided. Hence 
 flows the property of its three angles being together equal to two 
 right angles. The form or cause of heat, according to Bacon, 
 is motion.' 
 
 § 1063. The logician on the other hand cannot distinguish 
 between causes. He interrogates not merely 'nature', with its 
 clear demarcation of kinds, but the infinite range of possible 
 predication. If I say, ' Faulty spelling is more venial than 
 faulty punctuation ', and you ask why, and I reply that the latter 
 is a mark of slovenly thought, while the former only shows 
 ignorance (arising nowadays, it is true, from want of observation), 
 and may (as in the picturesque Elizabethan and Jacobean spell- 
 ing) be a sign of character, I am assigning general characteristics, 
 which may perhaps be called the form of the phenomenon. 
 
 ' There is a useful summary of Bacon's doctrine in Veitch's Logic, 
 pp. 469-83. Mill observes that ' a more efficacious mode of interrogating 
 nature has since Bacon's time shown that throughout one of the most 
 extensive departments of natural philosophy there does not exist that sort 
 of connexion between different truths which would enable us to deduce one 
 of them from another as the schoolmen attempted to do ' (on Whately's 
 Elements). 
 
520 Universals, How Obtained? 
 
 But if we want to know why the cat breaks the china, and 
 discover by observation or experiment that she is trying to get 
 at the sardines in the cupboard, the generalization hardly rises 
 to the dignity of essential form. Even natural phenomena are 
 conditioned by a variety of antecedents, among which the mere 
 logician cannot discriminate, and which he cannot range or 
 graduate. The ixAa-ov ^i^Ttja-ii depends on the object in view. 
 What makes this apple to have tumbled ? If I am philosophizing 
 I shall bring the phenomenon under the law of gravitation. If 
 I am in a practical mood I say that the fruit was clearly ripe, or 
 that there was a high wind in the night. As Mill remarks, if 
 a man falls from a ladder we say nothing about the earth's 
 attraction, but only that his foot slipped. So the Village Wife 
 and her uncomforting visitor explain the death of her daughter 
 by primary and secondary causes respectively — ' I thowt 'twur 
 the will o' the Lord ; but Miss Annie she said it wur draains '. 
 
CHAPTER XXXII 
 
 PRINCIPLE OF CAUSALITY 
 
 § 1064. The tendency to subordinate the principles of Logic 
 to Natural Philosophy, and to make it conversant with the laws 
 of Things rather than those imposed by Reason upon Thought, 
 is evidenced by the ambiguous expression ' Uniformity of Nature ' 
 for the supreme Axiom of Induction. Why nature?^ The 
 word may, it is true, be taken to mean not merely the material 
 universe, but the entire circle of existences, actual and ideal. 
 ' Forewarned is forearmed ' ; ' Comparisons are odious ' ; 
 ' Small is the worth of beauty from the light retired ' ; ' The 
 Red Lion is a good inn ' ; ' duke est desipere in loco ' — these 
 and a myriad other everyday statements may possibly be com- 
 prised under the uniform properties of ' Nature ', but are hardly 
 intended by the phrase. 
 
 § 1065. The Inductive Method applies to everything that can 
 be predicated. But the illustrations of writers on the subject of 
 Induction are almost invariably taken from the domain of 
 physical science, and make us familiar with Leyden jars, the 
 planetary orbits, oxygen, and the properties of common salt. 
 The vast and ever- widening sweep of philosophic Induction they 
 base, then, on the * uniformity ', the stability, the permanence, 
 which we find to attend the great sequences of natural Law 
 —the 'Cosmical Order', typified by that rainbow which the 
 
 ' Mansel contrasts Nature with the self-determination of the conscious 
 Self. ' The course of Nature is thought as uniform, because, so long as 
 Nature is spoken of, that element is absent which alone we can think of 
 as originating a change, Intelligence. And for the same reason, so long 
 as the several phenomena of Nature are believed to be each under the 
 control of a separate intelligence, the axiom of her uniformity will admit 
 of perpetual modification. The winds may blow north or south, as suits 
 the" caprices of Aeolus ; Xanthus may neglect the laws of his periodic rise 
 and fall, to arrest the progress of Achilles ; and even the steady-going 
 coachman, Phoebus, may alter upon occasion the pace of his chariot, to 
 gratify the wishes of his roving parent' (Proleg. Logica, pp. 148, 149). 
 
522 Principle of Causality 
 
 Visionary saw round about the Throne. The Creator hath made 
 the round world so fast that it cannot be moved. His decrees are 
 fixed. His promises fail not. So long as the world endureth 
 seed time and harvest shall not cease. Man has his allotted 
 length of days. Death is the way of all the earth — hodie mihi, 
 eras tibi. The thing that hath been is that which shall be. 
 The ' God of Amen ' compares His sure mercies to the covenant 
 of day and night and the appointed ordinances of heaven and 
 earth. His righteousness standeth like the strong mountains ; 
 His judgements are like the great deep. Even the wind, which 
 bloweth where it listeth, observes its appointed seasons, and 
 meteorology becomes more and more a science.^ 
 
 § 1066. This imposing natural security, however, is entirely 
 irrelevant to logical theory. Bain, Mill, and others discuss at 
 length the bearing of the then newly discovered law of the 
 Conservation of Energy and Indestructibility of Matter upon 
 the Law of Causation. But how can a discovery about the 
 contingent properties of outward nature — for example, those 
 of radium — affect an Axiom of Thought? For the Law of 
 Causality, if analysed far enough, is but the cosmical aspect of 
 the metaphysical Law of Self-identity.^ Logic cannot distinguish 
 between the sequence of cause and effect and the inherence of 
 attributes in a substance. It is concerned only with the attri- 
 
 ' Nature well known, no prodigies remain ; 
 
 Comets are regular, and Wharton plain. 
 
 (Pope, Moral Essays, Ep. I.) 
 An assertion such as ' What Englishmen have done Englishmen can do ' 
 rests on the idea of the stability of national character. 
 
 ^ No doubt, the majority of writers mean by the ' Law of Causality ' 
 the doctrine that every event must have a cause — which, on the logical 
 side, is the Principle of Sufficient Reason — and employ the phrase ' Uni- 
 formity of Nature ' for the doctrine that the same cause is always followed 
 by the same effects. But, apart from any criticism of the word ' Nature ' 
 to cover all predication, we are left without any name for the stable 
 course and constant sequences of the universal frame. And it is this fact 
 of permanent stability to which the Empirical philosophy appeals. The 
 sequence of events has been observed hitherto to present such and such 
 uniformities, and there is no reason to suppose that their accustomed 
 course will be interfered with. If chaotic disorder were to supersede the 
 present regularity. Logic for the Empirical philosopher would cease to 
 exist. But no witches' frolic of confusion would make the least difference 
 to ours. 
 
' Uniformity of Nature "" 523 
 
 bution of predicates to subjects. The Inductive process rests on 
 the assumption that each thing abides as itself, in the special 
 and appHed form of the law that a cause is always followed by 
 its own effects, or that a substance maintains its inherent 
 qualities. Once show that Reality being determined in this 
 way is also determined in that way, — in other words, once 
 establish a principle, a law, a causal connexion, — and we are 
 sure that, apart from any counteracting event, it must always 
 be so. As Mill puts it, 'Change can only be produced by 
 change.' ' Grapes will not produce thorns nor figs thistles with- 
 out some very unusual grafting. Qui seme des chardons 
 recueille des Opines. 
 
 § 1067. But this principle of Causality does not require that 
 the course of Nature should continue stable and uniform. If, 
 instead of the new flood of customary morn, the sun one day did 
 not rise, it would be because something had occurred to prevent 
 it. Our expectation that the sun will rise to-morrow is grounded 
 not upon custom but upon our reasonable belief that no physical 
 cause sufficient to disturb the planetary system so suddenly 
 exists.'' But if the universe were a chaos of conflicting forces, 
 a whirling kaleidoscope of change, a welter of confusion, if facts 
 lay about like a child's spillikins, still the principle that what 
 nature a thing has it has would be in no way affected — though 
 it would be very awkward for the logician to have no general 
 propositions. A conflict of forces is not a flux. For a flux 
 means that a law — including the Law of Causality itself — may 
 be truly stated, and yet that it is not to be depended on in any 
 given instance. Neither is Causality affected by supernatural 
 agency. Gravitation, as a law, holds good if a man be suspended 
 in the air by a miracle as much as if he be suspended by a rope. 
 Nor again, if the principle of Causality (or persistence of the 
 Truth of things) is not disturbed by Divine action, is it set aside 
 
 ^ Logic, i. 407. 
 
 ^ ' The plowman from the sun his season takes.' Archbishop Thomson 
 says : — ' The inductive method proceeds in the faith that the universe — 
 the Cosmos — will ever be subject to strict order and general laws ; and 
 nothing has occurred hitherto to disturb a belief upon which science 
 builds her hopes of progress — her very existence ' {Laws of Thought, 
 p. 359). By this strict order, however, the archbishop means that ' under 
 the same circumstances and with the same substances the same effects 
 always result from the same causes ' (p. 358). 
 
524 Principle of Causality 
 
 by Man's free will — that link between miracle and uniformity. 
 Whatever the metaphysical difficulty of the ideas, yet either 
 Will is an originating cause or we must fall back upon Necessi- 
 tarianism. In either case cause produces its effects. Will; 
 indeed, is irregular and unaccountable.' ' Nil aequale homini 
 fuit illi ... nil fuit unquam Sic impar sibi.' Byron says : — 
 
 Nought 's permanent about the human race, 
 Except the Whigs' not getting into place.'' 
 
 But though a human being were unstable as water, never for 
 two instants in the same mind, to one thing constant never, 
 still, granting the freedom of the Will, we cannot conceive of 
 a change of purpose —or rather a new direction of the personality 
 — either as determined inexorably or as fortuitous,' but only as 
 spontaneous and self-creative. If there be no such thing as free 
 will, cadit quaestio. 
 
 § 1068. The Uniform Course of Nature, on the other hand, is 
 a contingent fact only, not an a priori law. It has been said 
 that such uniformitarianism can never be more than a working 
 hypothesis. It is but empirically universal, a on only. The 
 mediaeval, observes De Morgan, was never sure but that 
 there might be men planted in the ground like Polydorus^ 
 He believed that somewhere, ' in antres vast and deserts idle ', 
 there lived 
 
 ' If we allow a large enough cycle, events dependent on human will 
 may be expected to recur. In parts of British India, where female 
 infanticide is secretly practised, the Government has been accustomed 
 to impose a tax on districts where the proportion of male to female 
 births exceeded the ascertained average for a certain period. 
 
 ^ Shakespeare's Biron speaks of 'vane-like men of strange inconstancy '. 
 
 ' The Americans have a phrase, ' It just happened.' The Greeks did 
 not regard Fortune as blind Chance, to avToimrov, striking wildly right 
 and left. To Anaxagoras, tvxi) is abrikos ahia avBpomipai Xoywr/im — ' All 
 chance (is) direction which thou canst not see ' (cf. Ar. Phys. ii. 4, § 8). 
 Plato says t ^era deov tv)^j] kol Kaiprjs Tav$pa>7nva dLaKv^epvaci avfiiravTa 
 {De Legg. iv. p. 709). Pindar addresses Fortune as divine and adorable 
 — nai Zrjvas 'EX^udepiov, and Sooretpa Tixa. Boole (Laws of Thought, p. 20) 
 observes that ' the records of crime and pauperism present a degree of 
 regularity unknown in regions in which the disturbing influence of human 
 wants and passions are unfelt — such as eruptions, weather, epidemics, 
 and so forth '. Yet we do not question that the most variable phenomena 
 are really subject to regular law. To omniscience nothing is contingent 
 and accidental; and a monstrous birth or fickle breeze is just as 'neces- 
 sary ' as the dawn of day. 
 
Constancy of Things 525 
 
 The anthropophagi, and men whose heads 
 Do grow beneath their shoulders.^ 
 
 Occult influences, removed from all experience, were catalogued 
 by star-gazers and prognosticators. That nature is uniform was 
 actually denied by the Peripatetic school, including Aristotle 
 himself, who, says Grote, held some sequences to be irregular 
 and unpredictable. At the most, the even course of Nature was 
 but looked on as the expression of the stability of the good 
 pleasure of heaven. 
 
 § 1069. The Axiom of Causality, in the sense in which I take 
 the expression, does not allow us to predict, except provisionally, 
 unless we know all causes. Whereas the doctrine of nature's 
 guaranteed permanence enables man, so far as he relies on it, 
 to ' dip into the future far as human eyes can see ', and also to 
 reconstruct the past. 
 
 The former teaches that things will continue as they are until 
 something occur, to alter them. The latter is the belief that 
 nothing will, at any rate at present, occur to alter them. The 
 one is a truth which is native to the mind. The other, so far 
 as it is true, is a truth given in experience. But it might fail us 
 at any moment. The forces which seem so permanent are at 
 the mercy of other forces which we know not of The great 
 compacted framework of our universe might, nufu numinis, 
 crumble and sink into the void ; the solid earth might fail beneath 
 our feet; the great globe itself and all that it inherit might dissolve, 
 leaving not a wrack behind ; as in that Dies Irae when ' the 
 stars of heaven fell unto the earth, even as a fig tree casteth her 
 untimely figs when she is shaken of a mighty wind. And the 
 heaven departed as a scroll when it is rolled together ; and every 
 
 ^ 'Now I believe that there are unicorns' (Tempest). The lastingness 
 of earth and sky is constantly appealed to in literature as the type of what 
 is least fickle. Thus, in Julius Caesar, ' I am constant as the northern 
 star.' Hermione says : — 
 
 The sun was not so true unto the day 
 
 As he to me. 
 In Scott we have the lines — 
 
 Come one, come all, this rock shall fly 
 
 From its firm base as soon as I. 
 But the same perdurance has been found in the works of men's hands— 
 e. g. ' Quando cadet Colisaeus cadet et Roma ; et quando cadet Roma 
 cadet et mundus^ (Bede).^ 
 
526 Principle of Causality 
 
 mountain and island were moved out of their places.' We have 
 ourselves seen sure mountains and age-long hills melt in fiery 
 ruin, isles disappear, cities brandished like a torch in a giant's 
 hand, and we know that such cataclysms were not comparable 
 to the changes that have taken place, slowly or suddenly, in ages 
 past — 
 
 There where the long street roars hath been 
 
 The stillness of the central sea. 
 
 And yet though the ordered Kocr/ios should fall back into elemental 
 strife, though the firmament should be folded up and changed 
 as a vesture, the Law of laws would abide. Ego Deus et non 
 mutor. Ego sum Qui sum. 
 
 § 1070. It may be thought, however, a preposterous trans- 
 cendentalism to exalt into an absolute a priori axiom the 
 observed constant relation between cause and effect, substance 
 and attribute. If we find by observation that a piece of lead 
 sinks in water we conclude no doubt that lead will always sink 
 in water. If a selfish person is found to be inconsiderate, we 
 think that wherever selfishness is found inconsiderateness will 
 be found. But, it is argued, such constancy in things is a law 
 of things, not a formula of the Reason. The knowledge of the 
 recurrence of sequences is contingent merely. It might have 
 been otherwise. Mansel himself says : — 
 
 ' This is a principle of contingent truth only, not of necessary 
 truth, at least, not in the highest sense of the term. I can 
 suppose, though I cannot conceive, that in some other portion 
 of the universe the phenomena of matter may have no settled 
 relations to each other, or even no relation at all. Each may 
 be absolutely detached from, and independent of, every other. 
 Or there may be dependencies continually changing, so that 
 phenomena at one time and in one place connected as cause 
 and effect may at another time or in another place have no 
 connexion at all." 
 
 § 1071. I venture to think that this view of the Axiom of 
 Causality as a contingent law will not bear probing. Of course, 
 if the Will of the Creator be pre-supposed, that Will can change 
 water into wine or cause a human body to walk upon the waves. 
 But this is simply to introduce a new and counteracting cause. 
 If I fling a stone, or an earthquake hurls a mountain, into the 
 
 * Proleg. Logica, p. 147. 
 
Causality not Empirical 527 
 
 air, no one supposes that the law of gravity has been made 
 of none effect. Nor is the truth of things any the more destroyed 
 if the modifying force be occult and supernatural. Apart, how- 
 ever, from the idea of an invisible Hand, or of unknown dis- 
 turbing forces, the supposition of a world in which the phenomena 
 had no settled relation to each other, and in which causes some- 
 times did and sometimes did not produce their effects, is 
 impossible and unmeaning. Infinite variety of change there 
 may be, but the changes must be governed by law. To suppose 
 that anything should be thus or thus, and then without any reason 
 not be thus, is to bewilder oneself with words. What can cause 
 possibly mean apart from constancy of connexion with its 
 effect? 
 
 § 1072. The inductive process first by eliminations reduces 
 the possible reasons for a phenomenon to one. Next, since 
 the phenomenon must have a reason for existing, it assigns 
 to it what has been found to be the only possible reason. 
 No doubt a phenomenon, considered abstractedly, may have 
 more than one cause ; but in any supposed case the induction 
 reduces the possible explanations to one. We have thus proved 
 that a particular result is to be attributed to a particular cause, 
 or a particular quality to a particular substance. That and no 
 other is the truth of the existence of the subject at this moment. 
 It exists in that manner, with that property. But if it exist so 
 at one moment it must exist so always, unless some new cause 
 operate to make it otherwise. This is its mode of being, and that 
 mode of being cannot be reversed without some sufficient reason. 
 In other words, causes always have the same effects. Subjects 
 do not drop their attributes like partners in some ever-changing 
 dance. 
 
 § 1073. It is impossible, then, to admit that this Axiom of 
 Causality is merely given us by Experience. Thus Archbishop 
 Thomson observes : — 
 
 'AH our experience goes to convince us that under the same 
 circumstances and with ffie same substances the same effects always 
 result from the same causes. This great inductive principle 
 is itself proved by induction, and partakes of the same formal 
 defect that may be charged against other inductive results, viz. 
 that its terms are wider than our experience can warrant. Many 
 groups of facts, connected as cause and effect, have not been 
 examined ; and in them it is conceivable at least that there may 
 
528 Principle of Causality 
 
 be capricious causes producing opposite effects at different 
 times.' ' 
 
 Surely a capricious, freakish cause is really unthinkable, 
 Ueberweg, meeting the assertion that the objective causal 
 nexus is a circle, since the knowledge of the real nexus is 
 based upon incomplete inductions, replies that the causal nexus 
 as existing precedes our inductions; but the same nexus as 
 known to us is a generalization from a great number of special 
 inductions.^ Hamilton remarks : — 
 
 'It is possible only in one way to raise Induction and 
 Analogy from mere probability to complete certainty — viz. to 
 demonstrate that the principles which lie at the root of these 
 processes are either necessary laws of thought or necessary 
 laws of nature. To demonstrate that they are necessary laws 
 of thought is impossible ; for Logic not only does not allow 
 inference from many to all, but expressly rejects it. Again, 
 to demonstrate that they are necessary laws of nature is equally 
 impossible. This has indeed been attempted, from the uni- 
 formity of nature, but in vain , . . seeing that this law itself 
 can only be discovered by way of Induction and Analogy. In 
 this attempted demonstration there is thus the most glaring 
 petitio principii' ' 
 
 Hamijton brings the same charge, it will be remembered, 
 against the Syllogism. 
 
 § 1074. Hume, Locke, Condillac, and the empirical school, 
 explain the belief in the constancy of things by association. 
 Mansel speaks of 'the physical Law of Causality', which he 
 thus states : — ' Every phenomenon which takes place has, among 
 its immediate antecedents, some one fact or combination of facts, 
 which being repeated, the same phenomenon will invariably 
 recur'.* He identifies this law with the belief in the uni- 
 formity of nature. The law is not confined by him to physical 
 phenomena; but he desires to exclude from it the self-deter- 
 minations of the Will. He combats Mill's view that the Law of 
 Causality is an induction,^ and one of by no means the most 
 
 ^ Laws of Thought, p. 358. ''■ Logic, p. 490. 
 
 ' Lectures on Logic, ii. 174. * Proleg. Logica, p. 145. 
 
 ^ Mill says that ' the principle of the uniformity of the course of nature 
 will appear as the ultimate major premise of all inductions. ... I regard it 
 as itself a generalization from experience. ... In the infancy of science it 
 could not be known that all phenomena are regular in their course ' 
 {Logic, i. 356-8). ' It is not properly uniformity, but uniformities' (ibid. 
 
Is the Law of Causality Empirical? 529 
 
 obvious kind. For this is to overlook the fact that, when the 
 Law is found in apparent conflict with experience, 
 
 'it is invariably assumed to be in the right and experience in 
 the wrong, which is not the case with merely inductive laws ; 
 to say nothing of the paralogism of making the ground and 
 principle of all induction itself depend upon induction, and 
 upon induction only. Our earliest and unphilosophical induc- 
 tions appear as often to indicate variety in the operations of 
 nature as uniformity. The sun rises and sets, the tide ebbs 
 and flows, with regularity; but storm and calm, rain and sun- 
 shine, appear to observe no fixed order of succession. But, 
 in any instance whatever of physical causation, let an apparent 
 repetition of the cause not be followed by that of the effect, and 
 all men alike, philosophical or unphilosophical, will at once 
 assert that there was some latent variety in the circumstances, 
 and not a change in the uniformity of their succession.' ' 
 
 Nevertheless even this acute philosopher regards the Principle 
 of Causality not as a law of thought but as an empirical principle, 
 albeit one of a very peculiar character. 
 
 ' If we were told of an instance on our own globe in which 
 the repetition of exactly similar phenomena had apparently not 
 been followed by the same effect, we should without hesitation 
 account for it on one of two grounds. Either the phenomena were 
 not exactly similar, or the interposition of some intelligent being 
 had prevented the natural result. And if we were asked why 
 these two alternatives alone are admissible, we should probably 
 reply, "because matter cannot change of itself." Now why 
 cannot we think of matter as changing itself? Because power, 
 and the origination of change, or self determination, have never 
 been given to us save in one form, that of the actions of the 
 conscious self.' ^ 
 
 It would be better to say 'things' than 'matter', which 
 will not cover a fraction of the subjects to which attributes 
 are ascribed. The only subject then which can change its 
 predicates, itself unchanged, is the Ego. 
 
 p. 364). 'We make experience its own test' (ibid. p. 369). Of the 
 observed uniformities of Nature the one with most pretension to rigorous 
 jndefeasibility is the Law of Causation (ibid. pp. 375, 376). 
 
 * Op. cit. pp. 146, 147. 
 
 ^ Ibid. p. 148. It is disappointing to find Professor Case in the 190? 
 edition of the Encyclopaedia Britannica asserting that ' few men have 
 believed in uniformity, but all have induced from particulars to universals '. 
 ' The theory of Mill,' he remarks, ' need not detain us long. Most induc- 
 tions are made without any assumption of the uniformity of nature. For 
 
 M m 
 
530 Principle of Causality 
 
 § 1075. If the foregoing account of the relation of Induction 
 (as a special application of inference) to pure Logic be correct, 
 the ' possibility of bringing new truths out of old ' need not have 
 been, as Mill says it is, ' an eternal mystery and stumbling-block 
 to Formal Logic' ^ Anything really new, and not merely expli- 
 cated, in the truths must of course be given by experience and 
 insight, not by ratiocination, and the materials for the detection 
 of a law must be selected and arranged by the Intelligence which 
 judges rather than by the Reason which infers. But, the 'inter- 
 rogation of nature ' completed, and the result subsumed under 
 the Axiom of Causality, the proof of the inferior universal, the 
 generalization from the facts, takes place by a valid and inex- 
 pugnable logical illation. There is no need to ' catch the 
 mantle of the prophet ' for this part of the process. 
 
 § 1076. Scientific Induction is something more than Kant's 
 ' Syllogism of the Judgement '. What the Judgement does is 
 to compare, analyse, and decompose the presentations of experi- 
 ence, and deciding which circumstances are- material hand its 
 results over to the syllogistic mill to grind. A single Ivo-Tao-is 
 stops it. Una instantia cadit inductio. Gainsborough is said to 
 "have painted the ' Blue Boy ' to disprove Sir Joshua's teaching 
 that blue should not be the dominant note of a picture. 
 
 § 1077. 'The notion of Cause is the root of the whole theory 
 of Induction.' " In this and in his other saying that the ' Uni- 
 formity of nature ' — meaning the constancy of law — ' is the 
 ultimate major premise of all inductions'^ Mill goes to the 
 heart of the matter. Proof of the general from the particular, 
 then, has an element of pure form, and is a syllogism whose 
 elements are the Axiom of Causality and sifted experience. 
 
 whether it is itself induced, or a priori, or postulated, this like every 
 assumption is a judgment, and most men are incapable of judgment 
 on so universal a scale when they are quite capable of induction.' Yet 
 in the same article the President of Corpus rebukes Dr. Bradley for 
 supposing that the major premisses of our reasonings must necessarily 
 be explicitly formulated in our mind. 
 
 ^ In the same way Dr. Case, asking 'how from some particulars ol 
 experience do we infer all universally?', avers that 'the answer to this 
 question is still a desideratum'' (ibid.). But one fact cannot prove 
 another ; nor can any mere string of facts, ' with power to add to their 
 number,' give us a universal, unless there is a greater universal in the 
 background, viz. here the Axiom of Causality. 
 
 "^ Logic, i. 376, » Ibid. p. 356. 
 
Aristotelian Induction 531 
 
 Mill, in spite of his disparagement of syllogism, is nearer the 
 truth than the scholastic logicians, who, from the Peripatetics 
 onwards, overlooked the true nature of epagogic reasoning. 
 
 § 1078. Aristotle says distinctly that the method of proceeding 
 from a number of similars to a general uniformity is through 
 a minor term consisting of all the instances. ■^ yap ciraytoy^ 819. 
 irmirmv. ^ Though they be innumerable as leaves in Vallombrosa 
 or as the pebbles on the ' unnumbered beach ' of Chesil, every 
 instance must be examined : otherwise the inference will be but 
 «ri TO iroki, probable, but nothing more. The only ' pure ' induc- 
 tion, says De Morgan, is per simplicem enumerationem ubi non 
 reperitur instantia contradidoria? Every bead of the inductive 
 rosary must be told. Any other discovery of laws is ' beyond 
 the province of formal logic ' and only called logical induction 
 ' by a confused use of language '. And yet the result of a com- 
 plete enumeration is not a law but a mere fact. It is not, All 
 X% are Y, but, All the X's> are Y. 
 
 § 1079. According to Aristotle, the Inductive syllogism proves 
 the major of the middle term by means of the minor — 
 
 Every M is P Every M is P Every M is P 
 
 SisM S'isM 5" is M 
 
 Therefore 5 is P. S' is P. S" is P. 
 
 Retracing our steps, we prove the universal, Every M is P, 
 by ascertaining that S is P, S' is P, S" is P, &c. S, 5', S", 
 &c., are each of them M. But do they together make up all il/ ? ' 
 To take Aristotle's example, longevity (t6 fjiaKpo^iov) has to be 
 proved to accompany absence of gall (to axoXov) by means of 
 a number of gall-less animals which are ascertained to be long- 
 lived. 
 
 All these observed animals are long-lived. 
 
 All of them are without a gall. 
 
 ' An. Pr. ii. 23, 68^1 S- 
 
 ^ Such ' Inductions ', lacking all abstract character, unless a summary 
 has it, are mere matter, whereas the true causal universal is a blank 
 form waiting to be filled up. 
 
 ' Devey {Logic, p. 149) gives it thus : — 
 
 Deductive. Inductive. 
 
 bis a x,y,z,a.re:a 
 
 x,y, z are contained in b x, y, z represent the class b 
 
 :. x,y, z are a. •'• b is a. 
 
 M m 2 
 
532 Principle of Causality 
 
 This is in the Third Figure. But we cannot conclude that all gall- 
 less animals are long-lived, unless we are further certain that the 
 animals enumerated exhaust the long-lived class. The whole 
 and the parts must be absolutely convertible. The constituent 
 species must together make up the genus. The summed indi- 
 viduals must constitute the universal. If we are not sure of 
 this, a particular and probable conclusion alone is possible, and 
 the Induction is called Imperfect. 'An Induction,' says Hamilton, 
 ' is an enumeration of the parts in order to legitimate a judge-i 
 ment in regard to the whole.' ^ 
 
 § 1080. An ' Imperfect induction ', then, is such a one as the 
 above, where we are only entitled from the premisses to conclude 
 that some bile-less animals are long-lived, affording a ' philo- 
 sophical presumption ', greater or less according to the number 
 of cases examined, that all are so. Hamilton, Veitch and 
 others, however, give the name of Imperfect Induction to 
 a syllogism in the following form : — 
 
 This, that and the other magnet attract iron. 
 
 This, that and the other magnet represent all magnets.' 
 
 Therefore all magnets attract iron. 
 
 If we substitute are for represent, it is, as they call it. Perfect 
 Induction. But if these do represent all magnets, the conclusion 
 is not probable but certain. The premiss may be inaccurate, but 
 how can the logician know that ? If on the other hand ' repre- 
 sent' means 'are instances of, the universal conclusion is 
 unwarranted. No, it may be said, they are more than instances ; 
 they are samples, and in that sense representative. But ' This, 
 that and the other magnet are samples of all magnets ' should 
 mean not that they are taken at random from a pile of objects 
 called magnets, but that all such objects are known to have the 
 same characteristic properties. We know, then, already that all 
 magnets attract iron. Or, finally, the Induction maybe asserted 
 
 ^ Lectures on Logic, ii. 167. 
 
 ^ Aldrich describes Formal Induction as a kind of enthymeme in 
 Barbara, with the minor premiss suppressed — ' This, that and the other 
 magnet attract iron ; therefore all magnets attract iron ' — understand, ' All 
 magnets are this, that and the other magnet.' Whately, on the other 
 hand, states the syllogism as though there were a suppressed major 
 premiss, — ' Whatever is a property of this, that and the other magnet is 
 (certainly or probably) a property of all magnets. Attracting iron is 
 a property of this, that and the other magnet. Therefore,' &c. 
 
'Perfect' and ^Imperfect' Induction 533 
 
 to be imperfect if we take ' represent ' to mean that there is 
 a general similarity between these particular magnets and all 
 other magnets. From the general similarity we infer a probable 
 resemblance also in the property of attracting iron.^ But the 
 question what right we have to infer from a general similarity to 
 a hitherto unascertained resemblance is the problem of Induction. 
 Because forty-nine shillings on my table lie head upwards, what 
 right have I to assume that the fiftieth does so ? Is there 
 not a danger of undistributed middle ? Forty-nine shillings lie 
 face upwards. This is an exactly similar shilling. Then this 
 does so. The logicians, no doubt, unable to escape from their 
 narrow round of physical generalizations, are thinking, as usualy 
 of natural kinds. Hamilton states the major premiss of what he 
 calls Material or Philosophical Induction thus : — 
 
 'What is found true of some constituents of a natural class 
 is to be presumed true of the whole class (for nature is always 
 uniform).' 
 
 This is the old ambiguity — 'uniformity of nature' being made 
 to mean not constancy in the relation of cause and effect, but the 
 homogeneity of coexistences and the grouping of things according 
 to their inner nature in permanent natural classes. But the 
 logician as such knows nothing of natural classes. As far as he 
 knows, sows' ears might become silk purses. There is a story 
 of a countryman who, thatching a cottage in a thick fog, could 
 not see or feel where the roof ended, and proceeded to thatch 
 the fog. That man was a true logician, for how can mere logic 
 decide where classes of things end or where begin ? That is 
 for the natural philosopher. It is the latter who gets the 
 judgements ready for the logician to syllogize with. 
 
 § 1081. The Aristotelian Induction, then, is a mere marking 
 of time ; it carries one no further. Bacon calls it a childish 
 affair, ever at the mercy of a contrary instance. It assumes the 
 
 ^ ' This, that and the other magnet represent all magnets is founded on 
 the principle that nature is uniform and constant, and, on this general 
 principle, the reasoner is physically warranted in making a few parts 
 equivalent to the whole. But this process is wholly incompetent to the 
 logician. The logician knows nothing of any principles except the laws 
 of thought' (Hamilton, Lectures on Logic, i. 320). Hamihon obviously 
 understands by uniformity of nature a physical law or fact, not the axiom 
 on which logical Induction is based. 
 
534 Principle of Causality 
 
 real induction as already made, whether that be a quantitative 
 accumulation of instances or a qualitative selection of instances 
 so as to exhibit a general law. The element of illative proof in 
 the inductive process must be logical and formal. And upon the 
 data this leads to certainty, not to probability.^ But this formal 
 process is not the barren ' perfect ' induction of the old logicians. 
 It is, as already explained, the application of the Axiom of 
 Causality as major premiss to the successive hypotheses about 
 the cause of a phenomenon X, which (by the principle of 
 Sufficient Reason) must be found somewhere among the ante- 
 cedents or circumstances of X, viz. a, b, c, d, e,f, &c. Each of 
 these in turn is subsumed hypothetically as minor term under 
 the Law of Causality. Is it b that caused XI Then it must 
 always have X as an effect. But on examining another case in 
 which b occurs as antecedent it is not found to be followed by 
 X. Similarly with c, d, e, &c. Therefore none of these was 
 what caused X. Then by exclusions a is left in, as the only 
 possible explanation of the phenomenon X. But it would 
 have been simpler and shorter, instead of excluding the possible 
 causes one by one, to observe whether the phenomenon X 
 follows when all the antecedent circumstances except one, e.g. 
 a, remain as before ; whether, that is, its cause is to be found 
 somewhere in b, c, d, e, f, &c. Thus, to take the former illustra- 
 tion, the feeling of warmth is seen to be due to the direct rays 
 of the sun by our simply stepping into the shade. Every other 
 antecedent remains the same except the one. This is the 
 
 ^ Krug remarks : ' By the processes of Induction and Analogy a great 
 probability is all that we can reach, and this for the simple reason that it 
 is impossible, under any condition, to infer the unobserved from the 
 observed, the whole from any proportion of the parts, in the way of any 
 rational necessity. Even from the requisites of Induction and Analogy it 
 is manifest that they bear the stamp of uncertainty ; inasmuch as they 
 are unable to determine how many objects or how many characters must 
 be observed in order to draw the conclusion that the case is the same 
 with all the other objects or all the other characters ' (Logik, § i68 ; 
 quoted by Hamilton). Hamilton himself remarks that ' a competent 
 number of cases must be observed, but how many it is impossible to say 
 in general. It depends on the difference of essential and unessential 
 characters. The difference of essential and accidental is, however, one 
 itself founded on induction' (ii. 169). So useless is the Aristotelian 
 Enumerative Epagogy. The real difficulty is not how to infer from 
 the observed, but how to observe and select. 
 
Methods of Difference and of Agreement 535 
 
 Method of Difference, for which a single case suffices. The 
 only question is whether we can be sure that every antecedent 
 but one is the same.* We proceed then to verify the generaliza- 
 tion at which we have arrived, that a will invariably be followed 
 by the effect X, by examining a number of cases in which a 
 occurs. If we find that it is in every such case followed by 
 X, our belief that it is the cause of X is much strengthened. ^ 
 The formal defect of this, the Method of Agreement, is, as 
 already stated, that in itself, owing to possible plurality of 
 causes, it is merely enumerative and empirical, and since every 
 case of a cannot be examined it only yields a probability. The 
 instances, numerantur non ponderantur. The so-called Formal 
 Induction of the logical books is based on Agreement, which, 
 if rigorous enough to prove, ceases to be inductive. 
 
 § 1082. Practically, the surmise that a is the cause of X is 
 often arrived at by a flash of imaginative insight, by which 
 a mind trained and exercised in the analysis of phenomena 
 pierces suddenly to the heart of things and detects the One 
 in the Many, the law in the facts.' Such master minds, having 
 
 ^ One to whom it was said : ' Your father died in battle, your grand- 
 father and great-grandsire also ; are you not afraid to go into battle ? ' 
 replied :— ' Your father died in bed ; your grandfather died in bed ; and 
 your great-grandfather died also in bed. Are you not afraid to so 
 to bed?' ^ 
 
 ' The point of agreement may be not itself the cause of the phenomenon, 
 but an indication of a cause less easily exhibited. Thus the Spectator 
 has contended (June i6, 1900) that ' The drinking races have not only 
 conquered, but have moralized, the world. The Jew drank and gave us 
 monotheism; the Greek drank and gave us literature and art; the 
 Roman drank and gave us law ; the Teuton drank (hard) and gave us 
 the passion of freedom.' On the other hand Hindoo and Arab have 
 done little for the world. It is not of course suggested that drinking 
 habits themselves benefited mankind, but the character with which they 
 have been coupled. 
 
 ' 'It was Bacon's boast that Induction, as applied to nature, would 
 equalise all talents, level the aristocracy of genius, accomplish marvels 
 by co-operation and method, and leave little to be done by the force of 
 individual intellects. This boast has been fulfilled ' (Hamilton, Lectures 
 on Logic, ii. 138). It is astonishing that Sir William should not have 
 observed that the boast has been entirely falsified. The giants of genius 
 have played as great a part in later Natural Science as the captains of 
 industry in modern commerce. The appropriate conception is often 
 discovered by what seems at first sight a kind of accident. Whewell 
 says : — ' Such events appear to result from a peculiar sagacity and felicity 
 
536 Principle of Causality 
 
 obtained their general principle not by a slow process of* exclu- 
 sions but by a rapid intuition, proceed to verify it deductively. 
 This is so in matters of common life as much as in speculative 
 research. The man of masculine common sense is not he who 
 never sees beyond his nose, but he who by quick perception 
 rejects what is immaterial, and fastens on the root of the matter. 
 Rem acu tetigit. It was said critically of an eminent modern 
 statesman, ' He has no intuitions.' He saw too many aspects 
 of every question, and saw them disproportionately. 
 
 § 1083. On the other hand, though inquiry into the reason 
 of a thing {to Sioti) is an inquiry into its essential nature (ti 
 eo-Ttv ;), yet I must repeat that the phenomena with which Logic 
 deals are all things that happen, not only those organic genera 
 or kinds which have a fixed constitution and clearly marked 
 essence. The reason why the train went off the line is because 
 a boy put a stone on the rail. The reason why I laughed is 
 because you said something amusing, or looked so serious. The 
 reason why the lady put up her umbrella was that she felt a drop 
 of rain. The inductive ' search into the system of Reality ', the 
 ascent to ever higher concepts, the unravelling of the tangled 
 web of causes and effects, the scientific pursuit of Truth — vere 
 scire est per caussas scire — , this is not for the mere logician, who 
 leaves to others the tracing of the orderly development of the 
 universe, through a gradation of essential conceptions, from 
 formless matter to matterless form. The 'Logic of rational 
 belief is not Induction employed upon one department of things, 
 that which is commonly called Nature, but upon all. 
 
 § 1084. The Stoic School endeavoured to make Logic an 
 instrument of physical inquiry. Abailard and his followers had 
 the same aim in the Middle Ages. This, however, is not to 
 widen logic but to narrow it. The investigation of physical 
 nature is but a small part of human inquiry, and presents a much 
 
 of mind — never without labour, never without preparation ; yet with no 
 constant dependence upon preparation, upon labour, or even entirely 
 upon personal endowments.' Darwin tells us how, his mind being 
 already prepared by long observation of the habits of plants and animals 
 to appreciate the universal struggle for existence, the idea of the 
 tendency of favourable variations only to be preserved came into his 
 brain in reading Malthus on Population. ' Here then I had at last 
 got a theory by which to work' {Life and Letters, vol. i, Autobiog. 
 Chapter). 
 
Scientific Simpler than Untutored Inductions 537 
 
 easier and simpler problem to the logician than the extremely 
 complicated phenomena of politics, ethics, and conduct gene- 
 rally. Every moment of our lives we are building up inductions — 
 the child that is learning to lisp its mother tongue as much as 
 the savant deciphering an unknown hieroglyphic ; the beggar 
 judging by faces from which passenger to expect a penny, the 
 man wondering why his friend does not write, or what is the 
 explanation of his shares going down, or putting two and two 
 together about anything else, great or small, from Free Trade 
 to the weather, as much as the student establishing the author- 
 ship of a Shakespearean play by the line endings and syntax. 
 The illustrations of the Inductive Methods given in the logical 
 books disguise the extreme complexity of most of the actual 
 problems presented to human minds. They also encourage 
 a misleading belief that Logic is only justified by the assistance 
 it gives to mankind in subduing Nature and extending the 
 boundaries of useful Knowledge.^ The difficult inductions of the 
 vulgar, moreover, are usually quite as correctly formed as the 
 comparatively simple ones of the learned. Where men go 
 wrong is not through want of logic but through ignorance, pre- 
 judice and mal-observation. It is their materials which are 
 their difficulty. They compare and judge wrongly; they select 
 and arrange the facts unintelligently and unmethodically ; they 
 think they have all the material facts before them when this is 
 far from being the case. But the grinding of the mill of Reason 
 is performed almost mechanically. It is the understanding, not 
 the rational faculty, which errs. 
 
 § 1085. The usefulness of Inductive analysis is chiefly disci- 
 plinary and educational. Veitch, however, remarks : — 
 
 'As to the value of the rules of Induction in the matter of 
 culture, they are wholly secondary as compared with the high 
 abstract training, the precision of logical thinking, the orderli- 
 ness of thought, the power of consecution, which are developed 
 
 ' Ramus complained that he had given himself to the study of the 
 ' Organon ' for a decade without becoming a better geographer or a wiser 
 historian (see Animadversiones in Dialeciicam Aristoielis, i. iv). 
 Edmond Mariotte (ob. 1684) was one of the first to ' enlarge ' the Aristo- 
 telian Logic by engrafting upon it experimental methods. He considered 
 this new calculus to be a supreme and universal science, related to the 
 other sciences as algebra to mathematics (Essai sur la logique, qu. Devey, 
 Logic, p. 17). 
 
538 Principle of Causality 
 
 by the study of Formal or General Logic. Compared to this' 
 their influence is weak and unsteady, as is the swaying chaos of 
 fact in the world compared with the grasp of the universal laws 
 which regulate concepts, propositions, and reasonings. And 
 while in the world of physical phenomena — definite, visible, 
 tangible, or to be reached by microscope or telescope — they are 
 valuable and important, they cannot for a moment be placed on 
 the same high level as those laws which regulate all human 
 thinking in its very essence, its very possibility — which form, 
 in fact, the conditions of any concept, any judgement, any 
 reasoning whatever. These are the first things to be studied, 
 and the man who knows not these in their grounds and basis is, 
 whatever he may know of rules applied to so-called phenomena, 
 a mere empiric' ^ 
 
 § 1086. Philosophy is the loser not the gainer by confusion 
 between Reason and Experience, between the necessary con- 
 nexions of thought, the rational consequences of data, on the 
 one hand, and the objective connexions of empirical beliefs 
 on the other. The mind, it is often contended, must aim at 
 actual, not at merely relatively valid, truth. That may be so ; 
 but it must not aim at it in logical analysis. Methodology, we 
 are told, should be regarded as the special, final and chief aim 
 of science. Sigwart, however, says, 'of our science,''' which in 
 the interests of scientific thought must be strenuously denied. 
 Those who ask not merely for stability and consistency in our 
 thoughts but for the thoughts themselves, or for the arrange- 
 ment of the thoughts, must go elsewhere than to Logic, which 
 supplies nothing more than a conditioned necessity, avdyKriv i^ 
 vTro^eVews. It is true, as Sigwart observes, that 'AH real learn- 
 ing is mediated judgement'.' The Socratic Maieutic went 
 further, and, maintaining that there is no such thing as learning, 
 nothing but recollection, was ' content to call into consciousness 
 the ideas of subject and predicate by means of questions '.* But 
 the materials, whether gained by experience or by dva/Avr/o-is, and 
 their marshalled order also, must be given and provided, Reason 
 conducting the mediating process formally only. 
 
 § 1087. However far back you push the bare deliverance of 
 consciousness, the sensible which is not yet the intelligible, you 
 must come to it sooner or later for any synthetic extension of 
 
 ' Institutes of Logic, pp. 482, 483. ^ Logic, i. 21. ' Ibid. p. II3. 
 Aristotle says : — ■rraaa SiSa(rKa\ia Ka\ nacra uddqais diai'oijriK^ «K irpov- 
 Trapxova-ijs yiyverai yvaxreais (An. Post, i. l). 
 
Does Logic Offer a Criterion of Truth ? 539 
 
 your knowledge. The intelligence has built the predicate out of 
 previously experienced hoc aliquids before it can judge that any 
 intuition falls under it as subject, that This is of such a kind.^ 
 But Logic guarantees neither the reality of the intuition nor 
 the truth of the comparison. It is impossible then to agree 
 with those who, like Sigwart, hold that ' Logic proposes to set 
 forth those Criteria of true Thought which are due to the demand 
 for necessity and universal validity ', with the explanation that 
 ' in necessary and universally valid Thought knowledge of the 
 Existent is included '." Logic cannot tell which predicates are 
 grounded in the permanent nature of their subjects, disengaging 
 the constant element from casual and varying connexions. 
 Even mathematical and metaphysical necessity are foreign to 
 its analysis, and accepted by it as given. Sigwart admits this. 
 He says : ' Logic declines to give any judgement as to the 
 necessity and universal validity of the premises from which we 
 start at any time. Observance of logical rules ensures merely 
 the formal correctness of the procedure and not the material 
 truth of the results.' Yet by what rules we may have certain 
 knowledge of a knowable Existent, and how Thought correctly 
 mediates the perceptions of an external world, in what way 
 human Thought, whose end is the preservation of our well- 
 being, shall avoid missing its aim and falling into error, this he 
 conceives to be the province of logical inquiry. Logic, in his 
 view, which is the usual one, is a discipline which guides and 
 directs Thought, regulating Thought's procedure, and partially 
 including the art of correct observation. In other words Logic 
 directs us how to judge, not limiting itself to 'judgements ot 
 subsumption to the exclusion of the mere communication of 
 facts', the conditions of validity challenging logical investigation 
 in the one case as much as in the other. Sigwart appeals to 
 Aristotle's definition of judgement as implying truth or falsehood.' 
 
 ^ The Subject is thus first in consciousness, the Predicate idea only 
 second. Judgement, as Bradley observes, predicates an idea of a realityj 
 a what of a that. But the what has been formed by the intelligence out 
 of thats given by sensation and stored up by memory. 
 
 " Logic, i. 8, 10. A recent writer well observes that there is no half- 
 way house between regarding the whole question of existence as irrelevant 
 to Logic and pursuing metaphysics to the bitter end. 
 
 ' (Aoyos) airo<pavTiK6s ov iras, d\X' iv m to SKrjOevav f) i^evbeffQai inrapx^', 
 De Int. 4. 
 
540 Principle of Causality 
 
 Thus guided by Logic, ' we proceed in Thought from given 
 data in such a way that each step shall be accompanied by the 
 consciousness of necessity and universal validity.' ^ 
 
 § 1088. But the Tightness of a judgement is more than formal 
 correctness. It is correspondence to the reality of things. And 
 a Logic which takes cognizance of such correspondence deals 
 with the matter of our thinkings and not only with their form. 
 Sigwart takes an example from the rule of Conduct — 
 
 ' Before the court of Conscience the only evidence we have 
 as to whether the Thought which guides our action has attained 
 its purpose or not is the inner consciousness of the necessity of 
 our Thought, the certainty that the given mode of action follows 
 from the general rule ; the self-evidence which satisfies us that it 
 was right and good to act so under the circumstances because 
 the general principles of justice and morality demanded it.' ^ 
 
 If, however, the necessity of application of rule to case ' were 
 merely a matter of ' formal correctness ' it would be easy enough. 
 The difficulty lies in judging about the facts, in deciding whether 
 the circumstances have all been reviewed and none forgotten, 
 overlooked or misapprehended, and in knowing whether to 
 trust the final verdict of the moral sense, The hesitation whether 
 my conduct ought to conform to a given rule resides, in a word, 
 in the infirmity of the Faculty of Comparison. That infirmity 
 lies outside the logician's cognizance. 
 
 § 1089. 'Let us labour,' said Pascal, 'to think aright; this 
 is the foundation of morality.'* Logic, however, is only a 
 negative condition of right thinking. It compels us to think con- 
 nectedly and rationally. It is concerned not with the well-being 
 of Thought, but with its right to come into existence." It is 
 
 '^ Again, he correctly describes the logical synthesis as ' a synthesis of 
 ideas into unity . . . not in the sense of agreement with external reality, 
 but in the sense of the logical necessity of their synthesis '. 
 
 "^ Logic, i. 5. 
 
 ' Whately rightly complains of the vagueness ot the use by logical 
 writers of the word Induction, 'which is sometimes employed to designate 
 the process of investigation and of collecting facts ; sometimes the de- 
 ducing of an inference from those facts. The former ... is not a process 
 of argument ; the latter again is an argumentative process ; but then it 
 is, like all other arguments, capable of being Syllogistically expressed.' 
 There cannot, the Archbishop insists, be a process of Reasoning distinct 
 from Syllogism (Essay on the Province of Reasoning). 
 
 * Pens^es, Pt. I. Art. iv. § 6. " See Hamilton, op. cit. ii. 3. 
 
Analogy 541 
 
 incompetent to find appropriate conceptions wherewith to 
 colligate facts. But it insists that everything implicit in a, con-, 
 ception may be stated explicitly as a fact. 
 
 § 1090. Suppose I am at a loss to account for the high death- 
 rate of health-resorts. Inductive reasoning connects the pheno- 
 menon with the circumstance of this, that and the other town 
 being resorted to for health, as effect with cause. In another 
 set of cases the same kind of reasoning obliges us to connect 
 a high death-rate with insanitary conditions. Here is a puzzle, 
 till the logician bids me analyse my conceptions by my intelli- 
 gence. Bad drainage and numerous deaths are easily associated. 
 What, on the other hand, is a health-resort ? Clearly a place 
 to which people resort for health? What kind of people? 
 Intelligence answers, aiUng people, A health-resort, then, is 
 a place crowded with unhealthy people. And unhealthy people 
 die, even at a dusty spa or in a seaside lodging-house. Reason, 
 i. e. the logician, now again steps in and draws the inference. 
 And Plurality of Causes accounts for the same phenomenon 
 appearing under such opposite circumstances. 
 
 If mortality is said to be greater among moderate drinkers 
 than among total abstainers. Logic is about to draw an obvious 
 conclusion ; but first it begs Intelligence to make sure what it 
 means by its terms. It may turn out that many call themselves 
 moderate drinkers who are moderate drunkards. In the same 
 way, convictions for crime may in a certain district be remark- 
 ably few. But it does not follow that criminals are few till we 
 are certain that witnesses will come forward, or that juries are 
 not terrorized. Again the fact that fewer children are now sent 
 to gaol than formerly does not prove that juvenile morality is 
 higher; for it may be that they are sent to reformatories or 
 otherwise dealt with. 
 
 § 1091. In these and like cases the respective provinces of 
 Reason and of the Understanding are clear. How illusory, 
 again, are inferences based on statistics, and (it must be added) 
 pn history. For we know that nothing is so deceptive as figures 
 — except facts, seeing that the record of ninety-nine important; 
 facts out of every hundred has perished. 
 
 § 1092. Before leaving the subject of Induction something 
 should be said about Analogical Reasoning. Analogy has been 
 
542 Principle of Causality 
 
 defined as induction from a single instance, in which the absence 
 of number, is compensated for by the high degree of resemblance. 
 But the points of resemblance must not be isolated. 
 
 The differences between Analogy and ordinary Induction, how- 
 ever, are superficial. Induction, to explain a fact, tries to arrive 
 at a general principle. ' These be her very Cs, her A'5, and her 
 T^s.' It follows (from comparison) that the handwriting is 
 . Olivia's. This child has diphtheria. So have others. They 
 all drank milk from a certain dairy. That then is the cause. 
 Analogy, on the other hand, appears to be scarcely conscious of 
 any general law, and argues (seemingly) from particular to par^ 
 ticular.^ Of this nature is case law, based on precedents. It is 
 as though we argued affirmatively in the Second Figure — 
 This thing which has the characteristic Y is Z. 
 XisZ. 
 Then X (probably) has the characteristic Y. 
 
 This union of physical parts in which the welfare of the whole 
 is affected by the welfare of each part is an organic body. 
 
 The Church is revealed as an organic Body. 
 
 Then in the Church (we may conjecture) if one member suffer 
 all the members suffer with it. 
 
 § 1093. The analogy — though this is more properly induction — 
 might, no doubt, be from a number of instances to a further 
 instance; as, if Mercury, Venus, the Earth, Mars, &c., being 
 opaque bodies, are planets, we presume that Jupiter also, being 
 a planet, is opaque. In such cases a general law is directly 
 suggested. But when the inference is from an otherwise unique 
 instance to another like it, the law, though in the background of 
 
 ' ' Mr. Mill remarks that the syllogistic form of inference, from generals 
 to particulars, which supposes that each induction is made general, 
 is "a collateral security for the correctness of the generalization itself". 
 It increases the sense of responsibility on the part of the reasoner by 
 letting him know that his inference to one individual must equally apply 
 to a large host of individuals. A common device for checking a rash 
 inference is to point out the extent of the consequences involved. . . . If an 
 induction is unsound, the making it general is likely to suggest contra- 
 dictory instances' (Bain, Logic, i. 213). 'Analogy represents a phase 
 of thought in which we no longer count but weigh the examples. ... It 
 might be said therefore that it is a material and not a formal inference ' 
 (Bosanquet, Logic, ii. 90). On the contrary Analogy is formal as far as 
 it goes. It does not compel belief, but recommends and supports it when- 
 created. So does Induction. 
 
Analogy 543 
 
 the reasoning faculty, is unlikely to be made explicit.^ Thus 
 a harvest field is, taken as an entire picture, unique. But in 
 the sphere of ghostly things a phenomenon, equally unique, 
 resembles it — the Kingdom of God. Parabolically, then, we 
 argue direct from the one to the other. There is no need to 
 formulate a general principle, or logical conception, under which 
 ■these two solitary cases are to be brought ; but — ' The Seed is 
 the Word ' ; ' The Word is the Seed.' ' The reapers are the 
 angels ' ; ' The angels are the reapers.' ' The good ground ' (ot 
 soil, or of heart) ' brings forth some thirty, some sixty, some an 
 hundredfold.' Or again, there is only one spiritual thing like 
 a drag-net cast into the waters and gathering fish of every kind, 
 of which the bad are cast away and the good kept. In fables 
 again, as the Wolf and the Lamb, or the Dog in the Manger, we 
 have a complete story or set of facts with its analogue. Bishop 
 Butler's Analogy of Religion, Natural and Revealed, to the 
 Constitution and Course of Nature expounds laws in the spiritual 
 world which are the counterpart of observed natural laws. 
 The difficulties which beset belief pertain to both. It is the 
 ' kill or cure ' method of argument. 
 
 ^ Professor Case says that the types of Induction and of Analogy are 
 respectively these : — 
 
 Induction. Analogy. 
 
 SisF S^isP 
 
 Every M is similar to S S^ is similar to S^ 
 
 Therefore every M is P. Therefore S' is P. 
 
 He combat's Bradley's contention that ' Similarity is not a principle 
 which works. What operates is identity, and that identity is a uni- 
 versal.' For, says Bradley, the moment you observe that this magnet 
 attracts iron you ipso facto know that every magnet does so, and 
 all that remains is for deduction to identify a second magnet as the 
 same as the first, and conclude that it attracts iron. Prof. Case denies 
 this, remarking that 'The basis of Bradley's logic is the fallacious 
 dialectic of Hegel's metaphysics, founded on the supposition that two 
 things which are different but have something in common are the same '. 
 It follows that a man is the same as a man-of-war, and all things are the 
 same thing (Encycl. Brit., loth ed., art. 'Logic'). Both views appear 
 to be somewhat crudely expressed. We do argue from similar to similar, 
 but we must first satisfy ourselves that the point of resemblance — in the 
 case of Analogy not a mere point but an order of things— is probably the 
 cause of the phenomenon. There might be similarity in other respects, 
 yet no inference be possible. We have to establish an identity in the one 
 essential respect, and this, demonstrated of a single instance, is a 
 universal. 
 
544 Principle of Causality 
 
 § 1094. In Analogical Reasoning then we do not generalize 
 from a number of instances which may have only one material 
 circumstance in common — like the people who all got their milk 
 from the same dairy — , but comparing two things which are in 
 a number of important inter-related circumstances constituted 
 alike, in other words two systems, we venture on the conclusion 
 that a property possessed by the one, and which seems to flow 
 from its general constitution, is possessed also by the other. 
 
 Even, however, if we are quite sure that the characteristic is 
 a derivative property, yet because the two systems are only 
 alike, and not the same, we cannot be certain that the cause, 
 the fundamentum relationis, which produces an effect in the one 
 is not modified by the circumstances which differentiate the 
 other. The spheres of Nature and of Grace, for instance, are 
 profoundly different, whatever analogies exist between them. 
 Again, there is an analogy between the cooling of love and the 
 cooling of an igneous body. Yet it would be rash to infer, 
 because a planet becomes more solid and firm as it gets colder, 
 that affection and devotion do so likewise. 
 
 § 1095. Hamilton, following Kant, says : — 
 
 ' In Induction we look to the one in the many ; in Analogy we 
 look to the many in the one. And while in both we conclude 
 to the unity in totality, we do this in Induction from the 
 recognized unity in plurality, in Analogy from the recognized 
 plurality in unity. Thus, as induction rests upon the principle 
 that what belongs (or does not belong) to many things of the 
 same kind belongs (or does not belong) to all things of the same 
 kind, so analogy rests upon the principle that things which 
 have many observed attributes in common have other not 
 observed attributes in common likewise.'^ 
 
 ^ Lectures on Logic, ii. 166. ' It would be an analogical inference to 
 conclude that a disease corresponding in many symptoms with those 
 observed in typhus corresponds in all, or, in other words, is typhus ; 
 whereas it would be an induction to infer that a particular symptom 
 appearing in a number of typhus patients will appear in all ' (G. Croom 
 Robertson, art. 'Analogy' in Encycl. Brit.). The Grote Professor 
 rightly considered, however, that the distinction does not go below the 
 surface. The former case might be a good induction, and the latter 
 a mere analogy. If there is no ground for a good induction there 
 can be no ground for a particular inference either. Robertson held 
 with Mill that Induction and Analogy only differ in respect of their 
 degree of evidence. Analogy cannot prove a causal connexion between 
 the inferred properties and the common characteristics of universal 
 
Analogy 545 
 
 § 1096. For Analogies do not always run on all fours. ' Every 
 parable halts.' It is sufficient if the causal rather than the 
 casual connexions are parallel. In fables, gnomic sayings, and 
 parables the main point, the ' moral ', alone is looked to. The 
 parables of the Unjust Judge and the Thief in the Night are 
 instances of this. In an Allegory, like the Pilgrim's Progress or 
 the Faery Queene, a parallelism worked out too exactly and 
 conscientiously would get upon the reader's nerves. Bunyan's 
 detailed identification of Talkative with the hare of the Mosaic 
 code is an instance. Far more is this the case with metaphors or 
 even similes. Such as Pope's 
 
 Eternal smiles his emptiness betray. 
 
 As shallow streams run dimpling all the way — 
 
 or Bacon's 'Money is like muck, not good except it be spread'. 
 The resemblance must not be too ingenious. Having touched 
 the sentence with suggestiveness the allusion flits away and is 
 seen no more. There is a deep mystery in the good tree bring- 
 ing forth good fruit, but not in 'Your life is a vapour' — vita 
 fumus — or a shuttle, or a voyage, or a stage-play, or in ' Ephraim 
 is a cake half turned ', in the besom of destruction, or the fly 
 in ointment. In Latin countries, where riots quickly arise, 
 they say, 'Rain is the best gendarme.' Hobbes says, 'Words 
 are the counters of wise men and the money of fools.' Socrates 
 argued that, as the human body is animated by a consciousness, 
 so the material universe, the system and frame of things, must 
 be. This is an analogy. But 'fluctus populi fluctus maris' 
 carries us no further; nor 'amor, ut pila, vices exigit'; nor 
 Petrarch's ' II giorno la sera, la vita loda il fine ' ; nor yet the 
 Psalmist's comparison which speaks of fruitful valleys as laugh- 
 ing and singing. In fact. Metaphor transfers to one object 
 conceptions which belong to another resembling it. Shakespeare 
 
 application. It can only show that they are not incompatible.' Science 
 resorts to analogies provisionally. In common life Analogy is relied upon 
 greatly for the guidance of conduct. But the mind, in its eagerness to 
 bring things together, is apt to overlook material dissimilarities. The 
 danger of False Analogy is especially great when the things compared do 
 not belong to the same natural classes, but are alike only in some internal 
 relation of each to another thing of its own kind. ' The legs of the lame 
 are not equal : so is a parable in the mouth of fools ' (Prov. xxvi. 7). 
 
 N n 
 
546 Principle of Causality 
 
 says of a lady, ' She speaks poniards ; every word stabs.' Death 
 with him is a ' fell sergeant, most strict in his arrest '. Tennyson, 
 very finely, calls eyes of pure women ' wholesome stars of love'. 
 This poet is fruitful in similes— the dainty nose 'tip-tilted like 
 the petal of a flower ', or the feigned lady's handwriting (early 
 Victorian) — 
 
 In such a hand as when a field of corn 
 Bows all its ears before the roaring East — 
 
 besides his many grave and noble similitudes. Milton's com- 
 parison of Satan's sleeping followers to the autumnal leaves 
 lying thick in an Italian valley will spring to the mind, or his 
 humorous lines on Hobson the carrier, how Death — 
 
 Thinking now his journey's end was come. 
 
 And that he had ta'en up his latest inn. 
 
 In the kind office of a chamberlin 
 
 Showed him his room where he must lodge that night, 
 
 Pulled off his boots and took away the light. 
 
 If any ask for him it shall be said, 
 
 ' Hobson has supped, and 's newly gone to bed.' 
 
 But when we think of the grave as a lodging-house, a deversorium, 
 we do not necessarily extend the analogy to the chamber candle- 
 stick. If we call a camel the ship of the. desert no image of 
 masts and spars comes into the mind. Sometimes a simile is 
 reciprocal — a brow is arched, and an arch is ' a hoary eyebrow ' ; 
 we speak of a clouded face, and of a scowling or frowning sky ; 
 of a ' scolding hinge ' and a temper that needs oiling ; or youth 
 is life's springtime, and May is the year's ' sweet seventeen ' — 
 
 O juventute, primavera della vita ; 
 O primavera, juventute dell' anno ! 
 
 When Shakespeare speaks of 'the bubble reputation', he 
 means its iridescence, as well as its lightness and quick bursting. 
 Still, that is accidental. Reputation might be called a bubble, 
 even though a bubble had no colour. Lowliness might be 
 young ambition's ladder, even if the successful man, once 
 mounted, did not kick away the degrees by which he did ascend. 
 It is only in the regular analogy that from the presence of 
 a congeries of resembling qualities we can surmise others. On 
 the other hand, though Metaphor is not argument, it may, as 
 Mill says, suggest that an argument exists, and be useful for 
 expository purposes. A single word will sometimes flood 
 
Analogy 547 
 
 a subject with light. Thus, the ruler of a state is a gubernator, 
 or helmsman. 
 
 § 1097. Analogy thus presumes the existence of well-defined 
 classes of things and groups of attributes. It implies that 
 objects have an internal constitution. But, as we have seen, 
 logical inference cannot assume these coexistences. The cir- 
 cumstance that two things have ninety-nine attributes in 
 common affords no logical ground for concluding that they have 
 the hundredth, unless it is reasonably supposed to be derivative. 
 If two saucers are exactly alike in make and one is cracked, that 
 aifords no presumption that the other is cracked. Yet it may 
 be presumed, therefore, that the other is fragile. But Mansel 
 is wrong in saying of Analogy that while (quoting Butler's 
 Introduction) its moral fiDrce varies 'from the highest moral 
 certainty to the very lowest presumption ', its ' togical value is 
 zero'.' Moral presumption implies material knowledge; but 
 there would be no presumption if it were all knowledge and no 
 logic. Experience and reflexion prove that there is such a thing 
 as parallelism, and if the parallel goes as far as we can see we 
 may presume it goes further. Yet it would be ludicrous if we ex- 
 pected giants to ' talk big ', and to use only sesquipedalian words. 
 
 § 1098. 'Analogy' is for Aristotle proportion, or parity of 
 ratios (io-on?s Xoymv). As 3 is to 7 so is 15 to 35. Such a quan- 
 titative relation, however, in the modern Analogy takes a quali- 
 tative form. What parliament is for the nation, a parish council 
 is for the parish. What the safety-valve is to an engine, the 
 same relation, it may be said, is borne by platform oratory and 
 the newspapers to the State machine, which works in spite of 
 popular institutions rather than because of them. The intelli- 
 gence is the eye of the soul.'' Aristotle usually speaks of Example 
 
 ' Butler puts the question 'Whence it proceeds that likeness should 
 beget that presumptive opinion and full conviction which the human mind 
 is formed to receive from it ' {Introduction). The Twelve failed to argue 
 from the feeding of the five thousand in the wilderness to their Master's 
 ability to feed the four thousand, or to still the storm. ' Their heart 
 was hardened ' (St. Mark vi. 52, cf. St. Matt. xvi. 8-10). On the other hand 
 there may be a credulous eagerness to analogize, like that of Hazlitt, who 
 fully believed that the Duke of Cumberland had murdered his valet, in 
 spite of overwhelming evidence' to the contrary, because, he said, all the 
 princely Houses of Europe had the instinct of murder in their blood. 
 
 ^ This is Aristotle's own illustration {Eth. v. 3. ^)—&<\ns : o-S/io : : vovs : 
 ^vxTj. Whatever may be predicated of the one relation may be predicated 
 
 N n 2 
 
548 Principle of Causality 
 
 (TrapaSeiy/ia) rather than of Analogy. This corresponds to the 
 Socratic irapa^oXri. But the inference, even though based on 
 a single case, is through a suggested universal. 'Example is 
 when the extreme, or major, term is shown to belong to the 
 middle by means of a term like the third, or minor, term.'* 
 Thus in the syllogism — 
 
 All wars between neighbours are disastrous ; 
 
 The war between Athens and Thebes is between neighbour ; 
 
 Therefore it is disastrous — 
 the major premiss was suggested by an example resembling the 
 war between Athens and Thebes, viz. the war between the 
 Thebans and Phocians, which was disastrous and was a war 
 between neighbours. 
 
 § 1099. Inductive inference, on the other hand, as we saw, 
 proves, according to Aristotle, the major premiss by means of 
 the minor term. Thus — 
 
 All wars between neighbours are disastrous, 
 
 This, that, and the other war have been (the whole number 
 of) wars between neighbours. 
 
 Therefore they have been disastrous. 
 But the major premiss was proved by examining the several 
 \vars comprised in the minor term, and showing that they were 
 disastrous, and also between neighbours. 
 
 § 1 100. Aristotle's explanation is not particularly illuminating. 
 He had no grasp of the real principle of Induction. Similarly 
 the Socratic Analogy was too simply enumerative. 
 
 Archbishop Whately remarks : — ' It has been made a subject 
 of bitter complaint against Logic that it presupposes the most 
 difficult point to be already accomplished, viz. the sense of the 
 terms to be ascertained. A similar objection might be urged 
 against every Art in existence ; e. g. against Agriculture, that all 
 
 of the other. Because two sets of terms have certain relations in common 
 (in the case of example certain attributes), they have all in common. 
 
 ' HapaSetyfia 8' ftrrtv orrav t<S piam to aKpov vndp}(OV Sfix^S ^'" '''''" o/ioiov 
 Tijj Tp'iTW. . , . (jiavepov cvv on to napddeiypd icrnv otre as pepos trpbs oXov, owTe 
 tor oKov TTpos pepos, dW o)s pipos npos p^pos, oTav ap(j)a> pev 3 viro raird, 
 yvtapipov 5e Bdrfpov. Kal 8ia<p€pei rrjs iirayayris on tj pev i^ dirdpTOiV t5>v 
 aropav (the individual cases) to aKpov 'Be'iKwev iirapx^nv ra peirif Koi irpos 
 TO aKpov ov o-vvrJTrTe tov a-vWoyia-pov (Induction does not necessarily apply 
 the generalization to a new case), to Se Koi avvdiTTei, koi ovk e| dirdpriov 
 &eiKvva-iv. Art. Pr. ii. 24, 68''38. 
 
Example 549 
 
 the precepts for the cultivation of land presuppose the possession 
 of a farm ; or against Perspective, that its rules are useless to 
 a blind man.' ^ 
 
 iioi. Example, or Analogy, is used chiefly as a way of 
 meeting objections. Or the argument may controvert an 
 attempted analogy, as that because two things are alike in one 
 respect they cannot be unlike in another, by producing two 
 other things which have the same resemblance but admittedly 
 are unlike in the other respect. Thus the Puritans argued that, 
 as an impression is produced on listeners to a sermon by a 
 general delivery to all at once, so the words of Administration 
 should be repeated once only. Hooker answered : ' The soft- 
 ness of wax may induce a wise man to set his stamp or image 
 therein ; it persuadeth no man that because wool hath the like 
 quality it may therefore receive the like impression.'^ If MX 
 is Y and MZ is Y it does not follow either that X is not Z or 
 that it is Z. It may be either. Butler did not try to show that 
 the difficulties of revealed truth prove its Divine origin (credo 
 quia absurdum), but only that they afford no logical presumption 
 against a Divine origin, seeing that they exist in the natural 
 order also, which the eighteenth-century opponent admitted to be 
 from God's hand. The example adduced is not sufficient to 
 establish a universal affirmative proposition, but it refutes the 
 universal negative. Such a thing has happened once ; therefore 
 it may happen again. And the larger the resemblance between 
 the two cases, considered as systematic wholes, the more prob- 
 able is it that what is true of the one is true of the other. Or 
 contrariwise, a negative instance refutes a universal affirmative 
 implied in a particular assertion. You choose statesmen by lot, 
 says Aristotle. But who chooses athletes by lot ? ' 
 
 » On Fallacies. ^ Ecd. Pol. Bk. V. cap. Ixviii. 
 
 = Rhet. ii. 3o, 1393*27. 
 
CONTENTS OF APPENDIX 
 
 PAGE 
 
 A. An Attack on the Inductive Methods . . 551 
 
 B. Analytical Deduction 554 
 
 C. Hypothetical Character of Universals . . 557 
 
 D. Indifference of the Quantity of the Minor . 560 
 
 E. Reduction per impossibile 562 
 
 F. Restrictive Form of Major Premiss . . . 567 
 
 G. Syllogisms in Comprehension 569 
 
 H. Some Syllogistic Variations 572 
 
 I. Cause and Sign 574 
 
 K. Idiomatic Forms 577 
 
APPENDIX A 
 
 AN ATTACK ON THE INDUCTIVE 
 METHODS 
 
 An attack, in what I am obliged to call the writer's style of 
 jocular truculence, is directed in Bradley's Logic against the 
 Inductive Methods, which 'are vicious and their Canons false '. 
 ' Inductive Logic is a superstition,' ' a fiasco,' and, since the 
 imperfections attendant on its rules are stated by Inductive 
 logicians themselves, ' a confessed fiasco.' The critic promises 
 to show three things — (i) That the Canons suppose universal 
 truths as the material upon which we are to work. (2) That the 
 process they prescribe is not inductive. (3) That they are them- 
 selves invalid. 
 
 As regards the first point, the raw material of Induction is 
 itself, we are told, a finished product, and presupposes universals 
 inductively obtained. If we expect to be given the material as 
 yet untouched by the Methods we are doomed to disappoint- 
 ment. 'A suspicion of the shock which we are destined to 
 receive may have come from the effrontery of the Method called 
 " Residues ". This estimable example of " our great mental 
 operation" comes up to us placarded as one of "the means 
 which mankind possess for exploring the laws of nature by 
 specific observation and experience ", and then openly avows 
 that it depends entirely on "previous inductions". Unless 
 supplied beforehand, that is, with one or more ready-made 
 universal propositions, it candidly declines to work at all. We 
 inquire of "Residues" where we are then to begin, and she 
 says, " I do not know; you had better ask 'Difference'." We 
 anxiously turn to consider "Difference" and are staggered at 
 once by the distressing extent of the family Hkeness. A chilling 
 idea now steals into the mind,' &c. 
 
 Well, it is true that this particular Method presupposes the 
 Method of Difference. And it is true that the latter Method 
 may often proceed from inductions already formed to a wider and 
 more general induction. If, instead of asking, Why does this 
 
552 Appendix A 
 
 object (an apple) now fall to the ground, and that object (smoke) 
 now rise towards the sky? I were to ask, Why do apples 
 always tumble and why does smoke always ascend ? the 
 materials for the general principle of gravitation would be 
 supplied to the thinker in a half-manufactured state/ But what 
 Dr. Bradley is concerned to show is that Inductive method 
 does not ultimately start from sense-material, from bare facts. 
 Surely the ascending property of smoke was generalized by me 
 originally from watching a particular cottage roof or factory 
 chimney ; and the law that apples, when anything releases them 
 from their hold of the tree, are sure to fall has been learnt by 
 my picking this one off the ground and by that one falling on 
 my head. Certainly, if ascertained results have once followed 
 from conditions exactly known, I am sure that, given the same 
 conditions, the same results will always follow; and so far the 
 ascertainment of every fact is the perception of a universal. 
 But this is conception rather than induction. The judging 
 faculty, comparing various manifestations of the phenomenon, 
 eliminates the immaterial features of the ease and thus abstracts 
 the law of the phenomenon. The eliminated features are not 
 necessarily inductions. They may be, and must ultimately be, 
 individual facts. It was not the prawns made me ill, for I took 
 some last week without ill effects. Nor was it the curry. And 
 so forth. Why should Dr. Bradley choose such an illustration 
 as that ' Oil and alkali, if combined under conditions be and de, 
 in each case produce soap ' ? 
 
 It is of little consequence whether I say, ' Curry never dis- 
 agrees with me,' or 'Curry did not disagree with me last week'. 
 In either case we eliminate an inconsequence. But the employ- 
 ment of a general rule adds security to the induction. The 
 imperfection of the Method of Difference is merely the difficulty 
 of being sure that the requirement of 'every circumstance in 
 common but one' has been fulfilled. This lends some 
 uncertainty to the conclusion. But so does uncertainty attach 
 to the conclusion of a deductive argument by the difficulty of 
 ensuring the exact truth of the premisses. Dr. Bradley demurs 
 to the induction from this that and the other dog barking that 
 
 ' ' It is worth noticing that Aristotle, when he speaks of Induction, is 
 hardly ever thinking of deriving a universal proposition from the observa- 
 tion of particular instances in the proper sense. His examples generally 
 have reference to concepts of species, and what he does is to combine, 
 not particular facts into a lowest concept, but specific concepts into 
 a more general concept, or specific rules into a general rule. That the 
 best driver is the man who understands it is itself a universal rule, but 
 he treats it as particular ; in the same way he takes as particulars that 
 man, horse, and mule are without gall, although these are already 
 universal judgements. He does not inquire how these have been obtained 
 from the observation of particular men, horses, and mules ' (Sigwart, 
 Logic, ii. 292). 
 
An Attack on Mill's Canons 553 
 
 all dogs bark, on the ground that we might as well infer, from 
 this that and the other dog having the mange, that all dogs have 
 it. They have ' only one circumstance in common ', viz. that 
 they are dogs. Certainly the Method of Agreement can never 
 supply more than a probability.^ But then life is made up of 
 probabilities ; and the difficulty of distinguishing the materials 
 of one induction from those of another demands not better logic 
 but better observation. The Canons, says Dr. Bradley, are not 
 hard to content. Neither is the Syllogism, which takes what 
 it can get. Why does not Dr. Bradley object to the syl- 
 logism that it deduces from the results of previous deductions 
 (until an ultimate intuited principle is reached), and uses 
 already made materials ? Every syllogism has for prosyllogism 
 another syllogism. 
 
 The second criticism is that the process of the Methods is not 
 really inductive. ' It is not of the essence of their process to 
 bring out a conclusion more general than the premisses. The 
 process is one of elimination. By removing one part of an ideal 
 construction you establish the remainder. And hence the result 
 will be more abstract than the whole original datum, but it need 
 not be more abstract than some of the premisses. On the con- 
 trary it may be less so.' ^ To be sure, if I want to know why 
 the dogs in the yard are barking, and conclude after considera- 
 tion that it is because they are chained up, I have eliminated 
 the circumstances that they are four-footed, or that Ponto is 
 handsome and Neptune worth more than ten pounds, all of 
 which portions of the ideal construction are wider than the fact 
 that they are at this moment chained. But all we are concerned 
 with is that ' chained ' is less particular than ' the dogs in the 
 yard barking'. Conversely, the conclusion of a syllogism is 
 often wider and more abstract than the minor premiss. 'A 
 ribston is subject to the law of gravitation ' (conclusion) is more 
 general than ' A ribston is an apple ' (minor premiss). But it 
 does not follow that in a deductive reasoning we are not 
 descending from the less to the more concrete. 
 
 The third objection to the Methods is that they are in them- 
 selves ' radically vicious '. Though ' recommended to us as a 
 sort of Gospel ' they are transparently ' false statements *. If 
 Dr. Bradley can show this of the Method of Difference, no doubt 
 he can do the business of the rest. What -does he say of it? 
 ' The foundation of the Method, " that whatever cannot be 
 eliminated is connected with the phenomenon by a law," is quite 
 false, unless we add to it " in this one case ", and thereby make 
 
 ' If all the many dogs I had ever observed had had the mange, 
 I should be justified in inferring the high probability that every dog is 
 liable to it, and that Diana's new puppy will have it some time 
 
 2 Lo£tc, p. 337. 
 
554 Appendix A 
 
 it ineffectual for the purpose of generalizing. ... In the 
 premisses ABC — def, BC — ef, you are supposed to know that 
 def is connected with ABC, and ef with BC; what you do not 
 yet know is if, in ABC, A is really a factor. For it might be 
 irrelevant, and BC without it might produce def. But now, 
 having BC — ef, and resting on the assumption which we call the 
 Principle of Identity, you are sure that, if BC — e/"is once true, it 
 will be true for ever. And you proceed from this to argue that 
 BC — def must be false. For to produce def B must have been 
 altered ; and since in ABC — def the result is produced with no 
 possible alteration except mere A, A there must be relevant to 
 the presence of def. Hence A in this case {pi ABC — def) must 
 be, directly or indirectly, relevant to d. . But you must not go 
 further. . . . And we must not forget that even this conclusion 
 depends on our having assumed in the premisses that, in ABC 
 — def, d is not irrelevant. Unless we are perfectly sure before- 
 hand that the whole def has been produced by ABC, we cannot 
 advance one single step.' ^ 
 
 I am, however, quite unable to discern the difference between 
 A being 'relevant to' d and being 'an indispensable part of 
 the cause ' of d. And if it is so in this case it must be so, as 
 Dr. Bradley himself says just before, in every case. What 
 subtler meaning lies in his contention is not easy to discover. 
 The threefold exposu;-e of the famous Methods is hardly so con- 
 vincing as to justify the scornful violence of the language directed 
 against them. But in the critic's opinion the Methods 'must 
 retire from the field, or withdraw their claims. Something like 
 a farce has been played before us, whether we consider the airs 
 and pretences of the Canons, or remember the promises and 
 boasts of their patron.' ^ Really one would suppose that the 
 late John Stuart Mill was the proud pontiff of some logical 
 Established Church. 
 
 APPENDIX B 
 
 ANALYTICAL DEDUCTION 
 
 Bradley's objection to Mill's exposition of the Methods that 
 they do riot start from facts but from inductions already formed, 
 might just as well be alleged against the inductive explanation 
 of a phenomenon ; for the general law, which has been induc- 
 tively reached, when applied to the phenomenon in question is 
 
 1 Op. cit. pp. 339, 341. 2 jj^j^j p_ ^^g^ 
 
Analytical Deduction 555 
 
 applied to it deductively, and yet the result is usually a generali- 
 zation and not a bare fact. Thus, the President of Corpus, 
 criticizing Whewell, Jevons and others, urges that the following 
 is not an induction but an ' analytical deduction ' — 
 
 Such and such spectra are effects of various gases. 
 
 Solar spectra are such spectra. 
 
 Therefore solar spectra are effects of those gases. 
 
 'In the same way,' he adds, 'to infer a machine from hearing the 
 regvdar tick of a clock, to infer a player from finding a pack of cards 
 arranged in suits, to infer a human origin of stone implements, and all 
 such inferences from patent eflfects to latent causes, are really deductions 
 which, besides the minor premiss stating the particular effects, require 
 a major premiss inducing the particular kind of effects of a particular 
 kind of cause. ... A deduction is often like an induction in inferring 
 from particulars ; the difference is that deduction combines a law in the 
 major with the particulars in the minor premiss, and infers syllogistically 
 that the particulars of the minor have the predicate of the major premiss ; 
 whereas induction uses the particulars simply as instances to generalize 
 a law. An infallible sign of an induction is that the subject and predicate 
 of the universal conclusion are merely those of the particular instances 
 generalized ; e. g. These magnets attract iron ; therefore all do.' ' 
 
 But the ' analytical deduction ' is merely the inductive gener- 
 alization applied to the phenomenon under investigation. We 
 are investigating the cause of the solar spectra. Examining 
 similar spectra which are more within our reach we find that 
 they are the effects of various gases. A causal connexion is 
 established, and we say, ' Such and such kinds of spectra are 
 effects of various gases.' This is the general law of which we 
 were in search. But the induction is not finished till we say, 
 deductively: 'Therefore solar spectra, being of that kind, are 
 the effects of those gases.' And, as such a discovery is itself 
 a generalization, it is often called the result of the induction, 
 or even the induction itself, though, strictly speaking, it is 
 a deductive application of the induced general principle. 
 
 In the other instances given by Dr. Case the phenomenon 
 investigated is not a uniformity but a single fact. What is the 
 explanation of the ticking which I hear, of this pack being 
 arranged in suits, of these flints being fashioned as implements? 
 Induction leads us to general principles — ticking implies 
 machinery; regular arrangement of cards proves a player; 
 artificial shapes of stones indicate human workmanship. But 
 we should more naturally say, ' The explanation of this pack 
 being found in suits is that it has been played with*; and so 
 forth. Similarly, the explanation of an apple falling may be 
 said to be either that it, being ponderable, is attracted by the 
 
 1 Encycl. Brit., loth ed., art. ' Logic' 
 
556 Appendix B 
 
 earth, or that all ponderable things are attracted by the earth, 
 or, more generally still, the universal law of gravitation. It 
 should be observed, however, that though we are here investi- 
 gating an individual fact, the explanation, 'This apple, being 
 ponderable, suffers the earth's attraction,' is really a generali- 
 zation and not a mere fact. And the same with the cards or 
 the flints, if we say that, being incapable of sorting or shaping 
 themselves, their condition is a sign of intelligent agency. The 
 statement of a cause is the statement of a law, even though it be 
 exhibited not abstractedly but as embodied in a phenomenon. 
 In induction we infer from particulars to particular, through a 
 detected law. But as the particulars from which we started 
 were themselves, as Bradley complains, ready-made uniformities, 
 so the particular to which we infer has a general character also. 
 We knew beforehand that terrestrial spectra had for antecedents 
 certain gases, and by the inductive canons we proved a fact of 
 causation. And now we deduce the same causal connexion in 
 the case of similar solar spectra. Only, until we used the canons, 
 the causal connexion between the gases and the terrestrial 
 spectra was not proved. The original materials of the induction 
 were mere empirical uniformities. Whereas in the case of the 
 solar spectra the causal nexus is proved — proved by the induction. 
 The process of proving it of the terrestrial spectra was the induc- 
 tion, not something prior to the induction. The proof that 
 a law exists is a generalization. It is true that the law that 
 terrestrial spectra are due to certain gases does not seem as 
 abstract and general as the law that spectra of that kind are due 
 to gases of that kind, for it might be that ' terrestrial ' would 
 make a difference. But in that case we could not have argued 
 to solar spectra, and the required induction or explanation is not 
 accomplished. We must assume that the examination of the 
 phenomena within our reach has proved a general and not 
 merely terrestrial connexion of cause and effect between gas 
 and spectrum. 
 
 Frequently we do not wait to demonstrate our general law, 
 but make a probable guess at it, assume it true, and then, 
 applying it deductively, verify the conclusion. The President 
 of Corpus, however, says : — 
 
 ' Jevons, Sigwart, and Wundt all think that induction contains a belief 
 in causation, in a cause or ground which is not present in the particular 
 facts of experience, but is contributed by a hypothesis added as a major 
 premiss to the particulars in order to explain them by the cause or 
 ground. Not so. When an induction is causal the particular instances 
 are already beliefs in particular causes, ^.g. A B C magnets attract iron, 
 and the problem is to generalize these causes, not to introduce them. 
 Induction is not introduction. . . . We first experience that particular, 
 causes have particular effects ; then induce that causes similar to those 
 have effects similar to these ; finally induce that when a particular cause 
 
Analytical Deduction 557 
 
 of the kind occurs it has a particular effect of the kind by synthetic 
 deduction, and that when a particular effect of the kind occurs it has 
 a particular cause of the kind by analytic deduction with a convertible 
 premiss ; as when Newton, from planetary motions like terrestrial 
 motions, analytically deduced a centripetal force to the sun like centri- 
 petal forces to the earth. ... In all induction the universal is the 
 conclusion, in none a major premiss, and in none the ground of either 
 the being or the knowing of the particulars. Induction is simply 
 generahzation.' 
 
 He adds that induction 'is not syllogism in the form of Mill's 
 syllogism from a belief in the uniformity of nature '. ' The fact 
 is that the uniformity of nature stands to induction as the axioms 
 of syllogism do to syllogism ; they are not premisses but con- 
 ditions of inference, which ordinary men use spontaneously. 
 . . . Induction is no species of deduction; they are opposite 
 processes.' 
 
 About this I have said what I have to say in the text, under 
 Induction. 
 
 APPENDIX C 
 
 HYPOTHETICAL CHARACTER OF UNIVERSALS 
 
 In the article already quoted from the new edition of the 
 Encyclopaedia Britannica, the distinguished writer criticizes 
 Sigwart's 'false reduction of categorical universals to hypo- 
 theticals ', which would explicate Barbara— ' M\. men are mortal ; 
 all professors are men ; therefore all professors are mortal ' — in 
 this way — 
 
 If anything is a man it is mortal ; 
 
 If anything is a professor it is a man ; 
 
 Therefore if anything is a professor it is mortal. 
 The President says: — 'This unnatural form, certainly not an 
 analysis of any conscious process of categorical reasoning, breaks 
 down at once, because it cannot explain those moods in the Third 
 Figure, e. g. Darapti, which reason from universal premisses to 
 a particular conclusion. 
 
 If anything is a professor it is good ; 
 
 If anything is a professor it is wise ; 
 
 Therefore something wise is good.' 
 This, Dr. Case observes, is a non-sequitur and admittedly 
 illogical. I presume he means that we have no right to con- 
 clude that wisdom and goodness are sometimes combined, since 
 
558 Appendix C 
 
 from the form of the premisses professors may, for all we know, 
 be non-existent. But this is merely the familiar objection to 
 ' All ^'s are B ' being converted as ' Some B's are A ', seeing 
 that ' All perfect things are as God designed them ' need not 
 imply that anything is perfect, nor 'All who make more than 100 
 marks will deserve a prize' imply that any will make more. 
 Darapti merely says that, granted the occurrence of the subject, 
 the predicated qualities then and there will be found in conjunc- 
 tion. They are, on the hypothesis, not incompatible. The 
 conclusion of the above syllogism should have been, ' If any- 
 thing is wise it may be good.' 
 
 Sigwart's view, however, destroys, we are told, the fabric of 
 inference, and reduces scientific laws to mere hypotheses. 
 
 'The greatest absurdity is that if all universals were hypothetical, 
 Barbara would become a purely hypothetical syllogism — a consequence 
 which seems innocent enough till we remember that all universal 
 affirmative conclusions in all sciences would with their premisses dissolve 
 into mere hypothesis. No logic can be sound which leads to the 
 following conclusion — 
 
 ' If anything is a body it is extended ; 
 If anything is a planet it is a body ; 
 Therefore if anything is a planet it is extended. 
 " Every M whatever is a /" " is a universal which we believe on account 
 of previous evidence without any condition about the thing signified by 
 the subject M, which we simply believe sometimes to be existent 
 (e.g. Every man existent) and sometimes not (e.g. Every centaur 
 conceivable). . . . 
 
 ' By " all " we mean every individual whatever of a kind ; and when 
 from the experience of sense and memory we start with particular 
 judgements of existence, and infer universal judgements of existence and 
 scientific laws, we further mean those existing individuals which we have 
 experienced, and every individual whatever of the kind which exists. 
 We mean neither a definite number of individuals, nor yet an infinite 
 number, but an incalculable number, whether experienced or inferred to 
 exist. We do not mean existing here and now, nor yet out of time and 
 place, but at any time and place {semper et ubique) — past, present, and 
 future, being treated as simply existing, by what logicians used to call 
 suppositio naturalis. We mean then by " all existing " every similar 
 individual whatever, wherever, whenever existing. 
 
 ' Hence Sigwart is right in saying that "All bodies are extended " 
 means, " Whatever is a body is extended," but wrong in identifying this 
 form with " If anything is a body it is extended "- " Whatever " is not 
 " If anything ". For the saine reason it is erroneous to confuse " all 
 existing " with a general idea. Nor does the use of abstract ideas and 
 terms make any difference. . When Bosanquet says that in " Heat is 
 a mode of motion " there is no reference to individual objects but a pure 
 hypothetical fornl which absolutely neglects the existence of objects, he 
 falls far short of expressing the nature of the scientific judgement ; for in 
 his Theory of Heat Clerk Maxwell describes it as "believing heat as it 
 exists in a hot body to be in the form of kinetic energy ",' 
 
 The doctrine which is here ascribed to Sigwart has appeared 
 in some form or other in every logical treatise, and is common, 
 
Hypothetical Character of Universals 559 
 
 in fact, to the whole human race. No one who ever lived has 
 at all times used ' all ' to mean merely a finite but incalculable 
 number. If we say 'All selfish persons are unhappy', or 'All 
 running waters tend to find their own level ', we mean more than 
 the entire number of actual instances, past, present, and future. 
 We give to ' all ' an abstract and ideal signification, judging not 
 only that every selfish person has been, is, or will be, as a con- 
 tingent fact, unhappy, but that there is a causal connexion; and 
 if, besides the actusd individuals seen or foreseen by the eye of 
 Omniscience, any other case of selfishness could be supposed, it 
 too would necessarily be attended byunhappiness. So also we 
 judge that it is the nature of running water to seek its own 
 level. 
 
 So far as science is the enunciation of general laws its catego- 
 rical universals are necessarily hypothetical. 
 
 But ' hypothetical ' need not imply a doubt as to the existence 
 of a real class of things about which the law is affirmed. It 
 merely implies that if anything is found to have the specified 
 attributes it has also the predicated attributes. ' A fast horse is 
 valuable ' means ' if any horse is fast it is valuable '. In this 
 sense quicquid and siquid mean the same thing. Compare 
 ' Whatsoever things (oo-a) are pure ; if there be any (ei rts) virtue 
 and if there be any praise '. 
 
 The ' all ', however, of which Professor Case is thinking does, 
 no doubt, assert by implication the existence of the subject, and 
 not leave it an open question. If the properties of heat are 
 described, the description is assumed to be of an existing thing. 
 'All bodies are extended' does convey to the hearer the idea 
 that bodies exist. Equally ' All three-headed giants breakfast on 
 babies' is meant to convey the idea that three-headed giants 
 exist. The difficulty, however, is a simple one. No one really 
 says that all universals are hypothetical — except so far as this 
 may be philosophically maintained of all subjects whatever. We 
 have to distinguish — as has been done above in the text, § 536 — 
 between abstract universals and concrete universals. 'AH ' may 
 be general and hypothetical, or it may be definite and assump- 
 tive. In the latter case it stands for ' All the '. ' All bodies are 
 extended ' is in a sense abstract. If anything comes under the 
 designation ' body ' it has the quality of extension. But it is 
 also a judgement of assumption, meaning 'All the class of bodies ', 
 referring to a definite and familiar thing. The ambiguity is 
 rather more noticeable in the use of ' Every '. In French, again, 
 there is not the same distinction as in English between ' All ' and 
 'All the', and Latin is more ambiguous, for want of a definite 
 article, than Greek. 
 
560 Appendix D 
 
 APPENDIX D 
 INDIFFERENCE OF QUANTITY OF THE MINOR 
 
 In order to exhibit the indifference of the quantity of the 
 minor term, and to simplify mood and figure as much as possible, 
 it may be worth while to suggest — 
 
 (i) That the quantity of the minor when aflHrmative, whether 
 universal or particular, should be symbolized by the letter U, 
 and when negative by the letter Y. 6/ will thus stand for^ or / 
 indifferently, and Y for E or O, minor and conclusion corre- 
 sponding quantitatively. 
 
 (2) That / and r be retained as the only non-significant con- 
 sonants, for the sake of euphony, after major and minor premiss 
 respectively. 
 
 (3) That the Second Figure be marked by the initial consonant 
 B, the Third by C, the Fourth by D. 
 
 (4) That Figures I and II be regarded as the double norm of 
 all syllogism, the former standing for the affirmation of the ante- 
 cedent, the latter for the denial of the consequent. It is to be 
 understood that direct moods of the Third Figure {C moods) 
 reduce to the form of the First, and moods of the Fourth Figure 
 (D moods) reduce to that of the Second ; in either case by 
 merely converting the minor premiss, no other reduction being 
 required. The conclusion, however, of moods in Figures III 
 and IV is not indifferent. 
 
 (5) That indirect moods, which, as they stand, give a conclusion 
 about P, and only about S by conversion of the conclusion, that 
 is, which require the premisses to be transposed in order to give 
 a direct conclusion about 5, be put on one side. These are, 
 Disamis and Bocardo in Figure III, and Bramanttp and Dimaris 
 in Figure IV. 
 
 We shall then get eight regular forms : — 
 
 Figure I. 
 Elury= {g^--^- 
 
 Figure II. 
 
 _ f Games 
 ~ \Baroa 
 
 n„!„^., ^ Camestres or 
 Balyry= y^Baroco. 
 
Indifference of Quantity of the Minor 561 
 
 Figure III. 
 
 Caluri^ [Dar'xptiox 
 \ Dattst. 
 
 Celuro^ {Felapton or 
 \ rertson. 
 
 Figure IV. 
 Dalere = Camenes. 
 
 Deluro^ ( |:^s«/o or 
 1 rrestson. 
 
 It will be observed that the conclusion in Figure III is / or O, 
 and in Figure IV is E or O, the quantity here of the minor 
 being indifferent but the conclusion always particular, except 
 Dalere [Camenes), which concludes in E as its minor is always E. 
 Looking at the reserved moods, the ones with transposed pre- 
 misses, it will be observed that in all of them the real major (the 
 seeming minor) premiss is the same, viz. Every M is S. It is 
 the quantity of the seeming major (but real minor) premisses 
 which is indifferent. Disamis [Cirali) will then, converting its 
 real minor premiss, group with Bramantip and Dimaris {Durali), 
 while Bocardo (Coralo) stands by itself, though it might be 
 placed under Felapton, if that mood were regarded as having 
 transposed premisses : — 
 
 Felapton. Bocardo, 
 
 No M is P= Some not-P's Some JJf s are not P = Some 
 
 (at least) are M. not-P's are M. 
 
 Every M is S. Every M is S. 
 
 Therefore Some not-Ps are S. 
 That is, Some S's are not P. 
 
 Camenes, if regarded as having transposed premisses, wants (the 
 pair being represented by Durely) a subaltern Cimenos, which, 
 however, is an invalid mood. 
 
 The above scheme, placing syllogistic forms on the simplest 
 basis, has the disadvantage of appealing better to the eye 
 than to the ear. On the other hand, while it gets rid of all 
 marks of reduction, it shows at once, by the initial letters, what 
 figure a mood is in, whereas in the ordinary Barbara Celarent 
 scheme this is only known memoriten 
 
 o o 
 
562 Appendix E 
 
 APPENDIX E' 
 REDUCTION PER IMPOSSIBILE 
 
 All moods may be proved indirectly by a reduction per 
 impossibile, i. e. per deductionem ad impossihile. 
 
 I. First, retaining the major premiss. It must for direct moods 
 concluding in ^ or £■ be retained as major premiss ; otherwise 
 the substituted premiss, which will be particular, must stand in 
 that place. 
 
 The contradictory of the inference supposed to be denied 
 standing as minor premiss, the new conclusion contradicts the 
 old minor, which is the omitted, premiss. 
 
 Figure I. Figure II. 
 
 Barbara. Baroco. 
 
 Every Y is Z Every Yis Z 
 Every X is Fs. Some ^'s are not Z 
 Every ^ is Z XSome ^'s are not Y. 
 
 Darii. Camestres. 
 
 Every Vis Z Every Fis Z 
 Some X's are F\ No X is Z 
 Some X's are Z \No X is Y. 
 
 Celarent. Festino. 
 
 NoYisZ No Fis Z 
 Every X is F\ Some X's are Z 
 No X is Z \Some X's are not F. 
 
 Ferio. Cesare. 
 
 NoYisZ No Fis Z 
 Some X's are F\ Every X is Z 
 Some X's are not Z \No X is F. 
 
 Reverse the two columns for the proof of the moods of 
 Figure II by those of Figure I. 
 
 Figure III. Figure II. 
 
 Darapti. Camestres. 
 
 Every F is Z Every F is Z 
 Every F is Z\ No if is Z 
 Some X's are Z \No XisY. 
 
 No X is F, converted to No F is X, is the contrary (which 
 includes the contradictory) of Every Y is X; but it is the con- 
 
Reduction per Impossihile 563 
 
 tradictory of the converse of Every F is X, viz. Some ^'s are Y. 
 Similar conversion is required in the three following cases— 
 
 Datisi. Camestres. 
 
 Every Vis Z Every Y\s Z 
 Some Y's are ^\ No JT is Z 
 Some X'a are Z \No X is Y. 
 
 Felapton. Cesare. 
 
 NoFisZ NoFisZ 
 Every Y is X\ Every X is Z 
 Some ^'s are not Z \No X is Y. 
 
 Ferison. Cesare. 
 
 NoYisZ NoFisZ 
 Some Y's are Z\ Every ^ is Z 
 Some ^'s are not Z \No X is Y. 
 
 The indirect moods Disamis and Bocardo have transposed 
 premisses, and therefore the old major must stand as the new- 
 minor — 
 
 Disamis. Festino. 
 
 Some y's are Z No X is Z. 
 
 Every Y is ^\ Some Y's are Z 
 Some ^'s are Z \Some Y's are not X. 
 
 Bocardo. Baroco. 
 
 Some Y's are not Z Every ^ is Z 
 
 Every Y is ^^^\ Some Y's are not Z 
 Some X's are not Z \Some Y's are not X. 
 
 It will be seen that the moods of Figure II can be proved by 
 those of Figure III, but not so directly as by those of Figure I. 
 The conclusions of Camestres and of Cesare must be simply con- 
 verted, and then proved by Datisi and Ferison respectively. 
 Festino and Baroco do not require any conversion of the conclu- 
 sion ; but it is the old minor premiss in their case which must 
 be retained in the major place. 
 
 Figure IV. Figure I. 
 
 Fesapo. Celarent. 
 
 No Z is Y No Z is Y 
 Every Y is X\ Every ^ is Z 
 Some X's are not Z \No X is Y. 
 
 Fresison. Celarent. 
 
 No Z is Y No Z is Y 
 Some Y's are Xs. Every X'xsZ 
 Some X's are not Z \No X is Y. 
 
 Here, again, the new conclusion is the contradictory ot the 
 
 002 
 
564 
 
 Appendix E 
 
 old minor converted. If the new conclusion be itself converted 
 simply, it is the contrary of the minor of Fesapo. Celarent 
 may be proved reversely by Fresison. 
 
 The indirect moods of Figure IV require the old major to be 
 retained as minor premiss — 
 
 Figure IV. Figure III. 
 
 Bramantip. Fesapo. Felapton. 
 
 Every Z is Y No ^'s are Z = No Z's are X 
 
 Every Y is ^^^V Every Z is Y 
 
 Z \Some Y's are not X. 
 
 Some X's are 
 
 Dintaris. 
 Some Z's are Y 
 
 Every Y is X\ 
 Some ^'s are Z 
 
 Fresison. Ferison. 
 
 No ^'s are Z = No Z's are X 
 Some Z's are Y 
 ■vSome y's are not X. 
 
 Camenes. Dimaris. Disamis. 
 
 Every Z is F Some X's are Z = Some Z's are X 
 No yisZ\ Every X is Y 
 No Z is Z \Some Y's are X. 
 
 II. Next let us try retaining 
 Figure I. 
 Barbara. 
 Every Y is Z\ 
 Every ^ is Y \ 
 Every X isZ 
 
 Darii. 
 Every Y is Z' 
 Some ^'s are Y 
 Some X's are Z 
 
 Celarent. 
 No YisZ 
 Every X is Y 
 No Z is Z 
 
 Ferio. 
 No YisZs 
 Some X's are Y 
 Some X's are not Z 
 
 Figure II. 
 
 Cesare. 
 No Z is Y\ 
 Every X is Y 
 No Z is Z 
 
 the Minor premiss : — 
 
 Figure III. 
 
 Bocardo. 
 
 Some X's are not Z 
 
 Every X is Y 
 
 \ Some Y's are not Z. 
 
 Ferison. 
 No ^'s are Z 
 Some X's are Y 
 vSome Y's are not Z. 
 
 Disamis. 
 Some ^'s are Z 
 Every XisY 
 Some Y's are Z. 
 
 Datisi. 
 Every X is Z 
 Some X's are Y 
 .Some Y's are Z. 
 
 Figure III. 
 
 Disamis. 
 Some X's are Z 
 Every X is Y 
 Some Y's are Z 
 = Some Z's are Y. 
 
Reduction per Impossihile 565 
 
 Festino. Datist. 
 
 No Z is y \ Every XisZ 
 
 Some X's are Y \ Some ^'s are Y 
 Some ^'s are not Z \ Some Y's are Z 
 
 \ = Some Z's are Y. 
 
 Camestres. Ferison. 
 
 Every Z is Y\ Some X's are Z \ . ^ j 
 No X is y\ No XisY ] '"^^'"' o'"'^^^- 
 
 No X is Z \Some Z is not Y. 
 
 Here the retained minor premiss must be made the new major. 
 But Camestres may, by privative conception, be regarded as a 
 direct mood. It will then be proved by Disamis — Some X's 
 are Z, Every X is non-F, therefore Some non-F is Z = Some 
 Z is not y. 
 
 Similarly — 
 
 Baroco. Datist. 
 
 Every Z is y\ Every X is Z 
 Some ^'s are not Y \. Some X's are not Y 
 Some ^'s are not Z \Some not- y's are Z = Some 
 
 Z's are not Y. 
 But, transposing premisses, Baroco may be proved by Bocardo. 
 
 Figure III. Figure I. 
 
 Darapti. Celarent. 
 
 Every Y is Z\ No X's are Z 
 Every yis X \^ Every Yis X 
 
 Some X's are Z \ No y is Z. 
 
 (Contraries, not contradictories.) 
 
 Datisi. Ferio. 
 
 Every Y is Z\ No X's are Z 
 Some y's are X \. Some y's are X 
 Some X's are Z \Some Ys are not Z. 
 
 Dimaris. Celarent. 
 
 Some y's are Zx No X's are Z 
 
 Every y is X \ Every y is X 
 Some X's are Z \No Y's are Z. 
 
 Felapton. Barbara. 
 
 No y is Z\ Every X is Z 
 Every y is X \ Every y is X 
 Some X's are not Z \ Every Y\s Z. 
 (Contraries again.) 
 
 Ferison. Darit. 
 
 No y is Z\ Every X is Z 
 Some y's are X \ Some Y's are X 
 Some X's are not Z \Some Y's are Z. 
 
566 Appendix E 
 
 Bocardo. Barbara. 
 
 Some Y's are not Z\ Every X'\%Z 
 Every Vis Z \ Every YlsX 
 Some ^^"'3 are not Z XEvery Yis Z. 
 
 Figure IV. Figure I. 
 
 Bramantip. Celarent. 
 
 Every Z is Yv No ^ is Z 
 Every Y is X \ Every Yis X 
 Some X's are Z \No Fis Z. 
 
 Dimaris. Celarent. 
 
 Some Z's are K No .X" is Z 
 
 Every F is X \ Every YisX 
 Some X's are Z \ No F is Z. 
 In these two the new conclusion contradicts theconverted premiss. 
 
 Camenes. Ferio. 
 
 Every Z is Fv Some ^'s are Z ) transpose and convert. 
 No y IS A \ No r IS ^ J ^ 
 
 No ..f is Z \Some Z's are not Y. 
 
 Fesapo. Barbara. 
 
 No Z is Fv Every X is Z 
 Every y is ^ N^ Every y is ^ 
 Some ^'s are not Z \ Every yis Z. 
 
 Fresison. Darii. 
 
 No Z is y\ Every ^ is Z 
 Some y's are X \^ Some y's are X 
 Some X's are not Z \Some y's are Z. 
 
 I submit the above rather as a school exercise than for any 
 other purpose. Proof of the third and fourth Figures by re- 
 duction per impossibile through the first or second is not an entire 
 waste of time, since the principle of ratiocination is seen most 
 clearly in Figures I and II. But what could be more anomalous 
 than to show that, if a person declines to be bound by reasoning 
 in Barbara or Cesare, he will incur the terrors of Bocardo or of 
 Disamisl Having committed the greater defiance he is not 
 likely to blench at the lesser. Demonstrative proof of syllogism 
 in itself by reductio ad absurdum is probare in circulo, seeing that 
 the proof assumes the truth of syllogistic reasoning. The prin- 
 ciple of rational illation is ultimate and undemonstrable. No 
 doubt in practice this kind of reduction is often useful, by show- 
 ing an opponent that rejection of your reasoning, because he 
 does not see his way through it, leads to a conclusion which he 
 has already admitted to be false. And the logical use of reductio 
 ad absurdum or ad impossibile, is, when the principle of a certain 
 Figure has been granted, to show thereby the truth of a con- 
 clusion in some other Figure. 
 
Kestrictive torm of Major Premiss 567 
 
 APPENDIX F 
 RESTRICTIVE FORM OF MAJOR PREMISS 
 
 Although it may seem far-fetched to express ' Every X is Y' in 
 the form ' No non- y is X', and still more far-fetched to state ' No ^ 
 is y in the form 'No not-not-V is X\ yet in common speech such 
 equivalents are quite usual. We can equally well say, ' Every- 
 thing which happens is in accordance with God's providence,' 
 or, ' Nothing which is not (nothing but what is) in accordance 
 with God's providence happens ' ; as well, ' Nothing came about 
 which was expected,' or, ' Nothing which was not unexpected 
 came about.' Again, ' No not-F is ^' can be phrased thus — No- 
 thing but Y is X, or. Only F is X. And ' No not-not-F is X' , 
 thus — Nothing but what is not Fis X, or, Only not- F is X. 
 
 With major premisses expressed thus in restrictive form, the 
 syllogistic Moods exhibit their principle in a new light. Thus — 
 
 Figure I. 
 Barbara {Darii). 
 
 Only what is P is If (or, Only P's are M). 
 But, All (Some) 5's are M. 
 Therefore All (Some) S's are P. 
 
 Celarent (Ferid). 
 
 Only what is not P is M. 
 But, All (Some) S's are M. 
 Therefore All (Some) S's are not P. 
 
 Figure II. 
 Cesare {Festino). 
 
 Only what is not M is P. 
 
 But, All (Some) 5's are M. 
 
 Therefore No 5 is P (Some 5's are not P). 
 
 Camestres (Baroco). 
 Only what is M is P. 
 But, No 5 is Af (Some 5's are not M). 
 Therefore No 5 is P (Some 5's are not P). 
 
 Figure III. 
 Darapti (Datisi). 
 
 Only what is P is M. 
 
 But, All (Some) things which are M are 5. 
 
 Therefore Some things (at least) which are 5 are P. 
 
 Felapton (Ferison), the same, substituting not-P for P. 
 
568 Appendix F 
 
 Disamis. 
 
 Some things that are M are P (Some things are at once 
 
 M and P). 
 But, Only what is S is M. 
 
 Therefore Some things that are S are P (are at once 5 
 and P). 
 Bocardo, the same, substituting not-P for P. 
 
 Figure IV. 
 Bramantip {Dimaris). 
 All (Some) P's are M. 
 But, Only what is 5 is M. 
 Therefore, Some things that are S are P. 
 
 (Some things are at once P and 5.) 
 
 Camenes. aliter. 
 
 Only what is M is P. All P% are M. 
 
 But, Nothing which is ilf is 5. But, Only what is not S is M. 
 
 Therefore, No S is P. Therefore, No P is S, and 
 
 No S is P. 
 Fesapo (Fresison). 
 
 Only what is not M is P. 
 
 But, All (Some) things which are M are 5. 
 
 It follows that Some things which are S are not P. 
 
 ' Only Y' (equivalent, as we have seen, to No not- Y) is restric- 
 tive of the sphere or extension of X by limiting it to Y, but 
 cannot restrict X's connotation. Thus, ' Bullies are always 
 cowards ' is as much as to say, Only cowards are bullies. But 
 for ' Cowardice is always an attribute of bullies ' we cannot sub- 
 stitute, ' Only cowardice is an attribute of bullies.' Similarly 
 ' None but Y' expresses an extension, a limited class. 
 
 On the other hand, ' Every X is Y' might be thus expressed 
 — Only y-ness enables X to exist, to be what it is. Only the 
 bereaved can sympathize (All who sympathize are of those who 
 have been bereaved). That is, Only bereavement causes a sym- 
 pathizer to be a sympathizer, brings sympathy into being. All 
 really noble persons are good. Only to be good is noble. 'Tis 
 only noble to be good. That is, Only goodness makes us call 
 a man noble. 
 
 It will be seen that by throwing propositions into this restric- 
 tive form, any Figure can be brought under any other. Mr. 
 Stock suggests the name, 'Converse Use of Reduction by 
 Negation.' Thus — 
 
 Barbara becomes Cesare. 
 
 Every M is P No not-P is M 
 
 Every S is M Every S is M 
 
 .: Every S is P .-. No 5 is not-P = Every S is P. 
 
Syllogisms m Comprehension 569 
 
 APPENDIX G 
 SYLLOGISMS IN COMPREHENSION 
 
 The opinion has been expressed in the text that the impor- 
 tance ascribed by Sir William Hamilton to the distinction 
 between Syllogisms expressed in Extension and Syllogisms 
 expressed in Intension is exaggerated. Possession of a quality 
 and inclusion in a class of things which possess a quality are 
 inseparable ideas. In any case, Hamilton fails to observe that, 
 understood intensively, mrapx^o' iv or eTvai h/ cannot mean 'is 
 part of a subject idea', but rather, 'is among the attributes 
 possessed by a subject.' 
 
 Nevertheless, reasoning may be expressed by attributes in 
 some such form as this — P'ness always accompanies M'ness, 
 and M'ness accompanies 5'ness ; therefore P'ness accompanies 
 5'ness. 'Co-exists with' is, we have seen, a little ambiguous, 
 since it may seem to imply that wherever the predicate quality 
 is found the subject quality will be found also ; which is more 
 than is intended. Similarly the phrase, 'P'ness is a mark of 
 5'ness,' is open to the objection attending the ratio cognoscendi, 
 that it may be taken to imply that wherever P is found we may 
 be sure of finding S. Using, then, ' goes with ' or ' accompanies ' 
 we may state the Syllogistic Moods thus : — 
 
 Figure I. 
 
 Barbara. P'ness always goes with M'ness (major premiss) 
 and Tlf' ness with 5'ness (minor) ; therefore P'ness always goes 
 with 5'ness. 
 
 Darii. ' Sometimes ' must be inserted in minor premiss and 
 conclusion. 
 
 Celarent. P'ness never goes with Tkf' ness, but M'ness always 
 goes with 5'ness ; therefore P'ness never goes with 5'ness. 
 
 Ferio. ' Sometimes ' in minor premiss for ' always ', and ' not 
 always ' for ' never ' in conclusion. 
 
 Figure II. 
 
 Cesare. M'ness never goes with P'ness but always with 
 5'ness ; therefore P'ness and 5'ness are never associated. 
 
 Festino. M'ness never goes with P'ness, but sometimes 
 with 5'ness. P'ness therefore is not always found where 5 
 is found. 
 
570 Appendix G 
 
 Camestres. M'ness always goes with ' P'ness but never 
 with S'ness ; therefore P'ness and 5'ness are never found 
 together. 
 
 Baroco. M'ness always goes with P'ness, but not always 
 with S'ness. P'ness, then, does not always accompany the 
 presence of 5'ness. 
 
 Figure III. 
 
 Darapti. ilf 'ness is always accompanied by both P'ness and 
 5'ness. P'ness and 5'ness, then, are sometimes (at least) found 
 united in a subject. 
 
 Datisi. ilf' ness is always accompanied by P'ness and some- 
 times by 5-ness; P'ness and 5'ness, then, sometimes go to- 
 gether. 
 
 Disamis. The same, with P and 5 interchanged. 
 
 Felapton. M 'ness is never accompanied by P'ness but always 
 by 5'ness. 5'ness, we infer, is sometimes (at least) found with- 
 out P'ness, 
 
 Ferison. ' Sometimes ' for ' always ' in minor premiss. 
 
 Bocardo, ' Not always' for 'never' in major premiss. 
 
 Figure IV. 
 
 Bramantip. P'ness is always accompanied by M'ness, and 
 il/'ness always by 5'ness. It follows that 5'ness is sometimes 
 accompanied by P'ness. 
 
 Dimaris. ' Sometimes ' for ' always ' in major premiss. 
 
 Camenes. ' Never ' for ' always ' in minor premiss, and for 
 ' sometimes ' in conclusion. 
 
 Fesapo. P'ness is never accompanied by J/'ness and il/'ness 
 is always accompanied by 5'ness. Accordingly 5'ness is not 
 always accompanied by P'ness. 
 
 Fresison. ' Sometimes ' for ' always ' in minor premiss. 
 
 The diagrams by which Inference is ordinarily exhibited in 
 logical treatises to the eye are based on class-inclusion, that is, 
 on extension. Is a reverse order of inclusion, based on com- 
 prehension, possible ? The import of the proposition, as we 
 have seen, is not that the predicate notion is included in, or part 
 of, the subject notion, but rather that the predicated quality is 
 included among the attributes of the subject thing. Thus, 
 ' William's aunt is a laundress ; laundresses earn money ; 
 earners of money are bipeds,' cannot mean that the notion of 
 two-footedness is part of the notion of earning money ; that 
 earning money is part of the notion of washing clothes ; and 
 that washing clothes is one of the ideas into which the conception 
 
Syllogisms in Comprehension 
 
 571 
 
 of being an aunt of William's may be analysed. The possible 
 notations, then, are these two— 
 
 whereby we see at a glance that William's aunt is a biped, and 
 that being a biped is an attribute predicable of William's aunt. 
 
 It is, however, impossible to represent a negative \ntensivQ 
 Syllogism by inclusive and exclusive lines. Thus — William's 
 aunt is a laundress ; no laundress is a duchess ; then William's 
 aunt is not a duchess. Intensively — the attributes of William's 
 aunt include that of being a laundress, and being a laundress 
 excludes the attribute of being a duchess. But the argument 
 cannot be represented thus — 
 
 On the other hand, while ' Every S is M, no M is P ; there- 
 fore no 5 is P ' cannot be shown intensively by circles (S attri- 
 butes include M, M attributes exclude P ; therefore S attributes 
 exclude P), we can depict, ' S attributes exclude M, M attributes 
 include P; therefore 5 attributes exclude P,' by circles thus — 
 
572 Appendix G 
 
 But this, though it looks correct on paper, is false reasoning — 
 No S is iJ/; Every M\&P; therefore no S is P. It is clear, 
 then, that qualitative relations cannot be represented in this 
 manner. 
 
 A quality or abstraction identified with another quality or 
 abstraction is not predicated of it. 'Time is money.* 'To labour 
 is to pray.' ' Punctuality is the politeness of princes.' ' Imitation 
 is flattery.' 'A kind of' we must often add in thought, for sub- 
 ject and predicate are not always convertible ; ,but this does not 
 make the predicate a common noun and so potentially adjec- 
 tival. We cannot say, 'Time is a money.' What is predicated 
 is ' identical with '. 
 
 APPENDIX H 
 SOME SYLLOGISTIC VARIATIONS 
 
 Representing ' Every X is Y' by ' No non- Y is X ', the recast- 
 ing of syllogistic moods will appear to give us in some cases two 
 negative premisses and in some a quaternio terminorum, or even 
 five or six terms. Thus, Barbara takes the form — No non-/' is 
 M, and No ■aon-M is S ; therefore, No non-/' is S. Celarent will 
 be, No P is M, No non-M is 5 ; therefore, No P is 5. Cesare 
 will be expressed thus — No M is P, and No non-M is S ; there- 
 fore No non-P is S. Darapti thus — No non-P is M, and Every 
 non-S is non-M ; therefore. Some S is P. 
 
 Roundabout as these forms may seem, arguments are often so 
 expressed. If we wish to show that there is no reason why the 
 wholesome and the entertaining should not be found together, 
 we may equally well premise, ' This entire book is at once 
 wholesome and entertaining,' or, ' There is nothing but what is 
 entertaining in this book, and for unwholesomeness you must 
 look elsewhere ' [Darapti). 
 
 The illative principle in such cases of (seeming) double nega- 
 tion is not perhaps so obvious as in the syllogism as ordinarily 
 expressed. But, if we take Barbara, ' No non-P is M, No non- 
 M is S' clearly means that anything which is not P is not M, 
 and anything which is not M is not S ; therefore if anything is 
 not P it cannot be S. That is. Everything which is .S is P. 
 Similarly Darapti — No non-P is M, and no non-S is M. In 
 other words, if anything is M it must be something which is not 
 not-P and at the same time is not not-S. Either then nothing at 
 all is M, or what is M must be some thing or things of those in 
 which the attributes of P and S are combined. The conclusion 
 here is particular. 
 
Some Syllogistic Variations 573 
 
 The President of Corpus^ quotes the following (among other) 
 quasi-syllogisms proposed by Schuppe : — 
 (i) No M is P (ii) Some M is P 
 
 S is not M Some S is If [or, All S is M] 
 
 .: S may be P. .•. Some S may be P. 
 
 Equally, of course, it may not — there is indifferent contin- 
 gency of the conclusion. So far as there is any inference at 
 all it is in the case of (i) merely this, that the fact of no M being 
 P establishes no presumption against S being P, since S and 
 M are totally unconnected. In the case of (ii) it is argued that 
 the fact of some M being P shows that there is nothing to forbid 
 S (which is in some [or all] cases M, being P- If no M were 
 P, then those 5's which are mentioned as being M could not 
 possibly be P, though other S's might be. 
 
 ^ Encycl. Brit., art. ' Logic' 
 
574 
 
 Appendix I 
 
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 CO 
 
 g^s 
 
 Q 
 
 8^£; 
 
 Z 
 
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 trate t: 
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 ; also 
 
 
 W 
 C/2 
 
 P 
 
 
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 O 4J 
 
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 ni 
 
 
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 VI 
 
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 L^ *^ r* • 
 
 S "5 > m 
 
 rH c "B -a 
 
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 3.2 
 
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 rt c I 
 
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Cause and St'gn 575 
 
 The Good are inwardly Happy. 
 Inductive reasoning, followed by a Deduction {ratio essendi). 
 
 I. A. How is this fact to be accounted fori Because they 
 are easy in conscience (minor), and such are inwardly happy 
 (major). 
 
 B. How do you account for their being easy in conscience 
 (minor) ? Because they are doers of right (sub-minor), and such 
 have easy consciences (sub-major). 
 
 C. What makes them doers of right? Because they are 
 God-fearing (sub-sub-minor), and such do right (sub-sub-major). 
 
 D. What makes doers of right to have an easy conscience ? 
 Because they are able to give account (sub-sub-minor), and such 
 have an easy conscience (sub-sub-major). 
 
 E. But now, to return, What makes those whose conscience 
 is at ease to be inwardly happy (major) ? Because, &c. (See 
 Chart.) 
 
 In the foregoing reasonings a Middle Term is sought as a 
 Cause to account for each alleged fact. Being given it, we say 
 deductively that the fact must be, is sure to be, as alleged. The 
 actual finding of the Middle Term or Cause is the work of 
 Induction, and is a material inquiry, an inquiry into the nature 
 of things, though as involving a reasoning process it has a 
 formal or rational element. 
 
 II. Let us now look below the line. The triangles here are 
 syllogisms which answer the question, What ground there is 
 for a judgement ? not. What cause there is for a fact ? The 
 answer is found not, as above, deductively, — 'The good have 
 an easy conscience, and such are happy ; therefore they must 
 be happy' — but from observed signs {^atio cognoscendi). This 
 is the other side of Induction— the asking what facts a 
 generalization rests upon. Afterwards from these facts, as 
 signs, the general principle is inferred. 
 
 The Good are inwardly Happy. 
 
 A. What ground is there for this statement! What makes 
 you say so? Because the good are (found to be) cheerful 
 (minor), and cheerfulness is a sign of happiness (major). 
 
 B. What ground is there for saying the good are cheerful 
 (minor)? Because they (are seen to) have sunny faces (sub- 
 minor), and that is a sign of cheerfulness (sub-major). 
 
 C. Why do you say they have sunny faces ? Because they 
 often smile, and that marks a sunny face [&c.]. 
 
 D. Why is a sunny face a sign of cheerfulness ? Because 
 
576 Appendix I 
 
 it goes with sweet-temperedness, which is an indication of 
 cheerfulness. 
 
 E. But now, to return, what is the ground for saying .that 
 the cheerful are inwardly happy (major)? Because, &:c. (See 
 Chart.) 
 
 The student is invited to improve upon the above illustrations, 
 and to make pro-syllogisms for himself. 
 
 Below the line the middle term sought is some fact of 
 observation. Such facts will be of a less and less general 
 character, until we get to intuitions, whereas above the line, each 
 new middle term becomes more and more abstract. 
 
 Having found the ground of a statement, the argument is 
 then turned round, and the statement, which was a probandum 
 and is now a conclusion, is inferred from the ground, deduc- 
 tively. 
 
 All inference is syllogistic. The word Induction is used 
 either to mean the search for middle terms, which is a material 
 inquiry, or else proof from observed signs as contrasted with 
 proof from abstract principles. But the major premiss of every 
 argumentative process must have a certain abstract character. 
 The weakness of the proof from an observed sign is that it ought 
 to be, in the major premiss, not merely an effect, but one that 
 never appears apart from the given cause. Thus, cheerfulness 
 is an invariable sign of inward happiness only if cheerful people 
 are always happy. But a circus clown has to be professionally 
 cheerful, when perhaps he has an only child lying at home 
 at the point of death. In dealing with natural classes, however, 
 we so often find qualities which ^re propria, and which reciprocate 
 with their subject, that the argument from a sign frequently 
 carries conviction. 
 
 In the above Chart, in the triangles above the line, any dotted 
 line (representing a fact of experience) may be taken as a base 
 line and made a probandum, having the apex of the triangle 
 below it for its ground, i. e. the a posteriori reason for asserting 
 it. The line opposite to the predicate will then give the observed 
 fact, the other line the general principle or sign (regarding the 
 predicate as a proprium). Thus, — What ground is there for 
 saying that the good fear God? This, that they are doers of 
 right, and right-doing is a sign of Godfearingness. Again, in 
 the triangles below the central line, any dotted line may be 
 made a base line, and find its cause in the apex of the triangle 
 above it. Thus, — What makes the good to be cheerful ? This, 
 that they are inwardly happy, and such inward happiness 
 produces cheerfulness. 
 
 In a universal affirmative proposition the extension of the 
 predicate is greater than that of the subject, and the intension 
 less. Apart from any question of convertibility between pro- 
 perties and subjects, a glance at the diagram, above the line, 
 
Cause and Sign 577 
 
 will show how many predicates intervene between 'the good' 
 and 'inwardly happy', and of course the triangles might be 
 multiplied indefinitely. It is the same below the line if we are 
 sure that by ' Cheerfulness is a sign of inward happiness ' we 
 mean all cheerfulness. 
 
 APPENDIX K 
 
 IDIOMATIC FORMS 
 
 The following are additional illustrations of the prepositional 
 A form, Every non-X is F: — 
 Vae mihi nisi evangelizavero. 
 
 Extra Christum Satanas animam occupat. (Calvin.) 
 Tout est perdu fors I'honneur. 
 Animum rege, qui nisi paret imperat. 
 Without him you are lost. 
 Perdition seize my soul, but I do love thee. 
 Offendatur Deus ne (so long as not) contristetur amicus. 
 Save back to England, all the world 's my way. 
 Absent le chat, les souris dansent. 
 
 More common is the E form, No non-.^ is Y (Every non-.X' 
 is non-Y). 
 
 What 's a table richly spread Without a woman at its head ? 
 
 Nullum magnum ingenium sine mixtura dementiae. 
 
 Get thee to church o' Thursday, or never look me in the face 
 again. 
 
 In rufa pelle non est animus sine felle. 
 
 If God be not, nothing is. (Hegd.) 
 
 Si mundus universus non est Deus, ne stellae quidem. 
 
 Nihil ardet in inferno nisi propria voluntas. 
 
 The world cannot be governed without laws, and laws without 
 a compulsory signify nothing. (Jer. Taylor.) 
 
 Where there is no law there is no transgression. 
 
 Nothing 's so hard but search will find it out. 
 
 Earth has no sorrow that Heaven cannot cure. 
 
 Sine cruce sine luce. 
 
 Avarus, nisi cum moritur, nil recte facit. 
 
 Extra Ecclesiam nulla salus. 
 
 There is no world without Verona's walls But purgatory, 
 torturing hell itself. 
 
 It never rains but it pours. 
 
 Shall there be evil, and the Lord hath not done it ? 
 
 No smoke without fire. 
 
 No rose without a thorn. 
 
 None think the great unhappy but the great. 
 
 No commonwealth can flourish without learning. 
 
 pp 
 
578 Appendix K 
 
 All I don't know is not knowledge. 
 
 There 's nothing bad but thinking makes it so. 
 
 Without revelation men know nothing. {Pense'es.) 
 
 No sermon without Augustine. (Spanish.) 
 
 Nihil est in intellectu quod non prius fuerit in sensu. (If we 
 add, ' nisi ipse intellectus,' the formula is, No non-Z non-.^ is Y) 
 
 On ne se d^tache jamais sans douleur. 
 
 What else is Plato than Moses speaking Attic Greek ? 
 
 Without an Ego there is no non- Ego. 
 
 Nemo laeditur nisi a se ipso. 
 
 If a man strive for masteries, yet is he not crowned except 
 he strive lawfully. 
 
 Out of sight out of mind. 
 
 Who abstains from meat that is not gaunt ? (Gaunt.) (Or 
 this will illustrate the form, ' No not-X is non- Y.') 
 
 A few further examples of the ordinary E judgement, No X 
 is Y, are here given. 
 
 Where happiness is, there am I not. 
 
 Tts 6 (Toj^o/tevos TrXouertos ," 
 
 With Stupidity even the gods cannot contend. 
 
 Venus smiles not in a house of tears. 
 
 'Tis not the many oaths that make the truth, &c. 
 
 Necessity has no law. 
 
 Te docente, nil obscurum. 
 
 I dare do all that may become a man ; Who dares do more 
 is none. 
 
 Non habet peccatum ideam. 
 
 In this place, most master wears no breeches. (Eleanor.) 
 
 Never too late to mend. 
 
 To-morrow never comes: 
 
 Gratia non ligatur mediis. 
 
 No two persons think exactly alike. 
 
 Use every man after his desert, and who will scape whipping? 
 
 Nil desperandum, Teucro duce. 
 
 Sint Maecenates, non deerunt, Flacce, Marones. 
 
 Uni navi ne committas omnia. 
 
 Non amo Te ut salves me. 
 
 If they were all one Body, where were then the Body ? 
 
 May his highness live in freedom and this man out of prison? 
 
 One example may be given of a duplex or reciprocating 
 judgement (Hamilton's 'All X is all Y')— He that hath the Son 
 hath life ; he that hath not the Son hath not life. 
 
 In the following list of general Affirmative Judgements, the 
 student may usefully cast each proposition in the form, ' Every 
 ZX is Y' — X being the assumed sphere of discourse, and Z the 
 conditioning element (see above, § 487). Such analysis is simple 
 in propositions like 'vis (X) consili expers (Z) mole ruit sua', 
 
Idiomatic Forms 579 
 
 or, ' Least (Z) said (X) soonest mended/ or, ' All hope abandon 
 ye {X) who enter here (Z),' or, ' florent concordia (Z) regna 
 \X).' But it will exercise thought in some of the following 
 examples of the A form of Universals : — 
 
 Dare quam accipere. 
 
 Where thou art, there is the world itself. 
 
 Woe to that land that 's governed by a child. 
 
 Timidi est optare necem. 
 
 God and one make a majority. 
 
 In great cities all men are more or less alike. 
 
 Men are nothing ; a man is everything. 
 
 Mos pro lege. 
 
 One touch of nature makes the whole world kin. 
 
 Christmas comes but once a year. 
 
 The world is made up of the vulgar. 
 
 Cineri gloria sera venit. 
 
 Unusquisque, quodcunque fecerit bonum, hoc recipiet a 
 Domino, sive servus sive liber. 
 
 Sublata omni quantitate tollitur spatium. 
 
 Mihi vivere Christus, mori lucrum est. 
 
 If every one would mend one, we should have a new world. 
 
 One man in his time plays many parts. 
 
 Unum corpus multi sumus, omnes qui de uno Pane parti- 
 cipamus. 
 
 Cavil, if it do not find a hole, will make one. 
 
 The one remains, the many change and pass. 
 
 A little fire is quickly trodden out. 
 
 Cuius regio eius religio. 
 
 To whom much is forgiven the same loveth much. 
 
 Nihil moror colorem, modo gratus sit sapor. 
 
 Quanto doctior eo iracundior. 
 
 Handsome is as handsome does. 
 
 Needs must when the devil drives. 
 
 Alius alii subsidium. 
 
 Once bitten twice shy. 
 
 All work and no play makes Jack a dull boy. 
 
 Quisque suos patimur Manes. 
 
 Time must friend or end. 
 
 Clay and clay differs in dignity, Whose dust is all alike. 
 
 Jack 's as good as his master. 
 
 Of bad the least. (Spanish.) 
 
 The rain it raineth every day. 
 
 Essex is all flat. 
 
 Credo ut intelligam. 
 
 'Wisdom and justice and equity are the invariable charac- 
 teristics of the dealings of the United States.,' 
 
 Brag's a good dog. 
 
 Gentillesse cometh of God alone. 
 
 p p 2 
 
580 Appendix K 
 
 Les Anglois s'amusent tristement. 
 One sinner destroyeth much good. 
 
 Every one that (R. V. whosoever) findeth me shall slay me. 
 Well begun is half done. 
 Mighty contests rise from trivial things. 
 Sal sapit omnia. 
 
 Every man is a scoundrel when he is sick. (Johnson.) 
 Tout passe ; I'Art seule a l'6ternit6. 
 
 He who serveth God with fear, it is good ; he who serveth Him 
 with love, it is better ; he who with both, that is best of all. 
 
 5 X .7 = 35- 
 
 A friend is one soul in two bodies. 
 Enough is as good as a feast. 
 Genius is always intolerant. 
 AvSpuiv iTn(f>av!ov iratra y^ Tac^os. 
 One star differeth from another star in glory. 
 Bate me some and I will pay you some. 
 Mundum regunt numeri. 
 Pessima republica plurimae leges. 
 Ut ameris ama. 
 
 Everybody's business is nobody's business. 
 Trade follows the flag. 
 When Caesar says do this, it is performed. 
 One pain is lessen'd by another's anguish. 
 Les nerfs, voila tout I'homme. 
 Seek ye the Lord while He may be found. 
 There must be such a thing as an orthpdoxy and a deposit 
 of truth, if there is to be a theology. 
 
 0<7Tt9 av ^pOTU>V 
 
 /caKos iri<l>vKri t,rjiJLiov(nv ol 6eoi. 
 L'homme ne meurt qu'une fois. 
 Felicium multi cognati. 
 Diversos diversa iuvant. 
 Ingratum si dixeris, omnia dicis. 
 Inter duas sellas decidimus. 
 Novus rex nova lex. 
 Plus vident oculi quam oculus. 
 Ex ungue leonem. 
 Tanti quantum habeas fis. 
 Truditur dies die. 
 
 It is the nature of War Offices to be inefficient. 
 Ut quisque est vir optimus, ita difficillime esse alios improbos 
 suspicatur. 
 
 Vitia erunt donee homines. 
 Meya /iijSXiov fieya KaKov. 
 Asse.2-t6t, si bien. 
 Multi societate tutiores. 
 Multa petentibus desunt multa. 
 
Idiomatic Forms 581 
 
 HaOTj/jLara fiaO-q/juiTa, 
 
 Clariora cariora. 
 
 Soon hot soon cold. 
 
 We mortal millions live alone. 
 
 Any stick will do to beat a dog with. 
 
 As a man sows, thus shall he reap. 
 
 La propri6t6 c'est le vol. 
 
 Silet sapit. 
 
 Pectus facit theologum. 
 
 A la guerre comme a la guerre. 
 
 Like people like priest. 
 
 They manage things better in France. 
 
 Accidents will happen. 
 
 Qualis vita finis ita. 
 
 Which way I fly is hell, myself am hell. 
 
 Near to sword near to God. 
 
 More things are wrought by prayer Than this world dreams of. 
 
 Remember me when thou comest. 
 
 Vetera religio commendat. 
 
 Fast-won fast lost. 
 
 When Greek meets Greek, then is the tug of war. 
 
 There 's small choice in rotten apples. 
 
 Homo, Deo solo dominante, liberrimus. 
 
 Never star Was lost here but it rose afar (no X is non-F). 
 
 Nemo praeter Christum sine peccato (no non-X is non-Y 
 = every non-X is Y). 
 
 Is any sick? The Man of Ross relieves. 
 
 If two ride one horse, one must ride behind. 
 
 The reader is invited to throw the following into symbolic 
 form — 'Alia sunt quae nisi intellegantur non credimus, et alia 
 quae nisi credamus non intellegimus '. (Aug.) 
 
 VERBAL PARADOXES 
 
 The examples given in the text (§§ 48, 133, 134, 236 seq., 512) 
 of verbal paradox may be supplemented by the following : — 
 
 An Englishman is never happy unless he is miserable ; a 
 Scotsman never at home unless he is abroad; an Irishman 
 never at peace unless he is at war. 
 
 The way to avoid obstacles is to crush them. (Robespierre.) 
 
 Every man has a right to say what he pleases; and every 
 other man has a right to knock him down for it. (Johnson.) 
 
 An Irishman, praising ancient architecture, asked, 'Where 
 do you ever see a modern building that has stood for five 
 centuries ? ' 
 
 Men, said Sancho Panza, are as God made them, and some- 
 times a great deal worse. 
 
582 Verbal Paradoxes 
 
 The captains of two St. Lawrence steamers declared that they 
 were not racing, but only trying which could go the faster. 
 
 An American politician said he was in favour of the Pro- 
 hibition Law, but against enforcing it. 
 
 ' Those, gentlemen,' said another politician, ' are my lifelong 
 convictions, and if they don't please you they can of course be 
 changed.' 
 
 Most of the above are really self-contradictory, as much as 
 ' stationary advance '. But the following are merely epigram- 
 matic : — 
 
 Busy people have most time. 
 
 Lazy people give themselves most trouble. 
 
 Lowly pomp. 
 
 An aggressive peace-policy. 
 
 Tyranny of free thought. 
 
 The multitudinous desolation of East London. 
 
 A parliament without debate. (The Quakers' Meeting in ' Elia'.) 
 
 Obscure notoriety. 
 
 The luminous obscure (contrast ' the palpable obscure '). 
 
 Darkness visible. 
 
 Fanatical in his moderation. 
 
 Improvident thrift. (J. Morley.) 
 
 Meek implacability. 
 
 A foreigner at home. (Johnson. Compare 'intra eadem 
 moenia exilium '.) 
 
 An old maid's husband. (George Eliot.) 
 
 Sympathetic loneliness. 
 
 Nunquam minus solus quam quum solus. 
 
 Cruel only to be kind. 
 
 Killing the slain. 
 
 Our friend the enemy. 
 
 Awful mirth. (looth Psalm, Tate and Brady.) 
 
 A law of liberty. 
 
 A pet aversion. 
 
 Brilliant flashes of silence. 
 
 Libido tacendi. (Cicero.) 
 
 A debauch of unselfishness. 
 
 A careless-ordered garden. 
 
 Helots of Park-lane. 
 
 The only chance of distinction in a democracy is to be un- 
 distinguished. 
 
 A grave jest. 
 
 Insatiate made from mere satiety. (Is. Williams.) 
 
 Secret de Polichinelle (an open secret). 
 
 Dining with Duke Humphrey (i. e. not at all). 
 
 A Newgate pastoral. (Swift.) 
 
 Monologue a deux. 
 
Verbal Paradoxes 583 
 
 A distinction without a difference. 
 
 Cruel, irreligious piety. {T. Andr.) 
 
 The Colonies responded to the call before it was made. 
 
 Cheap labour is dear labour. 
 
 Granite on fire (a character). 
 
 To be proud in that you are not proud is a phoenix pride. 
 (Manchester al Mondo.) 
 
 A deep below the deep, and a height beyond the height ; 
 
 Our hearing is not hearing, and our seeing is not sight. 
 
 The most of this world spend their days in a serious jesting 
 and busy doing of nothing. (Baxter.) 
 
 ' Love's sorwes glade.' (Gower.) 
 
 yewolov i/reCSos. 
 
 Magnas inter opes inops. 
 
 St. Gregory said of Benedict of Nursia that he was learnedly 
 ignorant and wisely untaught. The De Docta Ignorantia, 
 however, of Nicholas of Cusa (1438) is about educated 
 agnosticism. This Nicholas has the following analytic judge- 
 ments in his scheme of church reformation — ' The bishop is to 
 oversee, the canon to keep rules, the eremite to be a solitary, 
 the rector to rule, the curate to care for his flock, the cardinals 
 to be the church's hinges '. 
 
 An illustration of a name being employed in a changed sense 
 is Homer's use of ' hecatomb ' for a sacrifice of twelve oxen (//. vi. 
 93, 115) and for one of eighty-one {Od. iii. 59), as well as for 
 a sacrifice of rams (//. i. 315 ; Od. i. 25). 
 
 As an example of the necessity of mediation between ex- 
 pressions before we can pronounce the one to be implied in, or 
 incompatible with, the other, take such a phrase as 'beneficed 
 curate'. This may seem as obvious a-'contradiction in terms 
 as ' unbeneficed incumbent '. Yet a curate in Prayer Book lan- 
 guage means an incumbent. Few would rule out the phrases 
 'a farmer owning his own land', or 'a third alternative'. Yet 
 the former ignores the meaning of ' farmer ', and the latter that 
 of 'alter'. In 'Roman Catholic 'the two parts of the expres- 
 sion have been diversely regarded as mutually quahfying, 
 mutually creative, and mutually destructive. Milton argues 
 that it is ' one of the Pope's bulls : it is particular-universal or 
 catholike-schismatike '. The late Dr. Liddon, objecting to the 
 phrase ' Episcopal Church ', used to say it was like talking of 
 a biped man. A ' laughing philosopher ' is a contradiction in 
 terms, if the conceptions of Johnson's old college friend, Oliver 
 Edwards, were correct — ' I have tried too in my time to be a 
 philosopher; but, I don't know how, cheerfulness was always 
 breaking in '. 
 
 But Thought without Middle Terms is at a standstill. And 
 this is the conclusion of the whole matter. 
 
OXFORD : HORACE HART 
 PRINTER TO THE UNIVERSITY