MASTER NEGATIVE NO. 91-80063 MICROFILMED 1991 COLUMBIA UNIVERSITY LIBRARIES/NEW YORK a as part of the Foundations of Western Civilization Preservation Project Funded by the ATIONAL ENDOWMENT FOR THE HUMANITffiS R- 1 ^ %^ Y" "Auctions may not I -- \^ f . 1 ^ut permission from Columbia University Library COPYRIGHT STATEMENT The copyright law of the United States - Title 17, United States^ Code - concerns the making of photocopies or other reproductions of copxTighted maicri;il... Columbia U: iv'ersity Library reserves the right to refuse to accept a copy order if, in its judgement, fulfillment of the order wouia involve violation of the con- rklit law AUTHOR: READ, CARVETH Til IE: LOGIC. AND INDUCTIVE PLA CE LONDON DATE 1898 Master Negative # COLUMBIA UNIVERSITY LIBRARIES PRESERVATION DEPARTMENT BIBLIOGRAPHIC MICROFORM TARGET Original Material as Filmed - Existing Bibliographic Record Restrictions on Use: '•:" Read, Qarvetlu 1848- .4 s^t)04 Logic, deauctive and inductive. By Carveth Read, .... l^hrtd edition,- revised-and^nlarged. London, A. Moring, ltd., l^eS: 1898 ymr^.p.^ diagrs. 20«°'. XVi, 3iJ3 p. :;-u- -*«4y- ■M60^ -^^2^ 3d - r e v » and e nl » od > — London » Moring — 1 9 & 355303 TECHNICAL MICROFORM DATA REDUCTION RATIO:__iX FILM SlZE:_3_Sl)V_t^ IMAGE PLACEMENT: IA'QiA) IB IIB DATE FILMED •_i:_r_5i^'__5;z INITlALS_^L_^a_ HLMEDBY: RESEARCH PUBLICATIONS. INC WOODBRIDGE. cf n Association for information and Image IManagement 1100 Wayne Avenue, Suite 1100 Silver Spring, Maryland 20910 301/587-8202 Centimeter liU llllilllMlllllllllllllllllllllllllllll lllllllllll 5 6 7 8 9 Mill 10 11 12 13 14 15 mm iiiiiiiiiiiiiiiiiiiniiiiiiiiiiiii iiiiiiiiiiiiiiiiiiiiii I I Inches Ml T 1.0 I.I 1.25 TTJ lii 1 5.0 16 3 2.8 3.2 |7J 180 3.6 ■ 4.0 1.4 2.5 2.2 2.0 1.8 1.6 I T T T MnNUFPCTURED TO fillM STRNDPRDS BY nPPLIED IMRGE, INC. ^. O .V -b 1. # 9>' Columbia ^initiergitp in ti)t Citp of iSetu |9orfe LIBRARY I ■ ffiB \\ (r- i If LOGIC DEDUCTIVE AND INDUCTIVE LOGIC DEDUCTIVE AND INDUCTIVE (■ BY CARVETH READ, M.A. LONDON GRANT RICHARDS 9 HENRIETTA STREET. COVENT GARDEN 1898 I k' • • • •• • • • • ••• • Vi • • • • •• • *l • • • • • • • • • • • .• • • • • • • • • ••-•• • ►•••,•• • •• • •« • • • • ^ • • • • • • • •• • • • • • • • •• • I • • • • • • ••• • 'x9 1 \ Printed by Ballantyne, Hanson &> Co. At the Ballantyne Press ^ PREFACE SEPARATION Of the facts and laws of Nature into departments for the convenience of study, has been one of the chie con- ditions of scientific progress. It is true that such separation^ made for our convenience and does not exist in Natu e. Yet it has been the means of revealing the ""'^V^f. Mature he connection of facts, the harmony of laws: analysis ha been the necessary preliminary to an intelligent synthesis No further apology need be offered for the separation "f Logic^^m the present volume, from all other studies, and especial^ tar. Psvchology and Metaphysics, with greater rigour than has been usual in logical treatises : carrying out the plan that elsewhere has always proved advantageous. The instructed reader will easily see that I have been chiefly indebted to Mill's SysUm of Logic, Professor Bains Logtc^r Venn's Smprual Logic, and Dr. Keynes' For,naUog>c. What- ever is due to other authors has been acknowledged as occasion arose. /In every case I have tried to make the property con- veyed my own : an excuse for theft that must seem odd to a lawyer, but is well recognised in the courts of literature. > For the comprehensive study of contemporary opinion on Logic, several books besides the above-mentioned are needed : especially Mr. Bradley's FrinciJ,/es of Logic, Mr. Alfred S.dg- v^^ckl Process of Argument, and Mr. BosanqUet's Logrc : or the Morphology of Knowledge. The last author's ^— / Lojc is expressly intended to popularise his views. M . Hob house's Theory of Kno^.Mge, an original and valuable treatise, 263408 QC VI PREFACE did not come into my hands until this book was finished (now some time ago) : else, probably, I should often have referred to It. Those who, not reading German, desire to see a sample of the present state of Logic in the empire, may be referred to Professor Sigwart's Zoo^i^, recently translated. Ueberweg's Sysfem of Logic, atid History of Logical Doctrines is invaluable in its historical passages. I owe a great deal to Mr. Alfred Sidgwick, Mr. Thomas Whittaker and Professor C. M. Thompson, who have been at pams to advise me upon portions of the MS. and proofs. Most of the chapters, however, no one but myself has seen ; so that whatever errors the critic may find must occur in those unsponsored chapters; and it is, therefore, needless to say which they are. CARVETH READ. London, May 1898. CONTENTS Preface CHAPTER I INTRODUCTORY lAGE V § I. Definition of Lx)gic § 2. General character of proof . § 3. Division of the subject . § 4. Uses of Logic . . . • § 5. Relation of Logic to other sciences to Mathematics (p. 7) ) to concrete Sciences (p. 8) ; to Metaphysics (p. 8) ; to regulative sciences (p. 10) § 6. Schools of Logicians Relation to Psychology I' 2 3 4- 7 10 II' CHAPTER II GENERAL ANALYSIS OF PROPOSITIONS § I. Propositions and Sentences . § 2. Subject, Predicate and Copula § 3. Compound Propositions § 4. Import of Propositions . § 5. Form and Matter . § 6. Formal and Material Logic . § 7. Symbols used in Logic . 14 }^ 15 16 19- 20 • 21 Vlll CONTENTS CONTENTS CHAPTER III OF TERMS AND THEIR DENOTATION § I . Some Account of Language necessary . § 2. Logic, Grammar and Rhetoric . . . . § 3. Words are Categorematic or Syncategorematic § 4. Terms Concrete or Abstract § 5. Concrete Terms, Singular, General or Collective . CHAPTER IV THE CONNOTATION OF TERMS § I. Connotation of General Names § 2. Question of Proper Names other Singular Names § 3- Question of Abstract Terms . § 4. Univocal and Equivocal Terms Connotation determined by the suppositio § 5. Absolute and Relative Terms § 6. Relation of Denotation to Connotation . § 7. Contradictory Terms .... § 8. Positive and Negative Terms Infinites Privatives Contraries CHAPTER V CLASSIFICATION OF PROPOSITIONS § I. As to Quantity Quantity of the Predicate § 2. As to Quality . . . . Infinite Propositions PAGE 24 25 26 27 29 32 33 34 35 35 37 37 39 40 43 43 43 43 45 47 48 48 § 3. A. I. E. O. . § 4. As to Relation Change of Relation . § 5. As to Modality § 6. Verbal and Real Propositions CHAPTER VI CONDITIONS OF IMMEDIATE INFERENCE 8 I Meaning of Inference § 2. Immediate and Mediate Inference § 3. The Laws of Thought . 84. Identity . • • • • ' § 5 Contradiction and Excluded Middle § 6. The Scope of Formal Inference . CHAPTER VII IMMEDIATE INFERENCES Plan of the Chapter . • • • Subalternation . • • • ' Connotative Subalternation . Conversion .••••■ Obversion . • • • " " Contrary Opposition . • • • Contradictory Opposition . § 8. Subcontrary Opposition § 9 The Square of Opposition . § 10. Secondary modes of Immediate Inference §11. Immediate Inferences from Conditionals § I. 2. 3- 4 5 6. 7- IX PAGE 49 50 51 54 55 57- 58 60- 61 62 64 , • • * 67 67 68 69 71 72 73 74 74 , 75 77 CONTENTS CHAPTER VIII ORDER OF TERMS. EULER's DIAGRAMS. LOGICAL EQUATIONS. EXISTENTIAL IMPORT OF PROPOSITIONS PAGE § I. Order of Terms in a proposition 79 § 2. Euler's Diagrams .80 §3. Propositions considered as Equations 83 § 4. Existential Import of Propositions 86 CHAPTER IX FORMAL CONDITIONS OF MEDIATE INFERENCE § I. Nature of Mediate Inference and Syllogism .... 89 § 2. General Canons of the Syllogism 90 Definitions of Categorical Syllogism ; Middle Term ; Minor Term ; Major Term ; Minor and Major Pre- mise (p. 91) Illicit Process (p. 92) ; Distribution of the Middle (p. 92) ; Effects of Negative Premises (p. 93) ; of Particular Premises (p. 94) § 3. Dictum de omni et niillo 95 § 4. Syllogism in relation to the Laws of Thought ... 96 § 5. Other Kinds of Mediate Inference 98 CHAPTER X CATEGORICAL SYLLOGISMS § I. Illustrations of the Syllogism § 2. Of Figures § 3. Of Moods ^ 4. How valid Mocds are determined 99 100 lOI 102 CONTENTS XI § 5. Special Canons of the Four Figures . § 6. Ostensive Reduction and the Mnemonic Verses § 7. Another version of the Mnemonic Verses § 8. Indirect Reduction . . • . • § 9. Uses of the several Figures. § 10. Scientific Value of Reduction. . . § II. Euler's Diagrams for the Syllogism . PAGE 103 104 108 108 IIO III 112 CHAPTER XI ABBREVIATED AND COMPOUND ARGUMENTS § I. Popular Arguments Informal . . • • • § 2. The Enthymeme ' § 3. Monosyllogism, Poly syllogism. Prosyllogism. Episyllog § 4. The Epicheirema •••••• § 5. The Sorites § 6. The Antinomy . • , • • " • ' ;ism 114 115 116 117 118 120 CHAPTER XII CONDITIONAL SYLLOGISMS § I . The Hypothetical Syllogism § 2. The Disjunctive Syllogism § 3. The Dilemma . 122 126 127 CHAPTER XIII TRANSITION TO INDUCTION SI Formal Consistency and Material Truth . " ' ' § 2. Real General Propositions assert more than is directly known . • • • • • 132 133 r "'"--'iffliiritiiiiTiniiirrift'iiiTffrifl Xll CONTENTS CONTENTS Xlll / % 3. Hence, formally, a Syllogism's Premises seem to beg the Conclusion ......... § 4. Materially, a Syllogism turns upon the resemblance of the Minor to the Middle Term ; and thus extends the Major Premise to new cases § 5. Restatement of the Dictinn : equivalent to the Nota nota; § 6. Material Subalternation § 7. Uses of the Syllogism § 8. Materially, a Syllogism trusts to the Uniformity of Nature § 9. The Uniformity of Nature analysed .... CHAPTER XIV CAUSATION' § I. The most important aspect of Uniformity in relation to In- duction is Causation § 2. Definition of " Cause " explained. The five marks of Causa- tion § 3. How strictly the conception of Cause can be applied depends upon the subject under investigation .... § 4. Scientific conception of Effect. Plurality of Causes . § 5. Some condition, but not the whole cause, may long precede the Effect ; and some co-effect, but not the whole effect, may long survive the Cause § 6. Mechanical Causes and the homogeneous Intermixture of Effects ; Chemical Causes and the heteropathic Inter- mixture of Effects § 7. Tendency, Resultant, Counteraction, Elimination, Resolu- tion, Analysis, Reciprocity CHAPTER XV INDUCTIVE METHOD § I. Outline of Inductive investigation . § 2. Induction defined ..... PAGE 135 136 137 138 138 140 141 145 ^ 146 — 153 155 — 156 — 139-^ § 3. " Perfect " Induction § 4. Imperfect Induction methodical or immethodical . § 5. Observation and Experiment, the material ground of Induc- tion, compared ...»••••• § 6. The principle of Causation is the formal ground of Induction § 7. The Inductive Canons are derived from the principle of Causation, the more readily to detect it in facts observed ^/ CHAPTER XVI THE CANONS OF DIRECT INDUCTION § I. The Canon of Agreement Negative Instances (p. 174) ; PluraUty of Causes (p. 174) ; Agreement may show connection without direct Causa- tion (p. 175) § 2. The Canon of Agreement in Presence and in Absence . • It tends to disprove a Plurality of Causes (p. 178) § 3. The Canon of Difference May be applied to observations (p. 183) §4. The Canon of Variations How related to Agreement and Difference (pp. 185-6) ; The Graphic Method (p. 187) § 5. The Canon of Residues PAGH 165 166 167 168^- 170— • 172 176 180 184 189 161 164 CHAPTER XVII COMBINATION OF INDUCTION WITH DEDUCTION § I. Deductive character of Formal Induction § 2. Further complication of Deduction with Induction § 3. The Direct Deductive (or Physical) Method . f . § 4. Opportunities of Error in the Physical Method § 5. The Inverse Deductive (or Historical) Method ^ § 6. Precautions in using the Historical Method . 192 194 195 198 200 204 y 1/ XIV CONTENTS CHAPTER XVIII HYPOTHESES § I . Hypothesis defined and distinguished from Theory Employed in common reasoning (p. 209) § 2. An Hypothesis must be verifiable . .... § 3. Proof of Hypotheses (i) Must an hypothetical agent be directly observable (p. 211) ; Vera causa (p. 212) (2) An Hypothesis must be adequate to its pretensions (p. 213) ; Exceptio prohat regidam (p. 214) (3) Every competing Hypothesis must be excluded (p. 215) ; Crucial instance (p. 217) § 4. Hypotheses necessary in scientific investigation . §5. The Method of Abstractions Method of Limits (p. 222) ; In what sense all knowledge is hypothetical (p. 223) PAGE 208 1. 210 211 218 221 CHAPTER XIX LAWS CLASSIFIED ; CO-EXISTENCE ; EXPLANATION ; ANALOGY § I. Axioms; Primary Laws; Secondary Laws, Derivative or Empirical ; Facts 225 § 2. Secondary Laws either Invariable or Approximate Generali- sations . ......... § 3. Secondary Laws trustworthy only in ' Adjacent Cases ' § 4. Secondary Laws of Succession or of Co-existence Natural Kinds (p. 231), Co-existence of concrete things to be deduced from Causation (p. 232) § 5. Explanation consists in tracing resemblance, especially of Causation ........ § 6. Three modes of Explanation Analysis (p. 236) ; Concatenation (p. 236) ; Subsumption (P- 237) § 7. Limits of Explanation ....... § 8. Analogy 228 229 231 234 236 238 240 CONTENTS XV CHAPTER XX PROBABILITY § I. Meaning of Chance and Probability § 2. Probability as a fraction or proportion . § 3. Probability depends upon experience and statistics § 4. It is a kind of Induction, and pre-supposes Causation §5. Of Averages and • Errors ' Personal Equation (p. 250) ; meaning of ' E.xpectation ' (p. 250) § 6. Rules of the combination of Probabilities : . . . . Detection of a hidden Cause (p. 251); oral tradition (p. 252) ; circumstantial and analogical evidence (p. 253) PAGE 242 244 244 247' 249 251 CHAPTER XXI DIVISION AND CLASSIFICATION ^ § I . Classification, scientific, special and popular . - . . 254 § 2. Uses of classification 256 §3. Classification, Deductive and Inductive .... 257' § 4. Division, or Deductive Classification : its Rules . . . 258 § 5 Rules for testing a Division 260 § 6. Inductive Classification 261 §7. Difficulty of Natural Classification 262 § 8. Darwin's influence on the theory of Classification 264 § 9. Classification of Inorganic Bodies also dependent on Causa- tion 267 CHAPTER XXII NOMENCLATURE ; DEFINITION ; PREDICABLES § I. Precise thinking needs precise language § 2. Nomenclature and Terminology in popular Language (p. 272) § 3^. Definition § 4. Rules for testing a Definition 269 270 272 273 XV] CONTENTS 1 J 1 ) > > > > 5 5 § 5. Every Definition is relative to a Classification § 6. Difficulties of Definition .... Proposal to substitute the Type (p. 276) § 7. The Limits of Definition .... § 8. The five Predicables Porphpyry's Tree (p. 280) § 9. Realism and Nominalism .... § 10. The Predicaments .... CHAPTER XXIII DEFINITION OF COMMON TERMS § I The rigour of scientific method must be qualified . § 2. Still, Language comprises the Nomenclature of an imperfect Classification, to which every Definition is relative ; § 3. and an imperfect Terminology § 4. Maxims and precautions of Definition § 5. Words of common language in Scientific use . . . § 6. How Definitions affect the cogency of arguments CHAPTER XXIV FALLACIES § I. Fallacy defined and divided . § 2. Formal Fallacies of Deduction § 3. Formal Fallacies of Induction § 4. Material Fallacies classified . § 5. Fallacies of Observation § 6. Begging the Question § 7. Surreptitious Conclusion § 8. Ambiguity • § 9. Fallacies, a natural rank growth of the Human Mind, not easy to classify, or exterminate Questions PAGE 274 276 277 278 282 283 286 287 290 291 295 300 300 303 306 307 308 310 311 313- 315 > 3 CHAPTER I INTRODUCTORY § I. Logic is the science that explains what conditions must be fulfilled in order that a proposition may be proved, if it admits of proof. Not, indeed, every such proposition ; for as to those that declare the equality or inequality of numbers or other magnitudes, to explain the conditions of their proof belongs to Mathematics: they are said to be quantitative. But as to all other propositions, called qualitative^ like most of those that we meet with in conversation, in literature, in politics, and even in the sciences that are not treated mathe- matically (say, Botany and Psychology); propositions that merely tell us that something happens (as that salt dissolves in ivater\ or that something has a certain property (as that the east wind is batieful), or that something is related to a class of things (as that Englishmen are good sailors) : as to these, it belongs to Logic to show how we may judge whether they are true, or false, or doubtful. When propositions are expressed with the universaHty and definiteness that belongs to scientific statements, they are called laws ; and laws, so far as they are not laws of quantity, are tested by the principles of Logic, if they at all admit of proof. But it is plain that the process of proving cannot go on for ever ; something must be taken for granted ; and this is usually considered to be the case with those highest laws that are called axioms or first principles, of which we can only say that we know of no exceptions to them, that we cannot help believing them, and that they are indispensable to science and A • • • « • • ••• t •• • • • •• • • • • ••• •«, , •••••• '• • • • • » • •• • as ,?....l.€lGi<3!:-J3EDWi;iVE AND INDUCTIVE • ;••• • I #.2 • • •• • •• t(5 consistent thou^ht^ J^ogic, then, may be briefly defined the 3:(;;ef\Ce.*(5f Sf^l^ witlj respect to qualitative laws and propo- sitioirs, ^^fc'ept \hose tnat are axiomatic. § 2. Proof may be of different degrees or stages of com- pleteness. Absolute proof would require that a proposition should be shown to agree with all experience and with the systematic explanation of experience, to be a necessary part of an all-embracing and self-consistent philosophy or theory of the universe ; but as no one hitherto has been able to frame such a philosophy, we must at present put up with something less than absolute proof. Logic, assuming certain principles to be true of experience, or at least to be conditions of con- sistent discourse, distinguishes the kinds of propositions that can be shown to agree with these principles, and explains by what means the agreement can best be exhibited. These principles will be found in chaps, vi., ix., xiii., xiv. To bring a proposition or an argument under them, or to show that it agrees with them, is logical proof. The extent to which proof is requisite, again, depends upon circum- stances ; whether our aim be general truth for its own sake, or merely to compare a proposition with our own convictions, or to satisfy the doubts of a friend. If A and B are conversing, and A asserts that some white races have straight black hair, and B doubts this, but is willing to grant that some races n'ith straight black hair are ivhite, A may perhaps prove his point to the satisfaction of B by showing that these two pro- positions are intrinsically the same, as only differing in the order of the words. This is called proof by Immediate Inference, or by e(4uivalence of meaning. Again, if B is ready to admit that the Basques and Finns are white races, and that they also have straight black hair, then, when A puts these two propositions together thus — The Basques and Finns have straight black hair ; The Basques and Finns are white races ; Therefore, some white races have straight black hair — the truth of the last proposition is not likely to be disputed any longer. And this is called proof by Mediate Inference ; that is to say, a con- nection between ' some white races ' and * straight black hair ' is sup- posed not to be directly perceivable, but to be discovered by finding that both are connected in a certain way with ' Basques and Finns. ' If, however, B does not grant that the Basques or the Finns are a INTRODUCTORY 3 vvhite race, or that they have straight black hair, and A tries to prove these propositions, his difficulties greatly increase and may become msuperable. He must collect ethnological evidence, and convince B of Its sufficiency ; and if his friend be of a sceptical turn of mind, or desire a reputation for ingenuity rather than for good sense, the conclusion that some white races have straight black hair may be indefinitely postponed In fact, to follow out this illustration would be altogether unsuitable to an introductory chapter ; we had better turn to a simpler case Suppose that A holds in his hand a piece of yellow metal, which he asserts to be copper, and that B doubts this, perhaps suggesting that it IS really gold. Then A may propose to dip it in vinegar ; and we will suppose B to agree that, if it then turns green, it is copper and not gold On trying this experiment the metal does turn green ; so that we may put A s argument in this way ;— IVhatever yellow metal turns green in vinegar is copper ; This yellow metal turns green in vinegar ; Therefore, this yelloiv metal is copper. Now. however, it may occur to B that the liquid in which the metal was dipped was not vinegar, or not pure vinegar, and that the greenness was due to the impurity. A must thereupon show by some means that the vinegar was pure ; and then his argument will be that since nothing but the vinegar came in contact with the metal, the greenness was due to the vinegar ; or, in other words, that contact with the vinegar was the cause of the metal turning green. Still, on second thoughts. B may suspect that he had formerly con- ceded too much ; he may reflect that, although it had often been shown that copper turned green in vinegar, whilst gold did not. yet the same niight not always happen. How do we know, he may ask. that just at this moment, and perhaps always for the future gold turns, and will turn green in vinegar, whilst copper does not and never will again ? A will probably reply that this is to doubt the uniformity of causation- he may hope that B is not serious : he may point out to his friend that in every action of his life he takes such uniformity for granted. But he will be obliged to admit that, whatever he may say to induce his friend to assent to the principle of Nature's uniformity, his arguments will not amount to logical proof, because every argument in some way assumes that principle. He has come, in fact, to the limits of Logic Just as the mathematician does not try to prove that • two magnitudes equal to the same third are equal to one another.' so the Logician (as such) does not attempt to prove the uniformity of causation and the other orin ciples of his science. ^ § 3- Two departments of Logic are usually recognised. De- duction and Induction ; that is, to describe them briefly, proof from principles, and proof from facts. * Classification is' some- 4 LOGIC: DEDUCTIVE AND INDUCTIVE times made a third department; sometimes its topics are dis- tributed amongst those of the former two. In the present manual the order adopted is, Deduction, in chaps, ii. to xiii. ; Induction in chaps, xiii. to xx. ; and lastly. Classification. This order has been followed partly from some real convenience it has, partly in deference to custom ; but no formal division of the subject has here been made into parts or books, because (however convenient such a grouping may be in a larger treatise) it seemed desirable to avoid giving students the im- pression that such divisions represent fundamentally distinct and opposed aspects of the science. Although in discussing any question with an opponent who makes admissions, it may be posssible to combat his views with merely deductive argu- ments based upon his admissions; yet in any question of general truth, induction and deduction are mutually dependent and imply one another. This may be seen in one of the above examples. A argues that a certain metal is copper, because every metal is copper that turns green when dipped in vinegar. So far his proof appeals to a general proposition, and is deductive. But if B asks how he knows the general proposition to be true, A alleges experiments or facts ; and this is inductive evi- dence. Deduction then depends on Induction. But when B asks, again, how any number of past experiments can prove a general pro- position, which must be good for the future as well as for the past, A in- vokes the uniformity of causation ; that is, he appeals to a principle, and that is again deductive proof. Induction then depends upon Deduction. We may put it in this way : Deduction depends on Induc- tion, if general propositions are only known to us through the facts. Induction depends on Deduction ; because one fact can never prove another, except so far as what is true of the one is true of the other and of any other of the same kind ; and because, to exhibit this resemblance of the facts, it must be stated in a general proposition. § 4. The use of Logic is often disputed : those who have not studied it, often feel confident of their ability to do without it; those who have studied it, are sometimes disgusted with INTRODUCTORY As to those who, not hav ^ i^f t ' """""f' '^^'^''^• there will be time enough to Sfscuss ts „ ^ f"' '^' ^ ^'^''' ''' they know soniething abouMt "nd a Ti ^u'"' ^^'''^" studied it, turn away in d 1st fh Z ' ^''°' ''^^''"S able to judge whethef thev ' ,'^' ''"'^^'" ^^"' himself be juu^c wnetner they are justified, when he hr,« nffo* ^ to equal proficiency in the subiect Af. km ! '^^ ing considerations may be oS f'T^''^ ^^^ ^^"«- severe: ^ inducements to per- 00 Logic states, and partly exnhin^; nr./\ r abstract principles which ill o he" sci Ls l^'r ' '"'"" namely, the axioms above mentioned ^ '''"''" ' (^) By exercising the student \n tu^ ^ u • tions. It educates the power of abstract thnnahf ^ u -son Logic is the best propedeutic tlphi o o : tha^is t'o^ Metaphysics and speculative Ethics ' and i S';":^"""^^' :''"' «-" expounded, is a model of method and a d,sc^l,„e m close and consecutive thinking. This meX' Lo^ic ought to possess in a high degree 1 re Observe . the ^wm;/ nature of such evidenrp t^ would e absurd of the Logician to pretend to sru" ti Chem,st, Economist and Merchant, as to the ./../, "char'tr o he evidence requisite in their several spheres oHudgne t S .11, by investigating the general conditions of proo he 1.^ every man upon his guard against insufficient evi.l"' reaso,rWe' I '" '°" "°^' '" "'^ «^^' P'^^' ^-^h us to reason. We learn to reason, as we learn to walk and t.ll by the nautral growth of our powers, with some assfst nc^; from nends and neighbours. But, to be frank, f^w of u L go tail"""."""''"^ '''''■' ^"'^' - '° ---ng Logic cettamly quickens our sense of bad reasoning, bott 6 LOGIC: DEDUCTIVE AND INDUCTIVE in others and in ourselves. It helps us to avoid being misled by others, and to correct our own mistakes. A man who reasons deliberately, manages it better after studying Logic than he could before— if he tries to, if he has not a perverse liking for sophistry, and if he has the sense to know when formalities are out of place. There are some mental qualities that a man can only get from his father and mother. (uth as an end desired, and points out some of the means of attaining it; namely, to proceed by a regular method, to test any proposition by the principles of Logic, and to distrust whatever cannot be made consistent with them. It does not give any one originality and fertility of invention; but it enables us to check our inferences, revise our conclusions, and chasten the vagaries of ambitious speculation. On account of this corrective function, Logic is sometimes called a Regulative Science. (/) Finally, Logic is at least a refined mental exercise. And it needs no telescopes, microscopes, retorts or scalpels; no observatories, laboratories, or museums : it is, therefore, cheap and convenient. Moreover, it is of old and honourable descent; a man studies Logic in very good company. It is the warp upon which nearly the whole web of ancient, INTRODUCTORY 7 medieval and modern philosophy has been woven; and is therefore manifestly indispensable to a liberal education. § 5. The relation of Logic to other sciences may be indicated thus : (^7) Logic is regarded by Spencer as co-ordinate with Mathe- matics, both being Abstract Sciences— that is, sciences of the relations in which things stand to one another, whatever the ^ particular things may be that are so related; and this view seems to me to be, on the whole, just— subject, however, to a qualification that will appear presently. Mathematics treats of the relations of all sorts of things considered as quantities, namely, as equal to, or greater, or less than, one another. Things may be quantitatively equal or unequal in degree, as in comparing the temperature of bodies; or in duration; or in spatial magnitude, as with lines, superficies, solids; or in number. And it is assumed that the equality or inequality of things that cannot be direcdy compared, may be proved indirectly on the assumption that ' things equal to the same thing are equal ' &c. Logic also treats of the relations of all sorts of things, but not as to their quantity. It considers (i) that one thing may be like or unlike another in certain attributes, as that a shark is in many ways like a ray, and in many ways unlike a star-fish : (ii) that attributes co-exist or coinhere (or not) in the same subject, as the having several rows of teeth and a backbone prolonged into the upper lobe of the tail coinhere in a shark : and (iii) that one event follows another (or is the effect of it), as that the placing of iron in water causes it to rust. The relations of likeness and of coinherence are most prominent in the department of Classification ; for it is by resemblance of coinhering attributes that things form classes : the relation of succession, in the mode of causation, is the chief subject of the department of Induction. It is usual to group together these relations of attributes and of order in time, and call them qualitative, in order to contrast them with the quantitative which belong to Mathematics, And it is w 8 LOGIC: DEDUCTIVE AND INDUCTIVE assumed that qualitative relations of things, when they cannot be directly perceived, may be proved indirectly by assuming the axiom of the Syllogism (chap, ix.) and the law of Causa- tion (chap. xiv.). So far, then, Logic and Mathematics appear to be co- ordinate and distinct sciences. But we shall see hereafter that the satisfactory treatment of that special order of events in time which constitutes Causation, recjuires a combination of Logic with Mathematics. On the other hand. Logic may be said to be in some respects 'prior to' or * above' Mathematics as usually treated. For the Mathematics assume that one magnitude must be either equal or unequal to another, and that it cannot be both equal and unequal to it, and thus take for granted the principles of Contradiction and Excluded Middle; but the statement and elucidation of these principles is left to Logic (chap, vi.) The Mathematics also classify and define magnitudes, as (in Geometry) triangles, squares, cubes, spheres; but the principles of classification and definition remain for Logic to discuss. (/>) As to the concrete Sciences, such as Astronomy, Chemistry, Zoology, Politics— Logic (as well as Mathematics) is implied in them all; for all the propositions of which they consist involve causation, coexistence, and class-likeness. Logic is therefore said to be prior to them or above them : meaning by * prior ' not that it should be studied earlier, for that is not a good plan ; meaning by * above ' not in dignity, for distinctions of dignity amongst liberal studies are absurd.' But it is a philosophical idiom to call the abstract ' prior to,' or 'higher than,' the concrete (see Porphyry's Tree, chap, xxii. § 8) ; and Logic is more abstract than Astronomy or Politics. Philosophy may thank that idiom for many a foolish notion. (c) But, as we have seen. Logic does not investigate the truth, trustworthiness, or validity of its own principles; nor does Mathematics : this task belongs to Metaphysics, the criticism of knowledge and beliefs. INTRODUCTORY 9 Logic assumes, for example, that things are what to a careful scrutiny they seem to be ; that animals, trees, mountams, planets, are bodies with various attributes, existing m space and changing in time; and that certain principles, such as Contradiction and Causation, are true of things and even s. But Metaphysicians have raised many plausible obje^ctions to these assumptions. It has been urged that natural objects do not really exist on their own account, but only in dependence on some mind that contemplates them, and that even space and time are only our way of perceiving things ; or, again, that although things do really exist on their own account, it is in an entirely different way from that in which we know them. As to the principle of Contradiction-that if an object has an attribute, it cannot at the same time and in the same way be without it (..A^, if an animal is conscious, it is false that it is not conscious)-it has been contended that the speciousness of this principle is only due to the narrowness of our minds or even to the poverty of language, which cannot make the fine distinctions that exist in Nature. And as to Causation it is sometimes doubted whether events always have ph>^ical causes ; and it is often suggested that, granting they have physical causes, yet these are such as we can neither perceive nor conceive ; belonging not to the order of nature as we know it but to the secret inwardness and reality of Nature to the wells and reservoirs of power, not to the spray of the fountain that glitters in our eyes-' occult causes, in short Now these doubts ^nd surmises are metaphysical spectres which it remains for Metaphysics to lay. Logic has no direct concern with them (although of course meta- nhvsical discussion is usually expected to be logical), bu. keeps the plain path of plain beliefs, level with the com- prehension of plain men. Metaphysics, as examining the grounds of Logic itself, is sometimes regarded as the higher °S The relation of Logic to Psychology will be discussed in the next section. '° I^OGIC: DEDUCTIVE AND INDUCTIVE tru?intrent';"t" ''""'"' ""'"''"^ °"' ''^^ -"^itions of with ) Ethic, •;'' °"'" ^P'^*^")' ^-"^"'^ i» — dinate right Iduc ; T" .'7' " ^"'^"'"^ 'he conditions of Jn n.^h ' -1 "'"^ <"> -■'■^"^^"■^^' considered as deter- niimng the pnncples of criticism and good taste. rectms d Vn'""r' ^''°°'^ "' ''°Sicians are commonly differ to' «hr;';i;h.T"^'"^"'^'' •^-'^ ^'•^'-''^"■^'' "■•- nalists sav° o7 h "^" "'''''"y "''^''"^ "^^ »he Nomi- the ■Mat:?i;,is^ "SLn's 'o^ ^7'^'''' i"' ''°"«'^' ' ^ these positions author r ''"' "' ^''^^ '" '""«'«»« have the e" ^ s ^ Z k'/ ""'^ °' "i^'" ""^ """^ "^S'-'^-^' "7 -t ,ater ^^reStl^dT rtr^ "'^ ^ ^■•-•"- sc!: crtd"^:t":?t'°"" '""-'r""' '-'''''' ^-^^^ - -^^ ana Art of Reasoning, but at the same time is shai" ulthf T" "^°^<^"^°des of statement which he u"i c iT'"^' '■' "' '"«""^"'' "" --«'- "hat may be • uc buoject under discussion Thu^ ,'f ^^ // /r / 7 , , , mm „„v,»,r nf,^ ' °""'' inference /'v the \ A 7 "^ '■'^''"'■"" ' '■>"d «]ually sound is the inference i he latter propos.fon may be false, but it follows • and tsistnf '° ''? '°"""'^) '■°^"'^ ■•^ ->• concerned V th t e =::T;;e:tirz;ot;™'^ °^ '-'^^^ °^ - — •■ (^) Hamilton, our best-known Conceptualist, regards I ode as the scence of the "formal laws of thought " and '^f ■ thought as thought" thnt io -.i " °' thought about. Just a Whl, . 7"' '° "^'^ """^^ merdy with co^e, t flrn , f ' ''^"■''' ''"^'c as concerned as concerned reiT^;/.!''''^'-'"^'^"'' - "»-'■'- '-'s it This doctrine TcaLd Cone "TT' u '''""'' °' "^°"ght. element of .houg.:t s^he C ncm th. """ u'' ^™^'^^' such as is signified bv the ' "' "" "^''^""^ '"^'^' INTRODUCTORY 11 { attributes common to any class of things. Men, planets colours, virtuous actions or characters, have, severally, some- thing in common on account of which they bear these general names ; and the thought of what they have in common as the ground of these names is a Concept. To affirm or deny one con- cept of another, as S^me men are virtuous. No man u perfectly virtuous Mo form a judgment, corresponding to the ProposUions of which the other schools of Logic discourse. Conceptuahsm, then investigates the conditions of consistent judgments. To distinguish Logic from Psychology is most important m connection with Conceptualism. Concepts and Judgments being mental acts, or products of mental activity, it is often thought that Logic must be a department of Psychology. It is recognised, of course, that Psychology deals with much more than Logic does, with sensation, pleasure and pain, emotion, volition ; but in the region of the intellect, especially in its most deliberate and elaborate processes, namely, con- ception, judgment, and reasoning, it is supposed that Logic and Psychology occupy some common ground. In tact, however, the two sciences have little in common except a few aeneral terms, and even these they employ in different senses. !t is usual to point out that Psychology tries to explain the subjective processes of conception, judgment and reasoning (say, according to the Laws of Association) and to give their natural history ; but that Logic is wholly concerned with the results of such processes, with concepts, judgments and reasonings, and merely with the validity of the results, that is, with their truth or consistency ; whilst Psychology has nothing to do with their validity, but only with their causes. Besides, the logical judgment is (in Formal Logic at least) quite a different thing from the psychological : the latter involves feel- ing and belief, whereas the former is merely a given relation of concepts 5 is P: that is a model logical judgment, there can be no question of believing it ; but it is logically valid if M is P and 5 is M. If, again, belief has any place in Logic, it depends upon evidence ; whereas, in Psychology belief is M 12 LOGIC: DEDUCTIVE AND INDUCTIVE shown to depend upon causes, which may have evidentiary value or may not ; for Psychology explains quite impartially the growth of scientific insight and the growth of prejudice. (r) Mill, Bain, and Venn, are the chief Materialist logicians ; and to guard against the error of confounding Materialism in Logic with the ontological doctrine that nothing exists but Matter, it may suffice to remember that in Metaphysics all these philosophers are Idealists. Materialism in Logic consists in regarding propositions as affirming or denying relations {cf. § 5) between matters-of-fact ; in treating the first principles of Contradiction and Causation as true of things so far as they are known to us, and not merely as conditions or tendencies of thought ; and, indeed, in taking these principles as conditions of right thinking, because they seem to hold good of Nature. To these differences of opinion it will be necessary to recur in the next chapter (§ 4) ; but here I may observe that it is easy to exaggerate their importance in mere Logic. Whoever feels an interest in any subject upon which opinions differ, knows how hard it is not to take sides about it. How often in pure science and philosophy we witness the ludicrous spectacle of partisans engaging with as much rancour as if they- were politicians with the interests of taxation at stake ! If such a scene is ever witnessed under the dry light of Logic, let it pass for a bad dream. There is really little at issue between schools of logicians as such, and as far as their doctrines run parallel ; it is on the metaphysical grounds of their study, or as to its scope and comprehension, that they find a battle-field. As for this manual, it generally proceeds upon the third, or Materialist doctrine. If Deduction and Induction are regarded as mutu- ally dependent parts of one science, uniting the discipline of consistent discourse with the method of investigating laws of physical phenomena, the Materialist doctrine, that the prin- ciples of Logic are founded on fact, seems to be the most natural way of thinking. But if the unity of Deduction and Induction is not disputed by the other schools, the Materialist may regard them as allies exhibiting in their own way the same INTRODUCTORY 13 A body of truths. The Nominalist may certainly claim that his doctrine is indispensable : consistently cogent forms of state- ment are necessary both to the Conceptualist and to the Materialist ; neither the relations of thought nor those of fact can be arrested or presented without the aid of language or some equivalent system of signs. The Conceptualist may urge that the Nominalist's forms of statement and argument exist for the sake of their meaning, namely, judgments and reasonings ; and that the Materialist's laws of Nature are only judgments founded upon our conceptions of Nature ; that the truth of observations and experiments depends upon our powers of perception ; that perception is inseparable from understanding, and that a system of induction may be con- structed upon the axiom of Causation, regarded as a principle of Reason, just as well as by considering it as a law of Nature, and upon much the same lines. The Materialist, admitting all this, may say that the other schools have not hitherto been eager to recognise the unity of Deduction and Induction or to investigate the conditions of trustworthy experiments and observations within the limits of human understanding ; that thought is itself a sort of fact, as complex in its structure, as profound in its relations, as subtle in its changes as any other fact, and therefore at least as hard to know ; that to turn away from the full reality of thought in perception, and to confine Logic to artificially limited concepts, is to abandon the effort to push method to the utmost and to get as near truth as possible ; and that as to Causation being a principle of Reason rather than of Nature, the distinction escapes his apprehension, since Nature seems to be that to which our private minds turn upon questions of Causation for correction and instruction; so that if he does not call Nature the Universal Reason, it is because he loves severity of style. k 4 %, CHAPTER II GENERAL ANALYSIS OF PROPOSITIONS § I. Since Logic discusses the proof or disproof, or (briefly) the testing of propositions, we must begin by explaining their nature. x\ proposition, then, may first be described in the language of grammar as a sefitence indicative ; and it is usually expressed in the present tense. It is true that other kinds of sentences, optative, imperative, interro- gative, exclamatory, if they express or imply an assertion, are not beyond the view of Logic ; but before treating such sentences. Logic, for greater precision, reduces them to their equivalent sentences indi- cative. Thus, / iLish it were summer may be understood to mean. The coming of summer is an object of my desire. Thou shalt not kill may be inter- preted as Murderers arc in danger of the judgment. Interrogatories, when used in argument, if their form is affirmative, have negative force, and affirmative force if their form is negative. Thus, Do hypocrites love virtue ? anticipates the answer, No. Are not traitors the vilest of mankind ? anticipates the answer. Yes. So that the logical form of these sentences is, Hypocrites are not lovers of virtue ; Traitors are the vilest of mankind. Impersonal propositions, such as It rains, are easily rendered into logical forms of equivalent meaning, thus: Rain is falling ; or, if this be tauto- logy, The clouds are raining. Exclamations may seem capricious, but are often part of the argument. Shade of Chatham ! usually means Chatham, being aware of our present foreign policy, is much disgusted. It is, in fact, an appeal to authority, without the inconvenience of stating what exactly it is that the authority declares. § 2. But even sentences indicative may not be expressed in the way most convenient to logicians. SaU disso/ves in water is a plain enough statement for ordinary purposes ; but the logician prefers to have it thus : Sa/t is soluble in water. For he says that a proposition is analy sable into GENERAL ANALYSIS OF PROPOSITIONS 15 three elements : (i) a Subject (as Salt) about which something is asserted or denied; (2) a Predicate (as soluble in water) which is asserted or denied of the Subject, and (3) the Copula {is or are., or is not or are not), the sign of relation between the Subject and Predicate. The Subject and Pre- dicate are called the Terms of the proposition : and the Copula may be called the sign of predication, using the verb ' to predicate ' indefinitely for either ' to affirm ' or ' to deny.' Thus 5 is P means the term P is given as related in some way to the term S. We may, therefore, further define a Proposition as *a sentence in which one term is predicated of another.' In such a proposition as Salt dissolves, the copula {is) is contained in the predicate, and, besides the subject, only one element is exhibited : it is therefore said to be secundi adjacentis. When all three parts are exhibited, as in Salt is soluble, the proposition is said to be tertii adjacentis. § 3. The sentences of ordinary discourse are, indeed, for the most part, longer and more complicated than the logical form of propositions ; it is in order to prove them, or to use them in the proof of other propositions, that they are in Logic reduced as much as possible to such simple but explicit ex- pressions as the above {tertii adjacentis). A Compound Pro- position, reducible to two or more simple ones, is said to be exponible. The means by which sentences are compounded may be seen analysed in any book of grammar. One of the commonest forms is the copula- tive, such as Salt is both savoury and ivholesome, equivalent to two simple propositions: Salt is savoury; Salt is ivholesomc. Pure water is neither sapid nor odorous, equivalent to Water is not sapid; Water is not odorous. Or, again. Tobacco is injurious, but not when used in moderation, equivalent to Much tobacco is injurious ; A little ts not. (The word but, however, sometimes needs a third proposition to bring out its meaning, as in this case : Other nations change, but not the Chinese — an assertion of superiority.) Another form of Exponible is the Exceptive, as Kladderadatsch is pub- lished daily, except on week-days, equivalent to Kladderadatsch is published on Sunday ; it is not published any other day. Still another Exponible is the / i6 LOGIC: DEDUCTIVE AND INDUCTIVE Exclusive, as Only men use /ire, equivalent to Men arc users of fire ; No other animals are. There are other compound sentences that are not exponible, since, though they contain two or more verbal clauses, the construction shows that these are inseparable. Thus, // cats arc scarce, mice are plentiful, contains two verbal clauses ; but // cats are scarce is conditional, not indicative; and mice are plentiful is subject to the condition that cats are scarce. Hence the whole sentence is called a Conditional Proposition. For the various forms of Conditional Propositions see chap. v. § 4. But, in fact, to find the logical force of recognised grammatical forms is the least of a logician's difficulties in bringing the discourses of men to a plain issue. Metaphors, epigrams, innuendos and other figures of speech present far greater obstacles to a lucid reduction whether for approval or refutation. No rules can be given for finding everybody's meaning. The poets have their own way of expressing themselves ; sophists, too, have their own way. And the point often lies in what is unexpressed. Thus, " barbarous nations make, the civilised write his- tory," means that civilised nations do not make history, which none is so brazen as openly to assert. Or again, " Alcibiades is dead, but X is still alive." The whole meaning of this ' Exponible ' is that X would be the lesser loss to society. Even an epithet or a suffix implies a pro- position. This personage may mean A' is a pretentious nobody. How shall we discover such illusive predications except by cultivating our literary perceptions ? The obtuse man who misses the meaning of an epigram may escape some pain ; but ' the higher pain ' is good for him. At any rate, to disentangle the compound propositions, and to expand the abbreviations of literature and conversation, is a useful logical exercise. And if it seem a laborious task thus to reduce to its logical elements a long argument in a speech or treatise, it should be observed that, as a rule, in a long discourse only a few sentences are of principal importance to the reasoning, the rest being explanatory or illustrative digression, and that a close scrutiny of these cardinal sen- tences will frequently dispense us from giving much attention to the rest. § 4. But now, returning to ihe definition of a Proposition given in § 2, that it is 'a sentence in which one term is predicated of another/ we must consider what is the import of such predication. Foi the definition, as it stands, seems to be purely Nominalist. Is a Proposition nothing more than a certain synthesis of words ; or, is it meant to correspond with something further, a synthesis of ideas, or a relation of facts ? < GENERAL ANALYSIS OF PROPOSITIONS 17 Conceptualist logicians, who speak of Judgments instead of Propositions, of course define the Judgment in their own language. According to Hamilton, it is "a recognition of the relation of congruence or confliction in which two concepts stand to each other." To lighten the sentence, I have omitted one or two qualifications (Hamilton's Lectures on Logic% xiii.). " Thus," he goes on, " if we compare the thoughts water , iron^ and rusting, we find them congruent, and connect them into a single thought, thus : water rusts iron — in that case we form a judgment." When a judgment is expressed in words, he says, it is called a proposition. There seems at first to be a merely verbal difference upon this point between the three Schools (chap. i. § 6) ; for Whately begins by describing a Proposition as "a judgment expressed in words," though he prefers to define it as "a sentence indicative." Mill, again, defines it as "a portion of discourse in which a predicate is affirmed or denied of a subject." {Logic, Book I., chap. iv. § i.) But further differences come to light when Whately observes that his definition "relates entirely to the words," and when Mill goes on to inquire into the import of propositions. (Book I., chap, v.) Mill finds three classes of propositions : (a) those in which one proper name is predicated of another ; and of these Hobbes's Nominalist definition is adequate, namely, that a proposition asserts or denies that the predicate is a name for the same thing as the subject, as Tul/y is Cicero. (b) Propositions in which the predicate means a part (or the whole) of what the subject means, as Horses are ani?nais, Man is a rational animal. These are Verbal Propositions (See below: chap. v. § 6), and their import consists in affirming or denying a coincidence between the meanings of names, as The meaning of" animal^ is part of the ?neaning of ' horse '. But {c) there are also Real Propositions, whose predicates do not mean the same as their subjects, and whose import / 1: I •' i8 LOGIC: DEDUCTIVE AND INDUCTIVE consists in affirming or denying one of five different kinds of matter of fact: (i) That the subject exists, or does not; as if we say The bison exists^ The great auk is exti?icf. (2) Co-existence, as Ma?i is mortal ; that is, the Imng; subject to death coinheres with the qualities Ofi account of which we call certai?i objects 7?ien. (3) Succession, as The military precedes the industrial regime. (4) Causation (a particular kind of Succession), as Water rusts iron. (5) Resemblance, as The colour of this geranium is like that of a soldier's coat. On comparing this list of real predications with the list of logical relations given above (chap. i. § 5^), it will be seen that the two differ only in this, that I have there omitted simple Existence. In fact nothing simply exists, unrelated either in Nature or in knowledge. Still, such a proposition as The bison exists may, no doubt, be used in Logic (subject to interpretation) for the sake of custom or for the sake of brevity. Into the question of the Import of Propositions it would be unsuitable to enter further. This controversy really turns upon a difference of opinion as to the scope of Logic and the foundations of knowledge. Mill was dissatisfied with the " congruity " of concepts as the basis of a judgment. Clearly, mere congruity does not justify belief. In the pro- position Water rusts iron, the concepts water, 7'ust and iron may be congruous, but does any one assert their con- nection on that ground? in the proposition Murderers are haunted by the ghosts of their victims, the concepts victim, murderer, ghost have a high degree of congruity ; yet, un- fortunately, I cannot believe it : there seems to be no such cheap defence of innocence. Now, Mill held that Logic is concerned with the grounds of belief, and that the scope of Logic includes Induction as well as Deduction ; whereas, according to Hamilton, Induction is only Modified Logic, a mere appendix to the theory of the "forms of thought as thought." Indeed, Mill endeavoured in his Logic to probe the grounds of belief deeper than the science should pretend GENERAL ANALYSIS OF PROPOSITIONS 19 to penetrate, and Introduced a good deal of Metaphysics— certainly, either too much or not enough. But, at any rate, his great point was that belief, and therefore (for the most part) the Real Proposition, is concerned not merely with the relations of words, or even of ideas (though, of course, propositions are judgments expressed in words), but with matters of fact; that is, both propositions and judgments point to something further, to the relations of things which we can examine, not merely by thinking about them (com- paring them in thought), but by observing them with the united powers of thought and perception. This is what convinces us that water rusts iron: and the difficulty of doing this is what prevents our feeling sure that murderers are haunted by the ghosts of their victims. Hence, although Mill's definition of a Proposition, given above, is adequate for propositions in general; yet that kind of proposition (the Real) with regard to which Logic (in Mill's view) in- vestigates the conditions of proof, may be more explicitly and pertinently defined as 'a predication concerning the relation of matters of fact.' § 5. This leads to a very important distinction to which we shall often have to refer in subsequent pages— namely, the distinction between the Form and the Matter of a pro- position or of an argument. The distinction between Form and Matter, as it is ordinarily employed, is easily understood. An apple growing in the orchard and a waxen apple on the table may have the same shape, but consist of different materials; two real apples may have the same shape, but contain distinct ounces of apple-stuff, so that after one is eaten the other remains to be eaten. Similarly, tables may have the same shape, though one be made of marble, another of oak, another of deal. The form is common to several things, the matter is peculiar to each. Metaphysicians have, by analogy, carried the distinction further : apples, they say, may have not only the same outward shape, but the same inward constitution, which, therefore, may be called the Form 20 LOGIC: DEDUCTIVE AND INDUCTIVE of apple-stuff^namely, a certain pulpiness, juiciness, sweetness, etc. ; qualities common to all dessert apples : yet their matter is different, one being here, another there— differing in place or time, if in nothing else. To apply this distinction to the things of Logic : it is easy to see how two Propositions may have the same Form but different Matter: not using 'Form' in the sense of 'shape,' but for that which is common to many things, in contrast with that which is peculiar to each. Thus, All 7nale lions have tufted tails and All ivater is liquid at ^o"" Fahrenheit, are two propositions that have the same form, though their matter is entirely different. They both predicate something of the whole of their subjects, though their subjects are different, and so are the things predicated of them. Again, All male lions have tufted tails and All ??iale lions have 7nanes, are two propositions having the same Form and in their Subjects the same Matter, but different Matter in their Predicates. If, however, we take two such propositions as these : All male lions have manes and Some jnale lions have manes, here the Matter is the same in both, but the Form is different— in the former, predication is made concerning every male lion ; in the latter of only some male lions ; the former is universal, the latter is particular. Or, again, if we take Some tigers are man-eaters and Some tigers are not man-eaters, here too the Matter is the same, but the Form is different ; for the former proposition is affirma- tive, whilst the latter is negative. § 6. Now, according to Hamilton and Whately, pure Logic has to do only with the Form of Propositions and arguments. As to their Matter, whether they are really true in fact, that is a question, they said, net for Logic, but for experience, or for the special sciences. But Mill desired so to extend logical method as to test the material truth of propositions : he thought that he could expound a method by which experience itself and the conclusions of the special sciences may be examined. To this method, however, some critics persistently object, that the claim to determine Material Truth takes for granted GENERAL ANALYSIS OF PROPOSITIONS 21 that the order of Nature will remain unchanged, that (for ex- ample) water not only at present is a liquid at 50° Fahrenheit, but will always be so ; whereas (although we have no reason to expect such a thing) the order of Nature may change — it is at least supposable — and in that event water may freeze at such a temperature. On the other hand, they urge that a certain kind of Formal Truth may be placed beyond even the suppo- sition of possible error. An apple, for example, is either green all over, or it is not : if we affirm the one alternative we must deny the other ; this is necessary to all intelligible use of language and to all clearness of thought. But upon the ques- tion of material truth, as to the apple being really green all over, a certain dubiousness is defensible and not undignified. For what, after all, is meant by an apple * green all over'? What is 'green'? To whom is it green? Not to the colour-blind. In what circumstances? Not in the dark. Any matter of fact must depend on observation, either directly, or by inference — as when some- thing is asserted about atoms or ether. But observation and material inference are subject to the limitations of our faculties; and however we may aid observation by microscopes and micrometers, it is still observation ; and however we may correct our observations by repetition, comparison and refined mathematical methods of making allowances, the correction of error is only an approximation to accuracy. Outside of Formal Reasoning, suspense of judgment is your only attitude. It is not to be supposed that such reflections did not occur to Mill, though he may have thought them strained and negligible. Here, however, it seems to me right to give them some weight ; and accordingly prominence will be given to the character of Logic as a Formal Science. At the same time it will be shown that Induction may be included in Logic and treated formally ; and it will be assumed that logical forms are only valuable so far as tjaey represent the actual relations of natural phenomena. § 7. Symbols are often used in Logic instead of concrete terms, not only in Symbolic Logic where the science is treated t*^ 22 LOGIC: DEDUCTIVE AND INDUCTIVE algebraically (as by Dr. Venn in his Symbolic Logic)^ but in ordinary manuals ; so that it may be well to explain the use of them before going further. It is a common and convenient practice to illustrate logical doctrines by examples : to show what is meant by a Proposition we may give salt is soluble, or water rusts iron : the copulative exponible is exemplified by salt is savoury and wholesome ; and so on. But this procedure has some disadvantages : it is often cumbrous ; and it may distract the reader's attention from the point to be explained by exciting his interest in the special fact of the illustration. Clearly, too, if Logic is only formal, no particular matter of fact can adequately illustrate any of its doctrines. Accordingly, writers on Logic employ letters of the alphabet instead of concrete terms (say), X instead of salt or instead of iron, and (say) Y instead of so/M^/t' or instead of rusted by water; and then a proposition may be represented by X is Y. It is still more usual to represent a proposition by S is {or is not) P, S being the initial of Subject, and P of Predicate ; though this has the drawback that if we argue— S is P, therefore P is S, the symbols in the latter proposition no longer have the same significance, since the former Subject is now the Predicate. Again, negative terms frequently occur in Logic, such as not water, or 7iot iron, and then if water or iron be expressed by X, the corresponding negative may be expressed by x ; or, generally, if a capital letter stand for a positive term, the corresponding small letter represents the negative. And as terms are often compounded, it may be convenient to express them by a combination of letters : instead of illustrating such a case by boiling water or water that is boiling, we may write XY , or, since positive and negative terms may be compounded, instead of illustrating this by water that is not boiling, we may write Xy. The convenience of this is obvious ; but it is more than con- venient ; fors if one of the chief uses of Logic is to discipline the power of abstract thought, this can be done far more effectually by symbolic than by concrete examples ; and if such discipline were the only use of Logic it might be best to discard concrete illustrations altogether, at least in advanced Text-books, though no doubt the practice would be too severe for an elementary Manual. But on the other hand, to teach the practical applicability of Logic to the arguments and proofs of actual life, or even of the concrete sciences, merely symboUc illustration may be not only useless but even mis- GENERAL ANALYSIS OF PROPOSITIONS 23 leading. When we speak of politics, or poetry, or species, or the weather, the terms that must be used can rarely have the distinctness and isolation of X and Y ; so that the perfunctory use of symbolic illustration makes argument and proof appear to be much simpler and easier matters than they really are. Indeed, in this connection, it is impossible to illustrate Logic sufficiently : the student who is in earnest about the cogency of arguments and the limitation of proofs, and is scrupulous as to the degrees of assent that they require, must constantly look for illustrations of the science in his own experience and rely at last upon his own sagacity. CHAPTER III OF TERMS AND THEIR DENOTATION § I. In treating of Deductive Logic it is usual to recognise three divisions of the subject : first, the doctrine of Terms, words, or other signs used as subjects or predicates ; secondly, the doctrine of Propositions, in which terms are combined ; and, thirdly, the doctrine of the Syllogism in which proposi- tions are combined as the grounds of a conclusion. The terms employed are either letters of the alphabet, or the words of common language, or the technicalities of science; and since the words of common language are most in use, it is necessary to give some account of common language as sub- serving the purposes of Logic. It has been urged that we cannot think or reason at all without words, or some substitute for them, such as the signs of algebra; and although this opinion is too sweeping, since we draw many simple inferences by means of mental imagery, and even animals do so when judging of prey, or enemies, or friends by their scent or by the noises they make ; yet the more elaborate inferences, and especially the grouping and concatenation of inferences, which we call reasoning, seem to be impossible without language or some equivalent system of signs. It is not merely that we need language to express our reasonings and commu- nicate them to others : in solitary thought we depend on words— 'talk to ourselves,' in fact; though the words or sentences that then pass through our minds are seldom fully formed or articulated. In Logic, moreover, we have carefully to examine the grounds (at least the formal and proximate / i OV TERMS AND THEIR DENOTATION 25 grounus) of our conclusions ; and plainly this cannot be done unless the conclusions in question are explicitly stated and recorded. Conceptualists say that Logic deals not with the process of thinking (which belongs to Psychology) but with its results; not with conceiving but with concepts ; not with judging but with judgments. Is the concept self-consistent or adequate, Logic asks; is the judgment capable of proof? Now, it is only by recording our thoughts in language that it becomes possible to distinguish between the process and the result of thought. As a mere train of mental imagery, the act and the product of thinking would be identical and equally evanescent. But by carrying on the process in language and remembering or otherwise recording it, we obtain a result which may be ex- amined according to the principles of Logic. § 2. As Logic, then, must give some account of language, it seems desirable to explain how its treatment of language differs from that of Grammar and from that of Rhetoric. Grammar is the study of the words of some language, their classifica- tion and derivation, and of the rules of combining them according to the usage at any time recognised and followed by those who are considered good authors. Composition may be faultless in its grammar, though dull and absurd. Rhetoric is the study of language with a view to obtaining some special effect in the communication of ideas or feelings, such as pic- turesqueness in description, vivacity in narrative, lucidity in exposition, vehemence in persuasion, or literary charm. Some of these ends are often gained in spite of faulty syntax or faulty logic ; but since the few whom bad grammar saddens or incoherent arguments divert are not carried away as they else might be by an unsophisticated orator. Gram- mar and Logic are necessary to the perfection of Rhetoric. Not that Rhetoric is in bondage to those other sciences ; for foreign idioms and such figures as the ellipsis, the anacoluthon, the oxymoron and the hyperbole, and violent inversions have their places in the magnificent style ; but authors unacquainted with Grammar and Logic are not likely to place such figures well and wisely. Indeed, common idioms, though both grammatically and rhetorically justifiable, both correct and effective, often seem illogical. 'To fall asleep,' for example, is a perfect English phrase ; yet if we examine severally the words it con- 26 LOGIC: DEDUCTIVE AND INDUCTIVE seem strange that their combination should rfiean sists of, it may anything at all. But Logic only studies language so far as necessary in order to state, understand, and check the evidence and reasonings that are usually embodied in language. And good Logic is compatible with false con- cords and inelegance of style. If any one argues thus: All men is animals; therefore, some animals is men — the mode of expression may be deprecated, bat we know what he means, and the argument is sound. - § 3. Terms are either Simple or Composite : that is to say, they may consist either of a single word, as * Chaucer,' 'civili- sation '; or of more than one, as ' the father of English poetry,' or * modern civilised nations.' Logicians classify words accord- ing to their uses in forming propositions ; or, rather, they classify the uses of words as terms, not the words themselves ; for the same word may fall into different classes of terms according to the way in which it is used. (C/. Mr. Alfred Sidg wick's Distinction and the Criticism of Beliefs^ chap, xiv.) Thus words are classified as Categorematic or Syncategore- matic. A word is Categorematic if used singly as a term without the support of other words : it is Syncategorematic when joined with other words in order to constitute the subject or predicate of a proposition. If we say Venus is a planet whose orbit is inside the Earth's^ the subject, ' Venus,' is a word used categorematically as a simple term ; the predicate is a composite term whose constituent words (whether sub- stantive, relative, verb, or preposition) are used syncategorema- tically. Pre pos itions, conjunctions, articles, adverbs, relative pro nouns, in their ordinary use, can only enter into terms along with other words having a substantive, adjectival or participial force ; but when they are themselves the things spoken of and are used substantively {suppositio viaterialis), they are categorematic. In the proposition. Of was used more indefinitely three hundred years ago than it is now, 'of is categorematic. On the other hand, all substantives may be used categorematically ; and the same self-sufficiency is usually recognised in adjectives and partici- ples. Some, however, hold that the categorematic use of adjectives and participles is due to an ellipsis which the logician should fill up ; that instead of Gold is heavy, he should say Gold is a heavy metal ; instead of The sun is shining, The sun is a body shining. But in these cases the I i OF TERMS AND THEIR DENOTATION 2-f words • metal ' and ' body ' are unmistakable tautology, since ' metal ' is implied in gold and ' body ' in sun. But, as we have seen, any of these kinds of words, substantive, adjective, or participle, may occur syncate- gorematically in connection with others to form a composite term. § 4. Terms may be classified, first, according to what they stand for or denote ; and this is called their Denotation. In this respect, the use of a term is said to be either Concrete or Abstract. A term is Concrete when it denotes a ' thing ' ; that is, any person, object, fact, event, feeling or imagination, considered as capable of having (or consisting of) qualities and a deter- minate existence. Thus * cricket ball' denotes any object having a certain size, weight, shape, colour, etc. (which are its qualities), and being at any given time in some place and related to other objects— in the bowler's hands, in a box, in a shop window. Any ' feeling of warmth,' has a certain intensity, as pleasurable or painful, occurs at a certain time, and affects some part or the whole of some animal. An imagination, indeed, (say, of a fairy) cannot be said in the same sense to have locality ; but it depends on the thinking of some man who has locality, and is definitely related to his other thoughts and feelings. A term is Abstract, on the other hand, when it denotes a quality (or qualities), considered by itself and without deter- minate existence in time, place, or relation to other things. 'Size,' * shape,' 'weight,' 'colour,' 'intensity,' 'pleasurableness,' are terms used to denote such qualities, and are then abstract in their denotation. -'Weight,' you observe, is not something with a determinate existence at a given time; it exists not merely in some particular place, but wherever there is a iieavy thing ; and, as to relation, at the same moment it combines in iron with hardness and in mercury with liquidity. In fact, a quality is a point of agreement in a multitude of different things ; as all heavy things agree in weight, all round things in roundness, all red things in redness; and an abstract term denotes such a point (or. points) of agreement among the things 2S LOGIC: DEDUCTIVE AND INDUCTIVE denoted by concrete terms. Thus the use of abstract terms results from the analysis of concrete things into their qualities ; and conversely a concrete term may be viewed as denoting a synthesis of qualities in individual things. When several things agree in more than one quality, there may be an abstract term denoting the union of qualities in which they agree, but not their peculiarities ; as ' human nature ' denotes the 'common qualities of men, * civihsation ' the common conditions of civilised peoples. Every general name, if used as a concrete term, has, or may have, a corresponding abstract term. Sometimes the concrete term is modified to form the abstract, as 'greedy-greediness.' 'vain- vanity ' ; sometimes a word is adapted from another language as ' man-humanity ' ; sometimes a composite term is used, as ' mer- cury-the nature of mercury,' etc. The same concrete may have several abstract correlatives, as ' man -manhood, humanity, human nature ; 'heavy-weight, gravity, ponderosity'; but in such cases the abstract terms are not used quite synonymously ; that is, they imply different ways of considering the concrete. Whether a word is used as a concrete or abstract term is in most instances plain from the word itself, the use of most words being pretty regular one way or the other; but sometimes we must judge by the context. ' Weight ' may be used in the abstract for ' gravity ' or in the concrete for a measure ; but in the latter sense it is syncategore- matic (in the singular), needing at least the article • a (or the) weight ' ' Government ' may mean ' supreme political authority,' and is then abstract ; or, the set of men who happen to be ministers, and is then concrete ; but in this case, too, the article is usually prefixed. ' The life ' of any man may mean his vitality (abstract), as in " Thus follow- ing life ID creatures we dissect " ; or, the series of events through which he passes (concrete), as in ' the life of Nelson as narrated by Southey.' It has been made a question whether the denotation of an abstract term may itself be the subject of qualities. Apparently ' weight ' may be greater or less, * government ' good or bad, * vitality' intense or dull. But if every subject is modified by a quality, a quality is also modified by making it the subject of another ; and, if so, it seems then to become a new quality : 'greatness of weight,' 'badness of government,' *dulness of vitality.' Or if we say ' great weight,' ' bad government,' ' dull OF TERMS AND THEIR DENOTATION 29 vitality,' these phrases may be regarded as denoting some con- crete experience, such as the effort felt in lifting a trunk, disgust at the conduct of officials, sluggish movements of an animal when irritated. At any rate, it is to such concrete terms that w^e have always to refer in order fully to realise the meaning of abstract terms, and thereof, of course, to under- stand any qualification of them. § 5. Concrete terms may be subdivided according to the number of things they denote and the way in which they de- note them. A term may denote one thing or many : if one, it is called Singular; if many, it may do so distributively, and then it is General ; or, as taken all together, and then it is Collective : one, then ; any one of many : many in one. Among Singular Terms, each denoting a single thing, the most obvious are Proper Names, such as Gibraltar or George Washington, which are merely marks of individual things or persons, and often form no part of the common language of a country. They are thus distinguished from other Singular Terms, which consist of common words so combined as to restrict their denotation to some individual, such as, 'the strongest man on earth.' Proper Terms are often said to be arbitrary signs, because their use does not depend upon any reason that may be given for them. Gibraltar had a meaning among the Moors when originally conferred ; but no one now knows what it was, unless he happens to have looked it up ; yet the name serves its purpose as well as if it were " Rooke's Nest.'' Every Newton or Newport year by year grows old. but to alter the name would cause only confusion. If such names were given by mere caprice it would make no difference; and they could not be more cumbrous, ugly, or absurd, than many of those that are given 'for reasons.' The remaining kinds of Singular Terms, drawn from the common resources of the language, derive their denotative force from their usual meanings. Thus the pronouns 'he,' 'she.' 'it.' are singular terms, whose present denotation is determined by the occasion and context of discourse: so with demonstrative phrases— ' this man,' 'that horse.' Descriptive names may be more complex, as 'the wisest man of Gotham.' which is limited to some individual by the superlative suffix ; or ' the German Emperor,' which is Hmited by the definite article— the fr^^ 30 LOGIC: DEDUCTIVE AND INDUCTIVE general term ' German Emperor ' being thereby restricted either to the reignmg monarch or to the one we happen to be discussing. Instead of the definite, the indefinite article may be used to make general terms smgular. as • a German Emperor was crowned at Versailles ' (individua vaga). ^ Abstract terms are ostensively singular: * whiteness' {e.^.) is one quality. But their full meaning is general : * whiteness ' stands for all white things, so far as white. Abstract terms, in fact, are only formally singular. (General terms are words, or combinations of words, used to denote any one of many things that resemble one another in certain respects. 'CJeorge III.' is a Singular Term denoting one man; but *King' is a General Term denoting him and all other men of the same rank ; whilst the compound ' crowned head ' is still more general, denoting kings and also emperors. It is the nature of a general term, then, to be used in the same sense of whatever it denotes ; and its most characteristic form is the Class-name, whether of objects, such as 'king,' 'sheep,' 'ghost'; or, of events such as 'accession,' 'purchase,' ^mani- festation.' Things and events are known by their qualities and relations; and every such aspect, being a point of re- semblance to some other things, becomes a ground of general- isation, and therefore a ground for the need and use of general terms. Hence general terms are far the most important sort of terms in logic, since in them general propositions are ex- pressed, and, moreover (with rare exceptions), all predicates are general. For. besides these typical class-names, attributiye words are general terms, such as 'royal.' 'ruling,' 'woolly,' 'bleating,' 'impalpable.' ' yanishing.' Infinitiyes may also be used as general terms, as "To err is human " ; but are best translated into equivalent substantive forms, as Foolish actions are characteristic of mankind. Abstract terms, too, are fas I observed) equivalent to general terms : ' folly ' is abstract for ' foolish actions.' ' Honesty is the best policy ' means people who are honest may hope to find their account in being so; that is, in the effects of their honest actions, provided they are wise in other wavs, and no misfortunes attend them. The abstract form is often much the more succinct and forcible, but for logical treatment it needs to be interpreted in the general form,' OF TERMS AND THEIR DENOTATION 31 M By autonomasia proper names may become general terms, as if we say 'A Johnson' would not have written such a book— i.e., any man of his genius for elaborate eloquence. A Collective term denotes a multitude of similar things, not distributive^, but considered as forming one whole, as 'regi- ment,' 'fiock,' 'nation.' If a multitude of things have no resemblance, except the fact of being considered as parts of one whole, as 'the world,' or 'the town of Nottingham' (meaning its streets and houses, open spaces, people, and civic organisation), the term denoting them as a whole is Singular; but 'the world' or 'town of Nottingham,' meaning the inhabitants only, is Collective. In their strictly collective use, all such expressions are equivalent to Singular Terms; but many of them may also be used as General Terms, as when we speak of 'so many regiments of the line,' or discuss the 'plurality of worlds'; and in this general use they denote any of a multitude of things of the same kind— regiments, or habitable worlds. Names of substances, such as 'gold,' 'air,' 'water,' may be employed as Singular, Collective, or General terms ; though, perhaps, as Singular Terms only figuratively, as when we say Go/d is ki?ig. if we say with Thales, ' Water is the source of all things; 'water' seems to be Collective. But substantive names are frequently used as General Terms. For example, Go/d is heavy means ' in comparison with other things,' such as water. And, plainly, it does not mean that the aggregate of gold is heavier than the aggregate of water, but only that its specific gravity is greater; that is, bulk for bulk, any piece of gold is heavier than water. Finally, any class-name may be used collectively if we wish to assert something of the things denoted by it, not distri- butively but altogether, as that Sheep are more numerous than ivolves. ♦ I CHAPTER IV THE CONNOTATION OF TERMS § I. Terms are next to be classified according to their Connotation — that is, accf»rding lo what they imply as characteristic of the things denoted. We have seen that general names are used to denote many things in the same sense, because the things denoted resemble one another in certain ways : it is this resemblance in certain points that leads us to class the things together and call them by the same name ; and therefore the points of resemblance constitute the sense or meaning of the name, or its Connotation, and limit its applicability to such things as have these characteristic qualities. ' Sheep,' for example, is used in the same sense, to denote any of a multitude of animals that resemble one another : iheir size, shape, woolly coats, cloven hoofs, innocent ways and edibility are well known. When we apply to anything the term ' sheep ', we imply that it has these quali- ties : ' sheep,' denoting the animal, connotes its possessing these characteristics ; and, of course, it cannot, without a figure of speech or a blunder, be used to denote anything that does not possess all these qualities. It is by a figure of speech that the term ' sheep ' is applied to some men ; and to apply it to goats would be a blunder. All general names, and therefore not only class-names, like ' sheep,' but all attributives, have some connotation. * Woolly ' denotes anything that bears wool, and connotes the fact of bearing wool ; ' innocent ' denotes anything that habitually does no harm (or has not been guilty of a particular offence), THE CONNOTATION OF TERMS 33 and connotes a harmless character (or freedom from particular guilt); 'edible' denotes whatever can be eaten with good results, and c^notes its suitability for mastication, deglutition, digestion, and assimilation. § 2. But whether all terms must connote as well as denote something, has been much debated. Proper names, according to what seems the better opinion, are, in their ordinary use, not connotative. To say that they have no meaning may seem violent : if any one is called Alphonso Schultze (a name which I invent, hoping that no man bears it), this name no doubt means a great deal to his friends and neighbours, reminding them of his stature and physiognomy, his air and gait, his wit and wisdom, some queer stories, and an indefinite number of other things. But all this significance is local or accidental ; ,it only exists for those who know the individual or have heard him described: whereas a general name gives information about any thing or person it denotes to everybody who under- stands the language, without any particular knowledge of the individual. We must distinguish, in fact, between the peculiar associations of the proper name and the commonly recognised meaning of the general name. This is why proper names are not in the dictionary. Such a name as London, to be sure, or Napoleon Buonaparte, has a significance not merely local ; still, it is accidental. ' London ' suggests very diffe- rent things to a Londoner, to his country cousin, and to a merchant in Buenos Ayres. 'Napoleon Buonaparte" excites different ideas in France and in Germany, and had another meaning for our grandfathers than it has for us. Moreover, these names are borne by other places and persons than those that have rendered them famous. There are Londons in various latitudes, and, no doubt, many Napoleon Buona- partes in Louisiana ; and each name has in its several denotations an altogether different suggestiveness. For its suggestiveness is in each application determined by the peculiarities of the place or person denoted, and had any other name been given it would have gathered much the same associations. If the French hero had gone by some fiat and vulgar appellation, it would have impoverished the romance of history ; but the great bulk of its significance for us would now be the same. However, the scientific grounds of the doctrine that proper nfames are non-connotative, are these : The peculiarities that c 34 LOGIC: DEDUCTIVE AND INDUCTIVE distinguish anln dividual person or thing are admitted to be infinite, and anything less than a complete enumeration of these peculiarities may fail to distinguish and identify the individual. For, short of a complete enumeration of them, the description may be satisfied by two or more individuals; and in that case the term denoting them, if limited by such a description, is not a proper but a general name, since it is applicable to two or more in the same sense. The existence of other individuals to whom it might apply may be highly improbable ; but, if it be logically possible, that is enough. On the other hand, the enumeration of infinite peculiarities is certainly impossible. Therefore proper names have no assignable connotation. The only escape from this reasoning lies in falling back upon time and place, the principles of individuation, as constituting the connotation of proper names. Two things cannot be at the same time in the same place : hence ' the man who was at a certain spot on the bridge of Lodi at a certain instant in a certain year,' suffices to identify Napoleon Buonaparte for that instant. Supposing no one else to have borne the name, then, is this its^onnotation ? No one, I think, has ever thought or said so. And at any rate, time and place are only extrinsic determination^f^itable indeed to events like the battle of Lodi, or to ^ftaces themselves like London) ; whereas the connotation of a general term, like * sheep,' consists of intrinsic qualities. Hence, then, the scholastic doctrine 'that individuals have no essence' (see chap. xxii. § 9), and Hamilton's dictum ' that every concept is inadequate to the individual,' are justified. General names, when used as proper names, lose their connotation, as Euxine or Newfoundland. Singular terms, other than Proper, have connotation ; either in themselves, like the singular pronouns * he,' * she,' it,' which are general in their applicability, though singular in applica- tion ; or, derivatively, from the general names that combine to form them, as in * the first Emperor of the French ' or the ' Capital of the British Empire.' 4 THE CONNOTATION OF TERMS 35 § 3- Whether Abstract Terms have any connotation is another disputed question. We have seen that they denote a quahty or quah'ties of something, and that is precisely what general terms connote : ' honesty ' denotes a quality of some men; 'honest' connotes the same quality, whilst denoting the men who have it. The denotation of abstract terms thus seems to exhaust their force or Z^Z.fu; It ?" P':°P°^«<^' however, to regard them as connoting the qualities they directly stand for, and not denoting anything • but T:11 " T "°'r ■ ""^ "'""'' ^°'"^«""« -^ "'^ same'thini as to be the name of something (whether real or unreal), which every term must be. It IS a better proposal to regard their denotation and conn^- m a°n"s ^toT/l f ' '^°".g^°P«" '° '"« objection that 'connote' means to mark along with ' something else, and this plan leaves nothing else. Mill thought that abstract terms are connotative whin besides denoting a quality, they suggest a quality of that quality (as fault implies ■ hurtfulness ' ; but against this it may be urged that one quality cannot bear another, since every qualiHcation of a quality con! titutes a distinct quality in the total (■ millc-whi.eness ■ is distinct from whiteness,' c/. chap. iii. § 4). After all. if it is the most consis en" nltatio^f ""' ''''' "'^' ^'''"■'"' "''" P™P"^' '^™= ^^^ "o ^on- Bitt if abstract terms must be made to connote something should It not be those things, indefinitely suggested, to which the qualities belong.? Thus, 'whiteness' may be supposed to connote either snow or vapour, or any white thing, apart from one or other of which the quality has no existence ; whose existence therefore it implies. By this course the denotation and connotation of abstract and of general names would be exactly reversed. But the whole difficulty may be avoided by makmg it a rule to translate, for logical purposes, all abstract mto the corresponding general terms. § 4- If we ask how the connotation of a term is to be known, here again the answer depends upon the way it is used If used scientifically, its connotation is determined by, and is the same as, its definition ; and the definition is determined by examming the things to be denoted, as we shall see in chap. xxii. If the same word is used as a term in different 36 LOGIC: DEDUCTIVE AND INDUCTIVE sciences, as 'property' in Law and in Logic it will be dif- ferently defined by them, and will have, in each use, a corres- nondindy different connotation. But terms used m popular discourse should, as far as possible, have their connotations determined by classical usage, i.e., by the sense in which they are used by writers and speakers who are acknowledged masters of the language, such as Dryden and Burke. In this case the classical connotation determines the definition ; so that to define terms thus used is nothing else than to analyse their accepted meanings. It must not, however, be supposed that in popular use the connotation of any word is invariab'e. Logicians have at- tempted to classify terms into Univocal (having only one meaning) and ^:quivocal (or ambiguous) ; and no doubt some words (like civil, natural, proud, liberal, humorous), are more manifestly liable to ambiguous use than some others. But m truth all general terms are popularly and classically used in different senses. Figurative or tropical language chiefly consists in the transfer of Hguratue or I ^^^^ , „.j„uor or metonymy. In the course of words to new ^^'X^ZLT^^ks-^nA before the time of Dryden years too. words c^hangethe^rmeanmg^^^^ ^^ ^^^^ .^ ^^ Z:t^:oLTt:i'::ZTZ Bacon, MiUon. and.Sir Thomas Browne since become. j= some tense they originally haTin lltif^ough in En U^h they had ..^.^^ another meaning. Spenser and' Shakespeare, besides this practiceysometimes use words fn a way that can only be justified by their choosing to have it so. St.U. in a way «at ca y variation in the sense of words. Tr^lr ^ch '^^tZ:^ to denote are often so complicated or T aZ he assemblac^e interfusion, or gradation of their qualities . tZo. the tMn^ ^: -- - ^-' ™^I -~-4 Cy t.'. and the only escape fro. it short ^^^^^ -rv^wt ? t or to The resources of the literary art, to convey the true meaning. oT^;Cstinruateadecep^ Against this evil the having bee'n boTn Ice Dryden is no protection. It behoves us. then, to THE CONNOTATION OF TERMS 37 remember that terms are not classifiable into Univocal and /Equivocal, but that all terms are susceptible of being used aequivocally. and that honesty and lucidity require us to try, as well as we can, to use each term univocally in the same context. The context of any proposition always proceeds upon some assumption or understanding as to the scope of the discussion? which controls the interpretation of every statement and of every word. This has been called the " universe of discourse": an older name for it, revived by Dr. Venn, and surely a better one, is siippositio. If now we are talking of children, and 'play' is mentioned, the suppositio limits the suggestiveness of the word in one way ; whilst if Monaco is the subject of conversa- tion, the same word ' play,' under the influence of a different supposition excites altogether different ideas. Hence to ignore the suppositio is a great source of fallacies of equivocation- * Man ' is generally defined as a kind of animal ; but ' animal ' is often used as opposed to and excluding man. * Liberal ' has one meaning under the suppositio of politics, another with regard to culture, and still another as to the disposal of one's private means. Clearly, therefore, the connotation of general terms is relative to the suppositio^ or "universe of dis- course." § 5. Relative and Absolute Terms. — Some words go in couples or groups : like ' up-down,' ' former-latter,' ' father- mother-children,' ' hunter-prey,' * cause-effect,' etc. These are called Relative Terms, and their nature, as explained by Mill, is that the connotations of the members of such a pair or group are derived from the same set of facts (the fundament um re- lationis). There cannot be an ' up ' without a ' down,' a 'father' without a ' mother ' and ' child ' ; there cannot be a ' hunter ' without something hunted, nor ' prey ' without a pursuer. What makes a man a ' hunter ' is his activities in pursuit ; and what turns a chamois into ' prey ' is its interest in these activities. The meaning of both terms, therefore, is derived from the same set of facts \ neither term can be explained without exDlaining the other, and neither can with propriety be 38 LOGIC: DEDUCTIVE AND INDUCTIVE used without reference to the other, or to some equivalent, as * game ' for * prey.' In contrast with such Relative Terms, others have been called Absolute or Non-relative. Whijst ' hunter ' and * prey ' are relative, ' man ' and ' chamois ' have been considered abso- lute, as there may be no special connection between their meanings. However, if we believe in the unity of Nature and in the relativity of knowledge (that is, that all knowledge depends upon comparison, or a perception of the resemblances and differences of things), it follows that nothing can be com- pletely understood except through its agreements or contrasts with everything else, and that all terms derive their connotation from the same set of facts, namely, from general experience. Thus both man and chamois are animals ; this fact is an im- portant part of the meaning of both terms, and to that extent they are relative terms ' Five yards ' and ' five minutes ' are very different notions, yet they are profoundly related; for their very difference helps to make both notions distinct ; and their intimate connection is shown in this, that five yards are traversed in a certain time, and that five minutes are measured by the motion of an index over some fraction of a yard upon the dial. The distinction, then, between relative and non-relative terms must rest not upon a fundamental difference between them (since, in fact, all words are relative) but upon the way in which words are used. We have seen that some words, such as 'up-down,' 'cause-effect,' can only be used relatively; and these might, for distinction, be called Correlatives. But other words, whose meanings are only partially interdependent, may often be used without attending to their relativity, and may then be considered as Absolute. We cannot say ' the hunter returned empty handed,' without implying that ' the prey escaped ' ; but we may say ' the man went supperless to bed,' without implying that ' the chamois re- joiced upon the mountain.' Such words as ' man ' and ^chamois' may, then, in their use, be, as to one another, non-relative. i THE CONNOTATION OF TERMS 39 To illustrate further the relativity of terms, we may mention some of the chief classes of them. Numerical order: ist, 2nd, 3rd, etc. Note that ist implies 2nd, and 2nd ist ; and that 3rd implies ist and 2nd, but these do not imply 3rd; and so on. Order in Time, or Place: early-punctual-late; right-middle-left; North-South, etc. As to Extent, Volume and Degree : greater-equal-less ; large- medium-small ; whole and part. Genus and Species {cf. chaps, xxi.-ii.-iii.). Sometimes a term con- notes all the attributes that another does, and more besides, which, as distinguishing it, are called differential. Thus 'man' connotes all that 'animal ' does, and also (as differenticB) the erect attitude, articulate speech, and other attributes. In such a case as this, where we have well-marked natural classes, the term whose connotation is included in the others' is called a Genus of that Species. Thus we have a Genus, triangle ; and a Species, isosceles, marked off from all other triangles by the differential quality of having two equal sides. Or, again : Genus, book ; Species, quarto; Difference, having each sheet folded into four leaves. There are other cases where these expressions, ' genus ' and ' species,' cannot be so applied without a departure from usage, as, e.g., if we call snow a species of the genus ' white ' (for ' white ' is not a recog- nised class), although the connotation of white {i.e., whiteness) is part of the connotation of snow, just as the qualities of ' animal ' are amongst those of ' man. ' For logical purposes, however, it seems desirable to use ' genus and species ' to express that relativity of terms which consists in the connotation of one being part of the connotation of the other. Two Terms whose connotations include that of a third, whilst at the same time exceeding it, are (in relation to that third term) called Co- ordinate. Thus in relation to ' white,' snow and silver are co-ordinate ; in relation to colour, yellow and red are co-ordinate. And when all three terms stand for recognised natural classes, the co-ordinate terms are called co-ordinate species ; thus man and chamois are (in Logic) co- ordinate species of the genus animal. § 6. From such examples of terms related as whole and part in connotation, it is easy to see the general truth of the doctrine that as connotation decreases, denotation increases : for ' animal,' with less connotation than man or chamois, denotes many more objects; 'white,' with less connotation than snow or silver denotes many more things. It is not, however, certain that this doctrine is always true in the concrete : as there may be a term connoting two or more qualities, all of which qualities 40 LOGIC: DEDUCTIVE AND INDUCTIVE are peculiar to all the things it denotes ; and, if so, by sub- tracting one of the qualities from its connotation, we should not increase its denotation. If ' man,' for example, has among mammals the two peculiar attributes of erectness and articu- late speech, then, by omitting 'articulate speech' from the connotation of man, we could not use the name of any more of the existing mammalia than we can at present. Still we might have been able to do so ; there might have been an erect inarticulate ape, and perhaps there once was one ; and, if so, to omit 'articulate' from the connotation of man would make the term ' man ' denote that animal (supposing that there was no other difference to exclude it). Hence, potentially, an mcrease of the connotation of any term implies a decrease of its denotation. And, on the other hand, we can only increase the denotation of a term, or apply it to more objects, by de- creasing its connotation ; for if the new things denoted by the term had already possessed its whole connotation they must already have been denoted by it. However, we may increase the knoivn denotation without decreasing the connotation, if we can discover the full connotation in things not formerly sup- posed to have it; or if we can impose the requisite qualities upon new individuals, as when by annexing some millions of Africans we extend the denotation of ' British subject ' without altering its connotation. Many of the things noticed in this chapter, especially in this section and the preceding, will be discussed at greater length in the chapters on Classification and Definition. § 7- Contradictory Relatives.— Every term has, or may have, another corresponding with it in such a way that whatever differential qualities (§5) it connotes, this other connotes merely their absence; so that one or the other is alwaxs formally predicable of any Subject, but both these terms are never predicable of the ^anie Subject in the same relation : such pairs of terms ar(L>^d Contradictories. Whatever Subject we take, it is either ^ible or invisible, but not both; either human or non-human, but not both. (A >x ^ Ai' THE CONNOTATION OF TERMS 41 ourselves trifled uith if any one told us that 'A mountain is either anTrtUr'r"'!'"'"",' '^°*-' '' '^ ^^-''°'- terms sh'fx subject white e/sTrt "f '° '' -"'-Victories in relation to any flourish a dumb hl'll^f ! u P^^e^-^-as if we ask whether to or impeccabmt^^te h ""^^'' °' '° ''"''" *^ '"'"^ ^^ '"'""i™. visibTe'^reMlr ,n ^h ""^ r"-""-"""- S™"^^'^- "^'"le and ]„: hold upon a sound or TiT' ° ""'^'=""*^ "^'''' ^° '^^^ '^^^ ^ave no «cation^s as • t^h IbJ ^^^l^ t^ : -traTiel:^- ^^ ^"" -^"- Again, the above definition of Contradictories tells us that relation that .s, at the same time or place, or under the same condu.ons. The lamp is visible to me now, but wH b tT ,' • '"" ' °"''- "" '"' °f '^ - "- visible, but the other ,s not : therefore, without this restriction, " i, the same relat.on," few or no terms would be contradictory, actiln -T d ?"'f '"'"■ " """' '"«^" • °" 'he whole ' or • in a certain that seem contradictor^are prldi abroHh"' ' '''\^"">T'y' '--= the same relation." In order to avo^thl ^^"' '"u^'"' '''" "°' " '" only to construct the tLm7„ f ambiguity, however, we have whole ■ 7nT.K . ^^ '° '"'P'""''' "^« relation, as ■ wise on the the^thde sti^rTv aT'' '""''" "' contradictory • nofw^L on another not btck hii; • IrtheTfif u" ""^^ ""''' ""^^"^ ''-"■ -' stating the age reftrred to """"" " "'"^^"'^^"^ ^^'"''-ble by dicto"; terrrdTfficull""'-"' ' V^' ''"^^""^ ■" *« "- °f -ntra- of nZX^enot^TTZ' " "'^ -"«-«- change or .flux' ratdrf5-"— JCL.L, ai least as last as we can ntfpr fV.orv, . r^ -r black, since (like everything elsJ) his haTr L I "' '"' -^ """'' ""^'^ '' not black though ft J}.. TJ ^ changing, it must now be liUL uiacK, tnough (to be sure) it may still seem hlart ti,^ ^-m i the terms of human discourse assume a certain fixity of things ^Ce" thing at every moment changes but for th^ rr^^o. . ^""^gs. every- perceive this change nor expS it P-t we can neither ^ 42 LOGIC: DEDUCTIVE AND INDUCTIVE This paradox, however, may, I suppose, be easily overstated. The change that continually goes on in nature consists in the movements of masses or molecules, and such movements of things are compatible with a considerable persistence of their qualities. Not only are the molecular changes always going on in a piece of gold compatible with its remaining yellow, but its persistent yellowness depends on the con- tinuance of some of those changes. And as much may be said for the blackness of a man's hair, though, no doubt, at a certain age its colour may begin to be problematical, and the applicability to it of ' black ' or ' not-black ' may become a matter of genuine anxiety. Whilst being on our guard, then, against fallacies of contradiction arising from the im- perfect correspondence of fact with thought and language, we shall often have to put up with it. Candour and humility being satisfied with the above acknowledgment of the subtlety of nature, this book will henceforward proceed upon the postulate— that it is possible to use contradictory terms such as cannot both be predicated of the same subject in the same relation, though one of them may be; that, for example, it may be truly said of a man for some years that his hair is black ; and, if so, that during those years to call it not-black is false or extremely misleading. It must be observed that the most opposed terms of the literary vocabulary, such as 'wise-foolish,' old-young,' 'sweet- bitter,' are rarely true contradictories : wise and foolish, indeed, cannot be predicated of the same man in the same relation ; but there are many middling men, of whom neither can be predicated on the whole. For the comparison of quantities, again, we have three correlative terms, greater, equal, less, and none of these is the contradictory of either of the others. In fact, the contradictory of any term is one that denotes the sum of its co-ordinates (§ 6) ; and to obtain a contradictory, the surest way is to coin one by prefixing to the given term the particle 'not' or (sometimes) 'non': as 'wise-not-wise,' 'human- non-human,' ' greater-not-greater.' The separate word ' not ' is surer to constitute a contradictory than the usual prefixes of negation, ' un- ' or 'in-', or even 'non.' Since compounds of these are generally warped by common use from a purely negative meaning. Thus, ' Nonconformist ' does not denote everybody who fails to conform. 'Unwise' is not equivalent to 'not-wise,' but means ' rather foolish ' ; a very foolish action is not-wise, but can only be called unwise by meiosis or irony. Still, negatives formed by ' in ' "< i I- THE CONNOTATION OF TERMS 43 or • un ' or ' non ' are sometimes really contradictory of their positives • as 'visible-m visible,' 'equal-unequal.' § 8. The distinction between Positive and Negative terms is not of much value in Logic, what importance would else attach to it being absorbed by the more definite distinction of contradictories. For con- tradictories are positive and negative in essence and. when least am- biguously stated, also in form. And. on the other hand, as we have seen, when positive and negative terms are not contradictory, they are misleading. As with 'wise-unwise,' so with many others, such as • happy-unhappy ; ' which are not contradictories ; since a man may be neither happy nor exactly unhappy, but indifferent, or (again) so miser- able that he can only be called unhappy by a figure of speech. In fact in the common vocabulary a formal negative often has a limited posi- tive sense ; and this is the case with unhappy, signifying the state of teeling in the milder shades of purgatory. But when a Negative term is fully contradictory of its Positive, it is said to be Infinite; because it denotes an unascertained multitude of things, a multitude only limited by the Positive term and the siippositio ; thus ' not-wise ' denotes all, except the wise, within the suppositio of ' intelligent beings.' Indeed, formally (disregarding any suppositio), such a Negative Term stands for all possible terms except its Positive: x denotes everything but X ; and ' not-wise ' may be taken to include stones, triangles and hippogriffs. In this sense, every Negative term has some positive meaning, though a very in- definite one, not a specific positive force like 'unwise' or ' unhappy.' It denotes any and everything that has not the attributes connoted by the corresponding Positive Term. Privative Terms connote the absence of a quality that normally belongs to the thing denoted, as ' blind ' or ' deaf.' We may predicate • blind ' or ' deaf of a man, dog or cow that happens not to be able to see or hear, because the powers of seeing and hearing generally belong to these species ; but of a stone or idol these terms can only be used figuratively. Indeed, since the contradictory of a privative carries with It the privative limitation, a stone is strictly ' not-blind ' ; that is, it is ' not-something-that-normally-having-sight-wants-it.' Contrary Terms are those that severally connote the absence of differential qualities possessed by the others, and therefore cannot be predicated of the same Subject in the same relation : ^ ps^l 44 LOGIC: DEDUCTIVE AND INDUCTIVE and, so far, they resemble Contradictory Terms, but differ from them in this, that each of them connotes some positive differential quality which limits it to part of the denotation excluded by the others; so that, possibly, neither of two contraries is truly predicable of a given subject. Thus ' blue ' and 'red' are Contraries, for they cannot both be predicated of the same thing in the same relation ; but are not Contradictories, since, in a given case, neither may be predicable : if a flower is blue in a certain part, it cannot in the same part be red ; but it may be neither blue nor red, but yellow ; though it is certainly either blue or not-blue. All Co-ordinate terms are formal Contraries ; but if, in fact, a series of Co-ordinates comprises only two (as male-female), they are Contradictories; since each includes all that area of the suppositio which the other excludes. The extremes of a series of co-ordinate terms are Opposites ; as, in a list of colours, white and black, the most strongly contrasted, are said to be opposites ; or as, among moods of feeling, rapture and misery are opposites. But this distinction is of slight logical importance. Imper- fect Positive and Negative couples, like ' happy and unhappy,' which (as we have seen) are not contradictories, are often called opposites. The members of any series of Contraries are all included by any one of them and its contradictory, as all colours come under ' red ' and ' not-red,' all moods of feeling under ' happy and not-happy.' ^ CHAPTER V THE CLASSIFICATION OF PROPOSITIONS § I. It is usual in Logic to classify Propositions according to Quantity, Quality, Relation and Modality. As to Quantity, propositions are either Universal or Par- ticular; that is to say, the predicate is affirmed or denied either of the whole Subject or of a part of it— of All or of Some S. All S IS P (that is, P is predicated of all S). Sojne S is P (that is, P is predicated of some S). An Universal proposition may have for its subject a Singular term, a Collective, a General term distributed, or an Abstract term. (i) A Proposition having a Singular term for its subject, as The Queen is gone to France, is called a Singular Proposition ; and some logicians regard this as a third species of proposition with respect to quantity, distinct from the Universal and the Particular ; but this is needless. (2) A Collective term may be the subject, as The Black Watch is ordeved to India. In this case, as well as in singular propositions, a pre- dication is made concerning the whole subject as a whole. (3) The subject may be a General term taken in its full denotation, as A II apes are sagacious ; and in this case a predication is made concerning the whole subject distributively ; that is, of each and every thing that the subject stands for. (4) Propositions whose subjects are Abstract terms, though they may seem to be formally Singular, are really as to their meaning distributive Universals ; since whatever is true of a quality is true of whatever thing has that quality so far as that quality is concerned. Truth will prevail means that All true propositions are accepted at last (by sheer force of being true, in spite of interests, prejudices, ignorance and indifference). To bear this in mind may make one cautious in the use of abstract terms. i» 46 LOGIC: DEDUCTIVE AND INDUCTIVE In the above paragraphs a distinction is implied between Singular and Distributive Universals ; but it is very important to remember that, technically, every term, whether Subject or Predicate, when taken in its full denotation (or universally), is said to be ' distributed,' although this word, in its ordinary sense, would be directly applicable only to General terms. In the above examples, then, ' Queen," ' Black Watch,' •apes,' and ' truth' are all distributed terms. Indeed, a simple defini- tion of the Universal Proposition is ' one whose subject is distributed.' A Particular Proposition is one that has a general term for its subject, whilst its predicate is not affirmed or denied of everything the subject denotes ; in other words, it is one whose subject is not distributed : as Some lions inhabit Africa. In ordinary discourse it is not always explicitly stated whether the predication is universal or particular ; it would be very natural to say Liom inhabit Africa, leaving it, as far as the words go, uncertain whether we mean all or some lions. Propositions whose quantity is thus left indefinite are technically called ' preindesignate,' their quantity not being stated or designated by any introductory expression ; whilst pro- positions whose quantity is expressed, 2iS All Foundling-hosjl^itals have a high death-rate, or Some nine is made from grapes, are said to be predesig- nate. Now, the rule is that preindesignate propositions are, for logical purposes, to be treated as particular; since it is an obvious precaution of the science of proof, in any practical application, not to go beyond the evidence. Still, the rule may be relaxed if the universal quantity of a preindesignate proposition is well known or admitted, as in Planets shine with reflected light, or Sinners are wretched; though, indeed, the former of these examples, I suppose, may not be true under all conditions. Again, such a proposition as Man is the paragon of animals is not a pre- indesignate, but an abstract proposition ; the subject being elliptical for Man according to his proper nature ; and the translation of it into a General proposition is not All men are paragons; nor can Some men be sufficient, since an abstract can only be adequately rendered by a distributed term ; bnt we must say All men who approach the ideal. The marks or predesignations of Quantity commonly used in Logic are: for Universals, All, Any, Every, Whatever (in the negative No or No one, see next §) ; for Particulars, Some. It should be carefully noted that Some, technically used, does not mean Some only, but Some at least (it may be one, or more, or all). If it meant ' some only,' every particular proposition would be an exclusive exponible (chap. ii. § 3) ; since Only some men are wis» implies that Some, men are not wise. Besides, it may often happen in an investigation that all the instances we have observed come under a certain rule, though i f r f I \ THE CLASSIFICATION! OF PROPOSITIONS 47 we do not yet feel justified in regarding the rule as universal ; and this situation is exactly met by the expression Some (it may be all). The words Many, Most, Few are generally interpreted to mean Some ; but as Most signifies that exceptions are known, and Few that the excep- tions are the more numerous, propositions thus predesignate are in fact exponibles, amounting to Some are and Some arc not. If to work with both forms is too cumbrous, so that we must choose one, apparently Feiv are should be treated as Some are not. The scientific course to adopt with propositions predesignate by Most or Few, is to collect statistics and determine the percentage ; thus, Few men are wise — say 2^ per cent. The Quantity of a Proposition, then, is usually determined entirely by the Quantity of the subject, whether all or soj?te. Still, the quantity of the predicate is often an important consideration ; and though in ordinary usage the predicate is never predesignate, Logicians agree that in every Negative Proposition (see § 2) the predicate is 'distributed,' that is to say, is denied altogether of the subject, and that this is in- volved in the form of denial. To say So??ie men are not brave., is to declare that the quality for which men may be called brave is not at all found in the Some men referred to : and, similarly, to say No men are proof agai?ist flattery., cuts off the being ' proof against flattery ' entirely from the list of human attributes. On the other hand, every Affirmative Proposition is regarded as having an undistributed predicate; that is to say, its predicate is not affirmed exclusively of the subject. Some men are wise does not mean that ' wise ' cannot be predicated of any other beings ; it is equivalent to Some men are wise (7vhoever else may be). And All elephants are sagacious does not limit sagacity to elephants : regarding ' sagacious ' as possibly denoting many animals of many species that exhibit the quality, this proposition is equivalent to ' All elephants are some sagacious animals.' Clearly, the affirmative predication of a quality does not imply exclusive possession of it as denial implies its complete absence; and, therefore, to regard the predicate of an affirmative proposition as distributed would be to go beyond the evidence and to take for granted what had never been alleged. 48 LOGIC: DEDUCTIVE AND INDUCTIVE Some Logicians, seeing that the quantity of predicates though not distinctly expressed, is recogn.sed, and holdm, rt is .he p.. or U.C ".o „^. »P;j-"J»S whatever is imphcit in thought, ha%e proposea the quantity of predicates by predes.gnafon, thus Son^e „,en are some wise (beings)'; '-"f »>-.;^^/°' "fhe Pre- (beings)'; etc. This is called the Quantification of the Pre d 1, a,;d leads to some modifications of Deductive Lo^c which will be referred to, but not developed, hereafter. (See ^ V ^AsIo'Quahty, propositions are either Affirmative or NeUivf An Affirm'ative Proposition is, —y, one whose copula is affirmative (or, has no negative sign), as SsP,Al Jn-are -partial to themselves. A Negative Iropo stion one whose copula is negative (or, has a -Sa -- -g"). ^^ 5 is not P Sole men-are not-proof agamst flattery. ^\ hen, fned a Negative Proposition is of Universal Qu-tay " - stated thus : No S is P, No men are proof agaunt flatter , t:t t this case, the detachment of the negative sign fron^h copula and its association with the subject is merely an acaden of our idiom ; the proposition is the same as ^/( J-j; j/ Proof a^^ainst flattery. It must be distinguished, therefore fTrlh an efpres^ion as Not every -« » f^f ^if flatterr : for here the negative sign really qualifies the sub^c and the proposition is Particular, being equivalent to Some men are not proof against flattery. -^u ,u. Predicate When the negative sign is associated with the Predicate so as to make this an Infinite Term (chap. iv. § 8) p°oposition is called an Infinite Proposition (though, perhaps, Se tL and the Proposition might be better called In- ■ defiS, as S is not-P (or ,), All men are-tncafaMe of resisting flattery, or are-notproof against flattery. •.•„„= ™hen the copula is affirmative, are, formally. t^:^:^X^;^^tT. hyphen. It has heen proposed, M THE CLASSIFICATION OF PROPOSITIONS 49 indeed, with a view to superficial simplification, to turn all Negatives into Infinites, and thus render all propositions Affirmative in Quality. But although every proposition both affirms and denies something according to the aspect in which you regard it (as Snow is white denies that it is any other colour, and Snow is not blue affirms that it is some other colour), yet there is a great difference between the definite affirmation of a true Affirmative and the vague affirmation of a Negative or Infinite; so that materially an Affirmative Infinite is the same as a Negative. Generally Mill's remark is true, that affirmation and denial stand for distinctions of fact that cannot be got rid of by manipulating words. Whether granite sinks in water, or not ; whether the rook lives to be a hundred, or not ; whether a man has a hundred dollars in his pocket, or not ; whether human bones have ever been found in tertiary strata, or not ; such alternatives require distinct forms of expression. At the same time, it may be granted that many facts admit of being stated with nearly equal propriety in either quality, as No man is proof against flattery, or All men are open to flattery. But whatever advantage there is in occasionally changing the Quality of a proposition may be gained by the process of obversion (chap. vii. § 5) ; whilst to use only one Quality would impair the elasticity of logical expression. It is a postulate of Logic that the negative sign may be transferred from the copula to the predicate, or from the predicate to the copula, without altering the sense of a proposition ; and this is justified by the experience that not to have an attribute and to be without it are the same thing. § 3. A. I. E. O. — Combining the two kinds of Quantity Universal and Particular, with the two kinds of Quality, Affirma- tive and Negative, we get four simple types of proposition » which it is usual to symboh'se by the letters A. I. E. O., thus : A. Universal Affirmative — All S is P. I. Particular Affirmative — Some S is P. E. Universal Negative^No S is P. O. Particular Negative — Some S is not P. These symbols are exceedingly useful in abbreviating the exposition of Logic; and they should be so learnt as to suggest their meaning without the least need for an effort of recollection. As an aid to this, obs"'Pl'«f '^e fur her alternative ■ or both,' except when both alternatives have the =am« ^"t'- ject whilst the predicates are contraries or <=°""*'^!<='°"^'- . " '^^ disjunctive A is either B or C (B and C being contraries '™Pl'«; *^' both alternatives cannot be true, it can only be adequately rendered in Hypotheticals by the two forms-(i) If A is B. it is not C, and {2)1/ A is not B. it is C. But if the disjunctive A is either B orC(B and C not being contraries) implies that both may be true, it will be adequately translated into a hypothetical by the single form, If A ,s "<" ^J '' " Y We cannot translate it mio-If A is B. it is not C ; for by o"-; »PP°;'- tion if • A is B ■ is true, it does not follow that ' A is C must be fa se. It'may be observed that these conditional forms often cojer assertions that are not true complex propositions, but arguments abbreviated and rhetorically disguised. The hypothetical, • If Plato was not mistaken poets are dangerous citizens,' may be considered as an argument agamst the laureateship, and may be expanded (informally) thus: All Plato s opinions deserve respect ; one of them was that poets are bad citizens^ therefore, it behoves us to be chary of encouraging poetry Or take the disjunctive, • Either Bacon wrote the works ascribed '° Shak^^P^^'^^ or there were two men of the highest genius in the same age and country.' This means that it is not likely there should be two such men, that we are sure of Bacon, and therefore ought to give him all the glory Now, if it is the part of Logic • to make explicit in language all that is impl cit in thought,' or to put arguments into the form in which they can best be examined, such propositions as the above ought to be analysed in the way suggested, and refuted according to their real intention. § 5 As to Modality, propositions are divided into Pure and Modal A Modal proposition is one in which the predicate is affirmed or denied, not simply but am modo, with a qualifica- tion And some Logicians have considered any adverb occur- ring in the predicate, or any sign of past or future tense, enough to "constitute a modal : as ' Petroleum is dangerously inflam- mable ' • ' English will be the universal language.' But far the most important kind of modality, and the only one we need consider, is that which is signified by some qualification of the predicate as to the degree of certainty with which it is affirmed or denied. Thus, ' The bite of the cobra is probably THE CLASSIFICATION OF PROPOSITIONS 55 mortal,' is called a 'Contingent' or 'Problematic' Modal: ' Water is certainly composed of oxygen and hydrogen ' is an Assertory or Certain Modal: 'Two straight lines cannot enclose a space ' is a Necessary or Apodeictic Modal (the opposite being inconceivable). Propositions not thus qualified are called Pure. Modal propositions have had a long and eventful history, but they have not been found tractable to the resources of ordinary Logic, and are now generally neglected by the authors of text-books. Accordingly. I shall not enlarge upon the merely logical treatment of them in the present work. No doubt such propositions are common m ordinary discourse, and in some rough way we combine them and draw inferences from them. It is understood that a combination of assertory or of apodeictic premises may warrant an assertory or an apodeictic conclu- sion • but that if we combine either of these with a problematic pro- position our conclusion becomes problematic ; whilst the combination of two problematic premises gives a conclusion less certain than either. But if we ask ' How much less certain ? ' we are left to sheer guessing. That the modality of a conclusion follows the less certain of the propositions combined, is inadequate for scientific guidance ; so that, as ordinary Logic can get no further than this, it is now generally agreed to abandon the discussion of Modals. The true scientific course with regard to them is, to endeavour to determine the degree of certainty attaching to a proposition by collecting statistics with regard to it. Thus instead of ' The cobra's bite is probably fatal,' we might find that it is fatal 80 times in loo. Then, if we know that of those who go to India 3 in looo are bitten, we can calculate what the chances are that any one going to India will die of a cobra's bite (chap. xx.). § 6. Verbal and Real propositions.—Another important division of propositions turns upon the relation of the predi- cate to the subject in respect of their connotations. We saw when discussing Relative Terms, that the connotation of one term often implies that of another ; sometimes recipro- cally, like ' master ' and ' slave ' ; or by inclusion, like species and genus ; or by exclusion, like contraries and contradictories. When terms so related appear as subject and predicate of the same proposition, the result is often tautology- ^.^-., The master has authority over his slave; A horse is an animal; Red is not blue ; British is not foreign. Whoever knows the meaning of ' master,' ' horse,' ' red,' ' British,' learns nothing from these I 56 LOGIC: DEDUCTIVE AND INDUCTIVE propositions. Hence they are called Verbal propositions, as only expounding the sense of words, or as if they were propo- sitions only by satisfying the forms of language, not by fulfilling the function of propositions in conveying a knowledge of facts. They are also called ' Analytic ' and ' Explicative ', because they separate and disengage the elements of the connotation of the subject. Doubtless, such propositions are very useful to one who does not know the language ; and Definitions, which are verbal propositions whose predicates analyse the whole connotations of their subjects, are indispensable instruments of science (see chap. xxii). On the other hand, when there is no such direct relation between subject and predicate that their connotations imply one another, but the predicate connotes something that cannot be learnt from the connotation of the subject, there is no longer tautology, but an enlargement of meaning— ^•a'-., Masters are degraded by their slaves; The horse is the tioblest animal ; Red is the favourite colour of the British army. Such propositions are called Real, Synthetic, or Ampliaiive, because they are propositions for which a mere understanding of their subjects would be no substitute, since the predicate adds a meaning of its own concerning matter of fact. It has been seriously questioned whether a verbal propo- sition deserves to be called a proposition at all. We may ask whether, to any one who understands the language, a verbal proposition can ever be an inference or conclusion from evidence; or whether a verbal proposition can ever furnish grounds for an inference, which might not just as well be found in the meaning of the subject? It hardly belongs to such a book as this to determine such disputed questions; but we shall see hereafter that, without an answer to them, some important problems must remain unsolved. The whole subject of real and verbal propositions will inevi tably recur in the chapters on Definition ; but Verbal Propositions are such common blemishes in composition, and such frequent and fatal pitfalls in argument that attention cannot be drawn to them too early or too often. \ \i .. 1! CHAPTER VI CONDITIONS OF IMMEDIATE INFERENCE § I. The word Inference is used in two different senses, which are often confused but should be carefully distinguished. In the first sense, it means a process of thought or reasoning by which the mind passes from facts or statements presented, to some opinion or expectation. The data may be very vague and slight, prompting no more than a guess or surmise; as when we look up at the sky and form some expectation about the weather, or from the trick of a man's face entertain some prejudice as to his character. Or the data may be important and strongly significant, like the footprint that frightened Crusoe, or as when news of war makes the City expect that Consols will fall. These are examples of the act of inferring, or of inference as a process ; and with inference in this sense Logic has nothing to do ; it belongs to Psychology to explain how it is that our minds pass from one perception or thought to another thought, and how we come to conjecture, conclude and believe {(/". chap. i. § 6). In the second sense, inference means not this process of guessing or opining, but the result of it ; the surmise, opinion, or belief when formed ; in a word, the conclusion : and it is in this sense that Inference is treated of in Logic. The subject- matter of Logic is an inference, judgment or conclusion con- cerning facts, embodied in a proposition, which is to be ex- amined in relation to the evidence that may be adduced for it, in order to determine whether, or how far, the evidence amounts to proof. Logic is the science of Reasoning in the 58 LOGIC: DEDUCTIVE AND INDUCTIVE sense in which ' reasoning' means giving reasons, for it shows :it sort of reasons aregood. Whilst Psychology exp.a.ns how the mind goes forward from data to conclusions, Loj 'akes a conclusion and goes back to the data, .nqunmg -hethe 1 o^e data together with any other evidence (facts or prmc.ple.) that can be collected, are of a nature to warrant the conclusion. I w' think that the night will be stormy, that A. Schu.tze rs of a- amiable disposition, that water expands m free.mg, o^ '^at one n,eans to national prosperity is popular education, and w. h o know whether we have evidence sufficient to justify us ,n holding these opinions, Logic can tell us what form tl^^-'^ence should assume in order to be conclusive. Observe : say what /.^ the evidence should assume, not that Logic tells us what facts are proper evidence in any of these cases ; that ,s a question : t'he man of special experience in life, or ^^^^^ business. But whatever the facts are that constitute the ev, dence, they must, in order to prove the point, adm t of being stated in conformity with certain principles or conditions and of these principles or conditions Logic is the science. It deals. In, not'with'the subjective process of inferring, but with the objective grounds that justify or discredit the >"f«ence. § 2 Inferences, in the Logical sense, are divided into t«o great classes, the Immediate and the Mediate, according to the character of the evidence offered in proof of them^ In fact ^ speak of Inferences, in the sense of conclusions, as immed ate or mediate is an abuse of language, derived from times befo the distinction between inference as P— ^^"f^ "l"^ ^"Jei result was generally felt. No doubt, we ought rather to speak of Lmediate and Mediate Evidence; but it would be out o place in a manual to attempt to alter the usual expressions of '" An immediate Inference, then, is one that depends for its proof upon only one other proposition which has the same, or more extensive terms (or matter). Thus that ' one means to nat.ona p osped is popular education ' is an immediate inference if ^evidence Zr it is no more than the admission that 'popular [ i\ CONDITIONS OF IMMEDIATE INFERENCE 59 education is a means to national prosperity ' : Similarly, it is an immediate inference that * Some authors are vain,' if it be granted that * All authors are vain.' An Immediate Inference, indeed, is little else than a verbal transformation ; and some Logicians dispute its claims to be called an inference at all, on the ground that it is identical with the pretended evidence. If we attend to the meaning, say they, an immediate inference does not really express any new judgment ; the fact expressed by it is either the same as its evidence, or is even less significant. If from No men are gods we prove that No gods are men, this is nugatory ; if we prove from it that Some men are not gods, this is to emasculate the sense, to waste valuable information, to lose the command- ing sweep of our universal proposition. Still, in formal Logic, it is often found that an immediate inference expresses our knowledge in a more convenient form than that of the evidentiary proposition, as will appear in the chapter on Syllogisms and elsewhere. And in transforming a Universal into a Particular proposition, as No men are gods, therefore. Some men are not gods, the latter statement, though weaker, is far more easily proved; since a single instance suffices. A Mediate Inference, on the other hand, depends for its evidence upon a plurality of other propositions (two or more) which are connected together on logical principles. If we argue — No men are gods ; Alexander the Great is a man ; .-. Alexander the Great is not a god : this is a Mediate Inference. The evidence consists of two propositions connected by the term ' man,' which is common to both (a Middle Term), mediating between 'gods' and 'Alexander.' Mediate Inferences comprise Syllogisms with their developments, and Inductions; and to discuss them further at present would be to anticipate future chaplers. We must now deal with the principles or conditions on which Go LOGIC: DEDUCTIVE AND INDUCTIVE Immediate Inferences are valid : commonly called the " Laws of Thought." § 3. The Laws of Thought are conditions of the logical statement and criticism of all sorts of evidence ; but as to Immediate Inference, they may be regarded as the only conditions it need satisfy. They are three : (i) The principle of Identity (usually stated as ' Whatever is, is' or ' A is A')\ (2) The principle of Contradiction {' Jt is impossible for the same thing to be and ?iot be,' or 'A is not not-A'); (3) The principle of Excluded Middle {'Anything must either be or not be,' or 'B is either A or not A'). These principles are manifestly not ' laws ' of thought in the sense in which * law ' is used in Psychology; they do not, like the laws of the association of ideas, profess to give an account of the actual mental processes that uniformly take place in judgment or reasoning. If they were such natural laws of thought, it would be impossible for anybody to mistake one thing for another or assume that the same thing may both be and not be; whereas we know that people frequently make such mistakes. In relation to thought, therefore, these principles can only be regarded as laws when stated as precepts, the observance of which (consciously or not) is necessary to clear and consistent thinking : e.g., Never assume that the same thing can both be and not be. However, in this book Logic is treated as the science of thought only as embodied in propositions, in respect of which evidence is to be adduced, or which are to be used as evi- dence of other propositions ; and, accordingly, the above laws or principles must be restated as the conditions of consistent argument in such terms as to be directly applicable to propo- sitions. Now, it was shown in the chapter on the connotation of terms, that terms are assumed by Logicians to be capable of definite meaning, and of being used univocally in the same context: if, or in so far as, this is not the case, we cannot understand one another's reasons, nor even pursue in solitary meditation any coherent train of argument. We saw, too *'* CONDITIONS OF IMMEDIATE INFERENCE 61 that the meanings of terms were related to one another : some being full correlatives ; others partially inclusive one of another, as species of genus ; others mutually incompatible, as contraries ; or alternatively predicable, as contradictories. We now assume that propositions are capable of definite meaning according to the meaning of their component terms and of the relation between them ; that the meaning, the fact asserted or denied, is what we are really concerned to prove or disprove ; that a mere change in the words that constitute our terms, or of construction, does not affect the truth of a propo- sition as long as the meaning is not altered, or (rather) as long as no fresh meaning is introduced ; and that if the meaning of any proposition is true, any other proposition that denies it is false. This postulate is plainly necessary to consistency of statement and discourse ; and consistency is necessary, if our thought or speech is to correspond wi^h the unity and coherence of Nature and experience ;and the Laws of Thought or Conditions of Immediate Inference are an analysis of this postulate; § 4. The principle of Identity is usually written symbolically thus : A is A ; not-A is ?wt-A. It assumes that something is, and that it may be represented by a term. We need not here raise any metaphysical question whether after all anything can be said really to be, to be self-identical and sempiternal. Logic takes for granted a certain relative identity and persistence of things. Socrates in his father's workshop, at the battle of Delium and in prison, is assumed to be the same man denotable by the same name; and similarly, elephant, or justice, or fairy, in the same context, is to be understood of the same thing under the same suppositio. But, further, it is assumed that of the same thing another term may be predicated again and again in the same sense. To symbolise this we ought to alter the usual formula for Identity and write it thus : If B is A, B is A ; if B is not-A, B is not-A. If Socrates is wise, he is wise ; if fairies frequent the moonlight, they do ; if Justice is not of this world, it is 62 LOGIC: DEDUCTIVE AND INDUCTIVE not. Whatever affirmation or denial we make concerning any subject, we are bound to adhere to it. Of course, if our assertion turns out to be false, we must not adhere to it; but then we must repudiate all that we formerly deduced from it and begin again with a clean slate. Again, whatever is true or false in one form of words is true or false in any other : this is undeniable ; but in formal Logic it is not very convenient. If Socrates is wise, is it an identity to say, ' Therefore the master of Plato is wise ' ; or, further, that he 'takes enlightened views of life'? U Every man is fallible, is it an identical proposition that Every man is liable to error 1 It seems pedantic to demand a separate proposition that Fallible is liable to error. But, on the other hand, the insidious substitution of one term for another spe- ciously identical, is a chief occasion of fallacy. How if we go on to argue : therefore. Every man is apt to blunder, prone to confusion of thought, addicted to self-contradiction ? Practi- cally, I am afraid that the substitution of identities must be left to candour and good-sense ; and may they increase among us. But formal Logic is, no doubt, safest with symbols; should, perhaps, content itself with A and B ; or, at least, hardly venture beyond Y and Z, § 5. The principle of Contradiction is usually written sym- bolically, thus . A is not not-A. But, since this formula seems to be adapted to a single term, and we want one that is applic- able to propositions, it may be better to write it thus : B is not both A and not-A. That is to say : if any term may be affirmed of a subject, the contradictory term may be denied of it in the same relation. A leaf that is green on one side of it may be not- green on the other ; but it is not both green and not-green on the same surface, at the same time, and in the same light. If a stick is straight, it is false that it is at the same time not- straight : having granted that two angles are equal, we must deny that they are unequal. But is it necessarily false that the stick is crooked ; must we deny that either angle is greater or less than the other? How CONDITIONS OF IMMEDIATE INFERENCE 63 far is it permissible to substitute any other term for the formal contradictory? Clearly, the principle of Contradiction takes for granted the principle of Identity and is subject to the same difficulties in its practical application. As a matter of fact and common sense, if we affirm any term, we are bound to deny not only the contradictory but all synonyms for this, and also all contraries and opposites ; which, of course, are included in its contradictory. But who shall determine what these are? Without an authoritative Logical Dictionary to refer to, where all contradictories, synonyms, and contraries may be found on record, formal Logic will hardly sanction the free play of common sense. The principle of Excluded Middle is usually written : B is either A or not-A ; that is, if any term be denied of a subject, the contradictory term may be affirmed in the same relation. Of course, we may deny that a leaf is green on one side without being bound to affirm that it is not green on the other. But in the same relation a leaf is either green or not green ; at the same time, a stick is either bent or not bent. If we deny that A is greater than B, we must affirm that it is not greater than B. Whilst, then, the principle of Contradiction (that * of contra- dictory predicates, one being affirmed, the other is denied ') might seem to leave open a third or middle course, the denying of both contradictories, the principle of Excluded Middle derives its name from the excluding of this middle course, by declaring that the one or the other must be affirmed. Hence the principle of Excluded Middle does not hold good of mere Contrary Terms. If we deny that a leaf is green, we are not bound to affirm it to be yellow; for it may be red; and, therefore, we may deny both con- traries, yellow and green. In fact two contraries do not between them cover the whole predicable area, but contra- dictories do : the form of their expression is such that (within the suppositio) each includes all that the other excludes ; so that the subject (if brought within the suppositio) must fall 64 LOGIC: DEDUCTIVE AND INDUCTIVE under the one or the other. It may seem absurd to say that Mont Blanc is either wise or not-wise ; but how comes your mind so ill-organised as to introduce Mont Blanc into this strange company? Being there, however, the principle is inexorable : Mont Blanc, alas ! is not-wise. In fact, the principles of Contradiction and Excluded Middle are inseparable; they are implicit in all distmct experience, and may be regarded as indicating the two aspects of Negation. The principle of Contradiction says : B is either A or not-A, as if not- A might be nothing at all ; this is abstract negation. But the principle of Excluded Middle says: Grantim^ that B is not A, it is still somethini^—n^mtXy, not-A ; thus bringing us back to the concrete experience of a con- tinuum in which the absence of one thing implies the presence of something else. Symbolically : to deny that B is A is to affirm that B is not A, and this only differs by a hyphen from B is not-A. But if any one holds that the hyphen makes all the difference, I give it up. These principles, which were necessarily to some extent antici- pated in chap. iv. § 7, the next chapter will further illustrate. § 6. But first we must draw attention to a maxim (also already mentioned), which is strictly applicable to Immediate Inferences, though (as we shall see) in other kinds of proof it may be only a formal condition : this is the general caution not to go beyond the evidence. An immediate inference ought to contain nothing that is not contained (or formally implied) in the proposition by which it is proved. With respect to quantity in denotation, this caution is embodied in the rule ' not to distribute any term that is not given distri- buted.' Thus, if there is a predication concerning * Some S,' or * Some men,' as in the forms I. and O., we cannot infer any- thing concerning ' All S,' or ' All men ; ' and, as we have seen, if a term is given us preindesignate, we are generally to take it as of particular quantity. Similarly, in the case of affirmative propositions, we saw that this rule requires us to assume that their predicates are undistributed. \\i CONDITIONS OF IMMEDIATE INFERENCE 65 As to the grounds of this maxim, not to go beyond the evidence, not to distribute a term that is given as undistri- buted, it is one of the things so plain that to try to justify is only to obscure them. We might indeed say that such a leap from the particular to the general is not sanctioned by any of the three Laws of Thought. The caution against it may particularly be viewed as supplementary to the principle of Identity, that whatever is true in one form of words is true in any other : since if for ' Some S ' we substitute ' All S ', we no longer have the same sense as the given form of words. It is a gratuitous assumption, a mere non-sequitur ; and if any controvertist demands permission to make it, the formal logician can only " hold up his hands in respectful amaze- ment." Still we must here state explicitly what Formal Logic assumes to be contained or implied in the evidence afforded by any proposition, such as 'All S is P '. If we remember that in chap. iv. § 7, it was assumed that every term may have a contradictory ; and if we bear in mind the principles of Contradiction and Excluded Middle, it will appear that such a proposition as ' Ail S is P ' tells us something not only about the relations of ' S ' and ' P ', but also of their relations to ' not-S ' and ' not P ' ; as, for example, that ' S is not not-P ', and that ' not-P is not-S.' It will be shown in the next chapter how Logicians have developed these implications in series of Immediate Inferences. If it be asked whether it is true that every term, itself significant, has a significant contradictory, and not merely a formal contradictory, generated by force of the word ' not,' it is difficult to give any better answer than was indicated in §§ 3-5, without venturing further into metaphysics. I shall merely say, therefore, that, granting that some such term as 'Uni- verse ' or ' Being ' may have no significant contradictory, if it stand for ' whatever can be perceived or thought of ' ; yet every term that stands for less than ' Universe ' or ' Being ' has of course, a contradictory which denotes the rest of the uni- E 66 LOGIC: DEDUCTIVE AND INDUCTIVE verse. And since every argument or train of thought is carried on within a special ' universe of discourse ' or under a certain supposition we may say that within the special universe or sup- positio every term has a contradictory, and that every predication concerning a term implies some predication concerning its con- tradictory. CHAPTER VII IMMEDIATE INFERENCES § I. Under the general title of Immediate Inference Logicians discuss three subjects, namely. Opposition, Con- version, and Obversion ; to which some writers add other forms, such as Whole and Part in Connotation, Contraposi- tion, Inversion, etc. Of Opposition, again, all recognise four modes : Subalternation, Contradiction, Contrariety and Sub- contrariety. The only peculiarities of the exposition upon which we are now entering are, that it follows the lead of the three Laws of Thought, taking first those modes of Immediate Inference in which Identity is most important, then those which plainly involve Contradiction and Excluded Middle; and that this method results in separating the modes of Oppo- sition, connecting Subalternation with Conversion, and the other modes with Obversion. To make up for this departure from usage, the four modes of Opposition will be brought together again in § 9. § 2. Subalternation.— Propositions of the forms A. and I. are said to be Subalterns in relation to one another, and so are E. and O. ; the universal of each quahty being distinguished as subalternans, and the particular as subalternate. It follows from the principle of Identity that, the matter of the pro- positions being the same, if A. is true I. is true, and that if E. is true O. is true ; for A. and E. predicate something of All S or All men ■ and since I. and O. make the same predication of Some S or Some men. the sense of these particular propositions has already^een predicated in A or E. If ^// 5 is P. Some S is P; if No S ts P, Some S is not P • or if All men are fond of laughing, Some men are; if No men are exempt from ridicule, Some men are not. \ it ) \ 68 LOGIC: DEDUCTIVE AND INDUCTIVE Similarly, if I. is false A. is false ; if O. is false E. is falye. If we deny any predication about Some S, we must deny it of All S; since in denying it of Some, we have denied it of at least part of All ; and what- ever is false in one form of words is false in any other. On the other hand, if I. is true, we do not know that A. is ; nor if O. is true, that E. is ; for to infer from Some to All would be going beyond the evidence. We shall see in discussing Induction that the great problem of that part of Logic is, to determine the conditions under which we may in reality transcend this rule and infer from Some to All; though even there it will appear that, formally, the rule is observed. For the present it is enough that I. is an immediate inference from A., and O. from E. ; but that A. is not an immediate inference from I., nor E. from O. ,/ § 3. Connotative Subalternation. — We have seen (chap. iv. ^ 6) that if the connotation of one term is only part of another's its denotation is greater and includes that other's. Hence genus and species stand in subaltern relation, and whatever is true of the genus is true of the species : If A// animal life is dependent on vegetation^ All human life is dependent on zegeta- tion. On the other hand, whatever is not true of the species or narrower term, cannot be true of the whole genus : If it is false that ' All human life is happy, ^ it is false that ' All animal life is happy. ^ Similar inferences may be drawn from the subaltern relation of predicates ; affirming the species we affirm the genus. To take Mill's example, if Socrates is a man, Socrates is a living creature. On the other hand, denying the genus we deny the species : if Socrates is not vicious, Socrates is not drunken. It cannot be said that such cases as these are generally recognised by Logicians as immediate inferences coming under the principle of Identity. They are so regarded by Mill and Bain ; but probably most authorities upon our science would treat them as imperfect syllogisms, requiring another premise to legitimate the conclusion, as thus : All animal life is dependent on vegetation ; All human life is animal life ; Therefore, All human life is dependent on vegetation. Or again : All men are living creatures ; Socrates is a man ; Therefore, Socrates is a living creature. The decision of this issue seems to turn upon the question [cf. IMMEDIATE INFERENCES 69 chap vi § %) how far a logician is entitled to assume that the terms he uses are' understood, and that the identities involved in their meanmgs will be recognised. And to this question, for the sake of consistency one of two answers is required, failing which there remams the rule of thumb First, it may be held that no term is understood except those that are defined in expounding the science, such as ' genus ' and ' species, •connotation.' and -denotation.' But very few logicians observe this limitation; few would hesitate to substitute 'not-wise ^^J J^^^^^^" Yet by what right ? Malvolio being foolish, to prove that he is not wise, we may construct the following syllogism : Foolish is not-wise ; Malvolio is foolish ; Therefore, Malvolio is not-wise. Is this necessary ? If not, why not? Secondly, it may be held that all terms may be assumed as under- stood (amongst those native to the language) unless a defini ion is challenged. This principle will justify the substitution of not-wise for 'foolish' ; but it will also legitimate the above cases (concerning ' human life ' and ' Socrates ') as immediate inferences, with mnumerable others that might be based upon the doctrine of relative names as for example The hunter missed his aim; therefore. The prey escaped. And from thi; principle it will further follow that all apparent syllogisnis having one premise a verbal proposition, are immediate inferences {cf r^sd;^connected with such cases as the above are those mentioned by Archbishop Thomson as " Immediate Inferences by added Determi- nants " {Lau. of Thought, § 87). He takes the case : ' A negro ts afello^^ creature ■ therefore, A negro in sujfering is a fellow creature m sujfermg. This re;ts upon the principle that to increase the connotations of two terms by th^same attribute or determinant does not -^-^ ;^-^ ^;-- ship of their denotations, since it must equally dimmish (if at all the denotations of both classes, by excluding the same individuals, if any want the given attribute. § 4. Conversion is Immediate Inference by transposing the terms of a given proposition without altering its quality. If the quantity is also unaltered, the inference is called ' Simple Conversion ' ; but if the quantity is changed from universal to particular, it is called 'Conversion by limitation' or 'per accidens: The given proposition is called the ' convertend ' ; that which is derived from it, the ' Converse.' Departing from the usual order of exposition. I have taken up Con- veys on nexf to Subalternation. because it is generally thought to res upon the principle of Identity, and because it seems to be a good \ N 70 LOGIC: DEDUCTIVE AND INDUCTIVE method to exhaust the forms that come only under Identity before going on to those that involve Contradiction and Excluded Middle. Some mdeed dispute the claims of Conversion to illustrate the principle of Identity ; and if the sufficient statement of that principle be • A is A ' I am at a loss to see how Conversion or any other mode of Inference can be referred to it. But if we state it as above (ch. vi § 3) that u-hateyer is true in one form of words is true in any other, there' is no difhculty in applying it to Conversion. Thus, to take the conversion of I Some S IS P ; .-. Some P is S. Some poets are men of business ; .-. Some men of business are foets Here the convertend and the converse say the same thing, and this is true if that is. We have then, two cases of Simple Conversion : of I. (as above) and of E, For E. : ' No S is P: .'. No P is S. No ruminants are carnivores ; .-. No carnivores are ruminants In converting I., the predicate (P) when taken as the new subject being preindesignate. is treated as particular, according to the rule ' noi to -o beyond the evidence ' (chap. vi. § 4) ; and in converting E.. the predicate in when taken as the new subject, is treated as universal, accordin- to the rule in chap. iv. §1. ° A. is the one case of Conversion by limitation : All S is P; .-. Some P is S. All cats are animals; .-. Some animals are cats. And here the treatment of the predicate as particular, when taking it for the new subject, is according to the rule in chap. iv. § i. Palpably to infer that All animals are cats would never do. O. cannot be truly converted. If we take the proposition • Some S is not P, to convert this \nio No P is S, or Some P is not S, would break the rule in chap. vi. § 4 ; since S. undistributed in the convertend, would be distributed in the converse. If we are told that Some men are not cooks we cannot infer that Some cooks are not men. This would be to assume' that 'Some men ' are identical with 'All men.' By quantifying the predicate, indeed, we may convert O. simply, thus: Some men are not cooks .-. No cooks are some men. And the same plan has some advantage in converting A. ■ for by the usual method per accidens, the converse of A. being I., if we convert this agam it is still I., and therefore means less than our original convertend 1 nus : All S is P .-. Some P is S :. Some S is P S^uch knowledge, as that All S (the whole of it) ts P, is too precious a thing to be squandered in pure Logic. On the other hand, quantifying the predicate, if we convert A to Y thus — ■' All S is P . \ Some P is all S-^ I IMMEDIATE INFERENCES 71 H, i i I we may reconvert Y. to A. without any loss of meaning. It is perhaps the chief use of quantifying the predicate that, thereby, every propo- sition is capable of Simple Conversion. ^ § 5. Obversion (otherwise called Permutation or /Equipol- lence) is Immediate Inference by changing the quality of the given proposition and substituting for its predicate the con- tradictory term. The given proposition is called the 'obver- tend ' and the inference from it the * obverse.' Thus the obvertend being — Some philosophers are consistent reasonerSy the obverse will be — Some philosophers are not inconsistent reasoners. The legitimacy of this mode of inference follows, in the case of affirmative propositions, from the principle of Contra- diction, that if any term be affirmed of a subject, the contra- dictory term may be denied (chap. vi. § 3). To obvert affirma- tive propositions, then, the rule is — Add the negative sign to the copula, and for the predicate substitute its contradictory, A. All S is P :. No S is not-P All men are fallible :. No men are infallible. I. Some S is P :. Some S is ?iot not-P Some philosophers are consistent :. So?ne philosophers are not inconsistent. In agreement with this mode of inference, we have the rule of modern English grammar, that 'two negatives make an affirmative.' Again, since by the principle of Excluded Middle, if any term be denied its contradictory may be affirmed, to obvert negative propositions, the rule is— Remove the negative sign from the copula, and for the predicate substitute its contra- dictory. E. No S is P :. All S ts not-P No matter is destructible :. All matter is indestructible. O. So??ie S is not P :. So??ie S is not-P Some virtue is not attainable :. Some virtue is unattainable. Thus, by obversion, each of the four propositions retains its quantity but changes its quality : A. to E., I. to O., E. to A.. O. to I. And all the obverses are Infinite Propositions, the affirmative infinities having the 72 LOGIC: DEDUCTIVE AND INDUCTIVE sense of negatives, and the negative infinities having the sense of amrmatives. Again, having obtained the obverse of a given proposition, it may be desirable to recover the obvertend ; or it may at any time be requisite to change a given Infinite into the corresponding direct Affirmative or Negative ; and in such cases the process is still obversion. Thus if No S IS not.p be given us to recover the obvertend or to find the correspond- ing Affirmative; the proposition being formallv Negative, we applv the rule for obverting Negatives : • Remove the negative sign from the copula, and for the predicate substitute its contradictory ' This yields the affirmative All S is P. Similarly, to obtain the obvertend of ^// 5 is not-P, apply the rule for obverting Affirmatives ; and this yields No S iS P. § 6. Contrariety.— We have seen in chap. iv. § 8, that con- trary terms are those which are never both predicable in the same way of the same subject, whilst perhaps neither may be predicable of it. Similarly, Contrary Propositions are defined as those that are never both true together, whilst perhaps neither may be true; or, in other words, both may be false. This is the relation between A. and E. when concerned with the same matter : as A.— A// meN are ivise : E.—No me?i are wise. Such propositions cannot both be true ; but they may both be false, for some men may be wise and some not. Contrary relation may be viewed as according with the principle of Con- tradiction : if it may be affirmed that Ail me?i are wise, it may be denied that All fnen are not-wise : and this is the obverse of No men are wise, which therefore may also be denied. At the same time we cannot apply to A. and E. the principle of Excluded Middle, so as to show that one of them must be true of the same matter. For if we deny that All men are wise, we do not necessarily deny the attribute ' wise ' of each and every man : to say that Not all are wise may mean no more than that Some are not. This gives a proposition in the form of O. ; which, as we have seen, does not imply its subal- ternans, E. If, however, two Singular Propositions, having the same matter, but of different quality, are to he treated as universale and therefore as A. and E., they are, nevertheless, contradic- IMMEDIATE INFERENCES 73 \ tories and not merely contraries ; for one of them must he false and the other true. § 7. Contradiction, however, is a relation between two pro- positions analogous to that between contradictory terms, such, namely, that one of them is false and the other true. This is the case with the forms A. and O., and E. and I., in the same matter. If it be true that All men are wise, it is false that Some men are not wise (equivalent by obversion to Some men are nof-2vise) ', or else, since the * Some men ' are included in the ' All men,' we should be predicating of the same men that they are both ' wise ' and * not-wise ' ; which would violate the principle of Contradiction. Similarly, No men are wise, being by obversion equivalent to All men are 7iot-wise, is incom- patible with Some men are wise, by the same principle of Con- tradiction. But, again, if it is false that All men are wise, it is always true that Some are not wise ; for though in denying that * wise ' is a predicate of ' All men ' we do not deny it of each and every man, yet we deny it of ' Some men.' Of ' Some men,' therefore, by the principle of Excluded Middle, ' not-wise ' is to be affirmed ; and Some men are not-wise, is by obversion equivalent to Sofne 7nen are not wise. Similarly, if it is false that No jnen are wise, which by obversion is equivalent to All men are 7iot-wise, then it is true at least that So77ie 77ien are wise, I may here observe that by extending and enforcing the doctrine of relative terms, certain other inferences are implied in the contrary and contradictory relation of propositions. We have seen in chap, iv., that the contradictory of a given term includes all its contraries : * not-blue,' for example, includes red and yellow. Flence, since The sky is blue becomes by obversion. The sky is 7iot 7tot-blue, we may also infer The sky is 7iot red, etc. From the truth, then, of any proposition predica- ting a given term, we may infer the falsity of all propositions predicating the contrary terms in the same relation. But, on the other hand, from the falsity of a proposition predicating a 74 LOGIC: DEDUCTIVE AND INDUCTIVE given term, we cannot infer the truth of the predication of any particular contrary term. If it is false that The sky is red, we cannot formally infer that The sky is blue (cf. chap. vi. § 3). § 8. Sub-contrariety is the relation of propositions, con- cerning the same matter, that may both be truth but are never both false. This is the case with I. and O. If it be true that Some me,i are 7vise, it may also be true that Some {other) men are not tvise. This follows from the maxim in chap. vi. § 4 not to go beyond the evidence. For if it he true that Some men are wise, it may indeed be true that All are (this hein- the siibahernans) : and if All are, it is (by contradiction) false that Some are not; but as we are only told that Some men are. it is illicit to infer the falsity of Some are not, which could only be justified by evidence concerninf,^ All men. But if it be false that Some men are vise, it is true that Some men are not wise: for, by contradiction, if Some men are wise is false, No men are wise IS true : and, therefore, by subalternation, Some men are not wise is true. § 9. The Square of Opposition.— By their relations of Subalternation, Contrariety, Contradiction, and Sub-contrariety, the forms A. I. E. O. (having the same matter) are said to stand in Opposition : and it is traditional amongst Logicians to re- present these relations by a square having A. I. E. O. at its corners, thus : A. Contraries fi: en CD (A % ^^. .<" ^ c^ .^^ 5- \ tfi or CO I, Sub-contraries ®; As an aid to the memory, this diagram is useful ; but as an attempt to represent the logical relations of propositions, it is useless, and indeed, • f IMMEDIATE INFERENCES 75 misleading. For, standing at corners of the same square. A. and'E., A. and I., E. and O., and I. and O., seem to be couples bearing tht same relation to one another ; whereas we have seen that their relations are entirely different. The following traditional summary of their relations in respect of truth and falsity, is much more to the purpose : (i) If A. is true. I. is true, E. is false, O. is false. (2) If A. is false, I. is unknown, E. is unknown, O. is true. (3) If I. is true, A. is unknown, E. is false, O. is unknown. (4) If I. is false, A. is false. E, is true, O. is true. (5) If E. is true, A. is false. I. is false. O. is true. (6) If E. is false. A. is unknown, I. is true, O. is unknown. (7) If O. is true. A. is false, I. is unknown, E. is unknown. (8) If O. is false, A. is true, I. is true, E. is false. Where, however, as in cases 2, 3, 6. 7, alleging either the falsity of Universals or the truth of Particulars, it follows that two of the three Opposites are unknown, we may conclude further that one of them must be true and the other false, because the two unknowns are always Con- tradictories. § 10. Secondary modes of Immediate Inference are obtained by applying the process of Conversion or Obversion to the results already obtained by the other process. The best known form of secondary Immediate Inference is the Contrapositive, and this is the converse of the obverse of a given proposition. Thus, A. A/ I S is P :. No S is not-P :. No not-P is S ^v- I. Sotne S is P :. Some S is not not-P :. (none) E. No S is P :. All S is not-P :. Some not-P is S O. Some S is not P / Some S is 7wt-P :. Some not-P is S There is no contrapositive of L, because the obverse of L is in the form of O., and we have seen that O. cannot be converted. O., however, has a Contrapositive {Some not-P is S) ; and this is sometimes given instead of the converse, and called the * converse by negation.' Contraposition needs no justification by the Laws of Thought, as it is nothing but a compounding of Conversion with Obversion, both of which processes have already been justified. I give a table of the other ways of compounding these primary modes of Immediate Inference. k (\' IMMEDIATE INFERENCES 77 1 In this table a and b stand for not- A and not-B, and had better be read thus: for No A is b, No A is not-B ; for All b is a (col. 6), All not-B is not- A ; and so on. It may not, at first, be obvious why the process of alternately obvert- ing and converting any proposition should ever come to an end ; though it will, no doubt, be considered a very fortunate circumstance that it always does end. On examining the results, it will be found that the cause of its ending is the inconvertibility of O. For E., when obverted, becomes A. ; every A., when converted, degenerates into I.; every I., when obverted, becomes O. ; O. cannot be converted, and to obvert it again is merely to restore the former proposition : so that the whole process moves on to inevitable dissolution. I. and O. are exhausted by three transformations, whilst A. and E. will each of them endure seven. Except Obversion, Conversion and Contraposition, it has not been usual to bestow special names on these processes or their results. But the form in columns 7 and 10 [Some a is B—Somc a is not B), where the original predicate is affirmed or denied of the contradictory of the original subject, has been thought by Dr. Keynes to deserve a distinctive title, and he has called it the Inverse. Observe, however, that, although the Inverse is one form. Inversion is not one process, but is obtained by different processes from E. and A. respectively. In this it differs from Obversion, Conversion, and Contraposition, each of which stands for one process. The Inverse form has been objected to on the ground that the infer- ence All A is B .'. Some not- A is not B, distributes B (as predicate of a negative proposition), though it was given as undistributed (as predicate of an affirmative proposition). But Dr. Keynes defends it on the ground that (i) it is obtained by Obversions and Conversions which are a legitimate; and (2) that although All A is B does not distribute B in relation to A, it does distribute B in relation to some not-A (namely, in relation to whatever not-A is not-B). This is one reason why in stating the rule in chap. vi. § 4, 1 have written ; " an immediate inference ought to contain nothing that is not contained, or formally implied, in the pro- position from which it is inferred"; and have maintained that every term formally implies its contradictory. § II. Immediate Inferences from Conditionals are those which consist— (i) in changing a Disjunctive into a Hypo- thetical, or a Hypothetical into a Disjunctive, or either into a Categorical ; and (2) in the relations of Opposition and the equivalences of Obversion, Conversion, and secondary or compound processes, which we have already examined in respect of Categoricals. As no new principles are involved, it may suffice to exhibit some of the results. 78 LOGIC: DEDUCTIVE AND INDUCTIVE ^^^^:^l^!^^^^^ ^ ^^f-^-s .ay be read as i; we recognise ^ourV^^lT^l:^^^^^^^ stand to one another in a Snn.r. '7^^^^'''^^ ^- '• E. O., these plainly Thus A. and E. (7/^^/ C ' n'^ Opposition, just as Categoricals do^ trades, but not Comradictdes s'in'^^ '' ^' "" " "'' ""^ ^'^ ^- tinges be D, and somet Is noO thn . ^^ ^^ '^''' ^^ ^^^ ^«-- And if they are both fahe the I S ht '''"' '""""^ ^^^^ be true, respectively the ContradtorilsTf fh 'n '"'' i '" '"'^ ^^"^' '^^"^^ namely. I. of E.. and O of rBut in^^ ^niversals of opposite Quaht^ set out a satisfactory Itrfoo '•''"' """^'""^^^^^^^^ (chap. v.§ 4). the forms reSf^E^^^^^^^ '^^^"^^' ^^ ^^ -- but Exponibles. ^ ^- ^""^ O. are not true Disjunctives. The Obverse, Converse anr? r- . exhibited thus: ' ^ ^ontrapositive of Hypotheticals are \ Obverse. I/A is B, C is not d Sometimes u-hen A is B, C is not d UA IS B, C isd Sometimes 'when A is B, C is d CONTRAPOSITIVE. // C is d, A is not B (none) Sometimes u7ien C is d, A ts B Sometimes u^hcn C is d, A is B Datum. A. If A is B. CisD I. Sometimes K-/icn A is B, C is D ^' If A isB,C isnotD ^- ^^'^^times K'/icn A is B,C is not D Converse. Sometimes ichen C is D, A is B Sometimes i^hen C is D, A is B If C is D, A is not B (none) any proposition in the loL A 7 euTsr '''''''''■ ^""- «'-" pos>t,o,>s that give the sense of Ob "slf r ' '": "^ ^'^'« "^« P™" Obve„« ^ '"''''™°"' Conversion, rt,-.. thus: CONVERSE._S»«rf/„>,. „•,;„, £ ;^ CONTRAPOSITIVF \7../; ., "^ '^ ^ . For a Disjunctive i o^; "' " '"" ^ ""' ''''■ a Disjunctive in the form' eiZTlsBlrT^ ^'''''''^'''''■^- ^'-n Obverse-./„ ,„ ,ase is A b. and C at tt ' "'^ "^^^ '""^^ ^r ils or Contrapositive of such a DisL t """, '""I '^ ^"' "° Converse casting It into the Hypothetica^^rcregS f:™ "^''' "^"^^P' ^^ «-' • CHAPTER VIII ORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL EQUATIONS, EXISTENTIAL IMPORT OF PROPOSITIONS § I. Which Term is the Subject and which the Predicate of a pro- position ? In most of the exemplary propositions cited by Logicians it will be found that the subject is a substantive and the predicate an adjective, as in Men aye Mortal. But, in literature, sentences in which the adjective comes first are not uncommon, as Loud n'as the applause, Dark is the fate of man, Great is the glory of the conquering sword. Here, then, ' loud,' ' dark ' and ' great ' occupy the place of the Subject. Are they really the subject, or must we alter the order of such sentences into The applause was loud, etc. ? If we do, and then proceed to convert, we get Loud was the applause, or (more scrupulously) Some loud noise was the applause. The last form, it is true, gives the subject a substantive word, but ' applause ' has become the predicate ; and if the substantive ' noise' was not implied in the first form, Loud is the applause, by what right is it now inserted ? The recognition of Conversion, in fact, re- quires us to admit that, in a logical proposition, the term preceding the copula is subject and the one following is predicate. And, of course, materially considered, the mere order of terms in a proposition can make no difference in the method of proving it, nor in the inferences that can be drawn from it. Still, if the question is, how we may best cast a literary sentence into logical form, good grounds for a definite answer may perhaps be found. We must not try to stand upon the naturalness of expression, for Dark is the fate of man is quite as natural as Man is mortal. When the pur- pose is not merely to state a fact, but also to express our feelings about it. to place the grammatical predicate first may be perfectly natural and most effective. But the grounds of a logical order of statement must be found in its adaptation to the purposes of proof and inference. Now general propositions are those from which most inferences can be drawn, which, therefore, it is most important to establish if true ; and they are also the easiest to disprove if false, since a single negative instance suffices to establish the contradictory. It follows that, in 8o LOGIC: DEDUCTIVE AND INDUCTIVE re-casting a literary or colloquial sentence for logical purposes, we should try to obtain a form in which the subject is distributed— is either a singular term or a general term predesignate as * All ' or ' No.' Seeing, then, that most adjectives connote a single attribute, whilst most sub- stantives connote more than one attribute; and that therefore the denotation of adjectives is usually wider than that of substantives ; in any proposition, one term of which is an adjective and the other a substantive, if either can be distributed in relation to the other, it is nearly sure to be the substantive ; so that to take the substantive term for Subject is our best chance of obtaining an universal proposition. These considerations seem to justify the practice of Logicians in select- ing their examples. For similar reasons, if both terms of a proposition are substantive, the one with the lesser denotation is (at least, in Affirmative propositions) the more suitable subject, as Cats are caynivores. And if one term be abstract, that is the more suitable subject ; for, as we have seen, an abstract term may be interpreted by a corresponding concrete one distributed, as Kindness is infectious; that is, All kind actions suggest imitation. If, however, a controvertist has no other object in view than to refute some general proposition laid down by an opponent, a particular pro- position is all that he need disentangle from any statement that serves his purpose. § 2. Toward understanding clearly the relations of the terms of a proposition, it is often found useful to employ diagrams ; and the diagrams most in use are the circles of Euler. These circles represent the denotation of the terms. Suppose the proposition to he All Jiollon'-Jwrncd animals ruminate: then, if we could collect all ruminants upon a prairie, and enclose them with a circular palisade; and segregate from amongst them all the hollow-horned beasts, and enclose them with another ring-fence inside the other ; one way of interpreting the proposition (namely, in denotation) would be figured to us thus : Fig. I. An Universal Affirmative may also state a relation between two terms whose denotation is co-extensive. A definition always does this, as Vn EULER'S DIAGRAMS 8i Man is a rational animal; and this, of course, we cannot represent by two distinct circles, but at best by one with a thick circumference to suggest that two coincide, thus : Fig. 2. The Particular Affirmative Proposition may be represented in several ways. In the first place, bearing in mind that ' Some ' means ' some at least, it may be all,' an I. proposition may be represented by Figs, i and 2 ; for it is true that Some horned animals ruminate, and that Some men are rational. Secondly, there is the case in which the ' Some things ' of which a predication is made are, in fact, not all ; whilst the predicate, though not given as distributed, yet might be so given if we wished to state the whole truth ; as if we say Some men aye Chinese. This case is also represented by Fig. i, the outside circle representing 'Men,' and the inside one ' Chinese. ' Thirdly, .he predicate may appertain' to some only of the subject, but to a great many other things, as in Some horned beasts are domestic; for it is true that some are not, and that certain other kinds of animals are, domestic. This case, therefore, must be illustrated by overlapping circles, thus : Fig. 3. HORNED ANIMALS DOMESTIC /ANIMALS The Universal Negative is sufficiently represented by a single Fig. (4^ two circles mutually exclusive, thus : Fig. 4. That is. No horned beasts are carnivorous. 82 LOGIC: DEDUCTIVE AND INDUCTIVE Lastly, the Particular Negative may be represented by any of the Figs. I, 3 and 4 ; for it is true that Some ruminants are not hollow-horned, that Some horned animals are not domestic, ^nd that Some horned beasts are not carnivorous. \^- Besides their use in illustrating the denotative force of propositions, these circles may also be used to verify the results of Obversion, Con- version, and the secondary modes of Immediate Inference. Thus the Obverse of A. is clear enough on glancing at Figs, i and 2 ; for if we agree that whatever term's denotation is represented by a given circle, the denotation of the contradictory term shall be represented by the space outside that circle; then, of course, if it is true that All holloiv-horned animals are ruminants, it is at the same time true that No hollow-horned animals are not-ruminants; since none of the hollow-horned are found outside the palisade that encloses the ruminants. The Obverse of I., E., or O. may be verified in a similar manner' As to the Converse, a Definition is of course susceptible of Simple Conversion, and this is shown by Fig, 2 : ' Men are rational animals ' and ' Rational animals are men.' But any other A. proposition is pre- sumably convertible only by limitation, and this is shown in Fig. i ; where All hollow-horned animals are ruminants, but we can only say that Some ruminants are hollow-horned. That I. may be simply converted may be seen in Fig. 3, which repre- sents the least that an I. proposition can mean ; and that E. may be simply converted is manifest in Fig. 4. As for O., we know that it cannot be con\erted, and this is made plain enoug'i by glancing at Fig. i ; for that represents theO., Some ruminants are not holloji'-horned, but also shows this to be compatible with All hollow horned animals are ruminants (A.). Now in Conversion there is (by definition) no change of quality. The Converse, then, of Some ruminants are not hollow-horned must be a negative proposition, having 'hollow- horned' for its subject, either in E. or O. ; but there would be re- spectively the Contrary and Contradictory of ^// hollow-horned animals are ruminants; and, therefore, if this is true, they must both be false. But (referring still to Fig. i) the legitimacy of contrapositing O. is equally clear ; for if Some ruminants are not hollow-horned. Some animals that are not holloiv-horned are ruminants, namely, all the animals between the two ring-fences. Similar inferences may be illustrated from Figs. 3 and 4. And the Contraposition of A. may be verified by Figs, i and 2, and the contrapositive of E. by Fig. 4. Lastly, the Inverse of A. is plain from Fig. i—Some things that are not hollow-horned are not ruminants^ namely, all things that lie outside the outer circle and are neither ' ruminants ' nor ' hollow-horned. ' And the Inverse of E. may be studied in Fig. 4— Some things that are not-Jiorned beasts are carnivorous. Notwithstanding the facility and elegance of the demonstrations thus LOGICAL EQUATIONS 83 ^ obtained, there is much to be said for the opinion that such a dia- grammatic method is not properly logical. It seems to be agreed that fundamentally the relation asserted (or denied) to exist between the terms of a proposition, is a relation between the terms as determined by their attributes or connotation ; whether we take Mill's view, that a proposition asserts that the connotation of the subject is a mark of the connotation of the predicate ; or Dr. Venn's view, that things denoted by the subject (as having its connotation) have (or have not) the attribute connoted by the predicate ; or, the Conceptualist view, that a judgment is a relation of concepts (that is, of connotations). At any rate, it is certain that, with a few artificially framed exceptions (such as ' kings now reigning in Europe '), the denotation of a term is never directty known, but consists merely in 'all things that have the connotation.' And I venture to think that the value of logical training depends very much upon our habituating ourselves to construe propositions, and to realise the force of inferences from them, according to the connotation of their terms ; and that, therefore, a student does well not to turn too hastily to the circles, but rather to regard them as a means of verifying in denotation the conclusions that he has already learnt to recognise as necessary in connotation. (Keynes : Formal Logic, Part II. c. 4.) § 3. The equational treatment of propositions is closely connected with the diagrammatic. Hamilton thought it a great merit of his plan of quantifying the predicate, that thereby every proposition is reduced to its true form— an equation. According to this doctrine, the proposition A/i X is all K(U.) equates X and Y; the proposition All X is some F(A.) equates X with some part of Y; and similarly with the other affirmatives (Y. and I.). And so far it is easy to follow his meaning: the Xs are identical with some or all the Ys. But, coming to the negatives, the equational interpretation is certainly less obvious. The proposition No X is V (E.) cannot be said in any sense to equate X and Y ; though, if we obvert it into All X is some not- F, we have (in the same sense, of course, as the above affirmative forms) X equated with part at least of ' not-Y.' But what is this sense? Clearly not the same as that in which Mathematical terms are equated, namely, in respect of some mode of quantity. For if we may say Some X is some Y, these Xs that are also Ys are not merely the same in number, 84 LOGIC: DEDUCTIVE AND INDUCTIVE or position, or figure, or other determination of space; they are the same in every respect, both quantitative and quali- tative, are in fact identical. The proposition 2 + 2-4 means that any two things added to any. other two are, in respect of number, equal to any three things added to one other ; and this is true of all things that can be counted, however much they may differ in other ways. But A/I X is all F means that Xs and Ys are the same things, although they have different names when viewed in different aspects or relations. Thus all equilateral triangles are equiangular triangles ; but in one case they are named from the equality of their angles and in the other from the equality of their sides. Similarly, 'British subjects ' and ' subjects of Queen Victoria ' are the same people, named in one case from the person of the Crown, and in the other from the Imperial Government. These Logical equations, then, are in truth identities of denotation ; and they are fully illustrated by the relations of circles described in the previous section. When we are told that logical propositions are to be consi- dered as equations, we naturally expect to be shown some interesting developments of method in analogy with the equations of Mathematics ; but from Hamilton's innovations no such thing results. This cannot be said, however, of the equations of Symbolic Logic ; which are the starting-point of very remarkable processes of ratiocination. As the subject of Symbolic Logic, as a whole, lies beyond the compass of an ordinary manual, it will be enough to give Dr. Venn's equations corresponding with the four propositional forms of common Logic. According to this system, universal propositions are to be regarded as not necessarily implying the existence of their terms ; and therefore, instead of giving them a positive form, they are translated into symbols that express what they deny.' For example, the proposition All devils are ugly need not imply that any such things as Mevils ' really exist; but it rertainly does imply that D.nnls that are not-ugly do not exist. LOGICAL EQUATIONS 85 I Similarly, the proposition No angels are ugly implies that Angels that are ugly do not exist. Therefore, writing x for 'devils,' y for ' ugly,' and y for ' not-ugly,' we may express A., the universal affirmative, thus : A. x7 = o. That is, X that is not y is nothing; or. Devils that are not ugly do not exist. And, similarly, writing x for 'angels ' and y for ' ugly,' we may express E., the universal negative, thus : E. xy = o. That is, x that is y is nothing; or. Angels that are ugly do not exist. On the other hand, particular propositions are regarded as implying the existence of their terms, and the corresponding equations are so framed as to express existence. With this end in view, the symbol v is adopted to represent ' something ', or indeterminate reality, or more than nothing. Then, taking any particular affirmative, such as Some metaphysicians are obscure, and writing x for ' metaphysicians ', and y for ' obscure', we may express it thus : I. xy = v. That is, .V that is y is something; or. Metaphysicians that are obscure do occur in experience (however few they may be, or whether they be all obscure). And, similarly, taking any particular negative, such as Some giants are not cruel, and writing X for ' giants ' and 7 for ' not-cruel ', we may express it thus : O. xy = v. That is, .r that is not y is something; or, giants that are not cruel do occur— m romances, if nowhere else. Clearly, these equations, like those of Hamilton, are concerned with denotation. A. and E. affirm that the 'com- pound terms xy and xy have no denotation ; and I. and O. declare that xy and xy have denotation, or stand for something! Here, however, the resemblance to Hamilton's system ceases ; for the Symbolic Logic, by operating upon more than twj terms simultaneously, by adopting the algebraic signs of "4*-««| I S6 LOGIC: DEDUCTIVE AND INDUCTIVE operation, +, _, x, -^ (with a special signification), and manipulating the symbols by quasi-algebraic processes, obtains results which the common Logic reaches (if at all) with much greater difficulty. If, indeed, the value of logical systems were to be judged of by the results^ obtainable, formal deductive Logic would probably be superseded. And, as a mental discipline, there is much to be said in favour of the symbolic method. But, as an introduction to philosophy, the common Logic must hold its ground. (Venn's SymM'^ Logic, c. 7.) § 4. Whether Formal Logic involves any general assump- tion as to the real existence of the terms of propositions, is a question that has lately excited some interest ; so that a few remarks upon it will be expected here. But, as it is too abstruse a matter to be fully discussed in a manual, if my treatment of it seem somewhat dogmatic, the need of brevity must be my excuse. I observe, then, in the first place, that Logic treats primarily of the relations implied in propositions. This follows from its being the science of proof for all sorts of (qualitative) proposi- tions; since all sorts of propositions have nothing in common except the relations they imply. But, secondly, relations with- out terms of some sort are not to be thought of; and. hence even the most formal illustrations of logical doctrine comprise such terms as S and P, X and Y, or x and y, in a symbolic or representative character. Terms, therefore, of some sort are assumed to exist (together with their negatives or contra- dictories) >/- the purposes of logical manipulation. Thirdly, however, that Formal Logic cannot directly involve the existence of any particular concrete terms, such as ' man ' or ' mountain,' is implied in the word ' formal,' that is, ' con- fined to what is common or abstract ' ; since the only thing common to all terms is to be related in some way to other terms. The actual existence of any concrete thing can only be known by experience, as with ' man ' or ' mountain ' • or by methodically justifiable inference from experience, as with * atom ' or * ether.' ^ EXISTENTIAL IMPORT 87 Nevertheless, fourthly, the existence or non-existence of par- ticular terms may come to be implied, namely, wherever the very fact of existence, or of some condition of existence, is an hypothesis or datum. Thus, given the proposition All S is P, to be P IS made a condition of the existence of S ; whence it follows that an S that is not P does not exist (xy = o). On the further hypothesis that S exists, it follows that P exists. On the hypothesis that S does not exist, the existence of P is problematic ; but, then, if P does exist we cannot convert the proposition ; since Some P is S (P existing) would involve the existence of S ; which is contrary to the hypothesis. Assuming that Universals do not, whilst Particulars do, imply the existence of their subjects, we cannot infer the subalternate (I. or O.) from the subalternans (A. or E.), for that is to ground the actual on the problematic ; and for the same reason we cannot convert A. per accidens. Assuming, again, a certain suppositio or universe, to which in a given discussion every argument shall refer, then, any pro- positions whose terms lie outside that suppositio are irrelevant, and for the purposes of that discussion may be called false.' Thus propositions, which according to the doctrine of Opposi- tion appear to be Contradictories, may then cease to be so ; for of Contradictories one is true and the other false , but, in the case supposed, both are technically false. If the sub- ject of discussion is Zoology, all propositions about Centaurs or Unicorns are absurd ; and such specious Contradictories as No Centaurs play the lyre—Some Cetitaurs do play the lyre; or All unicor?is fight ivith lions—Some Unicorns do not fight with lions, are both false or meaningless, because in Zoology there are no Centaurs nor Unicorns ; and, therefore, in this reference, the propositions are not really contradictory. But if the subject of discussion or suppositio be Mythology or Heraldry, such propositions as the above are to the purpose, and form legitimate pairs of Contradictories. In Formal Logic, in short, we may make at discretion any assumption whatever as to the existence, or as to any condition 88 LOGIC: DEDUCTIVE AND INDUCTIVE of the existence of any term or terms ; and then certain impli- cations and conclusions follow in consistency with that hypo- thesis or datum. Still, our conclusions will themselves be only hypothetical, depending on the truth of the datum ; and, of course, until that is empirically ascertained, we are as far as ever from empirical reality. (Venn : Symbolic Logic, c. 6 ; Keynes: Formal Logic, Part II. c. 7.) CHAPTER IX FORMAL CONDITIONS OF MEDIATE INFERENCE § I. A Mediate Inference is a proposition that depends for proof upon two or more other propositions, so connected together by one or more terms (which the evidentiary propositions, or each pair of them, have in common) as to justify a certain conclusion, namely, the proposition in question. The type o. (more properly) the unit of all such modes of proof, when of a strictly logical kind, is the Syllogism, to which We shall see that all other modes are reducible. It may be exhibited symbolically thus : M is P ; S is M : .. Sis P. Syllogisms may be classified, as to quantity, into Universal or Particular, according to the quantity of the conclusion ; as to quality, into Attirmative or Negative, according to the quality of the conclusion ; and, as to relation, into Categorical, Hypothetical and Disjunctive, according as all their proposi- tions are categorical, or one (at least) of their evidentiary pro- positions is a hypothetical or a disjunctive. We will begin with Categorical Syllogisms, of which the following is a concrete example : All authors are vain ; Cicero is an author : .". Cicero is vain. Here e may suppose that there are no direct means of know- ing that Cicero is vain ; but we happen to know that all authors 90 LOGIC: DEDUCTIVE AND INDUCTIVE are vain and that he is an author ; and these two propositions put together unmistakably imply that he is vain. In other words, we do not at first know any relation between * Cicero ' and ' vanity ' ; but we know that these two terms are severally related to a third term, 'author,' hence called a Middle Term; and thus we perceive, by mediate evidence, that they are re- lated to one another. This sort of proof bears an obvious re- semblance to the mathematical proof of equality between two quantities, that cannot be directly compared, by showing the equality of each of them to some third quantity: A = B = C •'• A = C. Here B is a middle term. We have to inquire, then, what conditions must be satisfied in order that a Syllogism may be formally conclusive or valid. An apparent Syllogism that is not really valid is called a Parasyllogism. § 2. General Canons of the Syllogism. (i) A Syllogism contains three, and no more, distinct pro- positions. (2) A Syllogism contains three, and no more, distinct uni- vocal terms. These two Canons imply one another. Three propositions with less than three terms could only be connected in some of the modes of Immediate Inference. Three propositions with more than three terms do not show that connection of two terms by means of a third, which is the desideratum for proving a Mediate Inference. If we write- All authors are vain ; Cicero is a statesman ; there are four terms and no Middle Term, and therefore there is no proof Ur if we write — ^ All authors are vain ; Cicero is an author ; .'. Cicero is a statesman ; here the term • statesman ' occurs without any voucher; it appears in the inference but not in the evidence, and therefore violates the maxim of all formal proof. • not to go beyond the evidence ' (chap, vi S 4) it IS true that if any one argued— • b ^/. ai All authors are vain ; Cicero wrote on philosophy ; .•. Cicero is vain : CONDITIONS OF MEDIATE INFERENCE 91 this could not be called a bad argument or a material fallacy ; but it would be a needless departure from the form of expression in which the connection between the evidence and the inference is most easily seen • It would generally be called a formal fallacy. Still a mere adherence to the same form of words in the expression of terms is not enough : we must also attend to their meaning. For if the same word be used ambiguously (as 'author' now for ' father ' and anon for ' man of letters ') it becomes as to its meaning two terms ; so that we have four in all. Then, if the ambiguous term be the Middle, no connection is shown between the other two ; if either of the others be ambiguous, something seems to be inferred which has never been really given in evidence. The above two Canons are, indeed, involved in the definition of a Categorical Syllogism, which may be thus stated : A Cate- gorical Syllogism is a form of proof or reasoning (way of giving reasons) in which one categorical proposition is established by comparing two others that contain together only three terms, or that have one and only one term in common. The proposition established, derived, or inferred, is called the Conclusion : the evidentiary propositions by which it is proved are called the Premises. The term common to the Premises, by means of which the other terms are compared is called the Middle Term. For the other Terms, the Subject of the Conclusion is called the Minor Term ; the Predicate of the Conclusion, the Major Term. The Premise in which the minor term occurs is called the Minor Premise ; that in which the major term occurs is called the Major Premise. And a Syllogism is usually written thus : Major Premise— All Authors (Middle) are vain (Major) ; Minor Premise— Cicero (Minor) is an author (Middle) : ' Conclusion—.-. Cicero (Minor) is vain (Major). Here we have three propositions with three terms, each term occurring twice. The Minor and Major terms are so called, because when the conclusion is an universal affirmative (which only occurs in Barbara; see chap. x. § 6), its subject and predicate are respectively the less and the greater in extent or denotation. It should be carefully noticed that the premises 92 LOGIC: DEDUCTIVE AND INDUCTIVE are called after the peculiar terms they contain : the expressions * Major Premise' and 'Minor Premise' have nothing to do with the order in which the premises are presented ; though it is usual to place the Major tirst. (3) No term must be distributed in the conclusion unless it is distributed in the premises. It is usual to give this as one of the General Canons of the Syllogism ; but we have seen (chap. vi. § 6) that it is of wider application. Indeed, 'not to go beyond the evidence' belongs to the definition of formal proof. A breech of this rule in a Syllogism is the fallacy of Illicit Process of the Minor, or of the Major, according to which term has been unwarrantably distributed. The following parasyllogism illicitly distributes both terms of the conclusion : All poets are pathetic ; Some orators are not poets ; .•. No orators are pathetic. (4) The Middle Term must be distributed at least once in the premises. For the use of mediate evidence is to show the relation of terms that cannot be directly compared ; this is only possible if the Middle term furnishes the ground of comparison ; and this (in Logic) requires that the whole denotation of the Middle should be either included or excluded by one of the others ; since if we only know that the other terms are related to some of the Middle, their respective relations may not be with the same part of it. Indeed, if the Middle is undistributed in both premises, Whately regards it as ambiguous ; in which case the pretended syllogism depending on it has four terms : so that this 4th Canon may be regarded as reducible to the 2nd. It is true that in what has been strangely called the "numerically definite syllogism," an inference may be drawn, though our canon seems to be violated. Thus : 60 sheep in 100 are horned ; 60 sheep in 100 are black faced ; .*. at least 20 blackfaced sheep in 100 are horned. But such an argument, though I presume it may be correct Arithmetic, is not Logic at all ; and when such numerical evidence is obtainable the comparatively indefinite arguments of Logic are needless. Another apparent exception more to the purpose is the following : Most men are 5 feet high ; Most men are semi-rational : .*. Some semi-rational things are 5 feet high. Here the Middle Term (men) is distributed in neither premise, yet the I CONDITIONS OF MEDIATE INFERENCE 93 indisputable conclusion is a logical proposition. Observe, however, that the premises are really arithmetical ; for ' most ' means ' more than half,' or more than 50 per cent. For Mediate Inference depending on truly logical premises, then, it is necessary that one premise should distribute the Middle Term ; and the reason of this may be illustrated even by the above supposed ex- ceptions. For in them the premises are such that, though neither premise by itself distributes the Middle, yet they always do so between them, and that with a certain surplus. For if each premise dealt with exactly half the Middle., thus barely distributing it between them, there would be no logical proposition inferrible (though, of course, there might be a conclusion of numerical probability). We require that the Middle as used in one premise, should necessarily overlap the Middle as used in the other, so as to furnish common ground for comparing the other terms. Hence I have defined the Middle as ' that Term common to both premises by means of which the other terms are compared.' (5) One at least of the premises must be affirmative ; or, from two negative premises nothing can be inferred. The fourth Canon required that the Middle term should be given us distributed, or in its whole extent, in order to afford sure ground of comparison for the others. But that such comparison may be effected, something more is requisite ; the relation of the other terms to the Middle must be of a certain character. One at least of them must be, as to its extent or denotation, partially or wholly identified with the Middle; so that to that extent it may be known to bear to the other term, whatever relation we are told that so much of the Middle bears to that other term. Now, identity of denotation can only be predicated in an affirmative proposition : one premise, then, must be affirmative. If, however, both premises are negative, we only know that both the other terms are partly or wholly excluded from the Middle, or are not identical with it in denotation : where they lie, then, in relation to one another, we have no means of knowing. Similarly, in the mediate comparison of quantities, if we are told that A and C are both of them unequal to B, we can infer nothing as to the relation of C to A. Hence the premises — No electors are sober ; No electors are independent, howe'ver suggestive, do not formally justify us in inferring any connec- tion between sobriety and independence. F'ormally to draw a conclusion, we must have affirmative grounds, such as in this case we may obtain by obverting both premises : All electors are not-sober ; All electors are not-independent ; -\ Some who are not-independent are not-sober. II I 94 LOGIC: DEDUCTIVE AND INDUCTIVE (6) (a) If one premise is negative, the conclusion must be negative : and (<^) to prove a negative conclusion, one premise must be negative. (a) For we have seen that one premise must be affirmative, and that thus one term must be partly (at least) identified with the Middle. If then the other premise, being negative, predicates the exclusion of the other term from the Middle, this other term must be excluded from the first term, so far as we know the first to be identical with the Middle : and this exclusion will be expressed by a negative conclusion. The analogy of the mediate comparison of quantities may here again be noticed : if A is equal to B, and B is unequal to C, A is unequal to C. {b) If both premises are affirmative, the relations of both terms to the Middle are more or less inclusive, and therefore furnish no ground for an exclusive inference. This also follows from the function of the Middle term. For the more convenient application of these canons to the testing of syllogisms, it is usual to derive from them three Corollaries : (i) Two particular premises yield no conclusion. For if both premises are affirmative all their terms are undistributed, the subjects by predesignation, the predicates by position (chap. v. § i) ; and therefore the Middle must be undistributed, and there can be no conclusion. If one premise is negative, its predicate is distributed by position : the other terms remaining undistributed. But, by Canon 6, the conclu- sion (if any be possible) must be negative ; and therefore its predicate, the Major term, will be distributed. In the premises, therefore, both the Middle and the Major terms should be distributed, which is impos- sible : e.g., Some M is not P ; Some S is M ; .'. Some S is not P. Here, indeed, the Major term is legitimately distributed (though the negative premise might have been the Minor) ; but M, the. Middle term, is distributed in neither premise, and therefore there can be no con- clusion. (ii) If one premise is particular, so is the conclusion. For, again, if both premises are affirmative, they only distribute one term, the subject of the Universal premise, and this must be the Middle term. The Minor term, therefore, is undistributed, and the conclusion roust be particular. CONDITIONS OF MEDIATE INFERENCE 95 If one premise is negative, the two premises together can distribute only two terms, the subject of the Universal and the predicate of the negative (which may be the same premise). One of these terms must be the Middle ; the other (since the conclusion is negati\'e) must be the Major. The Minor term, therefore, is undistributed, and the conclusion must be particular. (iii) From a particular Major and a negative Minor premise, nothing can be inferred. For the Minor premise being negative, the Major premise must be affirmative (5th Canon) ; and therefore, being particular, distributes the Major term neither in its subject nor in its predicate. But since the conclusion must be negative (6th Canon), a distributed Major term is demanded: e.g., /fif^i Some M is P ; T y No S is M ; ^^ Here the Minor and the Middle terms are both distributed, but not the Major (P) ; and, therefore, a negative conclusion is impossible. § 3. First Principle or Axiom of the Syllogism. — Hitherto in this chapter we have been analysing the conditions of valid mediate inference. We have seen that a single step of such inference, a Syllogism, contains when fully expressed in lan- guage three propositions and three terms, and that these terms must stand to one another in the relations required by the fourth, fifth, and sixth Canons. We now come to a principle which conveniently sums up these conditions ; it is called the Dictum de om?ii et nullo^ and may be stated thus : Whatever is predicated (affirmatively or negatively) of a Term distributed, In which Term another is given as (partly or wholly) in- cluded, May be predicated in like manner of (part or all of) the latter Term. Thus stated (nearly as by Whately in die introduction to his Logic) the Dictum follows line by line the course of a Syllogism in the First Figure (see chap. x. § 2). To return to our former example : All authors are vain is the same as — Vanity is pre- dicated of all authors ; Cicero is an author is the same as— i %*..H| 96 LOGIC: DEDUCTIVE AND INDUCTIVE Cicero is included amongst authors : therefore, OV^z-^/V vain.ox — Vanity may be predicated of Cicero. The Dictuvi then requires : (i) three propositions; (2) three terms; (3) that the Middle be distributed ; (4) that one premise be affirmative, since only by an affirmative proposition can one term be given as included in another; (5) that if one premise is negative the conclusion be so too, since whatever is predicated of the Middle is predi- cated "in like manner" of the Minor term. Thus far, then, the Dictum is wholly analytic or verbal, expressing no more than is implied in the definitions ot ' Syllogism ' and ' Middle Term ' ; since (as we have seen) all the General Canons (except the third, which is a still more general condition of formal proof) are derivable from those definitions. However, the Dictum makes a further statement of a synthetic or real character, namely, that when these conditions are fulfilled, an inference is justified ; that then the Major and Minor terms are brought into comparison through the Middle, and that the Major may be predicated affirma- tively or negatively of all or part of the Minor. It is this real assertion that justifies us in calling the Dictum an Axiom. § 4. Whether the Laws of Thought may not fully explain the Syllogism without the need of any synthetic principle, has, however, been made a question. Take such a Syllogism as the following : All domesticated animals are useful ; All pugs are domesticated animals : .-. All pugs are useful. Here (an ingenious man might urge), having once identified pugs with domestic animals, that they are useful follows from the Law of Identity. If we attend to the meaning, and remember that what is true in one form of words is true in any other form, then, all domesticated animals being useful, of course pugs are. It is merely a case of Subalternation ; we may put it in this way : All domesticated animals are useful ; ,\ Some domesticated animals (e.g., pugs) are useful. CONDITIONS OF MEDIATE INFERENCE 97 The derivation of Negative Syllogisms from the Law of Contradiction (we might add) may be shown in a similar manner. But the force of this ingenious argument depends on the participial clause—' having once identified pugs with domestic animals.' If this is a distinct step of the reasoning, the above Syllogism cannot be reduced to one step, cannot be exhibited as mere subalternation, nor be brought directly under the law of Identity. If ' pug ', ' domestic ', and ' useful ' are distinct terms; and if 'pug' and 'useful' are only known to be connected because of their relations to ' domestic ' : this is something more than the Laws of Thought provide for : it is not Immediate Inference, but Mediate; and to justify it, scientific method requires that its conditions be generalised. The Dictum, then, as we have seen, does generalise these conditions, and declares that when such conditions are satisfied a Mediate Inference is valid. But, after all (to go back a little), consider again that proposition All pugs are domesticated aftimals : is it a distinct step of the reasoning ; that is to say, is it a Real proposition ? If it is ; if domesticated ' is no part of the definition of ' pug ', the proposition is Real, and is a distinct part of the argument. But take such a case as this : All dogs are useful ; All pugs are dogs. Here we clearly have, in the minor premise, only a verbal pro- position : to be a dog is certainly part of the definition of ' pug '. But, if so, the inference ' All pugs are useful ' involves no real mediation, and the argument is no more than this : All dogs are useful ; .'. Some dogs {e.g., pugs) are useful. Similarly, if the Major Premise be Verbal, thus : All men are rational ; Socrates is a man — to conclude that ' Socrates is rational ' is no Mediate In- ference; for so much was implied in the Minor Premise. G 98 LOGIC: DEDUCTIVE AND INDUCTIVE ' Socrates is a man,' and the Major Premise adds nothing to this. Hence I conclude (as by anticipation in chap. vii. § 3) that *any apparent syllogism, having one premise a Verbal Pro- position, is really an Immediate Inference ' ; but that, if both Premises are Real Propositions, the Inference is Mediate, and demands for its explanation something more than the Laws of Thought. I have not, however, always refrained from using Verbal Syllogisms as formal illustrations. § 5. Other kinds of Mediate Inference exist, yielding valid conclusions, without being truly syllogistic. Such are mathe- matical inferences of Equality, as— A = B = C .•.A = C. Here there are strictly four terms— (i) A, (2) equal to B, (3) B, (4) equal to C. Similarly with the argument a fortiori, A > B > C .•. (much more) A > C. This also contains four terms : (i) A, (2) greater than B, (3) B, (4) greater than C. Such inferences are nevertheless intuitively sound, may be verified by trial (within the limits of sense- perception), and are generalised in appropriate axioms of their own, corresponding to the Dictum of the Syllogism, as ' Things equal to the same thing are equal to one another,' etc. There are also cases of Order in Time and Place : A is before B, B IS before C; therefore, A is before C: or, again, A is to the left ofB, B is to the left of C ; therefore A is to the left of C. Some cases, however, that at first may seem equally obvious, are really delusive, unless further data be supplied. For instance, A is north of B, B is west of C : what is the relation of A to C ? One may be tempted to answer, ' North-east.' But suppose A is a mi.e to the north of B, and B a yard to the west of C, then A is practically north of C; at least, its eastward position uaniiot be expressed in terms of the mariner's compass. In sucn a case, then, we require to know not only the directions but the distances of A and C from B ; and then the exact direction of A from C is a matter of mathematical calculation. Ill CHAPTER X CATEGORICAL SYLLOGISMS § I. The type of logical, deductive, mediate, categorical Inference is a Syllogism directly conformable with the Dictum : as — All carnivorous animals (M) are of nervous temperament (P) ; Cats (S) are carnivorous animals (M) : /. Cats (S) are of nervous temperament (P). In this example P is predicated of M, a term distributed • in which term, M, S is given as included ; so that P may be pre^ dicated of S. Many arguments, however, are of a type superficially different from the above : as — No wise man (P) fears death (M); Dr. Johnson (S) fears death (M) : .-. Dr. Johnson (S) is not a wise man (P). In this example, instead of P being predicated of M, M is pre- dicated of P, and yet S is given as included not in P, but in M. The divergence of such a Syllogism from the Dictum may, however, be easily shown to be superficial, if instead of No wise man fears death we write the Simple Converse, JVo man who fears death is wise. Again : t^ Some dogs (M) are friendly to man (P) ; All dogs (M) are carnivorous (S) : .-. Some carnivores (S) are friendly to man (P). Here P is predicated of M undistributed ; and instead of S being included in M, M is included in S : so that the diver- loo LOGIC: DEDUCTIVE AND INDUCTIVE gence from the type of Syllogism to which the Dictum directly applies, is still greater. But if we transpose the premises, taking first All dogs (M) are carnivorous (P), then P is predicated of M distributed ; and, simply converting the other premise, we get — Some things friendly to man (S) are dogs (M) : whence it follows that — Some things friendly to man (S) are carnivores (P) ; and this is the simple converse of the original conclusion. Once more : No pigs (P) are philosophers (M) ; Some philosophers (M) are of those who approve of pleasure (S) : .-. Some of those who approve of pleasure (S) are not pigs (P). In this case, instead of P being predicated of M distributed, M is predicated of P distributed ; and instead of S (or part of it) being included in M, we are told that some M is included in S. Still there is no real difficulty. To show that it is all right, simply convert both the premises. Then we have : No philosophers (M) are pigs (P) ; Some who approve of pleasure (S) are philosophers (M). Whence the same conclusion follows ; and the whole Syllogism plainly conforms directly to the Dictum. Such departures as these from the normal syllogistic form are said to constitute differences of Figure (to be further de- fined in § 2) ; and the processes by which they are shown to be unessential differences are called Reduction (for a fuller account of which, see § 6). § 2. Figure is determined by the position of the Middle term in the premises ; of which position there are four possible variations. The Middle Term may be subject of the Major Premise, and predicate of the Minor, as in the first example above; and this position, being directly conformable to the requirements of the Dictum, is called the First Figure. Or the Middle Term may be predicate of both premises, as in the CATEGORICAL SYLLOGISMS lOl second of the above examples ; and this is called the Second Figure. Or the Middle may be subject of both premises, as in the third of the above examples ; and this is called the Third Figure. Or, finally, the Middle may be predicate of the Major premise, and subject of the Minor, as in the fourth example given above ; and this is the Fourth Figure. It may facilitate the recollection of this most important point if we schematise the Figures thus : in. IV. I. II. M P M 3 M M rP S The horizontal lines represent the premises, and at the angles formed with them by the slanting or by the perpendicular lines the Middle Term occurs. Note further that the schema of the Fourth and last Figure resembles Z, the last letter of the alphabet : this helps one to remember it in contrast with the First, which is thereby also remembered. § 3. The Moods of each Figure are the modifications of it which arise from different combinations of propositions accord- ing to Quantity and Quality. In the First Figure, for example, four Moods are recognised : A. A. A., E. A. E., A. J. I., E. L O. A. AllM isP; A. All S is M : A. .'. All Sis P. ^ E. No M is P ; /- A. Alls is M: E. .-. No S is P. ^V y V A. All M is P ; I. Some S is M : I. /. Some S is P. E. No M is P ; I. Some S is M : O. .-. Some S is not P. Now, remembering that there are four Figures, and four kinds 102 LOGIC: DEDUCTIVE AND INDUCTIVE of propositions (A. I. E. O.), each of which Propositions may be Major Premise, Minor Premise, or Conclusion of a Syllogism It appears that in each Figure there may be 64 Moods, and therefore 256 in all. On examinings these 256 Moods, how- ever, we find that only 24 of them are valid (/>., of such a character that the Conclusion strictly follows from the Pre- mises) ; whilst 5 of these 24 are needless, because their Con- clusions are 'weaker' or less extensive than the Premises warrant ; that is to say, they are particular when they might be universal. Thus, in the First Figure, besides the above 4 Moods, A. A. I. and E. A. O. are valid in the sense of being conclusive; but they are superfluous, because included in A. A. A. and E. A. E. Omitting then these 5 needless Moods, which are called Subalterns because their Conclusions are subaltern (chap. vii. § 2) to those of other Moods, there remain 19 Moods that are valid and generally recognised. § 4. How these 19 Moods are determined must be our next mquiry. There are several ways more or less ingenious and interesting; but all depend on the application, directly or indirectly, of the Six Canons, which were shown in the last chapter to be the conditions of Mediate Inference. (i) One way is to begin by finding what Moods of the First Figure conform to the Dictum. Now. the Dictum requires that, in the Major premise. P be predicated of a term distributed, from which it follows that no Mood can be valid whose Major premise is Particular, as in I. A. I., or O. A. O. Again, the Dictum requires that the Minor premise be affirmative (" in which term a third is given as included ") ; so that no Mood can be valid whose Minor premise is negative, as in A.' E. E. or A. O. O. By these considerations we find that in the First Figure out of 64 Moods possible, only six are valid, namely, those above m^'entioned m § 3. including the two Subalterns. The second step of this method is to test the Moods of the Second, Third and Fourth Figures, by trying whether they can be reduced to one or other of the four Moods of the First (as briefly illustrated in § i. and to be further explained in § 6) (2) Another way is to take the above six General or Common Canons and_to deduce from them Special Canons for testing each Figure : an interesting method, which, on account of its length, will be treated of separately in the next section. (3) Direct application of the Common Canons is. perhaps, the sim- CATEGORICAL SYLLOGISMS 103 plest plan. First write out the 64 Moods that are possible without regard to Figure, and then cross out those which violate any of the Canons or Corollaries, thus : AAA, 7^:iV«. (6th Can. \). AA I. T^%-e'(6th Can. h], -A-&A(6rtiCan. a) AE]^"^*«4.(6thCan. fl)^EO. ft4=A.(Cor. a.) n^t&(6th Can. o}^ 1 1. :W^(6th Can. *) -tc^Jc{ti\h C*a a) 3~0* (Cor. u ):ft-ai (6th Qua. «) A O O. The student will find it a useful exercise to go through the remaining 48 Moods, when he will discover that of the whole 64 only 11 are valid, namely : A. A. A., A. A. I.. A. E. E.. A. E. O., A. 1. 1., A. O. O., E. A. E.. E. A. O., E. I. O., I. A. I., O. A. O. These eleven Moods have next to be examined in each Figure, and if valid in every Figure there will still be 44 moods in all. We find, how- ever, that in the First Figure, A.vE.E., A.E.O., A.O.O., involve illicit process of the Major Term (3rd Can.) ; I. A. I., O. A. O. involve undistri- buted Middle (4th Can.) ; and A. A. I.. E. A. O. are Subalterns. In the Second Figure all the affirmative Moods, A. A; A., AM..!., A. 1. 1., LA. I., involve undistributed Middle; O. A. O. involves illicit process of the Major; and A. E. O., E. A. O are Subalterns. In the Third Figure, A. A. A., E.A. E., involve illicit process of the Minor (3rd Can.); A. E. E.. A. E. O., A. O. O. involve illicit process of the Major. In the Fourth Figure, A. A. A. involves illicit process of the Minor; A. 1. 1., A. O. O. involve Undistributed Middle; O. A O. involves illicit process of the Major ; and A. E. O. is Subaltern. Those moods of each Figure which, when tried by these tests, are not rejected, are valid, namely : Fig. I. — A. A. A., E. A. E., A. L L , E. A. O., Subaltern); Fig. IL— E. A ,E., A. El. E., E. I. O., A. E. O., Spbaltern) ; ^^ Fig. III.— A. A. L, I. A. J., A. LJ., E. LO.; Fig. T^L^=.>A. A. I., A. E.-E., I. A. L, (A. E. O., Subaltern). Thus, including Subaltern Moods, there are six valid in each Figure. In Fig. III. alone there is no Subaltern Mood, because in that Figure there can be no universal conclusion. § 5. Special Canons of the several Figures, deduced from the Com- mon Canons, enable us to arrive at the same result by a somewhat \. E. I.O. (A, A. I., ^^ A. 0,0. (E,A. O., E.A. 0., O.A.O., E.A. O, E. I.O. I04 LOGIC: DEDUCTIVE AND INDUCTIVE dififerent course. The Special Canons are not, perhaps, necessary to the Science, but they afford a very useful means of enabling a student to thoroughly appreciate the character of formal syllogistic reasoning. Accordingly, I shall indicate the proof of each rule, leaving its elabora- tion to the reader. In this he can find no difficulty, if he bears in mind that Figure is determined by the position of the Middle Term. Fig. I., Rule (a) : The minor premise must he affirmative. For, if not, in negative Moods there will be illicit process of the Major Term. Applying this rule to the eleven possible Moods given in § 4, as remaining after application of the Common Canons, it eliminates A. E. E, A. E.O., A. 0.0. {h) The major premise must he universal. For, if not, the minor being affirmative, the Middle Term will be undistributed. This rule eliminates I. A. I., O. A. O. ; leaving six moods, including two Subalterns. Fig. II. {a) One premise must he negative. For else neither premise will distribute the Middle Term. This rule eliminates A. A. A., A. A. I., A. 1. 1., I. A. I. {h) The major premise 7mist he universal. For else, the conclusion being negative, there will be illicit process of the Major Term. This eHminates I. A. I., O. A. O. ; leaving six moods, including two Subalterns. Fig. III. {a) The minor premise must he affirmative. For else, in negative moods there will be illicit process of the Major Term. This rule eHminates A. E. E., A. E. O., A. O. O. {b) The conclusion must he particular. For else, the minor premise being affirmative, there will be illicit process of the Minor Term. This eliminates A. A. A., A. E. E., E. A. E. ; leaving six Moods. Fig. IV. {a) When the major premise is affirmative, the minor must he universal. For else the Middle Term is undistributed. This eliminates All A. 0.0. {h) When the minor premise is affirmative, the conclusion must he particular. For else there will be illicit process of the Minor Term. This elimi- nates A. A. A., E. A. E. (c) When either premise is negative, the major must he universal. For else, the conclusion being negative, there will be illicit process of the Major Term. This eliminates O. A. O. ; leaving six Moods, including one Subaltern. § 6. Reduction is either— (i) Ostensive or (2) Indirect. Ostensive Reduction consists in showing that an argument given in one Mood can also be stated in another; the process I CATEGORICAL SYLLOGISMS 105 \> f r L is especially used to show that the moods of the second, third, and fourth Figures are equivalent to one or another Mood of the first Figure. It thus proves the validity of the former Moods by showing that they also essentially conform to the Dictum, and that all Categorical Syllogisms are only superficial varieties of one type of proof. To facilitate Reduction, the recognised Moods have all had names given them; which names, again, have been strung together into mnemonic verses of great force and pregnancy : Barbara, Celarent, Darii, Ferioque prioris : Cesare, Camestres, Festino, Baroco, secund^; Tertia, Darapti, -Disamis, Datisi, Felapton, Bocardo, Ferison, habet : Quarta insuper addit Bramantip, Camenes, Dimaris, Fesapo, Fresison. In the above verses the names of the Moods of Fig. I. begin with the first four consonants B, C, D, F, in alphabetical order; and the names of all other Moods likewise begin with these letters, thus signifying (except in Baroco and Bocardo) the Mood of Fig. I., to which each is equivalent, and to which it is to be reduced : as Bramantip to Barbara, Camestres to Celarent, and so forth. The vowels A, E, I, O, occurring in the several names, give the quantity and quality of Major Premise. Minor Premise, and Conclusion in the usual order. The consonants s and p, occurring after a vowel, show that the pro- position which the vowel stands for is to be converted either (s) simply or (p) per accidens ; except where s or p occurs after the third vowel of a name, the conclusion : then it refers not to the conclusion of the given Mood (say Disamis), but to the conclusion of that Mood of the first Figure to which the given Mood is reduced (Darii). M {mutare, metathesis) means ' transpose the premises ' (as of Cames- tres). C means ' substitute the contradictory of the conclusion for the fore- going premise,' a process of the Indirect Reduction to be presently explained (see Baroco, p. 109). The other consonants r, n, t, (with b and d, when not initial) occur- ring here and there, have no mnemonic significance. What now is the problem of Reduction ? The difference of Figures depends upon the position of the Middle Term. To reduce a Mood of any other Figure to the form of the First, then, we must so manipulate its premises that the Middle Term shall be subject of the Major pre- mise and predicate of the Minor. Now in Fig. II. the Middle Term is \ % io6 LOGIC: DEDUCTIVE AND INDUCTIVE predicate of both premises ; so that the Minor may need no alteration, and to convert the Major may suffice. This is the case with Cesare, which reduces to Celarent by simply converting the Major ; and with Festino, which by the same process becomes Ferio. In Camestres, however, the Minor premise is negative ; and, as this is impossible in Fig. I., the premises must be transposed, and the new Major premise must be simply converted : then, since the transposition of the premises will have transposed the terms of the conclusion (according to the usual reading of syllogisms), the new conclusion must be simply converted in order to prove the validity of the original Conclusion. The process may be thus represented (s. c. meaning ' simply convert ') : CATEGORICAL SYLLOGISMS Camestres. All P is M ; No S is M : No S is P. f fir Celarent. No M is S ; All P is M : No P is 8. The Ostensive Reduction of Baroco also needs special explanation. As it used to be reduced indirectly, its name gives no indication of the ostensive process. To reduce it ostensively let us call it Faksnoko, where k means ' obvert the foregoing premise. ' By thus obverting (k) and simply converting (s) (in sum, contrapositing) the Major Premise, and obverting the Minor Premise, we get a syllogism in Ferio, thus : Baroco or Faksnoko. All P is M ; Some S is not M : .-. Some S is not P. contrap.^ Ferio. -> No m (not-M) is P ; ah >fc'. -> Some S is m (not-M) : .*. Some S is not P. In Fig. III. the Middle Term is subject of both premises ; so that, to reduce its Moods to the First Figure, it may be enough to convert the Minor premise. This is the case with Darapti, Datisi, Felapton and Ferison. But, with Disamis, since the Major premise must in the First Figure be universal, we must transpose the premises, and then simply convert the new Minor ; and, lastly, since the Major and Minor Terms have now changed places, we must simply convert the new con- clusion in order to verify the old one. Thus : f 107 Disamis. Some M is P ; All M is S : .'. Some S is P. s.c. Darii. All M is S ; Some P is M •. Some P is S. Bocardo, like Baroco, indicates by its name the Indirect process. To reduce it ostensively let its name be Doksamrosk, and proceed thus : Bocardo or Doksamrosk. Some M is not P ; All M is S : So Darii. All MisS; Somep(not-P)isM .-. Some S is not P. < amveH & ohvert .^ g^^^ ^ ^^^^^^ .^ ^ In Fig. IV. the position of the Middle Term is, in both premises, the reverse of what it is in the First Figure ; we may therefore reduce its Moods either by transposing the premises, as with Bramantip, Camenes, and Dimaris ; or by converting both premises, the course pursued with Fesapo and Fresison. It may suffice to illustrate by the case of Bramantip : Bramantip. All P is M ; All M is S : Some Sis P. < c^yert.p^a^. Barbara. All M is S ; All P is M : •. All P is S. This case shows that a final significant consonant (s, p, or sk) in the name of any Mood refers to the conclusion of the new syllogism in the First Figure ; since p in Bramantip cannot refer to its own Conclusion in I., which, being already particular, cannot be converted /^r accidens. Finally, in Fig. I., Darii and Ferio differ respectively from Barbara and Celarent only in this, that their Minor Premises, and consequently their conclusions, are subaltern to the corresponding propositions of the universal Moods, a difference which seems insufficient to give them \ io8 LOGIC: DEDUCTIVE AND INDUCTIVE rank as distinct forms of demonstration. And as for Barbara and Cela- rent, they are easily reducible to one another by obverting their Major premises and the new conclusion, thus : Barbara. All MisP; obv. All S is M : All S is P. < obv. Celarent. No M is p (not P) ; All S is M : No S is p (not P). § 7. A new version of the mnemonic lines was suggested in Mind No. 27, with the object of (i) freeing them from all meaningless letters, (2) showing by the name of each Mood the Figure to which it belongs, (3) giving names to indicate the ostensive reduction of Baroco and Bocardo. To obtain the first two objects, / is used as the mark of Fig. I., 71 of Fig. II., r of Fig. III., t of Fig. IV. The verses (to be scanned discreetly) are as follows : Balala, Celalel, Dalii, Felioque prioris : _ ^ ^ . { Faksnoko secundae : Cesane, Camenes, Fesmon, - ^ i Banoco, Tertia, Darapri, Drisamis, Darisi, Ferapro, Doksamrosk | perisor habet : Quarta insuper addit Eocaro J Bamatip, Gametes, Dimatis, Fesapto, Fesistot. De Morgan praised the old verses as " more full of meaning than any others that ever were made " ; and in defence of the above alteration it may be said that they now deserve that praise still more. § 8. Indirect Reduction is the process of proving a Mood to be valid by showing that the supposition of its invalidity involves a contradiction. Take Baroco, and (since the doubt as to its validity is not concerned with the truth of the premises, but with their relation to the conclusion) assume the premises to be true. Then, if the conclusion be false, its contradictory is true. The conclusion being in O., its contradictory will be in A. Substituting this A. for the Minor premise of Baroco, we have the premises of a syllogism in Barbara, which will be found to give a conclusion in A., contradictory of the original Minor premise ; thus : 1 i 1 -i \ CATEGORICAL SYLLOGISMS 109 Baroco. All P is M ; Some S is not M : Some S is not P. Barbara. All P is M ; All S is P : All S is M. \ But the original Minor, Some S is nol M^ is true by hypothesis ; and therefore the conclusion of Barbara, All S is M^ is false. This falsity cannot, however, be due to the form of Barbara, which wc know to be valid ; nor to the Major premise, which is taken from Baroco, and is true by hypothesis : it must, therefore, be in the Minor premise of Barbara, All S is P ; and since this is contradictory of the conclusion of Baroco Some S is not P^ that conclusion was true. Similarly with Bocardo, the Indirect Reduction proceeds by substi- tuting for the Major Premise the contradictory of the Conclusion ; thus again obtaining the premises of a syllogism in Barbara, whose con- clusion is contradictory of the original Major premise. Hence the initial B in Baroco and Bocardo : it points to a syllogism in Barbara as the means of Indirect Reduction {Reductio ad impossibile). Any other Mood may be reduced indirectly : as, for example, Dimaris. If this is supposed to be invalid and the conclusion false, substitute the contradictory of the conclusion for the Major premise, thus obtaining the premises of Celarent : Dimaris. Some P is M ; ts All M is S : Some S is P. Celarent. No S is P ; All M is S : No M is P No P is M <- The conclusion of Celarent, simply converted, contradicts the original Major premise of Dimaris, and is therefore false. Therefore the Major of Celarent is false, and the conclusion of Dimaris is true. We might no LOGIC: DEDUCTIVE AND INDUCTIVE ^he MnS '°?f ""' "'"7°"ic names for the Indirect Reduction of all the Moods : the name of Dimaris would then be Cicari. § 9. The need or use of any Figure but the First, has been much discussed by Logicians. Since, in actual debate, argu- ments are rarely stated in syllogistic form ; and, therefore! if reduced to that form for closer scrutiny, generally have to be treated with some freedom ; why not always throw them at once into the First Figure ? That Figure has manifest advan- tages : it agrees directly with the Dictum; it gives conclusions m all four prepositional forms, and therefore serves every pur- pose of full affirmation or denial, of showing agreement or difference (total or partial), of establishing the contradictories of universal statements ; and it is the only Figure in which the subject and predicate of the conclusion occupy the same positions in the premises, so that the course of argument has in Its mere expression an easy and natural flow Still, the Second Figure has also a very natural air ,n some kinds of negative arguments. The parallelism of the two premises with the same predicate for Middle term, brings out very forcibly the necessary difference between the Major and Mmor terms that is involved in their opposite relations to the Middle. P ts not, whilst S is, M, says Cesare : that very neatly drives home the conviction that S is not P. Or perhaps even more naturally in Camestres : Deer do, oxen do not, shed their horns. What is the conclusion .' The Third Figure, again, furnishes in Darapti and Felapton the most natural forms of stating arguments in which the Middle term is singular : Socrates was truthful; Socrates was a Greek : .'. Some Greek was truthful. Reduchg this to Fig. I., we should get for the Minor premise. Some Greek was Socrates : which is certainly inelegant. Still, it might be urged that in the science of proof, elegance is an alto- gether extraneous consideration. And as for the other advantage CATEGORICAL SYLLOGISMS III { ! I claimed for Fig. III.— that, as ityields only particular conclusions, it is useful in establishing contradictories against universals— I do not see that for that purpose any of its Moods have a superiority over Darii and Ferio. As for Fig. IV., no particular advantage is claimed for it. It is of comparatively late recognition (sometimes called the *Galenian', after Galen, its supposed discoverer); and its scientific claim to exist at all is disputed. It is said to be a mere inversion of Fig. I. ; which is not true in any sense in which Figs. II. and III. may not be condemned as partial inversions of Fig. I., and as having therefore still less claim to recognition. It is also said to invert the order of thought ; as if thought had only one order, or as if the mere order of thought had anything to do with Formal Logic. The truth is that, if distinction of Figure be recognised at all, the Fourth Figure is scientifically necessary, because it is inevitably generated by an analysis of the possible positions of the Middle Term. § 10. Is Reduction necessary, however; or have not all the Figures equal and independent validity? In one sense not only every Figure but each Mood has independent validity : for any one capable of abstract thinking sees its validity by direct inspection. But this is true not only of the abstract Moods, but very commonly of particular concrete arguments. Science, however, aims at unifying knowledge; and after reducing all possible arguments that form categorical syllogisms to the nineteen Moods, it is but another step in the same direction to reduce these Moods to one form. This is the very nature of science : and, accordingly, I cannot look without wonder at the efforts of some Logicians to expound separate principles of each Figure. Grant that they succeed ; and what can the next step be, but either to reduce these principles to the Dictum, or the Dictum and the rest to one of these principles ? Unless this can be done there is no science of Formal Logic. If it is done, what is gained by reducing the principles of the other Figures to the Dictum, instead of 112 LOGIC: DEDUCTIVE AND INDUCTIVE CATEGORICAL SYLLOGISMS "3 the Moods of the other Figures to those of the first Figure ? It may, perhaps, be said that to show (i) that the Moods of the second, third, and fourth Figures flow from their own principles (though, in fact, these principles are laboriously adapted to the Moods) ; and (2) that these principles may be derived from the Dictum^ is the more uncompromisingly regular method ; but, on the whole, is not Formal Logic aheady sufficiently encumbered with formalities ? § II. Euler's diagrams may be used to illustrate the syllogism, thus : Fig. 8. Fig. 5. Barbara — Fig. 6. Celarent Fig. 7. Remembering that ' Some' means * It may be all,' it is plain that any one of these diagrams in Fig. 7, or the one given above for Barbara, may represent the denotative relations of P, M and S in Darii; though no doubt the diagram we generally think of as representing it is No. i. in Fig. 7. Ferio Here again, I suppose, we generally think of No. i as the diagram representing Ferio ; but 2, or 3, or that given above for Celarent, is compatible with the premises. Students will do well to work out the diagrams for the Moods of the other Figures, noticing how they stand related to the above. II CHAPTER XI ABBREVIATED AND COMPOUND ARGUMENTS § I In ordinary discussion, whether oral or written, it is but rarely that the forms of Logic are closely adhered to. We often leave wide gaps in the structure of our arguments, trust- ing the intelligence of those addressed to bridge them over ; or we invert the regular order of propositions, begmnmg with the conclusion, and mentioning the premises, perhaps, a good while after, confident that the sagacity of our audience will make all smooth. Sometimes a full style, like Macaulay's, may by means of amplification and illustration, spread the elements of a single syllogism over several pages-a penny- worth of logic steeped in so much eloquence. These practices give a great advantage to sophists ; who would find it very inconvenient to state explicitly in Mood and Figure the preten- tious antilogies which they foist upon the public ; and, indeed, such licences of composition often prevent honest men from detecting errors into which they themselves have unwittingly fallen, and which, with the best intentions, they strive to com- municate to others : but we put up with these drawbacks to avoid the inelegance (forsooth) and the tedium of a long dis- course in accurate syllogisms. Many departures from the strictly logical statement of reasonings, consist in the use of vague or figurative language, or in the substitution for one another of expressions supposed to be equivalent though, in fact, dangerously discrepant. Against such occasions of error the logician can provide no safeguard, except the advice to be careful and discriminating ABBREVIATED ARGUMENTS "5 in what you say or hear. But as to any derangement of the elements of an argument, or the omission of them, Logic effectually aids the task of restoration ; for it has shown what the elements are that enter into the explicit statement of most ratiocinations, namely, the four forms of propositions ; and what that connected order of propositions is which most easily and surely exposes the validity or invalidity of reasoning, namely, the Premises and Conclusion of the Syllogism. Logic has even gone so far as to name certain abbreviated forms of proof, which may be regarded as general types of those that actually occur in debate, in leading articles, pamphlets and other persuasive or polemical writings— namely, the Enthy- meme, Epicheirema and Sorites. § 2. The Enthymeme, according to Aristotle, is the Syllo- gism of probable reasoning about practical affairs and matters of opinion, in contrast with the Syllogism of theoretical de- monstration from necessary grounds. But, as now commonly treated, it is an argument with one of its elements omitted ; a Categorical Syllogism, having one or other of its Premises, or else its Conclusion, suppressed. If the Major Premise is sup- pressed, it is called an Enthymeme of the First Order ; if the Minor Premise is wanting, it is said to be of the Second Order; if the Conclusion is left to be understood, there is an Enthy- meme of the Third Order. Let the following be a complete Syllogism : All free nations are enterprising ; The Dutch are a free nation : .-. The Dutch are enterprising. Reduced to Enthymemes this argument may be put thus : In the First Order— The Dutch are a free nation : /. The Dutch are enterprising. In the Second Order — All free nations are enterprising : .-, The Dutch are enterprising. ii6 LOGIC: DEDUCTIVE AND INDUCTIVE In the Third Order- All free nations are enterprising ; And the Dutch are a free nation. It is certainly very common to meet with arguments whose statement may be represented by one or other of these three forms ; indeed the Enthymene is the natural substitute for a full Syllogism in oratory : whence the transition from Aristotle's to the modern meaning of the term. The most unschooled of men readily apprehend its force ; and a student of Logic can easily supply the proposition that may be wanted, in any case, to complete a Syllogism, and thereby test the argument's formal validity. In an Enthymene of the Third Order, especially, to supply the Conclusion cannot present any difficulty at all ; and hence it is a favourite vehicle of innuendo ; as in Hamilton's example — Every liar is a coward ; And Caius is a liar. The frankness of this statement and its reticence, together, make it a biting sarcasm upon Caius. To find the missing Premise in an Enthymene of either the First or Second Order, a simple rule may be given : Take that Term of the given Premise that does not occur in the Conclusion (and which must therefore be the Middle), and combine it with that Term of the Conclu- sion that does not occur in the given Premise; the proposition thus formed is the Premise which was requisite to complete the Syllogism. If the Premise thus constituted contain the predicate of the Conclusion, the Enthymene was of the First Order ; if it contain the Subject of the Conclusion, the Enthymene was of the Second Order. To reduce the argument of any ordinary discourse to logical forms, the first care should be to make it clear to oneself what exactly the Conclusion is, and to state it adequately but as succinctly as possible. Then look for the evidence. This may be of an inductive character, consisting of instances, examples, analogies ; and, if so, of course its cogency must be evalued by the principles of Induction, which we shall presently investigate. But if the evidence is deductive, it will probably consist of an Enthymene, or of several Enthymenes one depending on another. Each Enthymene may be isolated and expanded into a Syllogism. And we may then inquire; (i) whether the Syllogisms are formally correct according to Barbara (or whatever the appropriate Mood) ; (2) whether the Premises, or the ultimate Premises, are true in fact. § 3. A Monosyllogism is a syllogism considered as standing alone or without relation to other arguments. But, of course, ABBREVIATED ARGUMENTS 117 a disputant may be asked to prove the premises of any syllo- gism ; in which case other syllogisms may be advanced for that purpose. When the conclusion of one syllogism is used to prove another, we have a chain-argument ; which, stated at full length, is a Polysyllogism. In any Polysyllogism, again, a syllogism whose conclusion is used as the premise of another, is called in relation to that other a Prosyllogism ; whilst a syllo- gism, one of whose premises is the conclusion of another syllogism, is in relation to that other an Episyllogism. Two modes of abbreviating a Polysyllogism are usually discussed, the Epicheirema and the Sorites. § 4. An Epicheirema is a syllogism for one or both of whose premises a reason is added ; as — All men are mortal, for they are animals ; Socrates is a man, for rational bipeds are men ; .'. Socrates is mortal. The Epicheirema is called Single or Double, says Hamilton, according as an " adscititious proposition " attaches to one or both of the premises. The above example is of the double kind. The Single are said to be of the First Order, if the adscititious proposition attaches to the Major Premise ; if to the Minor, of the Second Order. (Hamilton : Lecture xix.) An Epicheirema then is an abbreviated chain of reasoning, or Polysyllogism, comprising an Episyllogism with one or two enthymematic Prosyllogisms. The Major Premise in the above case. All meti are mortal, for they are animals, is an Enthymeme of the First Order, suppressing its own Major Pre- mise, and may be restored thus : All animals are mortal \ All men are animals ; .*. All men are mortal. The Minor Premise, however, is an Enthymeme of the Second Order, suppressing its Minor Premise, and may be restored thus : ! ii8 LOGIC: DEDUCTIVE AND INDUCTIVE All rational bipeds are men ; Socrates is a rational biped : ;. Socrates is a man. § 5. The Sorites is a Pol> syllogism in which the Conclusions and even some of the Premises, are suppressed until the argu- ment ends. If the chain of arguments were freed of its enthymematic character, the suppressed Conclusions would of course appear as Premises of Episyllogisms. Two varieties of Sorites are recognised, the Aristotelian (so called, though not treated of by Aristotle), and the Goclenian (named after its discoverer, Goclenius of Marburg, who flourished about 1600 A.D.). In order to compare these two forms of argument, it will be convenient to place side by side Hamilton's classical examples of them. Aristotelian. Bucephalus is a horse ; A horse is a quadruped ; A quadruped is an animal ; An animal is a substance ; Bucephalus is a substance. Goclenian. An animal is a substance ; A quadruped is an animal ; A horse is a quadruped ; Bucephalus is a horse ; Bucephalus is a substance. The reader wonders what is the diff'erence between these two forms. Of course, in the Aristotelian Sorites the Minor Term occurs in the first Premise, and the Major Term in the last ; whilst in the Goclenian the Major Term occurs in the first, and the Minor in the last. But since the character of Premises is fixed by their Terms, not by the order in which they are written, there cannot be a better example of a distinction with- out a difference. At a first glance, indeed, there may seem to be a more important point involved: the Premises of the Aristotelian Sorites seem to proceed in the order of the Fourth Figure. But if that were really so the Conclusion would be, Some substance is Bucephalus. That, on the contrary, every one writes the Conclusion, Bucephalus is a substance, proves that the logical order of the Premises is in the First Figure. Logi- cally, therefore, there is absolutely no difference between these ABBREVIATED ARGUMENTS 119 two forms, and pure reason requires that the "Aristotelian Sorites" disappear from the text-books. It is the shining merit of Goclenius to have restored the Premises of the Sorites to the usual order of Fig. i . : whereby he has raised to himsel a monument more durable than brass, and secured indeed the very cheapest immortality. How expensive, compared with this, was the method of that Ephesian incendiary ! The common Sorites, then, being in the First Figure, its rules follow from those of the First Figure : (i) Only one Premise can be particular; and, if any, only that in which the Minor Term occurs. For, just as in Fig. I., a particular Premise anywhere else involves Undistributed Middle. (2) Only one Premise can be negative; and, if any, only that in which the Major Term occurs. For if there were two negative premises, at the point where the second entered the chain of argument there must be a Syllogism with two negative premises, which is contrary to Rule 5 ; whilst if one pre- mise be negative it must be that which contains the Major Term, for the same reason as in Fig. I. , namely, that the Conclusion will be nega- tive, and that therefore only a negative Major Premise can prevent Illicit Process of the Major Term. If we expand a Sorites into its constituent Syllogisms, the conclusions successively suppressed will reappear as Major Premises ; thus : (i) An animal is a substance ; A quadruped is an animal ; /. A quadruped is a substance. {2) A quadruped is a substance ; A horse is a quadruped ; .'. A horse is a substance. (3) A horse is a substance ; Bucephalus is a horse ; .'. Bucephalus is a substance. This suffices to show that the Protosyllogism of a Goclenian Sorites is an Enthymeme of the Third Order ; after which the argument is a chain of Enthymemes of the First Order, or even of the First and Third combined, since the Conclusions as well as the Major Premises are omitted, except in the last one. Lest it should be thought that the Sorites is only good for arguments so frivolous as the above, I subjoin an example collected from various parts of Mill's Political Economy : — I20 LOGIC: DEDUCTIVE AND INDUCTIVE The cost of labour depends on the efficiency of labour ; The rate of profits depends on the cost of labour ; The investment of capital depends on the rate of profits ; Wages depend on the investment of capital ; .-. Wages depend on the efficiency of labour. Had it occurred to Mill to construct this Sorites, he would have modified his doctrine of the Wages-Fund, and would have saved many critics from the malignant joy of refuting him. § 6. The Antinomy is a combination of arguments by which contradictory attributes are provtd to be predicable of the same subject. In symbols, thus : All U is P AH N is p All S is M All S is N All S is P All S is p Now, by the principle of Contradiction, S cannot be P and p (not-P) : therefore, if both of the above syllogisms are sound, S cannot exist at all. The contradictory conclusions are called, respectively, Thesis and Antithesis. To come to particulars, w^e may argue ; (i) that a constitu- tion which is at once a monarchy, an aristocracy and a de- mocracy, must comprise the best elements of all three forms ; and must, therefore, be the best of all forms of government ; the British Constitution is, therefore, the best of all. But (2) such a constitution must also comprise the worst elements of monarchy, aristocracy and democracy ; and, therefore, must be the worst of all forms. Are we, then, driven to conclude that the British Constitution, thus proved to be both the best and worst, does not really exist at all, being logically impos- sible ? For the proofs seem to me equally good. Again, (i) Every being who is responsible for his actions is free ; Man is responsible for his actions : .-. Man is free. (2) Every being whose actions enter into the course of nature is not free ; Man is such a being : .-. Man is not free. ABBREVIATED ARGUMENTS 121 Does it, then, follow that ' Man,' as the subject of contradictory attributes, is a nonentity ? This doctrine, or something like it, has been seriously entertained ; but if to any reader it seems extravagant (as it certainly does to me), lie will no doubt find an error in the above arguments. For other examples it is enough to refer to the Critique of Pure Reasoft, where Kant sets out the Antinomies of Rational Cosmology. But even if we do not agree with Kant that the human understanding, in attempting to deal with certain subjects beyond its reach, inevitably falls into such contradic- tory reasonings; yet it can hardly be doubted that we not unfrequently hold opinions which, if logically developed, result in Antinomies. And, accordingly, the Antinomy, if it cannot be imputed to Reason herself, may be a very fair, and a very wholesome, argumentum ad hominetn. J CHAPTER XII CONDITIONAL SYLLOGISMS § I. Conditional Syllogisms may be generally described as those that contain conditional propositions. They are usually divided into two classes, Hypothetical and Disjunctive. A Hypothetical Syllogism is one that consists of a Hypo- thetical Major Premise, a Categorical Minor Premise, and a Categorical Conclusion. Two Moods are usually recognised : (i) Modus J>onef IS, or Constructive. If A is B, C is D ; AisB: .-. C is D. If Aristotle's reasoning is conclusive, Plato's theory of Ideas is erroneous ; Aristotle's reasoning is conclusive : .'. Plato's theory of Ideas is erroneous. Rule of the Modus ponens : The Antecedent of the Major Premise being affirmed in the Minor Premise, the Consequent is also affirmed in the Conclusion. (2) Modus tollens, or Destructive. If A is B, Cis D; C is not D ; .". A is not B. If Pythagoras is to be trusted, Justice is a number; Justice is not a number: .*, Pythagoras is not to be trusted. Rule of the Modus tollens : The Consequent of the Major CONDITIONAL SYLLOGISMS 123 f Premise being denied in the Minor Premise, the Antecedent is denied in the Conclusion. By using negative Major Premises two other forms are obtainable: then, either by affirming the Antecedent or by denying the Consequent, we draw a negative Conclusion. Thus {Modus ponens) : {Modus tollens) : If A is B, C is not D; If A is B, C is not D; AisB: CisD: .'. C is not D. .-. A is not B. Further, since the Antecedent of the Major Premise, taken by itself, may be negative, it seems possible to obtain four more forms, two in each Mood, from the following Major Premises : (i) If A is not B, Cis D; (2) If A is not B, C is not D. But since the quality of a Hypothetical Proposition is determined by the quality of its Consequent, not at all by the quality of its Ante- cedent, I do not see how we can get from these two Major Premises any really new Moods, that is to say, Moods exhibiting any formal difference from the four previously expounded. Recognising these four, however, would it not be well to make the names ' Constructive ' and ' Destruc- tive • not synonymous with Modus ponens and Modus tollens respectively, but applicable thus : * Constructive ' to that form of the Modus ponens that has an affirmative Conclusion, and ' Destructive ' to the other three Syllogisms that conclude in the negative ? It must be carefully observed that, given the Hypothetical Major Premise — If A is B, C is D— we cannot by denying the Antecedent infer a denial of the Consequent. That A is B, is a mark of C being D ; but we are not told that it is the sole and indispensable condition of it. If men read good books, they acquire knowledge ; but they may acquire knowledge by other means, as by observation. For the same reason, we cannot by affirming the Consequent infer the affirmation of the Antecedent : Caius may have acquired knowledge ; but we cannot thence conclude that he has read good books. 124 LOGIC: DEDUCTIVE AND INDUCTIVE To see this in another light, let us recall chap. v. § 4, where it was shown that a Hypothetical Proposition may be translated into a Categorical one; whence it follows that a Hypothetical Syllogism may be translated into a Categorical Syllogism. Treating the above examples thus, we find that the Modus poncns takes the form of Barbara, and the Modus tollens the form of Camestres : Modus ponens. Barbara. If A is B, C is D ; The case of A being B is a case of C being D : A is B : This is a case of A being B : .-. C is D. .-. This is a case of C being D. Now if, instead of this, we affirm the Consequent, to form the new Minor Premise, This is a case of C being D, there will be a Syllogism in the Second Figure with two affirmative premises, and therefore the fallacy of Undistributed Middle. Again : Modus tollens. Camestres. If A is B, C is D ; The case of A being B is a case of C being D ; C is not D : This is not a case of C being D : .'. A is not B. .'. This is not a case of A being B. But if, instead of this, we deny the Antecedent, to form the new Minor Premise, This is not a case of A being B, there arises a Syllogism in the First Figure with a negative Minor Premise, and therefore the fallacy of Illicit Process of the Major Term. By thus reducing the Hypothetical Syllogism to the Categorical form, what is lost in elegance is gained in intelligibility. For, first, we may justify ourselves in speaking of the Hypothetical Premise as the Major, and of the Categorical Premise as the Minor ; since in the Categorical form they contain respectively the Major and Minor Terms. And, secondly, we may justify ourselves in treating the Hypothetical Syllogism as a kind of Mediate Inference, in spite of the fact that in the Hypo- thetical Syllogism there are not two Terms compared by means of a third ; since in the Categorical form such Terms distinctly appear : a new Term (' This') emerges in the position of the Minor ; the place of the Middle is filled by the Antecedent of the Major Premise in the Modus poncns, and by the Consequent in the Modus tollens. In fact, the mediate element of the inference in a Hypothetical Syllogism consists in asserting, or denying, the fulfilment of a given condition. In the Hypothetical Proposition, If A is B. C is D, the Antecedent, A is B, is the conditio sufficiens, or mark, of the Conse- quent, C is D ; and therefore the Consequent, C is D, is a conditio sine 1 CONDITIONAL SYLLOGISMS 125 qua non of the antecedent, A is B; and it is by means of affirming the former condition, or else denying the latter, that a conclusion is rendered possible. Indeed, we need not say that the element of mediation consists in affirming, or denying, the fulfilment of a given con- dition : It is enough to say 'in affirming.' For thus to explain the Modus tollens. reduce it to the Modus ponens (contrapositing the Major) : Celarent. If A is B, C is D : The case of C not being D is a case .-. It C IS not D, A is not B ; of A not being B ; C is not D : This is a case of C not being D : •'• ^ ^^ "°^ ^- •". This is a case of A not being B. The above four forms commonly treated of as Hypothetical Syllogisms, are called by Ueberweg and Dr. Keynes 'Hypo- thetico-Categorical.' Ueberweg restricts the name 'Hypo- thetical ' simply (and Dr. Keynes the name * Conditional ') to such Syllogisms as the following, having two Hypothetical Premises : IfCis D, EisF; If A is B, C is D : .'. If A is B, E is F. If we recognise Particular Hypothetical Propositions (see chap. V. § 4), it is obvious that such Syllogisms may be constructed in all the Moods and Figures of the Categorical Syllogism; and of course they may be translated into^'cate- goricals. We often reason in this hypothetical way. For example : If the margin ot cultivation be extended, rents will rise; If prices of produce rise, the margin of cultivation will be extended. .-. If prices of produce rise, rents will rise. But it may be noticed that the purpose of the Hypothetical Syllogism (commonly so called), as also of the Disjunctive (to be discussed in the next section) is to get rid of the conditional element and obtain a decisive Categorical Conclusion ; whereas these Syllogyisms with two Hypothetical Premises, leave us still with a Hypothetical Conclusion. This circumstance seems to 126 LOGIC: DEDUCTIVE AND INDUCTIVE me to ally them more closely with Categorical Syllogisms than with those that are discussed in the present chapter ; they are Categoricals in disguise: and, accordingly, in applying the name ' Hypothetical Syllogism,' I have not seen fit to depart from the older usage. ^ . § 2. A Disjunctive Syllogism consists of a Disjunctive Major Premise, a Categorical Minor Premise, and a Categorical Con- clusion. • 1 • J How many Moods are to be recognised in this kmd of argument depends on whether the alternatives of the Dis- junctive Premise are regarded as mutually exclusive or possibly coincident. In saying ' Either A is B, or C is D,' do we mean ' either, but not both,' or ' either, it may be both ' ? (See chap. v. When the alternatives of the Disjunctive are not exclusive, we have only the Modus tollendo pofiens. Either A is B, or C is D ; A is not B (or C is not D) : /. C is D (A is B). Either wages fall, or the weaker hands are dismissed ; Wages do not fall : .-. The weaker hands are dismissed. But we cannot argue — Wages fall : /. The weaker hands are not dismissed ; since in ' hard times ' both events may happen together. Rule of the Modus tollendo ponens : If one alternative is denied, the other is affirmed. When, however, the alternatives of the Disjunctive are mutually exclusive, we have also the Modus ponendo tollens. Either A is B, or C is D ; AisB; (orCisD): .-. C is not D (A is not B). CONDITIONAL SYLLOGISMS 127 Either the Tories or the Whigs win the election ; The Tories win : .'. The Whigs do not win. We may also, of course, argue as above in the Modus tollendo ponens— The Tories do not win : .*. The Whigs do. In this case, to make the Modus tollendo ponens materially valid, it must be impossible that the election should result in a tie. The danger of the Disjunctive proposition is that the alternatives may not, between them, exhaust the possible cases. Only contradictory alternatives are sure to cover the whole ground. Rule of the Modus ponendo tollens : If one alternative of the Disjunctive be affirmed, the other is denied. Since a Disjunctive Proposition may be turned into a Hypothetical Proposition (chap. v. § 4), a Disjunctive Syllogism may be turned into a Hypothetical Syllogism : Modus tollendo ponens. Modus ponens. Either A is B or C is D ; If A is not B, C is D ; A is not B : A is not B : ••• CisD. ... CisD. Similarly the Modus ponendo tollens is equivalent to that kind of Modus ponens that may be formed with a negative Major Premise; for if the alternatives of a Disjunctive proposition be exclusive, the corre- sponding Hypothetical may be affirmative or negative : Modus ponendo tollens. Modus ponens. Either A is B, or C is D ; If A is B, C is not D ; A is B : A is B ; .'. C is not D. .-. C is not D. Hence, finally, a Disjunctive Syllogism being equivalent to a Hypo- thetical, and a Hypothetical to a Categorical ; a Disjunctive is equiva- lent and reducible to a Categorical. It is a form of Mediate Inference in the same sense as the Hypothetical Syllogism is ; that is to say, the Conclusion depends upon an affirmation, or denial, of the fulfilment of a condition implied in the Disjunctive Major Premise. § 3. The Dilemma is perhaps the most popularly interesting of all forms of proof. It is a favourite weapon of orators and wits ; and " impaled upon the horns of a dilemma " is a painful situation in which every one delights to see his adversary. It seems to have been described by Rhetoricians before finding its way into works on Logic; and Logicians, to judge from i I 128 LOGIC: DEDUCTIVE AND INDUCTIVE their diverse ways of defining it, have found some difficulty in making up their minds as to its exact character. There is a famous Dilemma employed by Demosthenes, from which the general nature of the argument may be gathered : If ^.schines joined in the public rejoicings, he is inconsis- tent ; if he did not, he is unpatriotic : But either he joined, or he did not join : Therefore, he is either inconsistent or unpatriotic. That is, reduced to symbols : If A is B, CisD; and if E is F, G is H : ^ But either A is B, or E is F : ^ :. Either C is D or G is H {Complex Constructive). Now, plainly, this is a compound Conditional Syllogism, which may be analysed as follows : Either A is B or E is F. Suppose that E is not F : Suppose that A is not B : Then A is B. Then E is F. But if A is B, C is D; But if E is F, G is H; (AisB): (EisF:) .-. C is D. .-. G is H. .• Either C is D or G is H. A Dilemma, then, is a compound Conditional Syllogism, having for its Major Premise two Hypothetical Propositions, and for its Minor Premise a Disjunctive Proposition, whose ahernative Terms either affirm the Antecedents or deny the Consequents of the two Hypothetical Propositions forming the Major Premise. The Hypotheticals in the Major Premise, may have all four Terms distinct (as in the above example) ; and then the Con- clusion is a Disjunctive Proposition, and the Dilemma is said to* be Complex. Or the two Hypotheticals may have a common Antecedent or a common Consequent; and then the Conclusion is a Categorical Proposition, and the Dilemma is said to be Simple, CONDITIONAL SYLLOGISMS 129 Again, the alternatives of the Disjunctive Minor Premise may be Affirmative or Negative. If Affirmative, the Dilemma IS called Constructive ; and if Negative, Destructive. However, seeing that the Dilemma is a compound Conditional Syllogism' It would surely be better to name its Moods after the cor- responding Moods of the Hypothetical Syllogism— i^^^/^i- ponens and Modus tolleus. If, then, we use only affirmative Hypotheticals in the Major Premise, there are four Moods : I. The Simple Modus ponens (or, Constructive). If AjsJ, C is D; and if E is F, C is D : But either A is B, or E is F: .-. C is D. If the Tories win the election, the Government will avoid innovation ; and if the Whigs win, the House of Lords will prevent them innovating : But either the Tories or the Whigs will win ; .'. Innovation is improbable. 2. The Complex Modus pone?is (or, Constructive). If AisB^ CisD: andifE^F, GisH: But either A is B, or eITF: .-. Either C is D, or G is H. If Appearance is all that exists. Reality is a delusion ; and if there is a Substance beyond Consciousness, Know- ledge of Reality is impossible : But either Appearance is all, or there is a Substance beyond Consciousness : .-. Either Reality is a delusion, or a knowledge of it is im- possible. 3. Simple Modus tollens (or Destructive). If A is B, C is D; and if A is B, E is F : But either C is not D, or E is not F : .'. A is not B. If table-rappers are to be trusted, the departed are spirits; and they also exert mechanical energy : I30 LOGIC: DEDUCTIVE AND INDUCTIVE But either the departed are not spirits, or they do not exert mechanical energy : .'. Table-rappers are not to be trusted. 4. Complex Modus tollens (or, Destructive). If A is B, C is D ; and if E is F, (; is H : But either C is not D, or G is not H : .-. Either A is not B, or E is not F. If poetic justice is observed, virtue is rewarded ; and if the mirror is held up to Nature, the villain triumphs : But either virtue is not rewarded, or the villain does not triumph : /. Either poetic justice is not observed, or the mirror is not held up to Nature. These then are the four Moods of the Dilemma that emer-e if we use only affirmative Hypothetical for the Major Premise ; but. certainly it is often quite as natural to employ two negative Hypotheticals (indeed one might be affirmative and the other negative ; but waive that) ; and then four more Moods emerge, all having negative Conclusions. But it is needless to intimidate the reader by drawing up these four Moods in battle array. Of course, they always admit of reduction to the fore- going Moods by obverting the Hypotheticals ; but by the same process we may greatly decrease the number of Moods of the Categorical Syllogism ; so that I am afraid that this objection to them will be thought to prove too much. Just as some Syllogisms are most simply expressed in Celarent or Cesare, so some Dilemmas are most simply stated with negative Major Premises-^.^'. : The simple Modus Poncns above given would run more naturally thus: // the Tories win, the Government will not innovate; and if the Whigs, the Lords will not let them : and similarly Demosthenes' Dilemma— 7/ JEschines joined, he ts not con- sistent: and if he did not, he is not patriotic. Moreover, the propriety of recognising Dilemmas with negative Major Premises, follows from the above analysis of the Dilemma into a combination of Hypothetical Syllogisms, even if (as in § i of this chapter) we take account of only four Moods of the Hypothetical Syllogism. In the rhetorical use of the Dilemma, it may be observed that the Disjunction in the minor premise ought to be ob\-ious, or (at any rate) easily acceptable to the audience. Thus. Either the Tories or the Whigs will win ; Either ALschines joined in the rejoicings, or he did not; such propo- sitions are not likely to be disputed. But if the orator must stop to prove his Minor Premise, the smacking effect of this figure (if the expression be allowed) will be lost. Hence the Minor Premises of CONDITIONAL SYLLOGISMS stde^ntToTSlf ^t\ '' ^- ^ -^-t audience, ^ mechanical ..^r .^^^Tl^^ :;" ^'\ ^.^ '' ""'' ''''' taught by physical philosophers 7h!^ t P^^"^^?^^. generally energy; and that £.L jf ^^^^^ ^^ ^^e vehicle of consciousness, is a doctrine whtl! 1 ' '' ^^'''' '' ^ ^"^^^^^^^ ^^yond be expected to tde sta^d^ metaphysical philosophers could expected to agree Hot'^^^^^ "pon which they could not be junction may not'be reX t ^ ^^ ^""^'' ^' ^^^* ^ P^^^^^^le dis- does not allow fo^a ^eZ ^:::::z^::i SiS:^' - '^rr resistance would be vain • x.^f 1, / ^ ^ movement where sistent with subse'uenTcon' ra'o~ or.h^ " "f ""' "^ '"^- patible with patriotic reserve Zd "on a taeTth::';":","""'-'"^"™- premature and ominous ^^ rejoicings are way, sho„M ^^::^l^!::s:^^'77:^^::^''^''-'-- sistent or unpatriotic ■ : horrid words to a poiuldan' • Eitt '",°"" or no possible knowledge ■ ■ very disaDnoinHno. * ' "° ""^^'"y Thus the Disjunctive Conclu'on 'sTC lo .? ""°"' """""^ ' Categorical one in a Simple Dilemma °PP°"'"' ^^ *'^ Logicians further speak of the Trilemma, with three Hyno thetcals and a corresponding triple Disjunction; and of a Polylemma, w,th any further number of perplexities. But any one who has a taste for mere logical forms may haye it a L p ' gratified m numerous text-books. Indeed there are so Zy opportun,t,es of deyeloping such forms that, if i "e'ioZ enough, a .nan may still hope to discoyer some quUe " w one. and qu.te „,„ocently, as long as he does n't pu.^ ^ 1 TRANSITION TO INDUCTION CHAPTER XIII TRANSITION TO INDUCTION § I. Having now discussed Terms, Propositions, Immediate and Mediate ^Inferences, and investigated the conditions of Formal Truth or Consistency, we have next to consider the conditions of Material Truth : whether (or how far) it is possible to arrive at propositions that represent the course of nature and human life. Hitherto we have dealt with no sort of proof that gives any such assurance. A valid Syllogism guarantees the truth of its Conclusion, provided the Premises be true : but what of the Premises ? The relation between the Premises of a valid Syllogism and its Conclusion is indeed the same as the relation between the Antecedent and Conse- quent of a Hypothetical Proposition. If A is B, C is D : grant that A is B, and it follows that C is D ; and, similarly, grant the Premises of a Syllogism, and the Conclusion follows. Again, grant that C is not D, and it follows that A is not B ; and, similarly, if the Conclusion of a valid Syllogism be false, it follows that one, or other, or both of the Premises must be false, or else that they are illicitly connected. But, once more, grant that C is D, and it does not follow that A is B ; so neither, if the Conclusion of a Syllogism be true, does it follow that the Premises are. For example :— Geology is an exact science ; Mathematics is a branch of Geology ; . . Mathematics is an exact science. Here the conclusion is true although the Premises are absurd. Or again : — f ^33 Mathematics is an exact science ; Geology is a branch of Mathematics : .*. Geology is an exact science. Here the Major Premise is true, but the Minor is false, and the Conclusion is false. In both cases, however, whether the Con- clusion be true or false, it equally follows from the Premises, if there is any cogency in Barbara. The explanation of this is that Barbara has only formal cogency ; and that whether the conclusion of that, or any other valid Mood, shall be true according to fact and experience, depends upon how the form is filled up. How to establish the Premises, then, is the most important problem ; and it still remains to be solved. § 2. We may begin by recalling the distinction between the Denotation and Connotation of a General Term : the Denota- tion comprising the things or events which the Term is a name for; the Connotation comprising the common qualities on account of which these things are called by the same name. Obviously, there are very few General Terms whose denotation is exhaustively known ; since the denotation of a General Term comprises all the things that have its connotation, or that ever have had, or that ever will have it, whether they exist here, or in Australia, or in the Moon, or in the utmost stars. No one has examined all men, all dogs, all falling bodies, all cases of fever, all crystals, all mammoths, all revolutions, all stars— nor even all planets, since from time to time new ones are discerned. We have names for animals that existed long before there were men to observe them, and of which we know only a few bones the remains of multitudinous species: others may continue to exist when men have disappeared from the earth. If, indeed, we definitely limit the time, or place, or quantity of matter to be explored, we may sometimes learn, within the given limits, all that we are concerned about : as all the bones of a paiticular animal, or the list of English monarchs hitherto or the names of all the members of the House of Commons at the present time. Such cases, however, do not invalidate the above logical truth that few General Terms are exhaustively I ,34 LOGIC: DEDUCTIVE AND INDUCTIVE known in their denotation ; for the very fact of assigning limits of time and place impairs the generality of a Term. Ihe bones of a certain animal may be all examined, but not the bones of all animals, nor even of one species. The English monarchs that have reigned hitherto may be known, but there may be many still to reign. The General Terms, then, with which Logic is chiefly concerned, the names of Causes and Kinds, such as gravita- tion, diseases, social events, minerals, plants and animals, sfand for some facts that are, or have been, known, and for a great many other similar ones that have not been, and never will be, known. Hence the use of a General Term depends not upon our direct knowledge of everything comprised in its denotation, but upon our readiness to apply it to anything that has its connotation, whether we have seen the thing or not, and even though we never can see it ; as when a man talks freely of the ichthyosaurus, or of the central heat of planets, or of atoms and ether. , Hence Universal Propositions, which consist of General Terms, deceive us, if we suppose that their predicates are directly known to be related to all the facts denoted by their subjects. In exceptional cases, in which the denotation of a subject is intentionally limited, such exhaustive direct know- ledge may be possible ; as that " all the bones of a certain animal consist of phosphate of lime," or that every member of the present Parliament wears a black silk hat. But what predication is possible concerning the hats of all members of Parliament from the beginning? Ordinarily, then, whilst the relation of predicate to subject has been observed in some cases, in much the greater number of cases our belief about it depends upon other evidence than observation, or may be said (in a certain sense) to be taken on trust. ' All rabbits are herbivorous ' : why do we believe that ? We may have seen a few wild rabbits feeding ; or have kept tame ones, and tried experiments with their diet ; or have read of their habits in a book of Natural History ; or have studied I r TRANSITION TO INDUCTION 135 the physiology of digestion in many sorts of animals : but with whatever care we add testimony and scientific method to our own observation, it still remains true that the rabbits observed by ourselves and others are few in comparison with those that live, have lived and will live. And the same truth might be shown to hold good of any other General Proposition ; for it plainly follows from the fact that the General Terms of which such propositions consist, are never exhaustively known in their denotation. What right have we then to state Universal Propositions ? That is the problem of Inductive Logic. § 3. Universal Propositions, of course, cannot always be proved by Syllogisms; because to prove an Universal Pro- position^ by a Syllogism, its premises must be Universal Propositions ; and, then, these must be proved by others, and so on for ever. In fact the Formal Syllogism is itself mis- leading, if the Universal Proposition is so : if we think that the premises prove the conclusion because they have been established by detailed observation, we are mistaken. The consideration of any example will show this. Suppose any one to argue : All ruminants are herbivorous ; Camels are ruminants : .*. Camels are herbivorous. Have we, then, examined all ruminants? If so, we must have examined all camels, and cannot need a syllogism to prove their herbivorous nature : instead of the Major Premise proving the Conclusion, the Conclusion must then be part of the proof of the Major Premise. But if we have not examined all ruminants, having omitted most giraffes, most deer, most camels, how do we know that the unexamined (say, some camels) are not exceptional ? Camels are vicious enough to be carnivorous ; and indeed it is said that Bactrian camels will eat flesh rather than starve, though of course their habit is herbivorous. Or, again, it is sometimes urged that — 136 LOGIC: DEDUCTIVE AND INDUCTIVE All empires decay : .'. Britain will decay. This is manifestly a prediction : at present Britain flourishes, and shows no signs of decay. Vet a knowledge of its decay seems necessary, to justify any one in asserting the given premise. If it is a question whether Britain will decay, to attempt (whilst several empires still flourish) to settle the matter by asserting that all empires decay, seems to be ' a begging of the question.' But although this case is a manifest prediction, it does not really diff^er from the last one ; for the proof that camels are herbivorous has no limits in time. If valid, it shows not only that they are, but also that they will be, herbivorous. Hence, to revert to a dilemma, it may be urged : If aU the facts of the Major Premise of any Syllogism have been examined, the Syllogism is needless ; and if some of them have not been examined, it is a petltio principii. But either all have been ex- amined, or some have not. Therefore, the Syllogism is either useless or fallacious. § 4. A way of escape from this dilemma is provided, how- ever, by distinguishing between the formal and material aspects of the Syllogism considered as a means of proof. It begs the question formally, but not materially ; that is to say, if it be a question whether camels are herbivorous, and to decide it we are told that 'all ruminants are,' laying stress upon the 'all,' as if all had been examined, though in fact camels have not been, then the question as to camels is begged. The form of an universal proposition is then offered as evidence, when in fact the evidence has not been universally ascertained. But if in urging that ' all ruminants are herb- ivorous ' no more is meant than that so many other ruminants of diff'erent species are known to be herbivorous, and that the ruminant stomach is so well adapted to a coarse vegetable diet, that the same habit may be expected in other ruminants, such as camels, the argument then rests upon material evidence without unfairly implying the case in question. TRANSITION TO INDUCTION 137 4 • ' Now the nature of the material evidence is plainly this, that the resemblance of camels to deer, oxen, etc.^ in the fact of chewing the cud, justifies us in believing that they have a further resemblance in the fact of feeding on herbs ; in other words, we assume that 7'esemblance is a ground of inference. Another way of putting this difficulty with regard to syllo- gistic evidence, which we have just been discussing, is to object that by the Laws of Syllogism a Conclusion must never go beyond the Premises, and that therefore no progress in knowledge can ever be established, except by direct observa- tion. Now, taking the Syllogism formally, this is true : if the Conclusions go beyond the Premises, there must be either four Terms, or illicit process of the Major or Minor Term. But taking it materially, the Conclusion may cover facts which were not in view when the Major Premise was laid down ; facts of which we predicate something not as the result of direct observation, but because they resemble in a certain way those facts which had been shown to carry the predicate when the Major Premise was formed. *What sort of resemblance is a sufficient ground of in- ference ? ' is, therefore, the important question alike in material Deduction and in Induction ; and we shall presently endeavour to answer it. In the above cases, the fact of chewing the cud is a strong ground for inferring vegetarianism ; the resemblance of Britain to other empires is a much less substantial basis for expecting her ultimate downfall. § 5. If, now, the material character of syllogistic proof is such as we have above described, in order to generalise it the axiom de onini et nullo needs to be restated. "That whatever is true of a whole class is true of everything the class includes," seems from our present point of view to be a dictum designed to justify the begging of the question. That whatever is true of all is true of some, is a merely formal subaltern inference : knowing 'all,' how can there be any question about the * some ' ? But if we do not know ' all,' not really the ' whole class,' we must write the dictum thus : Whatever we have reason \ 138 LOGIC: DEDUCTIVE AND INDUCTIVE to regard as constantly connected ivith the nature or connotation of a class or class-name, we may expect to be similarly connected with whatever can be shoivn to have that nature or connotation. Thus the feeding upon herbage, being connected with the nature of ruminants, is connected with camels, because they ruminate. Another way of putting this principle \^—Nota notcB, nota ret ipsius, ' the mark of a mark is a mark of the thing itself,' or * whatever has a mark has what it is a mark of.' A mark is anything (A) that is never found without something else (B) \ so that where we find A, B may be expected. Now a camel is a mark of ruminating ; and ruminating is a mark of feeding upon herbage : therefore, a camel is a mark of feeding upon herbage. § 6 I must add that, as we distinguish between the formal and material character of the Syllogism, so we ought in the case of Sub- alternation. To infer I. from A. may imply a real advance of knowledge, if the ' Some ' of the I. were not in view when ' All ' was attached to the subject of the A. Thus Britain will decay goes beyond the material grounds of All empires decay, n3.me\y. those known to have decayed: nevertheless it is a subaltern not a mediate inference ; smce such a Minor premise as Britain is an empire (only true in the form-' the British empire is an empire') is a verbal proposition in disguise, and adds nothing to the argument. If the inference Britain uill decay is doubtful it is not because a false Minor premise has been omitted by Enthymeme, but because the Subalternans is doubtful, because the empires that have been known to decay may not be fair examples of all empires. It should be expressed-^// empires having such or such characteristics. There is then room for a real Minor premise-T/«^ British empire has these characteristics ; and on whether that is true, or not. depends the value of the inference Britain will decay. Similarly, the stock example— yl// men are mortal; therefore, Socrates is mortal, is a Subalternation : for although the Minor premise. Socrates is a man, is a real proposition under the rule that proper names have no connotation ; yet this rule is suspended by the context or suppositio : we are talking of men. § 7. The Syllogism has sometimes been discarded by those who have only seen that, as formally stated, it is either useless or fallacious : but those who also perceive its material grounds, retain and defend it. In fact, great advantages are gained by TRANSITION TO INDUCTION J 39 i J stating an argument as a formal Syllogism. For, in the first place, we can then examine separately the three conditions on which the validity of the argument depends : (i) Are the Premises so connected that, // they are true, the Conclusion follows ? This depends upon the formal principles of chap. X. (2) Is the Minor Premise true? This question can only arise when the Minor Premise is a real proposition. That Britain is an empire affords no matter for doubt or inquiry ; but whether Britain resembles Egypt, Assyria, Rome in those circumstances that led to their decay, is a very difficult subject for investigation. That Camels are rumitiatits is now a verbal proposition to a Zoologist, but not to the rest of us ; and even to the Zoologist the ascertaining of the relation in which camels stand to such ruminants as oxen and deer, is not a matter of analysing words but of dissecting stomachs. (3) Is the Major Premise true ? Are all ruminants herbi- vorous ? If there be any exceptions to the rule, camels are likely enough to be among the exceptions. And here the need of Induction is most conspicuous : how can we prove our Premises ? A second advantage of the Syllogism is, that it makes us fully aware of what an inference implies. An inference must have some grounds, or else it is a mere prejudice ; but what- ever the grounds are, if they are sufficient in a particular case, they must be sufficient for all similar cases, they must admit of being generalised ; and to generafise the grounds of the in- ference, is nothing else than to state the Major Premise. If the evidence is sufficient to justify the argument that camels are herbivorous because they are ruminants, it must also justify the Major Premise, All ruminants are herbivorous ; for else the inference cannot really depend merely upon the fact of rumi- nating. To state our evidence syllogistically, then, must be possible, if the evidence is mediate and of a logical kind ; and to state it in this formal way, as depending on the truth of a general principle, the Major Premise, increases our sense of I40 LOGIC: DEDUCTIVE AND INDUCTIVE responsibility for the inference that is thus seen to imply so much; and if there are any negative instances within our knowledge, we are the more likely to remember them. The use of Syllogisms therefore is likely to strengthen our reason- ings. A third advantage is, that an accurate generalisation may be useful to others : it is indeed part of the systematic procedure of science. The memoranda of our Major Premises, or reasons for believing anything, may be referred to by those who come after us, and either confirmed or refuted. When such a memo- randum is used for further inferences, these inferences are said, in the language of Formal Logic, to be dv:x\\n from it, as if the Conclusion were contained in our knowledge of the Major Premise ; but, considering the limited extent of the material evidence, it is better to say that the inference is drawn accord/// 1^ to the memorandum or Major Premise, since the grounds of the Major Premise and of the Conclusion are in fact the same. We shall see hereafter that Inductive proofs may be stated in Syllogisms, and that Inductive inferences are drawn according to the Law of Causation. § 8. Of the above three conditions on which the validity of an argument depends, namely, (i) its formal correctness as a Syllogism, (2) the truth of the Minor, and (3) of the Major Premise, the most difficult to ensure are clearly the second and third, and especially the third. And here lies one important connection between Deduction and Induction. How can we know whether the premises of a Deductive argument are true ? By Induction. Sometimes, indeed, premises moy be deduced by Prosyllogisms : All men are mortal, it may be said, because All animals are mortal ; and All animals are mortal, because All composite bodies are subject to dissolution. But if there were no limit to this process, proof would involve a regressus ad infinitum, for which life is too short; and, besides, con- venient Prosyllogisms are not always to be found. Accordingly, Logic accepts certain Principles, Axioms, or ultimate Major r TRANSITION TO INDUCTION 141 Premises, such as the Laws of Thought and Causation, as con- ditions of all reasoning, leaving it to Metaphysics to investigate their grounds ; whilst the common run of general propositions, laws, or premises, if they have any scientific grounds, are either obtained by Induction from facts with the aid of the ultimate Axioms and Principles, or else are Hypotheses (that is, pre- mises provisionally assumed). For example, how do we know that all ruminants are herbi- vorous ? We have only directly observed that great multitudes are so ; the examination of a few specimens shows that their organisation is adapted to a vegetable diet, and we infer that unobserved ruminants are also herbivorous, by assuming that resemblance (in ruminating) is a ground of inference (to the property of feeding on herbage). If you ask. Why ? the usual answer is, * Because of the Uniformity of Nature.' This is con- sidered to be an ultimate principle, for which it is needless and useless to ask a reason, but with the help of which our ordinary Major Premises may be obtained by Induction from facts. And in the same way (as we saw in § 4) the conclusion of a Syllogism is obtained from the material evidence embodied in the Major Premise, namely, by assuming that resemblance is a ground of inference, or that Nature is uniform. § 9. The Uniformity of Nature cannot be defined and is there- fore liable to be misunderstood. In many ways Nature seems not to be uniform : there is great variety in the sizes, shapes, colours and all other properties of things : bodies falling in the open air — pebbles, slates, feathers — descend in different lines and at different rates ; the wind and weather are proverbially uncertain ; the course of trade, or of politics, is full of surprises. Yet common maxims, even when absurd, testify to a popular be- lief that the relations of things are constant : the doctrine of St. Swithin and the rhyme beginning * Evening red and morning grey,' show that the weather is held to be not wholly unpre- dictable ; as to human affairs, it is said that * a green Yule makes a fat churchyard,' that 'trade follows the flag,' and that * history repeats itself ' ; and Superstition knows that witches 142 LOGIC: DEDUCTIVE AND INDUCTIVE cannot enter a stable-door if a horse-shoe ^f l^^.-^^^;;"^"^ that the devil cannot cross a ^^^^^^^''^^^^^^^^^^ pentagon. But the surest proof of a belief m the y-» If Nature is given by the conduct of men and an.rnals by tha adherence to habit, custom and tradition to ^^^^ ^^^^^^^ times they chiefly owe their safety, but which wou dai y d- appoint and destroy them, if it were not ^-^fl^lX thinc^s may be found where they have been left and that in similar circumstances there are similar events. Now this general belief, seldom distinctly conceived, for the most part quite unconscious (as a principle), merely imphed m :::; L l, is also the foundation of all the Sci^ are entirely occupied in seeking the Laws (that is, the Un olities) of NaL. And Philosophy, endeavou^^^^^ nature is to generalise to the utmost, whilst retaining the d ai:Jss of'scientiac thought, resolves the -mpr^^^^^^^^^^^^^^^ but indeterminate notion of Uniformity into a number of First Principles, which may be indicated as follows : (X) The Principles of Contradition and Excluded Middle (i^ ti \? 3).__These are called Laws of Thought ; and so they te • for in the f^rst place, it is true of thoughts, as of every- tl'c. el'se, that they have a certain content or not ; occur in a lel^: order, or dJnot ; and, in the second P^-,^^^^^^^^^^^^^ reference to an object thought about, is bound to observe these aw son pain of else going wrong. But the reason why the Ibove principles are laws of Thought in this secondary sense /tW is as rules or imperatives) is, that they are laws of things tV;^ of' 'laws' (as uniformities) ; for else they :ould rdirect us, and it would be (literally) madness to con- 'T)"certrn Axioms of Mediate Evidence: as, in Mathe- matics ' that magnitudes equal to the same magnitude are " ul to one another'; and, in Logic, the i^^^^-, or its I'T^M^^ the mark of a mark is a mark of the thing itself. T) That all Times and all Spaces are commensurable.-If Time really trotted with one man and galloped with another, TRANSITION TO INDUCTION 143 as it seems to; if Space really swelled in places, as De Quincey dreamed that it did; life could not be regulated, experience could not be compared, and science would be impossible. The Mathematical Axioms would then never be applicable to Space or Time, nor to the objects and processes that fill them. (4) The Persistence of Matter and Energy : the physical principle that, in all changes of the universe, the quantities of Matter and Energy (actual and potential, so-called) remain the same. — For example, as to Matter, although dew is found on the grass at morning without any apparent cause, and although a candle seems to burn away to a scrap of blackened wick, yet every one knows that the dew has been condensed from vapour in the air, and that the candle has only turned into gas and smoke. As to Energy, although a stone thrown up to the housetop and resting there has lost actual energy, it has gained such a position that the slightest touch may bring it to the earth again in the same time as it took to travel upwards; and in that position it is said to have potential energy. When a boiler works an engine, every time the piston is thrust forward (having actual energy), an equivalent in heat (molecular energy) is lost. But for the elucidation of these principles, readers must refer to treatises of Chemistry and Physics. (5) Causation, a special form of the foregoing principles (4), we shall discuss in the next chapter. (6) Certain Uniformities of Co-existence ; but for want of a general principle of Co-existence, corresponding to Causation, (the principles of Succession), we can only classify these Uni- formities as follows : {a) The Geometrical ; as that, in a four-sided figure, if the opposite angles are equal, the opposite sides are equal and parallel.— Countless similar Uniformities of Co-existence are disclosed by Geometry. The co-existent facts do not cause one another, nor are they jointly caused by something else ; they are mutually involved : such is the nature of Space. 144 LOGIC: DEDUCTIVE AND INDUCTIVE {b) Universal co-existences among the properties of concrete things. — The chief example is the co-existence of Gravity with Inertia in all material bodies. There is, I believe, no other entirely satisfactory case; but some good approximations to such uniformity are known to phyical science. {c) Co-existence due to Causation ; such as the positions of objects in space at any time. — The houses of a town are where they are, because they were put there; and they remain in their place as long as no other causes arise strong enough to remove or destroy them. Similarly, the relative positions of rocks in geological strata, and of trees in a forest, are due to causes. {d) The Co-existence of properties in Natural Kinds ; which we call the constitution, defining characters, or specific nature of such things.— Oxygen, platinum, sulphur and the other elements; water, common salt, alcohol and other com- pounds ; the various species of plants and animals : all these are known to us as different groups of co-existent properties. It may be conjectured, indeed, that these groupings of proper- ties are also due to causation, and sometimes the causes can be traced : but very often the causes are still unknown ; and, at any rate, these cases of Co-existence form a sufficiently Veil- marked class to be separately mentioned. {e) There are also a few cases in which properties co-exist in an unaccountable way, without being co-extensive with any one species, genus, or order : as most metals are whitish, and scarlet flowers are wanting in fragrance. So much, then, as to the Uniformity of Nature in general : some of its constituent principles have already been discussed ; and Causation is such an important one as to require a chapter to itself. (On this §, see Venn's Empirical Logic, c. 4.) 1 4. CHAPTER XIV CAUSATION § I. For the theory of Induction, the specially important aspect of the Uniformity of Nature is Causation. For (i) the Principles of Contradiction and Excluded ^Middle are implied in all logical operations, and need no further expli- cation. (2) That one thing is a mark of another (except in the ultimate modes of Uniformity— such as the Law of Causation Itself— which are assumed in Logic) must be established by Induction ; and the surest of all marks is a Cause. So that the application of the Nota nohc in particular cases requires, when most valid, a previous appeal to Causation. And if we find that the Nota 7iot(E is itself appealed to in showing that any given related phenomena are Cause and Effect, it will only be in the same way as in all Syllogisms, that is to say, as an Axiom. (3) The uniformity of Space and Time is, of course, involved in Causation, if we conceive Causation as essentially matter in motion ; for Motion is only known as a traversing of Space in Time ; so that if Space and Time were not uniform. Causation would be irregular. But, though always assumed, this principle need not be explicitly appealed to in any particular investigation; since it is only a formal condition ; for Time and Space are not agents or causes. (4) The general persistence of Matter and Energy, again, although it is nothing else than Causation in the movement of the world, is yet too wide a principle to use in esta Wishing the K 146 LOGIC: DEDUCTIVE AND INDUCTIVE cause of a particular limited phenomenon, such as a soap- bubble, or a thunder-storm, or the tide. (5) As to Co-existences, the Geometrical do not belong to Logic : those involved in the existence of plants, animals, and inorganic bodies, must, as far as possible, be traced to causes ; and so, of course, must the relative positions of objects in space at any time : and what Co-existences remain do not admit of methodical inductive treatment ; they will be briefly discussed in chap. xvii. We may assume, then, that Causation is that mode or aspect of the Uniformity of Nature which especially concerns us in Induction; and we must, therefore, make it as definite as possible. § 2. A Cause, according to Mill, is " the invariable uncondi- tional antecedent " of a given phenomenon. This definition needs careful attention. (i) A Cause is relative to a given phenomenon, called the Effect. Logic has no method for investigating the cause of the universe as a whole, but only of a part or epoch of it : any portion that is neither too large nor too small for a trained mind to comprehend. The magnitude of the phenomenon may be a matter of convenience. If the cause of disease in general is too wide a problem, can fevers be dealt with ; or, if that be too much, is typhus within the reach of inquiry? In short, how much can we deal with accurately ? (2) The given phenomenon is always an event: that is to say, not a new thing (nothing is wholly new), but a change in something or in the relative position of things. We may ask the cause of the phases ot the Moon, of the freezing of water, of a deposit of chalk, of the differentiation of species. To inquire the cause of France being a republic, or Russia an autocracy, imphes that these countries were once otherwise governed, or had no government : to inquire the cause of the earth being shaped like an orange, implies that the matter of the earth had once another shape. (3) The Cause is antecedent to the effect, which accordingly CAUSATION 147 t is often called its Consequent. This is often misunderstood and sometimes disputed. It has been said that the meaning of '• cause ' implies an ' effect,' so that until an effect occurs there can be no cause. But this is a blunder \ for whilst the word ' cause ' implies effect, it also implies the relative futurity of the effect ; and effect implies the relative priority of the cause. The connotation of the words^ therefore, agrees wxU enough with Mill's doctrine. In fact, the danger is that any pair of contrasted words may suggest too strongly that the phenomena denoted are separate in nature ; whereas every natural process is continuous. If water, dripping from the roof, wears away a stone, it fell on the roof as rain ; the rain came from a condensing cloud ; the cloud was driven by the wind from the sea, whence it exhaled ; and so on. There is no beginning to this, and no break in it. We may take any one of these changes, call it an effect, and ask for its cause ; or call it a cause, and ask for its effect. There is not in nature one set of things called causes and another called effects ; but everything is both cause of the future and effect of the past ; and whether we consider an event as the one or the other, depends upon the direction of our curiosity or interest. Still, taking the event as effect, its cause is the antecedent process ; or, taking it as cause, its effect is the consequent process. This follows from the conception of causation as essentially motion ; for that inotion takes time is (from the way our perceptive powers grow) an ultimate intuition. But, for the same reason, there is no interval of time between cause and effect ; since all the time is filled up with motion. Nor must it be supposed that the whole cause is antecedent to the effect as a whole : for we often take the phenomenon on such a scale that minutes, days, years, may elapse before we consider the cause as exhausted {e.g., an earthquake, a battle, an expansion of credit) ; and all that time the effect has been accumulating. But we may further consider such a cause as made up of moments or minute factors, and the effect as made up of corresponding moments ; and then the cause, taken in t 148 LOGIC: DEDUCTIVE AND INDUCTIVE its moments, is antecedent throughout to the effect, taken in its corresponding moments. (4) The Cause is the invariable antecedent of the effect; that is to say, whenever a given cause occurs it ahvays has the same effect : in this, in fact, consists the Uniformity of Causa- tion. Accordingly, not every antecedent of an event is its Cause : to assume that it is so, is the familiar fallacy of arguing ^ post hoc ergo propter hoc^ But every event has an infinite number of antecedents that have no ascertainable connection with it : if a picture falls from the wall in this room, there may have been, just before, an earthquake in New Zealand, an explosion in a Japanese arsenal, a religious riot in India, a political assassination in Russia and a vote of censure in the House of Commons, besides millions of other less noticeable events, between none of which and the falling of the picture can any direct causation be detected ; though, no doubt, they are all necessary occurrences in the general world-process, and remotely connected. The Cause, however, was that a door slammed violently in the room above, and that the picture was heavy and the cord old and rotten. Even if two events invariably occur one after the other, as day follows night, or the report follows the flash of a gun, they may not be Cause and Effect, though it is highly probable that they are closely connected by Causation ; and in these two examples the events are of course joint effects of a common Cause. Still, whilst it is not true that every antecedent, or that every invariable ante- cedent, of an event is its Cause, it is held to be true that the Cause is something, or some state and process of things, such that whenever it exactly recurs the same event invariably follows. At the same time, it must be acknowledged that, if we consider the antecedent state and process of things very widely and minutely, it never does exactly recur. So that to construe the Law of Causation too strictly, is to render it inapplicable not only in practice but also in scientific inquiry. The requisite qualifications will appear in the next paragraph. i L JL CAUSATION 149 (5) The Cause is the Unconditional Antecedent. — 'Con- dition ' means any necessary factor of a Cause : a positive Condition is one that cannot be omitted without frustrating the effect ; a negative Condition is one that cannot be intro- duced without frustrating the effect. In the falling of the picture, e.g.^ the positive conditions were the slamming door and the rottenness of the cord ; a negative condition was that it should have no support but the cord. When Mill, then, defines the Cause of any event as its "unconditional" ante- cedent, he means that it is that group of conditions (state and process of things) which, without any further condition, is followed by the event in question : it is the least antecedent that suffices, positive conditions being present and negative absent. Now this enables us to distinguish a true Cause from an unconnected antecedent. Earthquakes have happened in New Zealand and votes of censure in the House of Commons without a picture's falling in the room : they were not un- conditional antecedents ; something else was needed to bring down a picture. It also distinguishes a true cause from an invariable antecedent that is only a joint-effect : for when day follows night something else happens ; the earth rotates upon her axis : a flash even of gunpowder is not an unconditional antecedent of a report ; the powder must be ignited in a closed chamber. By common experience and more precisely by experiment, it is found possible to select from among the antecedents of an event a certain number upon which, so far as can be perceived, it is dependent, and to neglect the rest. Remote conditions may indeed modify the event in ways so refined as to escape our notice : business and science are alike subject to the limi- tations of our human faculties. Subject to these Hmitations, however, we are able in many cases to secure an unconditional antecedent upon which a certain event invariably follows. In ordinary affairs everybody takes this for granted : if the gas will not burn, or a gun will not go off, we wonder ' what can be 1 150 LOGIC: DEDUCTIVE AND INDUCTIVE wrong with it,' that is, what positive condition is wanting, or what negative one is present. And these conditions are de- finitely and narrowly conceived. No one now supposes that gunnery depends upon those "remotest of all causes," the stars, or upon the sun being in Sagittarius rather than in Aquarius, or that one shoots straightest with a silver bullet, or after saying the alphabet backwards. (6) That the Cause of any event is an Immediate Antecedent follows from its being an Unconditional one. For if there are three events, ABC, causally connected, it is plain that A is not the Unconditional antecedent of C, but requires the further condition of first giving rise to B. But that is not all ; for the B that gives rise to C is never merely the effect of A ; it involves something further. Take such a simple case as the motion of the earth round the sun (neglecting all other con- ditions, the other planets, etc^ ; and let the earth's motion at three successive moments be A B C : A is not the whole cause of B in velocity and direction ; we must add relation to the sun, say x. But then, again, the cause of C will not be merely Bx, for the relation to the sun will have altered ; so that we must represent it as Bx'. The series, therefore, is Ax Bx' C. What is called a " remote cause " is, therefore, doubly con- ditional ; first, because it supposes an intervening cause ; and, secondly, because it only in part determines the conditions that constitute this intervening cause. But although the Immediacy of a Cause is implied in its Unconditionalness, it is often so important a clue to it as to deserve separate mention. At the same time, it must be acknowledged that, as far as the detection of causes depends upon sense-perception, our knowledge of Immediacy is subject to the limitations of our perceptive powers, which are unequal to the subtlety of Nature. Between the event and what seems to us the Immediate Antecedent many things (molecular changes) may happen (say) in Chemistry. And where phenomena are treated upon a large scale, as in the Biological and Social sciences, Immediacy, as a mark of causation, must be liberally CAUSATION 151 1 interpreted. So far, then, as to the qualitative character of Causation. (7) But to complete our account of it, we must briefly con- sider its quantitative character. As to the matter contained, and as to the energy embodied, Cause and Effect are conceived to be equal. As to Matter, indeed, they may be more properly called identical; since the effect is nothing but the cause redistributed. When oxygen combines with hydrogen to form water, or with mercury to form red precipitate, the weight of the compound is exactly equal to the weight of the elements combined in it ; when a shell explodes and knocks down a wall, the materials of the shell and wall are scattered about. As to Energy, we see that in the heavenly bodies, which meet with no sensible impediment, it remains the same from age to age: with things * below the moon' we have to allow for the more or less rapid conversion of the visible motion of a mass into other forms of energy, such as sound and heat. But the right understanding of this point involves physical considerations of some difficulty, as to which the reader must refer to appropriate books, such as Balfour Stewart's on The Conservation of Energy. The comprehension of the quantitative aspect of Causation is, however, greatly aided by Professor Bain's analysis of any Cause into an Inciting Power and a Collocation. When a demagogue by making a speech stirs up a mob to a not, the speech is the Inciting Power ; the mo^ already in a state of smouldering passion, and a street convenient to be wrecked, are the Collocation. When a small quantity of strychnine kills a man, the strychnine is the Inciting Power; the nature of his nervo-muscular system, apt to be thrown into spasms by that drug, and all the organs of his body dependent on that system, are the Collocation. Now any one who thinks only of the speech, or the drug, in these cases, may express astonish- ment at the disproportion of Cause and Effect : " What great events from trivial causes spring ! " But, remembering that the whole cause of the riot included 152 LOGIC: DEDUCTIVE AND INDUCTIVE the excited mob, every one sees that its muscular power is enough to wreck a street ; and remembering that breathing depends upon the normal action of the intercostal muscles, it is plain that if this action is stopped a man must die. Thus, when suffi- cient energy to account for any Effect cannot be found in the Inciting Power, or manifestly active condition, we must look for it in the Collocation which is often supposed to be passive. And that reminds us of another common misapprehension, namely, that in Nature some things are passive and others active : the distinction between agent and patient. This is a merely relative distinction : in Nature all things are active. To the eye some things seem at rest and others in motion ; but we know that nothing is really at rest, that everything palpitates with molecular change, and whirls with the planet through space ; and the quietest looking object (say, a moss- covered stone), if we try to push or lift it, pushes or pulls us back, assuring us that ' action and reaction are equal and opposite.' * Inertia ' does not mean want of vigour, but the exact contrary ; and may be metaphorically described as the inex- pugnable resolve of everything to have its own way. Such reflec- tions enable any one to understand how cause and effect are equal when regarded as a transformation of Matter and Energy. This transformation of Matter and Energy, then, is the essence of causation : because it is continuous, causation is immediate ; and because in the same circumstances the trans- formation always follows the same course, a cause has invari- ably the same effect. If a fire is lit morning after morning in the same grate, with coal, wood and paper of the same quality and similarly arranged, there will be each time the same flaming of paper, crackling of wood and glowing of coal, followed in about the same time by the same reduction of the whole mass pardy to ashes and partly to gases that have gone up the chimney. The flaming, crackling and glowing are, physically, so many modes of energy ; and the change of materials into gas and ashes is a chemical and physical redis- tribution : and, if some one is present, he will be aware of all CAUSATION 153 v| [ i this ; and then, besides the physical changes, there will be sensations of light, sound and heat ; and these, again, will be always the same in the same circumstances. The Cause of any event, then, when exactly ascertainable, has five marks : it is (quantitatively) equal to the effect, and is (qualitatively) its immediate^ unconditional^i?ivanahIe antecedent. § 3. This scientific conception of causation, however, has been developed and rendered definite by the investigations of those physical sciences that can avail themselves of exact experiments and mathematical calculation ; and it is there, in Chemistry, Optics, Thermotics and Dynamics, that it is most completely applicable. The conception can indeed be carried into the Biological and Social sciences, even in its quantitative form, by making the proper allowances. For the limbs of animals are levers, and act upon mechanical principles ; and digestion and the aeration of the blood by breathing are partly chemical processes. There is a quantitative relation between the food a man eats and the amount of work he can do. The numbers of any species of plant or animal depend upon the food supply. The value of a country's imports is equal to the value of its exports and of the services it renders to foreigners. But, generally, the less experiment and exact calculation are practicable in any branch of inquiry, the less rigorously can the conception of Causation be applied there ; the more, too, will its application depend upon the quaUtative marks, and the more need there will be to use it judiciously. It is unreasonable to expect in any case more precise proofs than the subject admits of. Wherever mental action is involved, there is a special difficulty in applying the physical notion of Causation. For, clearly, if a Cause is conceived as matter in motion, a thought, * or feeling, or volition can be neither Cause nor Effect. And since mental action is involved in all social affciirs, and in the life of all men and animals, it may seem impossible to interpret social or vital changes according to laws of Causa- tion. Still, animals and men are moving bodies; and it is ii 154 LOGIC: DEDUCTIVE AND INDUCTIVE recognised that their thoughts and feelings are connected with their movements and with the movements of other things that act upon them, so that we can judge of one case by another ; although the connection is by no means well understood, and the best words (such as all can agree to use) have not yet been found to express even what we know about it. Hence, a regular connection being granted, I have not hesitated to use biological and social events and the laws of them, to illustrate causation and Induction ; because, though less exact than chemical or mechanical examples, they are to most people more familiar and interesting. In practical affairs, it is felt that everything depends upon Causation : how to play the fiddle, or sail a yacht, or get one's living, or defeat the enemy. The price of pig-iron six months hence, the prospects of the harvest, the issue in a Coroner's court. Home Rule and Socialism, are all questions of causation. But, in such cases, the conception of a Cause is rarely applied in its full scientific acceptation, as the unconditional ante- cedent, or ' all the conditions ' (neither more nor less) upon which the event depends. This is not because men of business are bad logicians, or incapable of scientific comprehension ; for very often the reverse is conspicuously true ; but because practical affairs call for promptitude and a decisive seizing upon what is predominantly important. How learn to play the fiddle ? *' Go to a good teacher." (Then, beginning young enough, with natural aptitude and great diligence, all may be well.) How defeat the enemy ? " Be two to one at the critical juncture." (Then, if the men are brave, disciplined, well armed and well fed, there is a good chance of victory.) Will the price of iron improve ? '* Yes : for the market is over- sold ": (that is, many have sold iron who have none to deliver, and must at some time buy it back ; and that will put up the price — if the stock is not too great, if the demand does not fall off, and if those who have bought what they cannot pay for are not in the meanwhile obliged to sell.) These prompt and decisive judgments as to what is the Cause, or predominantly CAUSATION 155 V, important condition, of any event, are not as good as a scientific estimate of all the conditions, when this can be obtained ; but, when time is short, the insight of trained sagacity may be much better than an imperfect theoretical treatment of such problems. § 4. To regard the Effect of certain antecedents in a narrow selective way, is another common mistake. In the full scientific conception of an Effect, it is the sum of the unconditional consequences of a given state and process of things : the consequences immediately flowing from that situation without further conditions. Always to take account of all the con- sequences of any Cause would no doubt be impracticable ; still the practical, as well as the scientific interest, often requires that we should enlarge our views of them. An important consequence of eating is to satisfy hunger, and this is the ordinary motive to eat ; but it is a poor account of the effect, including its physiological consequences. All sorts of food ' satisfy hunger ' ; but for health and strength some sorts are much better than others. An important consequence of firing a gun is the propulsion of the bullet or shell ; but there are many other consequences in the whole effect, and one of them is the heating of the gun, which, accumulating with rapid firing, may at last put the gun out of action. The tides have consequences to shipping and in the wear and tear of the coast that draw every one's attention ; but we are told that they also retard the rotation of the earth, and at last may cause it to present always the same face to the sun and, therefore, to be uninhabitable. Such concurrent consequences of any Cause may be called its co-effects : the Effect being the sum of them. The neglect to take account of the whole Effect (that is, of all the co-effects) in any case of causation, is perhaps the reason why many philosophers have maintained the doctrine of a " Plurality of Causes " : meaning not that more than one condition is operative in the antecedent of every event (which is true), but that the same event may be due at different times to different antecedents, that in fact there may be vicarious Causes. If, however, we take any Effect as a whole, this does 156 LOGIC: DEDUCTIVE AND INDUCTIVE not seem to be true. A fire may certainly be lit in many ways : with a match or a flint and steel, or by rubbing sticks together, or by a flash of lightning : have we not here a plurality of causes ? Not if we take account of the whole Effect ; for then we shall find it modified in each case according to the difference of the Cause. In one case there will be a burnt match, in another a warm flint, in the last a changed state of electrical tension. And similar differences would be found in cases of death under different conditions, as stabbing, hanging, cholera ; or of shipwreck from explosion, scuttling, tempest. In short, if we knew the facts minutely enough, it would be found that there is only one Cause (sum of conditions) for each Effect (sum of co-effects), and that the order of events is as uniform backwards as forwards. Still, as we are far from knowing events minutely, it is necessary in practical affairs and even in the more complex and unmanageable scientific investigations, especially those that deal with human life, to acknowledge a possible Plurality of Causes for any effect. Indeed, forgetfulness of this leads to many rash generalisations ; as that ' revolutions always begin in hunger ' ; or that ' myths are a disease of language.' Then there is great waste of ingenuity in reconciling such propositions with the recalcitrant facts. A scientific method recognises that there may be other causes of effects thus vaguely conceived, and then proceeds to distinguish in each class of effects the peculiarities due to different causes. § 5. The understanding of the complex nature of Causes and Effects helps us to overcome some other difficulties that perplex the use of these words. We have seen that the true cause is an immediate antecedent ; but if the cause is con- founded with one of its constituent conditions, it may seem to have long preceded the event which is regarded as its effect. Thus, if one man's death is ascribed to another's desire of revenge, this desire may have been entertained for years before the assassination occurred : similarly, if a shipwreck is ascribed to a sunken rock, the rock was waiting for ages before the ship CAUSATION 157 f ^ i sailed that way. But, of course, neither the desire of revenge nor the sunken rock was ' the sum of the conditions ' on which the one or the other event depended. We have also seen that the true effect of any state or process of things is the immediate consequence ; but if the effect is confounded with one of its constituent factors, it may seem to long outlive the cessation of the cause. Thus, in nearly every process of human industry and art, one factor of the effect— a road, a house, a tool, a picture— may, and generally does, remain long after the work has ceased : but such a result is not the whole effect of the operations that produce it. The other factors may be, and some always are, evanescent. In most of such works some heat is produced by hammering or friction, and the labourers are fatigued ; but these consequences soon pass off. Hence the Effect as a whole only momentarily survives the Cause. Consider a pendulum which, having been once set agoing, swings to and fro in an arc, under the joint control of the shaft, gravitation and its own inertia : at every moment its speed and direction change ; and each change may be considered as an effect, of which the antecedent change was one condition. In such a case as this, which, though a very simple, is a perfectly fair example of all causation, the duration of either Cause or Effect is quite insensible : so that, as Dr. Venn says, an Effect, rigorously conceived, is only "the initial tendency " of its Cause. § 6. Mill contrasted two forms under which causation appears to us : that is to say, the conditions constituting a cause may be modified or ' intermixed ' in the effect in two ways, which are typified respectively by Mechanical and Chemical action. In Mechanical causation, which is found in Astronomy and all branches of Physics, the effects are all reducible to modes of Energy, and are therefore commensurable with their causes. They are either directly commensurable, as in the cases treated of in the consideration of the mechanical powers; or, if different forms of energy enter into cause and effect, such as mechanical energy, electrical energy, heat, these different forms 158 LOGIC: DEDUCTIVE AND INDUCTIVE are severally reducible to units, between which equivalents have been established. Hence Mill calls this the ''homogeneous intermixture of effects," because the antecedents and conse- quents are fundamentally of the same kind. In Chemical causation, on the other hand, cause and effect (at least as they present themselves to us) differ in almost every way : in the act of combination the properties of the elements disappear, and are superseded by others in the com- pound. If, for example, mercury (a heavy, silvery liquid) be heated in contact with oxygen (a colourless gas), oxide of mercury is formed (red precipitate, which is a powder). The compound presents very different phenomena from those of the elements ; and hence Mill called this class of cases " the hetero- pathic intermixture of effects." Still, in chemical action, the effect is not (in Nature) heterogeneous with the cause : for the weight of a compound is equal to the sum of the weights of the elements that are merged in it ; and an equivalence has been ascertained between the energy of chemical combination and the heat, light, etc.y produced in the act of combination. The heteropathic intermixture of effects is also found in organic processes (which, indeed, are partly chemical) : as when a man eats bread and milk, and by digestion and assimilation converts them into nerve, muscle and bone. Such phenomena may make us wonder that people should ever have believed that ' effects resemble their causes.' A dim recognition of the equivalence of cause and effect in respect of matttr and motion, may have aided the belief; and the resemblance of offspring to parents may have helped ; but it has been thought to be chiefly a confusing of the order of images in the mind with the order of events m nature. After enough experience, the thought of any event makes us anticipate its consequences, or form a picture of them before they happen ; but again, any image in the mind often reminds us of something similar, and this may be mistaken for the anticipation of an effect. Hence, whistling is seriously regarded as a means of raising the wind, because the wind whistles ; and barbarous CAUSATION 159 rain-makers sometimes torment a child to tears that the clouds also may weep. (See Tylor's Primitive Culture, ch. 4.) §7. There is another consideration arising out of the complex character of causes and effects. When a cause consists of two or more conditions or forces, we may consider what effect any one of them would have if it operated alone, that is to say, its Tendency. This, now, is best illustrated by the Parallelogram of Forces : if two forces acting upon a point, but not in the same direction, be represented by straight lines drawn in the direction of the forces, and in length proportional to their magnitudes, these lines, meeting in an angle, represent severally the Tendencies of the forces ; whilst if the parallelogram be completed on these lines, the diagonal drawn from the point in which they meet represents their Resultant or effect. Again, considering the Tendency of any force if it operated alone, we may say that, when combined with another force (not in the same direction) in any Resultant, its Tendency is counteracted either partially or wholly. If the other force be equal and opposite, the Resultant is equilibrium ; if it be in the same direction, the two are merely added together. Counteraction is only one mode of combination. Sometimes the separate Tendencies of combined forces can only be theoretically distinguished : as when the motion of a projectile is analysed into a Tendency to travel in the straight line of its discharge, and a Tendency to fall straight to the ground. But sometimes a Tendency can be isolated : as when, —after dropping a feather in some place sheltered from the wind, and watching it drift to and fro, as the air, offering unequal resistances to its uneven surface, counteracts its weight with varying success, until it slowly settles upon the ground, — we take it up and drop it again in a vacuum, when it falls like lead. Here we have the Tendency of a certain Cause (namely, the relation between the feather and the earth) free from Counteraction : and this is called the elimination of the counter- acting circumstances. In this case indeed there is physical elimination ; whereas, in the case of a projectile, when we say 158 LOGIC: DEDUCTIVE AND INDUCTIVE are severally reducible to units, between which equivalents have been established. Hence Mill calls this the "homogeneous intermixture of effects," because the antecedents and conse- quents are fundamentally of the same kind. In Chemical causation, on the other hand, cause and effect (at least as they present themselves to us) differ in almost every way : in the act of combination the properties of the elements disappear, and are superseded by others in the com- pound. If, for example, mercury (a heavy, silvery liquid) be heated in contact with oxygen (a colourless gas), oxide of mercury is formed (red precipitate, which is a powder). The compound presents very different phenomena from those of the elements ; and hence Mill called this class of cases " the hetero- pathic intermixture of effects." Still, in chemical action, the effect is not (in Nature) heterogeneous with the cause : for the weight of a compound is equal to the sum of the weights of the elements that are merged in it ; and an equivalence has been ascertained between the energy of chemical combination and the heat, light, e/c, produced in the act of combination. The heteropathic intermixture of effects is also found in organic processes (which, indeed, are partly chemical): as when a man eats bread and milk, and by digestion and assimilation converts them into nerve, muscle and bone. Such phenomena may make us wonder that people should ever have believed that * effects resemble their causes.' A dim recognition of the equivalence of cause and effect in respect of matter and motion, may have aided the belief; and the resemblance of offspring to parents may have helped ; but it has been thought to be chiefly a confusing of the order of images in the mind with the order of events in nature. After enough experience, the thought of any event makes us anticipate its consequences, or form a picture of them before they happen ; but again, any image in the mind often reminds us of something similar, and this may be mistaken for the anticipation of an effect. Hence, whistling is seriously regarde"a as a means of raising the wind, because the wind whistles ; and barbarous CAUSATION 159 ^1 il 1 rain-makers sometimes torment a child to tears that the clouds also may weep. (See Tylor's Primitive Culture^ ch. 4.) § 7. There is another consideration arising out of the complex character of causes and effects. When a cause consists of two or more conditions or forces, we may consider what effect any one of them w^ould have if it operated alone, that is to say, its Tendency. This, now, is best illustrated by the Parallelogram of Forces: if two forces acting upon a point, but not in the same direction, be represented by straight Hnes drawn in the direction of the forces, and in length proportional to their magnitudes, these lines, meeting in an angle, represent severally the Tendencies of the forces; whilst if the parallelogram be completed on these lines, the diagonal drawn from the point in which they meet represents their Resultant or effect. Again, considering the Tendency of any force if it operated alone, we may say that, when combined with another force (not in the same direction) in any Resultant, its Tendency is counteracted either partially or wholly. If the other force be equal and opposite, the Resultant is equihbrium ; if it be in the same direction, the two are merely added together. Counteraction is only one mode of combination. Sometimes the separate Tendencies of combined forces can only be theoretically distinguished ; as when the motion of a projectile is analysed into a Tendency to travel in the straight line of its discharge, and a Tendency to fall straight to the ground. But sometimes a Tendency can be isolated : as when, — after dropping a feather in some place sheltered from the wind, and watching it drift to and fro, as the air, offering unequal resistances to its uneven surface, counteracts its weight with varying success, until it slow^ly settles upon the ground, — we take it up and drop it again in a vacuum, when it falls like lead. Here we have the Tendency of a certain Cause (namely, the relation between the feather and the earth) free from Counteraction : and this is called the elimination of the counter- acting circumstances. In this case indeed there is physical elimination ; whereas, in the case of a projectile, when we say i6o LOGIC: DEDUCTIVE AND INDUCTIVE that its actual motion is resolvable (neglecting the resistance of the air) into two Tendencies, one in the line of discharge, the other earthwards, there is only theoretical elimination of either Tendency, considered as counteracting the other ; and this is more specifically called the Resolution or Analysis of the total effect into its component conditions. Now Elimination and Resolution may be said to be the essential process of Induction in the widest sense of the term, as including the combination of Induction with Deduction. The several conditions constituting any cause, then, by aiding or counteracting one another's tendencies, jointly determine the total effect. Hence, viewed in relation one to another, they may be said to stand in Reciprocity or mutual influence. This relation is itself one of co-existence, though it is conceived with reference to a possible effect. As Kant says, all substances, as perceived in space at the same time, are in reciprocal activity. And what is true of the world of things at any moment (as connected, say, by gravity) is true of any selected group of circumstances which we regard as the particular cause of any event to come. But we must not think of Reciprocity as obtaining in the succession of cause and effect, as if the effect could turn back upon its cause ; for as the effect arises its cause disappears, and is irrecoverable by Nature or Magic. J r CHAPTER XV INDUCTIVE METHOD § I. It is necessary to describe briefly the process of investi- gaiing laws of causation, not with the notion of teaching any one the Art of Discovery, which each man pursues for himself according to his natural gifts and his experience in the methods of his own science, but merely to cast some light upon the contents of the next few chapters. Logic is here treated as a process of proof; proof supposes that some general proposition has been suggested as requiring proof; and the search for such propositions springs from scientific curiosity. We may, as Professor Bain observes, desire to detect a process of causation either, first, amidst circumstances that have no influence upon the process but only obscure it; as when, being pleased with a certain scent in a garden, we wish to know from what flower it rises ; or, being attracted by the sound of some instrument in an orchestra, we desire to know which it is : or, secondly, amidst circumstances that alter the effect from what it would have been by the sole operation of some Cause ; as when the air deflects a falling feather ; or in some more complex case, such as the problem now (1895) exciting so much interest, the fall of prices that has gone on during the last twenty years. To what, men ask, is this due ? The first step of Elimination (as Professor Bain further observes) is "to analyse the situation mentally," in the light of analogies suggested by our experience or previous know- ledge. Dew, for example, is moisture formed upon the surface of bodies from no apparent source. But two possible sources L J.\ i62 LOGIC: DEDUCTIVE AND INDUCTIVE are easily suggested by common experience : is it deposited from the air, like the moisture upon a mirror when we breathe upon it; or does it exude from the bodies themselves, like gum or turpentine ? Or, again, as to the fall of prices, a little experience in business, or knowledge of Economics, readily suggests two possible explanations : either cheaper production in making goods or in carrying them ; or a scarcity of that in which the purchasing power of the chief commercial nations is directly expressed, namely, gold. (Bain's Logic: B. III. c. v.) Having thus analysed the situation and considered the possibility of one, two, three, or more possible Causes, we fix upon one of them for further investigation ; that is to say, we frame an Hypothesis that this is the Cause. When an Effect is given to find its Cause, an inquirer nearly always begins his investigations by thus framing an Hypothesis as to the Cause. The next step is to try to verify this Hypothesis. This we may sometimes do by varying the circumstances of the phenomenon, according to the Canons of Inductive Proof to be discussed in the next chapter ; that is to say, by observing or experimettting in such a way as to get rid of or eliminate the obscuring or disturbing conditions. Thus, to find out which flower in a garden gives a certain scent, it is usually enough to rely on observation, going up to the likely flowers one after the other and smelling them : at close quarters, the greater relative intensity of the smell is sufficiently decisive. Or we may resort to a sort of experiment, plucking a likely flower, as to which we frame the Hypothesis (this is the Cause) and carrying it to some place where the air is free from con- flicting odours. But if the phenomenon is so complex and extensive as the recent fall of prices, direct observation or experiment is a useless or impossible method ; and we must then resort to Deduction. If, for example, we take the Hypothesis that the fall is due to a scarcity of gold, we must show that there is a scarcity ; what effect such a scarcity may be expected to have upon prices from the 'acknowledged laws of prices, and INDUCTIVE METHOD 163 from the analogy of other cases of an expanded or restricted currency; that this expectation agrees with the statistics of recent commerce ; and finally that the alternative Hypothesis that the fall is due to cheaper production is not true ; either because there has not been a sufficient cheapening of general production ; or because, if there has been, the results to be rationally expected from it are not such as to agree with the^ statistics of recent commerce. (Ch. xviii. ) But now suppose that, a phenomer^on having been suggested for explanation, we are unable at the time to think of any Cause— to frame any Hypothesis about it ; we must then wait for the phenomenon to occur again and, once more observing its course and accompaniments and trying to recall its ante- cedents, do our best to frame an Hypothesis about it, and proceed as before. Thus, in the recent epidemic of influenza, some doctors framed the Hypothesis that it was due to a deluge in China, others to a volcanic eruption near Java ; some thought it a mild form of Asiatic plague, and others caught a specific microbe. As the disease often recurred, there were fresh opportunities of framing Hypotheses. I do not know whether any one of them has been established. If not, we must wait for the next epidemic. Again, however, the investigation may take a different form : given a supposed Cause to find its Effect ; e.g., a new chemical element, to find what compounds it forms with other elements ; or, the spots on the sun, have they any influence upon our weather ? Here, then, if the Cause is under control, as a new element may be, it is possible to try experiments with it according to the Canons of Inductive Proof. The inquirer may form some hypothesis or expectation as to the effects, to guide his obser- vation of them, but will be careful not to hold his expectation so confidently as to falsify his observation of what actually happens. But if the Cause is, like the sun-spots, not under control, the inquirer will watch on all sides what events follow their appearance and development : he must watch for consequences 164 LOGIC: DEDUCTIVE AND INDUCTIVE of the new cause he is studying in many different circumstances, that his observations may satisfy the canons of Proof. But he will also resort for guidance to Deduction ; arguing from the nature of the Cause, if anything is known of its nature, what consequences may be expected, and comparing the results of this deduction with any consequent which he suspects to be connected with the cause; and of course, if the results of Deduction and Observation agree, ho will still consider whether the facts observed may not be due to some other cause. A Cause, however, may be under control and yet be too dangerous to experiment with ; such as a proposed change of the constitution by legislation ; or even some minor Act of Parliament, for altering the Poor Law, or regulating the hours of labour. Here the first step must be Deductive. We must ask what consequences are to be expected from the nature of the change (comparing it with similar changes), and from the laws of the special circumstances in which it is to operate? And sometimes we may partially verify our deduction by try- ing experiments upon a small scale or in a mild form. There are conflicting deductions as to the probable efi'ect of giving Home Rule to Ireland ; and experiments have been made in more or less similar cases, as in the Colonies and in some foreign countries. It has also been proposed to make eight hours the legal limit of a day's labour in all trades. We have all tried to forecast the consequences of this ; and by way of verification we might begin with nine hours; or we might induce some other country to try the experiment first. Still, no verification by experiments on a small scale, or in a mild form, or in somewhat similar yet very different circumstances, can be considered logically conclusive. What proofs are con- clusive we shall see in the following chapters. § 2.' To begin with the conditions of direct Induction. — An Induction is an universal real proposition, based on observa- tion, in reliance on the uniformity of nature : when well ascer- tained, it is called a Law. Thus, that all life depends on the presence of oxygen is (i) an universal proposition; (2) a real r. INDUCTIVE METHOD 165 one, since the 'presence of oxygen' is not connoted by 'life'; (3) it is based on observation ; (4) it relies on the uniformity of nature, since all cases of life have not been examined. It should be observed that such a proposition is here called an Induction, when it is inductively proved ; that is, proved by facts, not deduced from more general premises (except the premise of nature's uniformity) : and by the ' process of Induc- tion' is meant the method of inductive proof. The phrase * process of Induction ' is often used in another sense, namely, for the inference or judgment by which such propositions are arrived at. But it is better to call this the process of hypothe- sis, and to regard it as a preliminary to the process of Induc- tion (that is, proof), as furnishing the hypothesis which, if it can stand the proper tests, becomes an Induction or Law. § 3. Inductive proofs are usually classed as Perfect and Im- perfect. They are said to be Perfect when all the instances within the scope of the given proposition have been severally examined, and the proposition has been found true in each case. But we have seen (chap. xii. § i) that the instances included in universal propositions concerning Causes and Kinds cannot be exhaustively examined : we do not know all planets, all heat, all liquids, all life, eU. ; and we never can, since a man's life is never long enough. It is only in such cases as those formerly quoted from Jevons, that examination can be exhaustive; or else if a class is artificially limited, such as, 'the present House of Commons.' There perfect induction might show (say) that every member has two Christian names. The argument is sometimes exhibited as a Syllogism in Darapti with a Minor Premise in U., which legitimates a Conclusion in A., thus : A.B. to Z have two Christian names; A.B. to Z are all the present M.P.s : .*. All the present M.P.s have two Christian names. But in such an investigation there is no need of logical method to find the Major Premise ; it is mere counting : and to carry out the Syllogism is a hollow formality. Accordingly, our i66 LOGIC: DEDUCTIVE AND INDUCTIVE definition of Induction excludes the kind unfortunately called Perfect, by including in the notion of Induction a reliance on the uniformity of nature ; for this would be superfluous if every instance in question had been severally examined. Imperfect Induction, then, is what we have to deal with : the method of showing the credibility of an universal real proposition by an examination of some of the instances it includes, generally a small fraction of them. § 4. Imperfect Induction is either Methodical or Imme- thodical. Now Method is procedure upon a principle ; and if the method is to be precise or conclusive, the principle must be precise and definite. There is a Geometrical method, because the axioms of Geometry are precise and definite, and by their means, with the aid of definitions, laws are deduced of the equality of lines and angles and other relations of position and magnitude in space. The process of proof is purely Deductive (the axioms and definitions being granted). Diagrams are used not as facts for observation, but merely to fix our attention in following the general argument ; so that it matters little how badly they are drawn, as long as their divergence from the conditions of the proposition to be proved is not distracting. Even the appeal to *' superposition " to prove the equality of magnitudes (as in Euclid I. 4), is not an appeal to observation, but to our judg- ment of what is implied in the foregoing conditions. Hence no inference is required from the special case to all similar ones ; for they are all proved at once. There is also, as we have seen, a method of Deductive Logic resting on the principles of Consistency and the Dictum de omni et nuUo. And we shall find that there is a method of Inductive Logic, resting on the principle of Causation. But there are a good many general propositions, more or less trustworthy within a certain range of conditions, which cannot be methodically proved for want of a precise principle by which they may be tested ; and they, therefore, depend upon Immethodical Induction, that is, upon the examination ^'^ INDUCTIVE METHOD 167 i <• T i of as many instances as can be found, relying for the rest upon the mere undefinable principle of the Uniformity of Nature, since we are not able to connect them with any of its definite modes enumerated in chap. xiv. §1. To this subject we shall return in chap, xix , after treating of Methodical Induction, or the means of determining that a connection of events is of the nature of Cause and Effect, because the relation can be shown to have the marks of causation, or some of them. § 5. Observations and Experiments are the w^/^'/'/a/ grounds of induction. An experiment is an observation made under prepared, and therefore known, conditions ; and, when obtain- able, it is much to be preferred. Simple observation shows that the burning of the fire depends, for one thing, on the supply of air ; but it cannot show us that it depends on oxygen. To prove this we must make experiments ; as by obtaining pure oxygen and pure nitrogen (which, mixed in the proportion of one to four, form the air) in separate vessels, and then plunging a burning taper into the oxygen — when it will blaze fiercely, and again plunging it into the nitrogen — when it will be extinguished. This shows that the greater part of the air does nothing to keep the fire alight, except by diminishing its intensity and so making it last longer. Experiments, now, are more perfect the more carefully they are prepared, and the more completely the conditions are known under which the given phenomenon is to be observed. Plainly, however, experiments are only possible when some knowledge has already been gained by observation, or else the preparation which they require would be impossible. Observation, then, was the first material ground of induc- tion, and in some sciences it remains the chief ground. The heavenly bodies, the winds and tides, the strata of the earth, and the movements of history, are beyond our power to experi- ment with. Experiments upon the living body or mind are indeed resorted to when practicable, even in the case of man, as in Psycho-physics, and the investigation of Hypnotism ; but, if of a grave nature, they are usually thought unjustifiable. i68 LOGIC: DEDUCTIVE AND INDUCTIVE And in political affairs experiments are hindered by the reflec- tion, that those whose interests are affected must bear the con- sequences and may resent them. Hence, it is in physical and chemical inquiries that direct experiment is most useful. Where direct experiment is possible, however, it has many advantages over unaided observation. If one experiment does not enable us to observe the phenomenon satisfactorily, we may try again and again ; whereas the mere observer, who wishes to study the bright spots on Mars, or a commercial crisis, must wait for a favourable opportunity. Again, in making experiments we can often var}'the conditions of the phenomenon, so as to observe its different behaviour in each case : whereas he who depends solely on observation must trust the bounty of nature to supply him with a suitable diversity of instances. It is a particular advantage of experiment that a phenomenon may sometimes be "isolated," that is, removed from the influ- ence of all agents except that whose operation we desire to observe, or except those whose operation is already known : whereas a simple observer, who has no control over the con- ditions of the subject he studies, can never be quite sure that its movements or changes are not due to causes that have never been conspicuous enough to draw his attention. Finally, experiment enables us to observe coolly and circumspectly and to be precise as to what happens, the time of its occurrence, the order of successive events, their duration, intensity and extent. § 6. The principle of Causation is the for7tial ground of Induction; and the Inductive Canons derived from it are means of testing the formal sufficiency of observations to justify the statement of a Law. If we can observe the process of cause and effect in nature we may generalise our observation into a law, because that process is invariable. First, then, can we observe the course of cause and effect ? Our power to do so is plainly limited by the refinement of our senses, aided by instruments such as lenses, thermometers, balances, etc. If the causal process is essentially molecular change, as in the maintenance of combustion by oxygen, we INDUCTIVE METHOD 169 ^( cannot directly observe it ; if the process is partly cerebral or mental, as in social movements which depend on feeling and opinion, it can but remotely be inferred ; even if the process is a collision of moving masses (billiard-balls), we cannot really observe what happens, the elastic yielding and recoil and the internal changes that result ; though no doubt photography will throw some light upon this, as it has done upon the galloping of horses and the impact of projectiles. Direct observation is limited to the effect which any change in a phenomenon (or its index) produces upon our senses ; and what we believe to be the causal process is a matter of inference and calculation. It is to be regretted, if the meagre and abstract outlines of Induc- tive Logic foster the notion, that the evidence on which Science (or even common opinion) rests is simple: it is amazingly intricate and cumulative. Secondly, then, so far as we can observe the process of nature, how shall we judge whether a relation of Cause and Effect is before us ? By looking for the five marks of Causa- tion. Thus, in the experiment above described, showing that oxygen supports combustion, we find— (i) that the taper which only glowed before being plunged into the oxygen, bursts into flame when there— Sequence ; (2) that this begins to happen at once without perceptible interval — Immediacy ; (3) that no other agent or disturbing circumstance was present (the preparation of the experiment having excluded any such thing)— Unconditionalness; (4) the experiment may be repeated as often as we like with the same result — Invariableness. In- variableness, indeed, I do not regard as formally necessary to be shown, supposing the other marks to be clear; for it can only be proved within our experience ; and the very object of Induction is to find grounds of belief beyond actual experience. However, for material assurance, to guard against his ow^n liability to error, the inquirer will of course repeat his experiments. The above four are the qualitative marks of Causation : the fifth and quantitative mark is the Equality of Cause and Effect ; and this, in the above example, the Chemist deter- I70 LOGIC: DEDUCTIVE AND INDUCTIVE mines by showing, that instead of the oxygen and wood that have disappeared during combustion, an equivalent amount of carbonic acid, water, etc., has been formed. Here, then, we have all the marks of Causation ; but in the ordinary judgments of life, in history, politics, criticism, busi- ness, we must not expect such clear and direct proofs ; and we shall see in subsequent chapters how different kinds of evidence are combined in different departments of investigation. § 7. The Inductive Canons, to be explained in the next chapter, describe the character of observations and experiments that justify us in drawing conclusions about Causation ; and, as we have observed, they are derived from the principle of Causation itself. According to that principle, cause and effect are invariably, immediately and unconditionally antecedent and consequent, and are equal as to the matter and energy embodied. Invariability can only be observed, in any of the methods of induction, by collecting more and more instances, or repeating experiments. Of course it can never be exhaustively observed. Immediacy is also, in direct induction, a matter for the most exact observation that is possible. Succession, or the relation itself of antecedent and conse- quent, must either be directly observed ; or else ascertained by showing that energy gained by one phenomenon has been lost by another, for this implies succession. But the Unconditionality of Causation it is the great object of the methods to determine, and for that purpose its meaning may be further explicated by the following rules : I. — For Positive Instances. To find a Cause : (a) Any agent whose introduction among certain conditions (without further change) is followed by a given phenomenon ; or, (b) whose removal is followed by the ce«isation (or modification) of that phenomenon, is (so far) the cause or an indispensable condition of it. To find the Effect : (r) Any event that follows a given phenomenon, when there is no further change ; or, (d) that INDUCTIVE METHOD 171 1 >' V does not occur w^hen the conditions of a former occurrence are exactly the same, except for the absence of that phenomenon, is the effect of it (or is dependent on it). II. — For Negative Instances. To exclude a supposed Cause : (a) Any agent that can be introduced among certain conditions without being followed by a given phenomenon (or that is found without that pheno- menon) ; or (b) that can be removed when that phenomenon is present without impairing it (or that is absent when that phenomenon is present), is not the cause, or does not com- plete the cause, of that phenomenon in those circumstances. To exclude a supposed Effect: (r) Any event that occurs without the introduction (or presence) of a given phenomenon ; or (d) that does not occur w^hen that phenomenon is introduced (or is present), is not the effect of that phenomenon. Subject to the conditions thus somewhat cumbrously stated, the rules may be briefly put as follows : I. (a) That which (without further change) is followed by a given event is its cause. II. {a) That which is not so followed is not the cause. I. (b) That which cannot be left out without impairing a phenomenon is a condition of it. II. (b) That which can be left out is not a condition of it. Again, the Equality of Cause and Effect may be further explained by these rules : III. {a) When a cause (or effect) increases or decreases, so does its effect (or cause). III. (b) If two phenomena, having the other marks of cause and effect, seem unequal, the less contains an unexplored factor. III. (c) If an antecedent and consequent do not increase or decrease correspondingly, they are not cause and effect, so far as they vary. It will next be shown that these propositions are vaiiously combined in Mill's five Canons of Induction. CHAPTER XVI THE CANONS OF DIRECT INDUCTION § I. Let me begin by borrowing an example from Professor Bain {Logic : B. III. c. 6). The North-East wind is generally detested in this country : as long as it blows few people feel at their best. Occasional well-known causes of a wind being injurious, are violence, excessive heat or cold, excessive dryness or moisture, electrical condition, want of ozone, the being laden with dust or exhalations. Let the hypothesis be that the last is the cause of the North-East wind's unwholesome quality; since we know it is a ground current setting from the pole toward the equator and bent westward by the rotation of the earth ; so that, reaching us over thousands of miles of land, it may well be fraught with dust, effluvia and microbes. Now' examining many cases of North-East wind, we find that this is the only circumstance in which all the instances agree : for it is sometimes cold, sometimes hot ; generally dry, but some- times wet ; sometimes light, sometimes violent; of all electrical conditions, and is charged with ozone on the Norfolk coast. Each of the other circumstances, then, can be omitted without the N.E. wind ceasing to be noxious; but one circumstance is never absent, namely, that it is a ground current. That circumstance, therefore, is probably the Cause of its injurious- ness. This case illustrates : — (i) The Canon of Agreement. If two or more instances of a phenomenon under investigation have only one other circumstance (antecedent or consequent) in K V X THE CANONS OF DIRECT INDUCTION 173 common^ that circumstance is the cause {or an indispensable part of the cause) or the effect of the phenomenon. This rule of proof (so far as it is used to establish direct causation) depends first, upon observation of an invariable connection between the given phenomenon and one other circumstance ; and, secondly, upon 1. (a) and II. {b) among the propositions obtained from the unconditionality of causation at the close of the last chapter. Let us suppose two instances of the occurrence of a given phenomenon. A, an antecedent, or /, a consequent, with concomitant facts or events, and let us represent them thus : — ABC A D E (antecedents) p q r p s t (consequents) ; and let us suppose that, in this case, the immediate succession of events can be observed. Then A is the cause of/. For, as far as our instances go, A is the invariable antecedent of / ; and / is the invariable consequent of A. But the two instances of A or / agree in no other circumstance. Therefore A is (or completes) the unconditional antecedent of /. For B and C are not the causes of /, being absent in the second instance (Rule II. {b))\ nor are D and E, being absent in the first instance. Moreover, q ana r are not Effects of A, being absent in the second instance (Rule 11. (^)); nor are s and /, being absent in the first instance. It should be observed that the cogency of the proof depends entirely upon its tending to show the unconditionality of the sequence A-/. That/ follows A even immediately, is nothing by itself : if a man sits down to study and, on the instant, a hand-organ begins under his window, he must not infer malice in the musician : thousands of things follow one another every moment without traceable connection ; and this we call ' acci- dental.' Even invariable sequence is not enough to prove direct causation ; for, in our experience, does not night invari- ably follow day? The proof requires that the instances be such as to show not merely what events are m invariable sequence, but also what are not. From among the occasional /^ 174 LOGIC: DEDUCTIVE AND INDUCTIVE antecedents of p (or consequents of A) we have to eliminate the accidental ones. And this is done by finding or making 'negative instances' in respect of each of them. Thus the A D E . . . mstance p ^ ^ is a negative mstance of B and C considered as supposable causes of / (and of q and r as supposable effects of A) ; for it shows that they are absent when/ (or A) is present. To insist upon the cogency of * negative instances' was Bacon's great contribution to Inductive Logic. If we neglect them, and merely collect examples of the sequence A -/, this is * simple enumeration ' ; and although simple enumeration, when the instances of agreement are numerous enough, may give rise to a strong belief in the connection of phenomena, yet it can never be a methodical or logical proof of causation, since it does not indicate the unconditionalness of the sequence. For simple enumeration of the sequence A-/ leaves open the possibility that, besides A, there is always some other antecedent of/, say X ; and then X may be the cause of/. To disprove It, we must find, or make, a negative instance of X— where / occurs, but X is absent. If indeed (or whenever) we recognise the possibility of a Plurality of Causes, this method of Agreement cannot be quite satisfactory. For then, in such instances as the above, although D is absent in the first, and B in the second, it does not follow that they are not the causes of / ; for they may be alternative causes : B may have produced p in the first instance, and D in the second ; A being in both cases an accidental circumstance in relation to/. To remedy this shortcoming by the method of Agreement itself (we shall see other remedies hereafter) the only course is to find more instances of /. We may never find a negative instance of A ; and, if not, the probability that A is the cause of / increases with the number of instances. But if there be no antecedent that we cannot sometimes exclude, yet the collection of instances will probably give at last all the causes of// and by finding the proportion \ 5 THE CANONS OF DIRECT INDUCTION 175 of instances in which A, B, or X precedes/, we may estimate the probability of any one of them being the cause of / in any given case of its occurrence. Again, though we have assumed that, in the instances supposed above, immediate sequence is observable, yet in many cases it may not be so, if we rely only on the canon of Agreement; if instances cannot be obtained by experiment, and we have to depend on observation. The phenomena may then be so mixed together that A and / seem to be merely concomitant ; so that, though connection of some sort may be rendered highly probable, we may not be able to say which is Cause and which is Effect, We must then try (as Bain says) to trace the expenditure of energy : if / gains when A loses, the course of events is from A to/; but here we are anticipa- ting the method of Variations (§ 4). Moreover, where succession cannot be traced, the method of Agreement may point to a connection between two facts (perhaps as joint-effects of a remote cause) where direct causa- tion seems to be out of the question : e.g.^ that Negroes, though of different tribes, different localities, customs, etc.^ are both prognathous and dolichocephalic. But such an investiga- tion belongs to the theory of Definition rather than to our present subject. Men often use arguments which, if they knew it, might be shown to conform more or less to this canon ; for they collect many instances to show that two events are connected ; but usually neglect to bring out the negative side of their proof ; so that their arguments only amount to simple enumeration. Thus Ascham in his Toxophilus, insisting on the national importance of archery, argues that victory has always depended on superiority in shooting; and, to prove it, he shows how the Parthians checked the Romans, Sesostris conquered great part of the known world, Tiberius overcame Arminius, the Turks established their empire, and the English defeated the French (with many like examples)— all by superior archery. But having cited these cases to' his purpose, he is content ; whereas he might have greatly strengthened his proof by showing how one or the other instance excludes other possible causes of success. Thus : the cause was not discipline, for the Romans were better disciphned than the Parthians ; nor yet the boasted superiority of a northern habitat, for Sesostris issued from the south ; 176 LOGIC: DEDUCTIVE AND INDUCTIVE nor better manhood, for here the Germans probably had the advantage ot the Romans ; nor superior civiUsation. for the Turks were lels civihsed than most of those they conquered ; nor numbers, nor even a good cause, for the French were more numerous than the Enghsh and were shamefully attacked by Henry V. on their own soil. Many an argument from simple enumeration may thus be turned into an mduction of greater plausibility according to the canon of Agreement Still, in the above case, the effect (victory) is so vaguely conceived. that a plurality of causes must be allowed for : although, e.g., discipline did not enable the Romans to conquer the Parthians. it may have been heir chief advantage over the Germans ; and it was certainly important to the English under Henry V. in their war with the French. Here is another argument, somewhat similar to the above put forward by Mr. Spencer with a full consciousness oAts logical character States that make war their chief object, he says, assume a certain type of organisation, involving the growth of the warrior class and the treatment of labourers as existing solely to sustain the warriors • the complete subordination of individuals to the will of the despotic soldier- king, their property, liberty and life being at the service of the State • the regimentation of society not only for military but also for civil purposes ; the suppression of all private associations, etc. This is the case in Dahomey and in Russia, and it was so at Sparta, in Egypt and in the empire of the Yncas. But the similarity of organisation in ihese States cannot have been due to race, for they are all of different races • nor to size, for some are small, some large ; nor to climate or other circumstances of habitat, for here again they differ widely • the one thing they have in common is the military purpose ; and this, therefore must be the cause of their similar organisation. ^Political Institutions ) ' By this method, then, to prove that one thing is causally connected with another, say A with/, we show first, that in all instances of /> A is present ; and. secondly, that any other supposable cause of t may be absent without disturbing p. We next come to a method the use of which greatly strengthens the foregoing, by showing that where b is absent A is also absent, and (if possible) that A is the only supposable cause that is always absent along with /. § 2. The CanOx\ of the Joint Method of Agree- ment IN Presence and in Absence. If {\) two or more instances in which a phenomenon occurs have only one other circumstance {antecedent or consequent) in common, while (2) two or more instances in which it does not occur {though in some important points they resemble the former set of instances) have nothing else in common save the absence of THE CANONS OF DIRECT INDUCTION 177 that circumstance — the circu?tistance in which alone the two sets, of instances differ throughout {being present in the first set and^ absent in the second) is the effect or the cause, or an indispensable ■ part of the cause, of the pheno??ienon. The first clause of this Canon is the same as that of the . Method of Agreement, and its significance depends upon the. same propositions concerning Causation. The second clause, relating to instances in which the phenomenon is absent, depends for its probative force upon Prop. II. {a\ and I. {b). Let the two sets of instances be represented as follows : Instances of Presence. ABC p q r A D E, p s t AFG . ^ p u v Instances of Absence. C HF r X IV B D K q y z EG M // n Then A is the cause of/, or / the effect of A : first, by the Canon, of Agreement in Presence, as represented by the first set of. instances; and, secondly, by Agreement in Absence in the. second set of instances. For there we see that C H F B D K . E G M occur without the phenomenon /, and therefore (by. Prop. II. {a) ) are not its cause, or not the whole cause, unless, they have been counteracted (which is a point for further, investigation). We also see that r x iv q y z t f n occur without . A, and therefore are not the effects of A. And, further, if the . negative instances represent all possible cases, we see that, (according to Prop. I. {b) ) A is the cause of/, because it cannot . be omitted without the cessation of p. The inference that A . and/ are Cause and Effect, suggested by their being present, throughout the first set of instances, is therefore strengthened, by their being both absent throughout the second set. , As this Double Method, like the Single Method of Agree, ment, relies mainly on observation. Sequence may not be per- 178 LOGIC: DEDUCTIVE AND INDUCTIVE ceptible in the instances observed, and then, direct causation cannot be proved by it, but only the probability of causal con- nection. It has, however, one peculiar advantage, namely, that if the second list of instances (in which the phenomenon and its supposed antecedent are both absent) can be made exhaustive, it precludes any hypothesis of a plurality of causes ; since all possible antecedents will have been included in this list without producing the phenomenon. Thus, in the above symbolic example, taking the first set of instances, the suppo- sition is left open that B, C, D, E, F, G, may, at one time or another, have been the cause of / / but, in the second list, these antecedents all occur here or there without producing/, and therefore (unless counteracted in some way) cannot be the cause of/. A, then, stands out as the one thing that is present whenever/ is present, and absent whenever/ is absent. Stated in this abstract way, the Double Method may seem very elaborate, compHcated and difficult ; yet, in fact, we all use it in our ordinary reasonings. If a man finds that whenever he eats cucumber he suffers from indigestion, this indicates by Agreement that cucumber is the cause of his pain. But, if he is fond of cucumber, he will put the fault upon other ingredients of his diet taken at the same time, such as cheese, salmon or pastry, which he likes less. Making, however, a second list of dinners (say) when visiting, at which cucumber is not served, whilst cheese, salmon, pastry, etc., all occur, and finding that he does not suffer from indigestion, the conclusion seems to be forced upon him that cucumber is the only pleasure of the table that must be bought with pain. In this case sequence can be observed. Again, if, whilst a certain oarsman is stroke of a boat whose crew often changes, it always wins; whilst, after he retires, it always loses (in spite of other changes) ; his admirers will certainly argue according to this Method that, since his presence brought victory and his absence brings defeat, success was due to him and to him alone. There are some instructive applications of this Double Method in Dr. Wallace's Darwinism. In chap, viii., for example, on Colour in Animals, he observes, that the usefulness of their colouration to animals is shown by the fact that, " as a rule, colour and marking are constant in each species of wild animal, while, in almost every domesticated animal there arises great variability. We see this in our horses and cattle, our dogs and cats, our pigeons and poultry. Now the essential difference between the conditions of life of domesticated and wild animals is, that t THE CANONS OF DIRECT INDUCTION 179 the former are protected by man, while the latter have to protect them- selves." Wild animals protect themselves by acquiring qualities adapted to their mode of life. Now colouration is a very important quality, its chief, though not its only use, being concealment. Hence a useful colouration having been established in any species, though mdividuals may occasionally vary from it, they will generally perish ; whilst among domestic animals variation of colour or marking is subject to no check except the taste of owners. We have, then, two lists of instances : first, innumerable species of wild animals in which the colouration is constant and which depend upon their own qualities for existence ; secondly, several species of domestic animals in which the colouration is not constant, and which do not depend upon their own qualities for existence. In the former list two circumstances are present together (under all sorts of conditions) ; in the latter they are absent together. The argument may be further strengthened by adding a third list, parallel to the first, comprising domestic animals in which colouration is approximately constant, but where (as we know) it is made a condition of existence by owners, who only breed from those specimens that come up to a certain standard of colouration. Dr. Wallace goes on to discuss the colouring of arctic animals ; I will slightly condense his statement. In the arctic regions some animals are wholly white all the year round, such as the polar bear, the American polar hare, the snowy owl and the Greenland falcon : these live amidst almost perpetual snow. Others, who live where the snow melts in summer, only turn white in winter, such as the arctic hare, the arctic fox, the ermine and the ptarmigan. In all these cases the white colouring is useful, concealing the herbivores from their enemies, and also the carnivores in approaching their prey ; this usefulness, therefore, is the cause of the white colouring. Two other explanations have how- ever been suggested : first, that the prevalent white of the arctic regions directly colours the animals, either by some photographic or chemical action on the skin, or by a reflex action through vision (as in the chameleon) ; secondly, that a white skin checks radiation and keeps the animals warm. But there are some exceptions to the rule of white colouring in arctic animals which refute these hypotheses, and confirm the author's. The sable remains brown throughout the winter; but it frequents trees, with whose bark its colour assimilates. The musk- sheep is brown and conspicuous ; but it is gregarious, and its safety depends upon being able to recognise its kind and keep with the herd. The raven is always black ; but it fears no enemy and feeds on carrion, and therefore does not need concealment for either defence or attack. The colour of the sable, then, though not white, serves for concealment ; the colour of the musk-sheep serves a purpose more important than concealment; the raven needs no concealment. There are thus two sets of instances:— in one set, the animals are white; [a) all the year- 178 LOGIC: DEDUCTIVE AND INDUCTIVE ceptible in the instances observed, and then, direct causation cannot be proved by it, but only the probability of causal con- nection. It has, however, one peculiar advantage, namely, that if the second list of instances (in which the phenomenon and its supposed antecedent are both absent) can be made exhaustive, it precludes any hypothesis of a plurality of causes ; since all possible antecedents will have been included in this list without producing the phenomenon. Thus, in the above symbolic example, taking the first set of instances, the suppo- sition is left open that B, C, D, E, F, G, may, at one time or another, have been the cause of / ; but, in the second list, these antecedents all occur here or there without producing/, and therefore (unless counteracted in some way) cannot be the cause of/. A, then, stands out as the one thing that is present whenever/ is present, and absent whenever/ is absent. Stated in this abstract way, the Double Method may seem very elaborate, complicated and difficult ; yet, in fact, we all use it in our ordinary reasonings. If a man finds that whenever he eats cucumber he suffers from indigestion, this indicates by Agreement that cucumber is the cause of his pain. But, if he is fond of cucumber, he will put the fault upon other ingredients of his diet taken at the same time, such as cheese, salmon or pastry, which he likes less. Making, however, a second list of dinners (say) when visiting, at which cucumber is not served, whilst cheese, salmon, pastry, etc., all occur, and finding that he does 7iot suffer from indigestion, the conclusion seems to be forced upon him that cucumber is the only pleasure of the table that must be bought with pain. In this case sequence can be observed. Again, if, whilst a certain oarsman is stroke of a boat whose crew often changes, it always wins; whilst, after he retires, it always loses (in spite of other changes); his admirers will certainly argue according to this Method that, since his presence brought victory and his absence brings defeat, success was due to him and to him alone. There are some instructive appHcations of this Double Method in Dr. Wallace's Darwinism. In chap, viii., for example, on Colour in Animals, he observes, that the usefulness of their colouration to animals is shown by the fact that, " as a rule, colour and marking are constant in each species of wild animal, while, in almost every domesticated animal there arises great variability. We see this in our horses and cattle, our dogs and cats, our pigeons and poultry. Now the essential difference between the conditions of Ufe of domesticated and wild animals is, that THE CANONS OF DIRECT INDUCTION 179 the former are protected by man, while the latter have to protect them- selves." Wild animals protect themselves by acquiring qualities adapted to their mode of life. Now colouration is a very important quality, its chief, though not its only use, being concealment. Hence a useful colouration having been established in any species, though mdividuals may occasionally vary from it, they will generally perish ; whilst among domestic animals variation of colour or marking is subject to no check except the taste of owners. We have, then, two lists of instances: first, innumerable species of wild animals in which the colouration is constant and which depend upon their own qualities for existence ; secondly, several species of domestic animals in which the colouration is not constant, and which do not depend upon their own qualities for existence. In the former list two circumstances are present together (under all sorts of conditions) ; in the latter they are absent together. The argument may be further strengthened by adding a third list, parallel to the first, comprising domestic animals in which colouration is approximately constant, but where (as we know) it is made a condition of existence by owners, who only breed from those specimens that come up to a certain standard of colouration. Dr. Wallace goes on to discuss the colouring of arctic animals ; I will slightly condense his statement. In the arctic regions some animals are wholly white all the year round, such as the polar bear, the American polar hare, the snowy owl and the Greenland falcon : these live amidst almost perpetual snow. Others, who live where the snow melts in summer, only turn white in winter, such as the arctic hare, the arctic fox, the ermine and the ptarmigan. In all these cases the white colouring is useful, concealing the herbivores from their enemies, and also the carnivores in approaching their prey ; this usefulness, therefore, is the cause of the white colouring. Two other explanations have how- ever been suggested : first, that the prevalent white of the arctic regions directly colours the animals, either by some photographic or chemical action on the skin, or by a reflex action through vision (as in the chameleon) ; secondly, that a white skin checks radiation and keeps the animals warm. But there are some exceptions to the rule of white colouring in arctic animals which refute these hypotheses, and confirm the author's. The sable remains brown throughout the winter ; but it frequents trees, with whose bark its colour assimilates. The musk- sheep is brown and conspicuous ; but it is gregarious, and its safety depends upon being able to recognise its kind and keep with the herd. The raven is always black ; but it fears no enemy and feeds on carrion, and therefore does not need concealment for either defence or attack. The colour of the sable, then, though not white, serves for concealment ; the colour of the musk-sheep serves a purpose more important than concealment; the raven needs no concealment. There are thus two sets of instances:— in one set, the animals are white; (a) all the year; i8o LOGIC: DEDUCTIVE AND INDUCTIVE (6) in winter, and white conceals them (a) all the year, (b) in winter; in the other set. the animals are not white, and to them either whitenes' would not give concealment, or concealment would not be advantageous. And this second list refutes the rival hypothesis : for the musk-sheep and the raven are as much exposed to the glare of the snow, and to the cold, as the other animals are. § 3. The Canon of Difference. //an instance in ivhich a phenomenon occurs, and an instance tn ivhich it does not occur, have every other circumstance in common save one, that one {whether consequent or antecedent) occurring only in the former ; the circumstance in ivhich alone the two instances differ is the effect, or the cause, or an indispen- sable condition of the phenomenon. This follows from Props. I. {a) and (b), in chapter xv. § 7. Let two instances, such as the Canon requires, be represented thus : ABC BC P ^ r g r Then A is the cause of/. For, in the first instance, A being introduced (without further change), / arises (Prop I. (^) ); or, in the second instance, A having been removed (without other change),/ disappears (Prop. I. (b) ). Similarly we may prove, by the same instances, that/ is the effect of A. Which of two phenomena thus shown to be connected is Cause, and which Effect (if we have no prior knowledge of their nature, and are not experimenting, but relying on simple observation) must be determined by observing the order in which they occur ; and the immediacy of their connection is also a matter for observation, aided by whatever instruments and methods of inspection and measurement may be available. As to the invariability of the connection, it may of course be tested by collecting more instances or making more experi- ments ; but it has been maintained, that a single experiment accordmg to this method, if satisfactorily performed, is suf- ficient to prove causation, and therefore implies invariabi- lity (since causation is unifor.n), though no other instances 4 .-i^ THE CANONS OF DIRECT INDUCTION 181 should ever be obtainable; because a single perfect experi- ment establishes the unconditionality of the connection. Now, formally this is true; but in any actual investigation how shall we decide what is a satisfactory or perfect experiment ? Such an experiment requires that in the negative instance — , q r B C shall be the least assemblage of conditions necessary to co-operate with A in producing/; and that it is so cannot be ascertained without either general prior knowledge of the nature of the case or special experiments for the purpose. So that invariability will not really be inferred from a single expe- riment ; besides that every prudent inquirer repeats his experi- ments, if only to guard against his own liabihty to error. The supposed plurality of causes, does not affect the Method of Difference. In the above symbolic case, A is clearly one cause (or condition) of /, whatever other causes may be possible; whereas in the former case of the Single Method of Agreement, it remained doubtful (admitting a plurality of causes) whether A, in spite of being always present with/, was ever a cause or condition of it. Now this Method of Difference is perhaps oftener than any other, though without our being distinctly aware of it, the basis of ordinary judgments. That the sun gives light and heat, that food nourishes and fire burns, that a stone will break a window or kill a bird, that turning a tap hastens or checks the flow of water or of gas, and thousands of other propositions are known to be true by rough but often emphatic applications of this method in common experience. It should be noticed that there are two ways in which this application may be made : either (a) by observation, taking for our two instances distinct assemblages of conditions, differing only in one*pkrticular with its antecedent or consequent ; or {h) by experiment, regarding as our two instances the same assemblage of conditions, before and after the introduction of a certain agent. If, for example, there are two men of closely similar age, health, clothing and habits, one of whom stands in the shade and feels cool, whilst the other stands in the sun and feels warm, this shows in the former way, by observation, that the sun gives heat ; but if, instead of this, the man who stands in th^shade merely steps into the sunshine and feels warm, the same proposition is proved in the latter way by experiment. The experimental way is the better i8o LOGIC: DEDUCTIVE AND INDUCTIVE {b) in winter, and white conceals them {a) all the year, {b) in winter ; in the other set, the animals are ?wt white, and to them either whitenes would not give concealment, or concealment would not be advantageous. And this second list refutes the rival hypothesis : for the musk-sheep and the raven are as much exposed to the glare of the snow, and to the cold, as the other animals are. § 3. The Canon of Difference. Tfan instance in ivhich a phenojnenon occurs, and an insfa?tce in which it does not occur, have every other circumstance in common save one, that o?te {whether consequent or antecedent) occurrifig o?iiy in the former ; the circumstaiice in which aIo?te the two instances differ is the effect, or the cause, or an indispen- sable condition of the phenomeno7i. This follows from Props. I. {a) and (b), in chapter xv. § 7. Let two instances, such as the Canon requires, be represented thus : ABC BC p q r q r Then A is the cause of/. For, in the first instance, A being introduced (without further change),/ arises (Prop I. (a) ); or, in the second instance, A having been removed (without other change),/ disappears (Prop. I. (l))). Similarly we may prove, by the same instances, that/ is the effect of A. Which of two phenomena thus shown to be connected is Cause, and which Effect (if we have no prior knowledge of their nature, and are not experimenting, but relying on simple observation) must be determined by observing the order in which they occur ; and the immediacy of their connection is also a matter for observation, aided by whatever instruments and methods of inspection and measurement may be available. As to the invariability of the connection, it may of course be tested by collecting more instances or making more experi- ments ; but it has been maintained, that a single experiment according to this method, if satisfactorily performed, is suf- ficient to prove causation, and therefore implies invariabi- lity (since causation is unifor.n), though no other instances -ii»^ 1 THE CANONS OF DIRECT INDUCTION 181 should ever be obtainable ; because a single perfect experi- ment establishes the unconditionality of the connection. Now, formally this is true ; but in any actual investigation how shall we decide what is a satisfactory or perfect experiment? R C Such an experiment requires that in the negative instance > q r B C shall be the least assemblage of conditions necessary to co-operate with A in producing/; and that it is so cannot be ascertained without either general prior knowledge of the nature of the case or special experiments for the purpose. So that invariability will not really be inferred from a single expe- riment j besides that every prudent inquirer repeats his experi- ments, if only to guard against his own liability to error. The supposed plurality of causes, does not affect the Method of Difference. In the above symbolic case, A is clearly one cause (or condition) of /, whatever other causes may be possible ; whereas in the former case of the Single Method of Agreement, it remained doubtful (admitting a plurality of causes) whether A, in spite of being always present with/, was ever a cause or condition of it. Now this Method of Difference is perhaps oftener than any other, though without our being distinctly aware of it, the basis of ordinary judgments. That the sun gives light and heat, that food nourishes and fire burns, that a stone will break a window or kill a bird, that turning a tap hastens or checks the flow of water or of gas, and thousands of other propositions are known to be true by rough but often emphatic applications of this method in common experience. It should be noticed that there are two v%fays in which this application may be made : either (a) by observation, taking for our two instances distinct assemblages of conditions, differing only in one|particular with its antecedent or consequent ; or (6) by experiment, regarding as our two instances the same assemblage of conditions, before and after the introduction of a certain agent. If, for example, there are two men of closely similar age, health, clothing and habits, one of whom stands in the shade and feels cool, whilst the other stands in the sun and feels warm, this shows in the former way, by observation, that the sun gives heat ; but if, instead of this, the man who stands in th^shade merely steps into the sunshine and feels warm, the same proposition is proved in the latter way by experiment. The experimental way is the better i82 LOGIC: DEDUCTIVE AND INDUCTIVE when, as in this case, an immediate sequence can be obtained, because it gives a greater certainty of there being no difference between the two instances except the intervention of the given agent. For when there are two separate sets of conditions, it may be very difficuU to make sure that they are exactly similar except in one circumstance with its ante- cedent or consequent. On the other hand, the experimental method is unsatisfactory if some time must elapse between the introduction of the agent and the manifestation of its effects ; for then other changes may have occurred meanwhile to which these effects are really due. If you throw a stone at a window and the window breaks (nothing else having happened apparently), it will be thought pretty clear that the missile was the immediate unconditional antecedent of the fracture : but if, feeling out of sorts, you take a drug and some time afterwards feel better, it is not clear on this ground alone that the drug was the cause of recovery, for other curative processes may have been active mean- while — food, or sleep, or exercise. Any book on some branch of Physics or on Chemistry will furnish scores of examples of the Method of Difference ; such as Galileo's ex- periment to show that air has weight, by first weighing a vessel filled with ordinary air, and then filling it with condensed air and weighing it again ; when the increased weight can only be due to the greater quantity of air contained. The melting-point of solids is determined by heating them until they do melt (as silver at looo^ C, gold at 1250°, platinum at 2000°) ; for the only difference between bodies at the time of melting and just before is the addition of so much heat. Similarly with the boiling-point of liquids. That the transmission of sound depends upon the continuity of an elastic ponderable medium, is proved by letting a clock strike in a vacuum (under a glass from which the air has been withdrawn by an air-pump), and standing upon a non-elastic pedestal : when the clock may be seen to strike, but makes only such a faint sound as may be due to the imperfections of the vacuum and the pedestal. The experiments by which the chemical analysis or synthesis of various forms of matter is demonstrated, are simple or compound appli- cations of this Method of Difference, together with the quantitative mark of causation (that cause and effect are equal) ; since the bodies resulting from an analysis are equal in weight to the body analysed, and the body resulting from a synthesis is equal in weight to the bodies synthesised. That an electric current resolves water into oxygen and hydrogen may be proved by inserting the poles of a galvanic battery in a vessel of water ; when this one change is followed by another, the rise of babbles from each pole and the very gradual decrease of the water. If the bubbles are caught in receivers placed over them, it can be shown that the joint weight of the two bodies of gas thus formed is equal to the weight of the water that has disappeared ; and that the '^4^ I THE CANONS OF DIRECT INDUCTION 183 gases are respectively oxygen and hydrogen may then be shown by proving that they have the properties of those gases according to further experiments by the Method of Difference ; as {e.g.) that one of them is oxygen, because it supports combustion, and combines in certain definite proportions with carbon, sulphur, etc. In the more complex sciences the Method of Difference is not so generally applicable, because of the greater difficulty of being sure that only one circumstance at a time is altered ; still, it is frequently used. Thus, if by dividing a certain nerve certain muscles are paralysed, it is shown that normally that nerve controls those muscles. In his work on Earth li'oyms, Darwin argues that, though sensitive to mechanical tremors, they are deaf (or, at least, not sensitive to sonorous vibrations transmitted through the air) by the following experiment. He placed a pot containing a worm that had come to the surface, as usual at night, upon a table, w hilst close by a piano was violently played ; but the worm took no notice of the noise. He then placed the pot upon the piano whilst it was being played, when the worm, feeling the vibrations, hastily slid back into its burrow. When, instead of altering one circumstance in an instance (which we have done our best not otherwise to disturb) and then watching what follows, we try to find ready-made instances of a phenomenon, which only differs in one other circumstance, it is, of course, still more diffi- cult to be sure that there is really only one other circumstance in which they differ. It may be worth while, however, to do our best to find such instances. Thus, that the temperature of ocean currents influences the climate of the shores they wash, seems to be shown by the fact that the average temperature of Newfoundland is lower than that of the Norwegian coast some 15° further north. Both regions have great con- tinents at their back ; and as the mountains of Norway are higher and capped with perennial snow, we might expect a colder climate there : but the shore of Norway is visited by the Gulf Stream, whilst the shore of Newfoundland is traversed by a cold current from Greenland. Again, when in 1841 the railway from Rouen to Paris was being built, gangs of English and gangs of French workmen were employed upon it, and the English got through about one-third more work per man than the French. It was suspected that this difference was due to one other difference, namely, that the English fed better, preferring beef to thin soup. Now, logically, it might have been objected that the evidence was unsatisfactory, seeing that the men differed in other things besides diet — in ' race ' (say), which explains so much and so easily. But the Frenchmen, having been induced to try the same diet as the English, were, in a few days, able to do as much work: so that the "two instances" were better than they looked. It often happens that evidence, though logically questionable, is good when used by experts, whose familiarity with the subject makes it good. i84 LOGIC: DEDUCTIVE AND INDUCTIVE THE CANONS OF DIRECT INDUCTION 185 § 4. The Canon of Variations. Whatever phenomenon varies in any manner wherever another phenomenon (consequent or antecedent) varies in some particular yjianner [no other change having concurred] is either a cause or effect 0/ that phefiome?ion [or is connected with it through some fact of causation]. This is not an entirely fresh method, but may be regarded as a special case either of Agreement or of Difference, to prove the cause or effect, not of a phenomenon as a whole, but of some modification of it. There are certain forces, such as gravitation, cohesion, heat, friction, that can never be elimi- nated altogether, and therefore can only be studied in their degrees. To such phenomena the method of Difference can never be fully applied, because there are no negative instances. But we may obtain negative instances of a given quantity of such a phenomenon (say, heat), and may apply the method of Difference to that quantity. Thus, if the heat of a body in- creases 10 degrees, from 60 to 70, the former temperature of 60 was a negative instance in respect of those 10 degrees ; and if only one other circumstance (say, friction) has altered at the same time, that circumstance (if an antecedent) is the cause. Accordingly, if in the above Canon we insert, after ' particular manner ', " [no other change having concurred] ", it is a state- ment of the method of Difference as applicable to the in- crement of a phenomenon instead of to the phenomenon as a whole ; and we may then omit the last clause — *' [or is con- nected, f/r.]." For these words are inserted to provide for the case of part-effects of a common cause (such as the flash and report of a gun) ; but if no other change (such as the discharge of a gun) has concurred with the variations of two phenomena, there cannot have been a common cause, and they are therefore cause and effect. If, on the other hand, we omit the clause " [no other change' having concurred] ', the Canon is a statement of the method of Agreement as applicable to the increment of a phenomenon / r instead of to the phenomenon as a whole ; and it is then subject to the imperfections of that method : that is to say, it leaves open the possibilities, that an inquirer may overlook a plurality of causes ; or may mistake a connection of two phenomena, which (like the flash and report of a gun) are part-effects of a common cause, for a direct relation of cause and effect. It may occur to the reader that we ought also to distinguish Quali- tative and Quantitative Variations as two orders of phenomena to which the present method is applicable. But, in fact, Qualitative Variations may be adequately dealt with by the foregoing methods of Agreement, Double Agreement, and Diiference ; because a change of quality or property entirely gets rid of the former phase of that quality, or substi- tutes one for another ; as when the ptarmigan changes from brown to white in winter, or as when a stag sheds his antlers. The peculiar use of the Method of Variations, however, is (as already observed) to formulate the conditions of proof in respect of those causes or effects which cannot be entirely got rid of, but can be obtained only in greater or less amount ; and such phenomena are, of course, quantitative. We may then illustrate the two cases of the method thus : Agreement in variations — ABC A' D E A' F G p q r p' s t p" u V Here the accompanying phenomena change from time to time, and the one thing in which the instances agree throughout is that any increase of A (A' or A") is followed or accompanied by an increase of / (/' or /") : whence it is argued that A is the cause of/, according to Prop. III. {a) (ch. xv. § 7). Still, it is supposable that, in the second instance, D or E may be the cause of the increment of/ ; and that, in the third instance, F or G may be its cause. And, since an actual investigation of this type must rely on observation, it is further possible that some undiscovered cause, X, is the real determinant of both A and/, and of their concomitant variations. Professor Ferri, in his Criminal Sociology, observes: "I have shown that in France there is a manifest correspondence of increase and decrease between the number of homicides, assaults and malicious wounding, and the more or less abundant vintage, especially in the years of extraordinary variations, whether of failure of the vintage 186 LOGIC: DEDUCTIVE AND INDUCTIVE (1853-5.1859,1867, 1873, 1878-80), attended by a remarkable diminu- tion of crime (assaults and wounding), or of abundant vintages (1850, 1856-8, 1862-3, 1865, 1S68, 1874-5), attended by an increase of crime " (p. 117, Eng. trans). And earlier he had remarked that such crimes also " in their oscillations from month to month display a characteristic increase during the vintage periods, from June to December, notwith- standing the constant diminution of other ofJ'ences " (p. yj). This is a necessary appeal to the canon of Concomitant Variations, because France is never without her annual vintage, nor yet without her annual statistics of crime. We can only faintly imagine what would happen if there were no vintage ! Still, it is an argument whose cogency is only that of Agreement, showing that very probably the abuse of the vintage is a cause of crimes of violence, but leaving open the supposi- tion, that some other circumstance or circumstances, arising or varying from year to year, may determine the increase or decrease of crime ; or that there is some unconsidered agent which afiects both the vintage and crimes of violence. French sunshine, it might be urged, whilst it matures the generous grape, also excites a morbid fermentation in the human mind. Difference in Variations may be symbolically represented thus : AB A'B A ' B /^/' f ^I Here the accompanying phenomena are always the same — ; and the only point in which the successive instances differ is in the increments of A (A', A ") followed by corresponding incre- ments of / (/', / ') : hence the increment of A is the cause of the increment of/. For examples of the application of this method, the reader should refer to some work of exact science. He will find in Deschanel's Natural Philosophy, c. 32, an account of some experiments by which the connection between Heat and Mechanical Work has been established. It is there shown that " whenever work is performed by the agency of heat " [as in driving an engine], " an amount of heat disappears equiva- lent to the work performed ; and whenever mechanical work is spent in generating heat " [as in rubbing two sticks together], " the heat gene- rated is equivalent to the work thus spent." And an experiment of Joule's is described, which consisted in fixing a rod with paddles in a vessel of water, and making it revolve and agitate the water by means of a string wound round the rod, passed over a pulley and attached to a weight that was allowed to fall. The descent of the weight was , THE CANONS OF DIRECT INDUCTION 187 measured by a graduated rule, and the rise of the water's temperature by a thermometer. "It was found that the heat communicated to the water by the agitation amounted to one pound-degree Fahrenheit for every 772 foot-pounds of work " expended by the falling weight. As no other material change seems to take place during such an experiment, it shows that the progressive expenditure of mechanical energy is the cause of the progressive heating of the water. ''"^. The Thermometer itself illustrates this method. It has been found , that the application of heat to mercury expands it according to a law ; / and hence the volume of the mercury, measured by a graduated index, is used to indicate the temperature of the air, water, animal body, etc., in which the thermometer is immersed, or with which it is brought in contact. In such cases, if no other change has taken place, the heat of the air, water, or body, is the cause of the rise of the mercury in its tube. If some other substance (say spirit) be substituted for mercury in constructing a thermometer, it serves the same purpose, provided the index be graduated according to the law of the expansion of that sub- stance by heat, as experimentally determined. It may be added that instances of phenomena that do not vary together indicate the exclusion of a supposed cause (by Prop. III. (r)). The I^Graphic JNIethod is an interesting way of exhibiting Concomitant Variations to the eye. It is extensively used in physical and statistical inquiries. Along a horizontal line (the abscissa) is measured one of the conditions (or agents) with which the inquiry is concerned, called the Variable ; and along perpendiculars (ordinates) is measured some phenomenon to be compared with it, called the Variant. Thus, the expansion of a liquid by heat may be represented by measuring degrees of temperature along the horizontal, and the ex- FiG. 9. I' s •I 1 I 1 I L_L. 40 50 eo L I u 70 J I 1_ -1 1 L. J \ L. 80 90 roo De^jrees of Htuit pansion of a column of the liquid in units of length along the perpendicular. In the next Diagram, reduced from one given by Mr. C. H. i88 LOGIC: DEDUCTIVE AND INDUCTIVE Si 3 t; o CO 3 XI c o 0) H 2 o ca S-i 'a V C o -♦-* a B 3 CA) C O u 3 Q •■i-i o -• IV Xi c o CA 6 a u M ^ ^ " - CO t t 4 ? n •<> 1 5 1 1 1 5? 1^ ' 1 1 cr> 1 t ^ ^ ♦^. ^- * *• ^ 1 \ \ / 1 1 07 \ / • \ r i 1 : cr» , \ V i / 1 s \ \ • / • 4 • • • \ \ • / 1 • • • • • • If \ t 1 • • • • ■ > ■■ rr. / A \. • • • • 1 / / • \ V 9i i i t • • • * \ • / • f • a • ■ • > t \ • < * m • • • 5^ • / • / • • • • • • o y * • f • • • • • 1 • / / • • • • • • « • \ Z> V 1 «M C4 1 «0 t • \ <« 1 ft- § 1 § Ik ^ «0 ^ c? $- 1 C/3 0) O c 3 O o a 3 o * 0) c O C/3 U 4) »o u nJ CL, ■*-> C o N l-i o c O 1 J THE CANONS OF DIRECT INDUCTION 189 Denyer in an article on the price of tea {Economic Journal, No. 9), the condition measured horizontally is Time ; and, vertically, three variants are measured simultaneously, so that their relations to one another from time to time may be seen at a glance. From this it is evident that, as the Duty on Tea falls, the Price of Tea falls, whilst the Consumption of Tea rises ; and, in spite of some irregularity of correspondence in the courses of the three phenomena, their general causal connection can hardly be mistaken. It will be noticed that these three lines, especially those of Price and Consumption (which may be considered natural resultants, in contrast with the arbitrary fixation of a Tax), do not depart widely from regular curves ; and accordingly, assuming the causes at M^ork to vary con- tinuously during the intervals between points of measurement, curves may be substituted. In fact, a curve often represents the course of a phenomenon more truthfully than can be done by a line that zigzags along the exact measurements ; because it is less influenced by tem- porary and extraordinary causes that may obscure the operation of those that are being investigated. On the other hand, the abrupt deviations of a punctilious zigzag may have their own logical value, as will appear in the next section. § 5. The Canon of Residues. Subduct from any phe?iomenon such part as previous induc- tions have shown to be the effect of certain antecedents, and the residue of the phenomeno7i is the effect of the reinai?iing ante- cedents. The phenomenon is here assumed to be an effect : a similar Canon may be framed for residuary causes. This also is not a fresh method, but a special case of the method of Difference. For if we suppose the phenomenon to hep q r, and the antecedent to be A B C, and that we already know B and C to have (either severally or together) the con- sequents g r, in which their efificacy is exhausted ; we may B C regard as an instance of the absence of / obtained deduc- q r ABC tively from the whole phenomenon by our knowledge of P q r ' ABC the laws of B and C ; so that — is an instance of the P V ^ I90 LOGIC: DEDUCTIVE AND INDUCTIVE presence of/, differing otherwise from ^-^ in nothing except ^ r or that A is also present. By the Canon of Difference, therefore A is the cause of /. Or, again, when phenomena thus treated are strictly quantitative, the method may be based on Prop. III. (/O, ch. XV. § 7. Of course, if A can be obtained apart from B C and directly experimented with so as to produce/, so much the better; and this may often be done ; but the special value of the method of Residues appears, when some complex phenomenon has been for the most part accounted for by known causes, whilst there remains some excess, or shortcoming, or deviation from the result which those causes alone would lead us to expect, and this residuary fact has to be explained in relation to the whole. Here the negative instance is constituted by deduction, showing what would happen but for the interference of some unknown cause which is to be investigated ; and this prominence of the deductive process has led some writers to class the method as deductive. But we have seen that all the Canons involve deduction ; and, considering how much in every experiment is assumed as already known (what circumstances are * material,' and when conditions may be called ' the same '), the wonder is that no one has insisted upon regarding every method as concerned with residues. In fact, as scientific explanation progresses, the phenomena that may be considered as residuary become more numerous and the importance of this method increases. Examples : The recorded dates of ancient eclipses having been found to differ from those assigned by calculation, it has been surmised that the average length of a day may in the meanwhile have increased. If so, this is a residuary phenomenon not accounted for by the causes formerly recognised as determining the rotation of the earth on its axis ; and it may be explained by the doctrine that the tides, by their friction, are reducing the rate of the earth's rotation, and thereby lengthening the day. Capillarity seems to be a striking exception to the principle that water (or any liquid) ' finds its level,' that being the condition of equili- brium; yet capillarity proves to be only a refined case of equilibrium THE CANONS OF DIRECT INDUCTION 191 when account is taken of the forces of adhesion generated by different kinds of bodies in contact. " Many of the new elements of Chemistry," says Herschel, "have been detected in the investigation of residual phenomena." Thus, Lord Rayleigh found that nitrogen from the atmosphere was slightly heavier than nitrogen got from chemical sources. The search for the cause of this difference led to the discovery of argon. Darwin suggested Sexual Selection as a means of explaining certain modifications of animals in form, colouration, or habits, which did not seem to him to have resulted from their struggle for existence in relation to other species or to external conditions. The economist shows that when a country imports goods the chief means of paying for them is to export other goods. If this were all, imports and exports would be of equal value : but the United Kingdom imports about /40o,ooo,ooo annually, and exports about ;^3oo,ooo,ooo. Here, then, is a residuary phenomenon of ;^ 100,000,000 to be accounted for. But foreign countries owe us about ;^5o,ooo,ooo for the use of shipping, and £70,000,000 as interest on the capital we have lent them, and ;^ 1 5. 000, 000 in commissions upon business transacted for them. These sums added together amount to ;^ 1 35,000,000 ; and that is ;^35, 000,000 too much. Thus another residuary phenomenon emerges ; for whilst foreigners seem to owe us ;^435,ooo,ooo, they only send us ;^40o,ooo,ooo of imports. To account for these ;^35,ooo,ooo, we may suppose that they represent the annual investment of our capital abroad, in return for which no immediate payment is due ; and, these being omitted, exports and imports balance. When, in pursuing the method of Variations, the phenomena com- pared do not always correspond in their fluctuations, the irregular movements of that phenomenon which we regard as the effect may often be explained by treating them as residuary phenomena, and then seeking for exceptional causes, whose temporary interference has ob- scured the influence of the general cause. Thus, returning to the dia- gram of the Price of Tea in § 4, it is clear that generally the Price falls as the Duty falls; but in Mr. Denyer's more minutely wrought diagram, from which this is reduced, it may be seen that in 1840 the Price of Tea rose from 3s. gd. to 4s. gd. without any increase of Duty. This, how- ever, is readily explained by the Chinese War of that year, which, of course, checked the trade. Again, from 1869 to 1889 the Duty was constant, whilst the Price of Tea fell as much as 8^. per lb. ; but this residuary phenomenon is explained by the prodigiously increased pro- duction of Tea during that period in India and Ceylon. CHAPTER XVII COMBINATION OF INDUCTION WITH DEDUCTION § I. We have now reviewed Mill's five Canons of Inductive Proof. At bottom, as he observes, there are only two, namely. Agreement and Difference ; since the Double Method, Varia- tions and Residues are (as we have seen) only special forms of the other two. And indeed it may almost be said that in the final analysis they are all reducible to one, namely, Difference ; for the cogency of the Method of Agreement, as distinguished from a simple enumeration of instances agreeing in the coincidence of a supposed Cause and its Effect, depends upon the omission, in one instance after another, of all other circumstances; which omission is a point of difference. Now, the Canons are an analysis of the conditions of proving directly, by means of observation or experiment, any proposition that predicates causation. Rut if we say ' by means of observation or exoeriment,' it is not to be under- A. ' stood that these are the only means and that nothing else is involved ; for it has been shown that the Law of Causation is itself an indispensable foundation of the evidence. In fact Inductive Logic may be considered as having a purely formal character. It consists, first, in a statement of the Law of Cause and Effect ; secondly, in certain immediate inferences from this Law, expanded into the Canons ; thirdly, in the syllogistic application of the Canons to special proposi- tions of causation by means of minor premises, showing that certain instances satisfy the Canons. COMBINED INDUCTION AND DEDUCTION 193 At the risk of some pedantry, we may exhibit the process as follows (cf. Prof. Ray's Logic : Appendix D) : Whatever relation of events has certain marks is a case of Causation ; The relation A : /J has some or all of these marks (as shown by observation and by the conformity of instances to such or such a Canon) : Therefore, the relation A : / is a case of Causation. Now, the parenthesis, "as shown by the conformity, eU.," is an adscititious member of an Epicheirema, which may be stated, as a Prosyllogism, thus : If an instance, etc. (Canon of Difference) ; A B C BC are of the kind required : The instances P q r q r Therefore, the antecedent A, present where / occurs and absent where it does not occur, is the cause of/. Such is the bare Logic of Induction: so that, strictly speakmg, observation or experiment is no part of the logic, but a means of applying the logic to actual, that is, not merely symbolical, propositions. The Formal Logic of Induction is essentially deductive; and it has been much questioned whether any transition from the formal to the material conditions of proof is possible. As long as we are content to illustrate the Canons with symbols, such as A and /, all goes well ; but can we in any actual investigation show that the relevant facts or ' instances ' correspond with those symbols ? In the first place, as Dr. Venn shows, natural phenomena want the distinctness and capability of isolation that belong to symbols. Secondly, the observing whether instances conform to a Canon, must always be subject at last to the limits of our faculties. How can we ascertain exact equality, immediate sequence? The Canon of Difference, in its experimental application, is usually considered the most cogent sort of proof: yet when can the two sequent instances, before and after the introduction of a certain agent, be said to differ in nothing else ? Are not earth and stars always changing posi- N 194 LOGIC: DEDUCTIVE AND INDUCTIVE tion ; is not every molecule in the room and apparatus always oscillating? It is true that our senses are now aided by elaborate instruments ; but the construction of these depends on scientific theories, which again depend on experiments. It is right to touch upon this well-known sceptical topic ; but to insL much upon it is not a sign of good sense. The works of Herschel, Whewell, and Jevons should be consulted for the various methods of correcting observations, by repeating them, averaging them, verifying one experimental process by another, always refining the methods of exact measurement, multiplying the opportunities of error (that if any exist it may at last show itself), and by other devices of what may be called Material Logic. But, probably, only many years spent in the study and personal manipulation of scientific processes, can give a just sense of their effectiveness ; and to stand by, sug- gesting academic doubts, is easier and more amusing. § 2. Still, it is not so much in laws based upon direct obser- vation or experiment, that the material validity of scientific reasoning appears, as in the cumulative evidence that arises from the co-ordination of laws within each science, and the growing harmony and coherence of all sciences. This requires a more elaborate combination of deduction with observation and experiment. During the last three hundred years many departments of science have been reduced under prmciples of the greatest generality, such as the Law of Gravitation, the Undulatory theory of Light, the Conservation of Energy, and the Theory of Natural Selection ; connecting and explaining the less general laws, which, again, are said to connect and explain the facts. Meanwhile, those sciences that were the first to make progress have been useful in developing others which, like Biology and Sociology, present greater difticulties. In fact it is more and more apparent that the distinctions drawn among Sciences are entirely for the convenience of study and that all Sciences tend to merge in one universal Science of Nature. Now, this process of the ' unification of knowledge ' is almost another name for deduction ; but at the COMBINED INDUCTION AND DEDUCTION 195 same time it depends for its reality and solidity upon a constant reference to observation and experiment. Of the logical character of this process only a very inadequate notion can be given in the ensuing chapters. Let us begin by returning to some earlier considerations. We have seen in chap. xiv. § 6, that when two or more agents or forces combine to produce a phenomenon, their effects are intermixed in it, and this in two ways according to their nature. In chemical action and in vegetable and animal life, the causes concerned are blended in their results in such a way that most of the qualities which they exhibited severally are lost, whilst new qualities appear instead. Thus chlorine (a gas) and sodium (a metal), in a certain combination, form common salt; which is quite unlike either of them : a man eats bread, and it becomes muscle, nerve and bone. In such cases we cannot trace the qualities of the causes in the qualities of the effects ; given such causes, we can prove by experimental analysis and synthesis, according to the canons of induction, that they have such effects ; but we may not be able in any new case to calcu- late what the effects will be. On the other hand, in Astronomy and Physics, the causes treated of are mechanical ; at least, it is the aim of Physics to attain to a mechanical conception of phenomena ; so that, in every new combination of forces, the intermixed effect, or re- sultant, can be calculated beforehand ; provided that the forces concerned admit of being quantitatively estimated, and that the conditions of their combination are not so complex as to baffle the powers of mathematicians. In such cases, therefore, when direct observation or experiment is insufficient to resolve an effect into the laws of its causes, the general method is to ) calculate what may be expected from a combination of its r causes, either as known or hypothetically assumed, and to ! compare the anticipation with the actual phenomenon. J § 3. This is what Mill calls the Direct Deductive Method; or, the Physical Method, because it is so much relied on in treating of Light, Heat, Sound, etc.\ though it is also the 196 LOGIC: DEDUCTIVE AND INDUCTIVE usual method of Astronomy and Economics; Deduction leads the way, and its results are tested by f "<=''- 3", ments or observations. Given any complex mechanical phenomenon, the inquirer considers-(.) what laws already ascertained by induction seem likely to apply to .t (m default of known laws, hypotheses are substituted : cf. chap, xvni.) ; he then" (.) computes the effect that will follow from these laws in circumstances similar to the case before him ; and (3) be verifies his conclusion by comparing it with the actual pheno- menon. A ^ell-tried and staunch example of this method is the explanation of the rise of .ater in the •common pump.' We know three law aii^' able to this case: ,.) that the a.-sphere weighs upon the wte outside the pump with a pressure of 14 lb. to the square inch (i- tha a iTquid (and therefore the water) transmits pressure equally n al di cUon (upwards as svell as downwards and sideways) and (.) that nressure upon a body in any direction, if not counteracted by an oppo- site pressure, produces motion. Hence, when the rise of the p.stott of he pump r moves the pressure upon the water withm the cy mder tending to produce a vacuum there, this water is pushed up by he pres ure of^the air upon the water outside the cylinder, and follows the risfnepiston, until L column of water inside the cylinder exerts a pressure equkl to that of the atmosphere upon a given area. So much ?or the computation ; does it correspond with the fact ? It ,s found tha at the sea-level water can be pumped to the height of 32 feet and that such a column of water has a pressure of .4 lb. to the square inch. We ™^v show further that, at the sea level, spirits of wine may be pumped r.Lr a corig to it^ less speciBc gravity ; and that if we attempt to pump water at successive altitudes above the sea level, we can only raise Ft t^Us and less heights, corresponding with the lessened atmospheric prrssure at those aUitudes, where the column of air producing the ^esu e is shorter. Finally, if we try to work a pump, having first pro- duced a vacuum over the water outside the cylinder, we shall find that the water inside will not rise at all; the piston can be raised, but the watr does not follow it. The verification thus shows that the com- puted effect corresponds with the phenomenon to be explained that Ihe result does not depend upon the nature of water only, bu' s ' "e (allowing for differences of specific gravity) of other liquids , that if the pressure of the outside air is diminished, the height of pumping is so wo (canon of Variations) ; and that it that pressure is entirely removed, Dumping becomes impossible (canon of Difference). Any text-book of Astronomy or Physics furnishes numerous lUustra- i COMBINED INDUCTION AND DEDUCTION 197 tions of this method. Take, for example, the first chapter of Deschanel's Optics, where are given three methods of determining the velocity of Light. This was first deduced from observation of Jupiter's satellites. The one nearest the planet passes behind it, or into its shadow, and is eclipsed at intervals of about 42^ hours. But it can be shown that, when Jupiter and the Earth are nearest together on the same side of the Sun, an eclipse of this satellite is visible from the earth 16 min. 266 sec. earlier than when Jupiter and the Earth are furthest apart on opposite sides of the Sun : 16 min. 26' 6 sec, then, is the time in which light traverses the diameter of the Earth's orbit. Therefore, supposing the Earth's distance from the Sun to be 91^ millions of miles, light travels about 185,500 miles a second. Another deduction, agreeing with this, starts from the fact of aberration, or the displacement of the apparent from the actual position of the stars in the direction of the earth's motion. Aberration depends partly on the velocity of light, partly on the velocity of the Earth ; and the latter being known, the former can be computed. Now, these two deductive arguments, verify- ing each other, have also been verified experimentally. Foucault's experiment to measure the velocity of light is too elaborate to be described here : a full account of it will be found in the treatise above cited, § 687. When the phenomena to be explained are of such a character, so vast in extent, power or duration, that it is impossible, in the actual circum- stances of the case, to frame experiments in order to verify a deductive explanation, it may still be possible to reproduce a similar phenomenon upon a smaller scale. Thus Monge's explanation of mirage by the great heat of the desert sand, which makes the lowest stratum of air less dense than those above it, so that rays of light from distant objects are refracted in descending, until they are actually turned upwards again to the eye of the beholder, giving him inverted images of the objects as if they were reflected in water, is manifestly incapable of being verified by experiment in the natural conditions of the pheno- menon. But by heating the bottom of " a sheet-iron box, with its ends cut away," the rarefied air at the bottom of the box may sometimes be made to yield reflections ; and this shows at least that the supposed cause is a possible one (Deschanel, Optics, § 726). Similarly as to the vastest of all phenomena, the evolution of the stellar system, and of the solar system as part of it, from an immense cloudlike volume of matter : Mr. Spencer, in his Essay on The Nebular Hypothesis {Essays, I. vi.), says, amidst a great array of deductive arguments from mechanical principles, that " this ci priori reasoning harmonises with the results of experiment. Dr. Plateau has shown that when a mass of fluid is, as far as may be, protected from the action of external forces, it will, if made to rotate with adequate velocity, form detached rings ; and that these rings will break up into spheroids, which turn on their axes in the same direction 198 LOGIC: DEDUCTIVE AND INDUCTIVE Nvith the central mass." The theory of the evolution of species of plants and animals by Natural Selection, again, though, of course, it cannot be verified by direct experiment (since experiment implies arti- ficial arrangement), and the process is too slow for observation, is nevertheless, to some extent confirmed by the practice of gardeners and breeders of animals. Since, by taking advantage of accidental varia- tions of form and colour in the plants or animals under their care, and relying on the heritability of these variations, they obtain extensive modifications of the original stocks, and adapt them to the various purposes for which flowers and cereals, poultry, dogs and cattle are domesticated. This shows, at least, that living forms are plastic and extensively modifiable in a comparatively short time. § 4. Suppose, however, that, in verifying a deductive argu- ment, the effect as computed from the laws of the causes assigned, does not correspond with the facts observed : there must then be an error somewhere. If the fact has been accurately observed, the error must he cither in the process of deduction and computation, or else in the premises. As to the process of deduction, it may be very simple and easily revised, as in the above explanation of the common pump ; or it may be very involved and comprise long trains of mathe- matical calculation. If, however, on re-examining the compu- tations, we find them correct, it remains to look for some mistake in the premises. (I) We may not have accurately ascertained the laws, or the modes of operation, of the forces present. Thus, the rate at which bodies fall was formerly believed to vary in proportion to their relative weights ; and any estimate based upon this belief is not likely to have agreed with the facts. Again, the corpuscular theory of light, namely, that the physical cause of light is a stream of fine particles projected in straight lines from the luminous object, though it seemed adequate to the explanation of many optical phenomena, could not be made to agree with the facts of interference and double refraction. (2) The circumstances in which the agents are combined may not have been correctly conceived. When Newton began to inquire whether the attraction of the earth determined the orbit of the moon, he was at first disappointed. " According to Newton's calculations, made at this time " says Whewell. " the moon, by her motion in her orbit, was deflected from the tangent every minute through a space of thirteen feet. But by noticing the space which bodies would fall in one minute at the earth's surface, and supposing this to be diminished in the ratio of the COMBINED INDUCTION AND DEDUCTION 199 inverse square, it appeared that gravity would, at the moon's orbit, draw a body through more than fifteen feet." In view of this discre- pancy he gave up the inquiry for sixteen years, until in 1682, having obtained better data, he successfully renewed it. " He had been mis- taken in the magnitude of the earth, and consequently in the distance of the moon, which is determined by measurements of which the earth's radius is the base." It was not, therefore, a mistake as to the law or nature of the forces concerned (namely, the law of the inverse square and the identity of celestial with terrestrial gravity), but as to the cir- cumstances in which the agents (earth and moon) were combined, that prevented his calculations being verified. {Hist. Ind. Sc. : VII. ii. 3.) (3) One or more of the agents affecting the result may have been overlooked and omitted from the estimate. Thus, an attempt to explain the tides by taking account only of the earth and the moon will not entirely agree with the facts, since the sun also influences the tides. This illustration, however, shows that when the conclusion of a deduc- tive explanation does not entirely agree with the facts, it is not always to be inferred that the reasoning is, properly speaking, wrong ; it may be right as far as it goes, and merely inadequate. Hence (a) it is often in just such cases that an opportunity occurs of applying the Method of Residues, by discovering the agent that must be allowed for in order to complete the explanation. And {b) the investigation of a phenomenon is often designedly begun upon an imperfect basis for the sake of sim- plicity ; the result being regarded as a first approximation, to be afterwards corrected by including one by one the remaining agents or circumstances affecting the phenomenon, until the theory is complete ; that is. until its agreement with the facts is satisfactory. (4) We may have included among the data of our reasonings agents or circumstances that do not exist or do not affect the phenomenon in question. In the early days of science purely fanciful powers were much relied upon : such as the solid spheres that carried the planets and stars ; the influence of the planets upon human destiny ; the ten- dency of everything to seek " its own place," so that fire rises to heaven, and solids fall to the earth ; the " plastic virtue " of the soil, which was once thought to have produced fossils. It may be said, however, that when such conceptions hindered the progress of explanation, it was not so much by vitiating the deductive method as by putting men off from exact inquiries. More to our present purpose were the supposed cata- clysms, or extraordinary convulsions of the earth, a belief in which long hindered the progress of Geology. Again, in Biology. Psychology, and Sociology many explanations have depended upon the doctrine that any improvement of structure or faculty acquired by an individual may be inherited by his descendants : as that, if an animal learns to climb trees, his offspring have a greater aptitude for that mode of life ; that if a man tries to be good, his children find it easier to be virtuous ; 200 LOGIC: DEDUCTIVE AND INDUCTIVE that if the inhabitants of a district carry on cloth-work, it becomes easier for each successive generation to acquire dexterity in that art. But now the heritabiUty of powers acquired by the individual through his own efforts, is disputed ; and, if the denial be made good, all such explanations as the above must be revised. Clearly, then, if the premises of a deductive argument be vitiated in any of these four ways, its conclusion will fail to agree with the results of observation and experiment, unless, of course, one kind of error happen to be cancelled by another that is ' equal and opposite.' We now come to a variation of the method of combining Induction with Deduction, so important as to require separate treatment. § 5. The Inverse or Historical Method has of late years become remarkably fruitful. When the forces determining a phenomenon are too numerous, or too indefinite, to be com- bined in a direct deduction, we may begin by collecting an empirical law of the phenomenon (as that ' the democracies of City-states are arbitrary and fickle'), and then endeavour to show by deductions from " the nature of the case," that is, from a consideration of the circumstances and forces known to be operative (of which, in the above instance, the most important is sympathetic contagion), that such a law was to be expected. Deduction is thus called in to verify a previous Induction; whereas in the 'Physical Method' a Deduction was verified by comparing it with an Induction or an experi- ment; hence the Method now to be discussed has been named the Inverse Deductive Method. But although it is true that, in such inquiries as we are now dealing with, Induction generally takes the lead ; yet I cannot think that the mere order in which the two logical processes occur is the essential distinction between the two ways of combining them. For, in the first place, in investigations of any complexity both Induction and Deduction recur again and again in whatever order may be most convenient ; and, in the second place, the so-called 'inverse order' is sometimes resorted to in Astronomy and Physics. For example, Kepler's Laws were first collected empirically from observations of the planetary motions, and afterwards deduced by Newton from the Law of Gravitation : this, then, was the Inverse Method ; ]l COMBINED INDUCTION AND DEDUCTION 201 but the result is something very different from any that can be obained by the Historical Method. The essential difference between the Physical and Historical Methods is that, in the former, w^hether Direct or Inverse, the deductive process, when complete, amounts to exact demonstration ; whereas, in the latter, the deductions consist of qualitative reasonings, and the results are indefinite. They establish — (i) a priori a merely probable connection between the phenomena according to the empirical law (say, between City-democracy and fickle politics) ; (2) connect this with other historical or social generalisations, by showing that they all alike flow from the same causes, namely, from the nature of races of men under certain social and geographical conditions ; and (3) explain why such empirical laws may fail, according to the differences that prevail among races of men and among the conditions under which they live. Thus, seeing how rapidly excitement is propagated by the chatter, grimacing, and gesticulation of townsmen, it is probable enough that the democracy of a City- state should be fickle (and arbitrary, because irresponsible). A similar phenomenon of panic, sympathetic hope and despair, is exhibited by every stock-exchange, and is not peculiar to political life. And when political opinion is not manufactured solely in the reverberating furnace of a city, fickleness ceases to characterise Democracy ; and, in fact, is not found in Switzerland or the United States. This is called the Historical Method, then, because it is more useful than any other in explaining the movements of history, and in verifying the generalisations of political and social science. We must not, however, suppose that its use is confined to such studies. Only a ridiculous pedantry would allot to each subject its own method and forbid the use of any other ; as if it were not our capital object to establish truth by any means. Wherever the forces determining a phenomenon are too numerous or too indefinite to be combined in a deductive demonstration, there the Historical Method is likely to be useful; and this seems often to be the case in 202 LOGIC: DEDUCTIVE AND INDUCTIVE Geology and Biology, as well as in the Science of History, or Sociology, and its various subsidiary studies. Consider upon what causes historical events depend : the customs, character, and opinions of all the people concerned ; the organisation of their government, and the character of their religious institutions ; the development of industry among them, of the military art, of fine art, literature and science; their relations, commercial, political and social with other nations ; the physical conditions of climate and geographical position amidst which they live. Hardly an event of importance occurs among them that is not, directly or indirectly, influenced by every one of these circumstances, and that does not react upon. Now, from the nature of the Inductive Methods, it is plain that, in such a complex and tangled situation as history presents, no satisfactory employment of them is possible ; for they all require the actual or virtual isolation of the pheno- menon under investigation. They also require the greatest attainable immediacy of connection between cause and effect ; whereas the causes of social events may accumulate durmg hundreds of years. Clearly, therefore, in collecting empirical laws from history, only very rough inductions can be hoped for, and we may have to be content with simple enumera- tion. Hence the importance of supporting such laws by deduction from the nature of the case, however faint a pro- bability of the asserted connection is thereby raised ; and this even if each law is valued merely for its own sake. Still more, if anything worth the name of Historical Science is to be con- structed, must a mere collection of such empiricisms fail to content us; and the only way to give these a scientific character is to show deductively their common dependence upon various combinations of the same causes. Yet even those who profess to employ the Historical Method often omit the deductive half of it; and of course ' practical poHticians' boast of their entire contentment with what they call ' the facts.' ^ Sometimes, however, politicians, venturing upon deductive «i COMBINED INDUCTION AND DEDUCTION 203 reasoning, have fallen into the opposite error of omitting to test their resuhs by any comparison with the facts : arguing from certain ' Rights of Man,' or * Interests of Classes,' or ' Laws of Supply and Demand,' that this or that event will happen, or ought to happen, without troubling themselves to observe whether it does happen or ever has happened. This method of deduction without any empirical verification, is called by Mill the Geometrical ; and, plainly, it can be trust- worthy only where there is no actual conflict of forces to be considered. In pure mathematical reasoning about space, time, and number, provided the premises and the reasoning be correct, verification by a comparison with the facts may be needless, because there is no possibility of counteraction. But when we deal with actual causes, no computation of their effects can be relied upon without comparing our conclusions with the facts : not even in Astronomy and Physics, least of all in Politics. Burke, then, has well said that "without the guide and light of sound well-understood principles all our reasoning in politics, as in everything else, would be only a confused jumble of particular facts and details without the means of drawing any sort of theoretical or practical conclusion " ; but that, on the other hand, the statesman, who does not take account of circumstances, infinite and infinitely combined, " is not erroneous, but stark mad." There is, or ought to be, no logical difi*erence between the evidence required by a states- man and that appealed to by a philosopher ; and since, as we have seen, the combination of principles with circumstances cannot, in solving problems of social science, be made with the demonstrative precision that belongs to astronomical and physical investigations, there remains the Historical Method as above described. Examples of the empirical laws from which this method begins will occur to every one. They abound in histories, newspapers, and political discussions, atid are of all shades of truth or half-truth : as that ' His- tory consists in the biographies of great men ' ; in other words, that the I 204 LOCxIC: DEDUCTIVE AND INDUCTIVE movements of society are due to exceptional personal powers, not to general causes ; That at certain epochs great men occur in groups ; That every Fine Art passes through periods of development, culmination and decline ; That Democracies tend to change into Despotisms ; That the possession of power, whether by classes or despots, corrupts the pos- sessor ; That ' the governments most distinguished for sustained vigour and abilities have generally been aristocracies ' ; That ' revolutions always begin in hunger ' ; That civilisation is inimical to individuality ; That the civilisation of the country proceeds from the town ; That ' the movement of progressive societies has hitherto been a movement from Status to Contract' {i.e., from a condition in which the individual's rights and duties depend on his caste, or position in his family as slave, child, or patriarch, to a condition in which his rights and duties are largely determined by the voluntary agreements he enters into) ; and this last is treated by Mr. Spencer as one aspect of the law first stated by Comte, that the progress of societies is from the military to the industrial state. The deductive process we may illustrate by Mr. Spencer's explana- tion ci priori of the co-existence in the military state of those specific characters, the inductive proof of which furnished an illustration of the method of Agreement. The type of the military State involves the growth of the warrior class, and the treatment of labourers as existing solely to support the warriors ; the complete subordination of all indi- viduals to the will of the despotic soldier-king, their property, liberty and life being at the service of the State ; the regimentation of society, not only for military, but also for civil purposes ; the suppression of all private associations, etc. Now all these characteristics arise from their utility for the purpose of war, a utility amounting to necessity if war is the State's chief purpose. For every purpose is best served when the whole available force co-operates toward it : other things equal, the bigger the army the better ; and to increase it, men must be taken from industry until only just enough remain to feed and equip the soldiers. As this state of things is not to everybody's taste, there must be despotic control ; and this control is most effective through regimentation by grades of command. I'rivate associations, of course, cannot live openly Tn such a State, because they may have wills of their own and are con- venient for conspiracy. Thus the induction of characteristics is verified by a deduction of them from the nature of the case. § 6. The greater indefiniteness of the Historical, compared with the Physical Method, both in its inductions and in its deductions, makes it, perhaps, even more difficult to work with. It wants much sagacity and more sincerity; for the demon of Party is generally too much with us. Our first care '1 COMBINED INDUCTION AND DEDUCTION 205 should be to make the empirical law as nearly true as possible, collecting as many as we can of the facts which the law is supposed to generalise, and examining them according to the canons of Induction, wdth due allowance for the imperfect applicability of those canons to such complex, unwieldy, and indefinite instances. Turning to the examples of such laws given above, it is clear that in some cases no pains have been taken to examine the facts. What is the inductive evidence that Democracies change into Despotisms ; that revolutions always begin in hunger ; or that civilisation is inimical to individuality ? Even Mill's often cjuoted saying, " that the governments remarkable in history for sustained vigour and ability have generally been aristocracies", is oddly over-stated. For if you turn to the passage {J^e/>. Gov. chap, vi.), the next sentence tells you that such governments have always been aristocracies of public functionaries ; and the next sentence but one restricts, appa- rently, the list of such remarkable governments to two — Rome and Venice. Whence, then, comes the word " generally " into Mill's law ? As to deducing our empirical law from a consideration of the nature of the case, it is obvious that we ought — (a) to take account of all the important conditions ; (/^) to allow weight to them severally in proportion to their importance ; and {c) not to include in our estimates any condition which we cannot show to be probably present and operative. Thus the Great-Man-Theory of history must surely be admitted to assign a real condition of national success. The great man organises, directs, inspires : is that nothing ? On the other hand, to recognise no other condition of national success is the manifest frenzy of a mind in the mythopoeic age. We must allow the great man his due weight, and then inquire into the general conditions that (a) bring him to birth in one nation rather than another, and {d) give him his opportunity. Mill's explanation of the success of the aristocratic governments of Rome and Venice is, that they were, in fact, bureaucracies ; that is to 2o6 LOGIC: DEDUCTIVE AND INDUCTIVE say, their members were trained in the science and art of administration and command. Here, again, we have, no doubt, a real condition ; but is it the only one? The public mind, which little relishes the scaling down of Mill's original law to those two remote cases, is persuaded hat an aristocracy is the depository of hereditary virtue, especially with reference to government, and would at once ascribe to this circum- stance the greater part of the success of any aristocratic government. Now, if the effects of training are inherited, they must, in an hereditary aristocracy, increase the energy of the cause assigned by Mill ; but, if not, such heredity is a condition " not present or not operative." Still, if families are ennobled for their extraordinary natural powers of ad- ministration or command (and this sometimes happens), it is agreed on all hands that innate qualities are heritable ; at least, if care be taken to intermarry with families similarly distinguished, and if by natural or artificial selection all the failures among the offspring be eliminated. The Spartans had some crude notion of both these pre- cautions ; and if such measures had been widely adopted, we might deduce from the doctrine of heredity a probability in favour of Mill's original proposition, and thereby verify it in its generality, if it could be collected from the facts. The Historical Method may be further illustrated by the course adopted in that branch of Social Science which has been found sus- ceptible of the most extensive independent development, namely, Economics. First, by way of contrast, I should say that the general, abstract, or theoretical treatment of Economics is according to the Physical Method ; because, as Mill explains, although the phenomena of industry are no doubt influenced, like other social affairs, by all the other circumstances of Society, government, religion, war, art, etc. ; yet, where industry is most developed, as in England and the United States, certain special causes are so much the most important that, for the purpose at least of a first outline of the science, they may conveniently be considered as the only ones. These causes are : (i) the general dis- position of men to obtain wealth with as little trouble as possible, and (2) to spend it so as to obtain the greatest satisfaction of their various desires ; (3) the causes that determine population, and (4) the tendency of extractive industry, when pushed beyond a certain limit without any improvement in the industrial arts, to yield "diminishing returns." From these causes it is easy to infer the general laws of prices, of wages and interest (which are the prices of labour and of the use of capital), and of rent; and it remains to verify these by comparing them with the facts in each case ; and (if they fail to agree with the facts) to amend them, according to the Method of Residues, by taking account of those influential causes which were omitted from the first draft of the theory. Whilst, however, this is usually the procedure of those inquirers 'I COMBINED INDUCTION AND DEDUCTION 207 who have done most to give Economics its scientific character, to insist that no other plan shall be adopted would be sheer pedantry ; and Dr. Keynes has shown, in his Scope and Method of Political Economy, that Mill has himself sometimes solved economic problems by the Historical Method. With an analysis of his treatment of Peasant Proprietorship in Book n., cc. 7 and 8 of his Principles of Political Economy, we may close this chapter. Mill first shows inductively, by collecting evidence from Switzerland. Germany, Norway. Belgium, and France, that peasant proprietors are superhumanly industrious, intelligent culti- vators, and generally intelligent men, prudent, temperate, and inde- pendent, and that they exercise self-control in avoiding improvident marriages. This group of empirical generalisations as to the character of peasant proprietors is easily deduced from the nature of the case : for their industry is a natural consequence of the fact that, however much they produce, it is all their own ; they cultivate intelligently, because for generations they have given their whole mind to it ; they are generally intelligent men, because the variety of work involved in small farming, requiring foresight and calculation, necessarily promotes intelligence ; they are prudent, because they have something to save, and by saving can improve their station and perhaps buy more land ; they are temperate, because intemperance is incompatible with industry and prudence ; they are independent, because secure of the necessaries of life, and from having property to fall back upon ; and they avoid improvidence in marriage, because the extent and fertility of their fields is always plainly before them, and therefore how many children they can maintain is easily calculated. The worst of them is that they work too hard and deny themselves too much ; but, over the greater part of the world, other peasantry work too hard : though they can scarcely be said to deny themselves too much, since all their labour for others brings them no surplus to squander upon self-indulgence. CHAPTER XVIII HYPOTHESES § I. An Hypothesis, sometimes employed instead of a known law, as a premise in the deductive investigation of nature, is defined by Mill as "any supposition which we make (either without actual evidence, or on evidence avowedly insufticient) in order to endeavour to deduce from it con- clusions in accordance with facts which are known to be real ; under the idea that if the conclusions to which the hypothesis leads are known truths, the hypothesis itself either must be, or at least is likely to be, true." The deduction of known truths from an hypothesis is its Verification ; and when this has been accomplished in a good many cases, and there are no manifest failures, it is often called a Theory : though this term is also used for the whole system of laws of a certain class of phenomena, as when Astronomy is called the ' theory of the heavens.' Between hypothesis and theory in the former sense no distinct line can be drawn ; for the complete proof of a certain speculation may take a long time, and meanwhile the gradually accumulating evidence produces in different minds very different degrees of satisfaction; so that the sangume begin to talk of 'the theory,' whilst the melancholic continue to call it ' the hypothesis.' An Hypothesis may be made concerning an agent (such as the ether), or a collocation (such as the plan of our solar system-whether geocentric or heliocentric), or a law of an agent's operation (as that light is transmitted by a wave motion). II' HYPOTHESES ^^ as^L' T'™'' "!'.P'^"^"°" °f Light involves bcth an agent, the Ether as an all pervading elastic fluid, and also the law of its operation d fi itrrs "xhe '" ^'''' V''''' ^°™ ^"^ >"«''™ nnite velocity. The agreement between the calculated results nf ^^fZVT':s^^:''^r':' ''-"^--^ oflghtt .hi t z of taXrLdf '^'prt^'- '^ ^'' ^' ''^ '"^ -- ^ bodies on the Earth MnnnQ . , ^^'""' "^""'y' ^^"l^' f«"ing hypothesis :as thai f^.ttLTtgrte "Z^l^iT':^ - rxn^ro^ -rnafrtt^^^^^^^^ was the centre of the universe and L'm' '"t"""^' "'^' °" =^"'' .srT'J :2ri.z Lr,.7„" ,r;rcr ?*- positions and Drincinlps « tUo* r , , -^P^^^^^^es as to their dis- peculiarly absurd maxim as thl*' *°"'1°°' ""?"'« motives' is a human hfe. To iZ^'bad m.r °°.°"!f "^^ °^ understanding probable, is to be Zt ng fn the I'^iffit ' •^^'".^r ^" J"^' ^^ subject in . a dry light.' Nor can Te ^ ^ ' i" '.rn'^^ ""' selves'- fnrQ^lf i.T,^ 1 J . '^^^ ^^ "^^P judging others by our- se! out lot t erp?e h tes of oth:"'' Tf"'' ^'-ting-point wh'en we combinations o? wh ch he elents^f . " ""''"''''"' "'^ "'^"f"'" how these are <^etertitrJ,Xb eedtg^oTLTrS' '''^' T' various conditions, and again by the circuLl "rof Lch man'rUfe s": hlitro7°ht2 "sthl^Tf 1^ imaginaZ^J'ifh oi inought. Such should be the equipment of the O 2IO LOGIC: DEDUCTIVE AND INDUCTIVE historian, who pursues the same method of hypothesis when he attempts to explain (say) the state of parties upon the Exclusion Bill, or the policy of Louis XI. Problems such as the former of these are the easier ; because, amidst the compromises of a party, personal peculiari- ties obliterate one another, and expose a simple scheme of human nature with fewer fig-leaves. Much more hazardous hypotheses are necessary in interpreting the customs of savages, and the feelings of all sorts of animals. Thus the method of our every-day thoughts is identical with that of our most refined speculations. Literary criticisms, a-ain. abound with hypotheses: e.g., as to the composition of the Homeric poems, the order of the Platonic dialogues, the authorship of the C^dmonic poems, or the Ossianic. or of the letters of Junius. And in all these cases we have to ask whether the Hypothesis accounts for the facts. § 2. It follows from the definition of an hypothesis that none is of any use that does not admit of verification (proof or disproof), by comparing the results that may be deduced from it with facts or laws. If so framed as to elude every attempt to test it by facts, it can never be proved by them nor add anything to our understanding of them. Suppose that a conjurer asserts that his table is controlled by the spirit of your deceased relative of virtuous memory, and makes it rap out an account of some domestic adventure that could hardly have been expected to be within a stranger's knowledge. So far good. Then trying again, the table raps out some absurd blunder about your family history which the deceased relative could not have committed ; but the conjurer explains that ' a lying spirit' sometimes possesses the table Plainly, this amendment of the hypothesis makes it equally compatible with success and with failure. It has been said of a certain supposed biological agent, "It would seem that by a little skilful manipulation it can be made to account for anything that has ever been observed, or is ever likely to be observed. It is one of those con- venient invisibles that will do anything that you desire." And what- ever the justice of this criticism, it shows a sound conception of what is to be required of an hypothesis. Very similar was the case of the Ptolemaic Astronomy : by perpetual tinkering its hypothesis was made to correspond with accumulating observations of the celestial motions ; so that, until the telescope was invented, it may be said to have been almost unverifiable. Consider, again, the sociological hypothesis, that civil order was at first founded on a Contract which remains binding upon all mankind : this is reconcilable with the most opposite institu- tions. For we have no record of such an event ; and if the institutions HYPOTHESES 211 of one State (say the British) include ceremonies, such as the corona- tion oath and oath of allegiance, which may be remnants of an original contract, they may nevertheless be of comparatively recent origin: whereas if the institutions of another State (say the Russian) contain nothing that admits of similar interpretation, yet traces of the Contract once existing may long since have been obliterated. Moreover, the actual contents of the contract not having been preserved, every ad- herent of this hypothesis supplies them at his own discretion, 'accord- ing to the dictates of Reason ' ; and so one derives from it the duty of passive obedience, and another with equal cogency establishes the right of rebellion. To be verifiable, then, an hypothesis must be definite; if somewhat vague in its first conception (which is reasonably to be expected), it must become definite in order to be put to the proof. But, except this condition of verifiability, and definiteness for the sake of verifiability, without which a proposition does not deserve the name of an hypothesis, it seems inadvisable to lay down rules for a ' legitimate ' hypo- thesis. The epithet is infelicitous. It suggests that the Logician makes rules for scientific inquirers ; whereas his business is to discover the princi- ples which they, in fact, employ in what are acknowledged to be their most successful investigations. If he did make rules for them, and they treated him seriously, they might be discouraged in the exercise of that liberty of hypothesising, which is the condition of all originality ; whilst if they paid no attention to him, he must suffer some loss of dignity. To say that a ' legitimate hypothesis ' must explain all the facts, at least in the department for which it is invented, is decidedly discouraging. No doubt it may be expected to do this in the long run when (if ever) it is completely established ; but this may take a long time. Is it meanwhile illegitimate ? Or can this adjective be applied to Newton's corpuscular theory of Light, even though it has failed to explain all the facts ? § 3. Given a verifiable hypothesis, however, what constitutes proof or disproof? (i) If a new agent be proposed, it is desirable that we should be able directly to observe it, or at least to obtain some evidence of its existence of a different kind from the very facts which it has been invented to explain. Thus, in the 212 LOGIC: DEDUCTIVE AND INDUCTIVE discovery of Neptune, after the existence of such a planet outside the orbit of Uranus had been conjectured (to account for the movement of the latter), the place in the heavens which such a body should occupy at a certain time was calculated, and there by means of the telescope it was actually seen. Agents, however, are assumed and reasoned upon very successfully which, by their nature, never can be objects of perception : such are the Atoms of Chemistry and the Ether of Optics. Hence, the severer Methodologists regard them with suspicion : Mill was never completely convinced about the ether. He was willing, however, to make the most of the evidence that has been adduced as indicating a certain pro- perty of it distinct from those by which it transmits radiation, namely, mechanical inertia, whereby it has been supposed to retard the career of the heavenly bodies, as shown especially by the history of Encke's comet. This comet returns sooner than it should, as calculated from the usual data ; and this may be due to the influence of a resisting medium in reducing the extent of its orbit ; and such a medium may be the Ether. If this conjecture, or any similar one, should gain accept- ance, the Ether might be regarded as a vera causa (that is, a condition whose existence may be proved independently of the phenomena it was intended to explain), in spite of its being excluded by its nature from the sphere of direct perception. After all, it is very difficult, you know, to say what is within the sphere of direct perception. Waiving, however, this question (which is far from elementary). Science is not a way of perceiving things, but essentially a way of thinking about them. It starts, indeed, from per- ception and returns to it, and its thinking is controlled by the analogies of perception. Atoms and Ether are thought about as if they could be seen or felt ; and if they are found necessary to connect and explain perceptions, those who can understand the explanation will no doubt be reconciled to them. For most men of Science, I suppose, their existence is as good as axiomatic. On the other hand, a great many agents, once assumed in order to explain phenomena, have since been explained away. Of course, difact can never be • explained away ' : the phrase is properly applicable to the fate of erroneous hypotheses, when, not only are they disproved, but others are established in their places. Of the Aristotelian spheres, which were supposed to support and translate sun, moon and planets, no trace has ever been found : they would have been very much in the way of the comets. Phlogiston, again, an agent much in favour with the earlier Chemists, was found, Whewell tells us, when their theories were tested by exact weighing, to be not merely non-existent but a minus quantity ; that is to say, it required the assumption of its absolute HYPOTHESES 213 lightness "so that it diminished the weight of the compounds into which it entered." These agents, then, have been explained away, and instead of them we have gravitation and oxygen. (2) Whether the hypothetical agent be perceptible or not, it cinnot be established, nor can a supposed law of such an agent be accepted as suf^cient to the given inquiry, unless it is adequate to account for the effects which it is called upon to explain, at least so far as it pretends to explain them. The general truth of this is sufficiently obvious, since to explain the facts is the purpose of an hypothesis ; and we have seen that Newton gave up his hypothesis that the moon was a falling body, as long as he was unable to show that the amount of its deflection from a tangent (or its fall) in a given time, was exactly what it should be, if the Moon was controlled by the same force as falling bodies on the Earth. It is worth while, however, to observe the limitations to which this canon is subject. In the first place, it says that, unless adequate to explain the facts in question, an hypothesis cannot be ^established^ : but, for all that, such an hypothesis may be a very promising one. It may take a very long time fully to verify an hypothesis. Some facts may not be obtainable that are necessary to show the connection of others : as, for example, the hypothesis that all species of animals have arisen from earlier ones by some process of gradual change, can be only imperfectly verified by collecting the fossil remains of extinct species, because immense depths and expanses of fossiliferous strata have been destroyed. Or, again, the general state of culture may be such as to prevent men from tracing the consequences of an hypothesis : for which reason, apparently, the doctrine that the Sun is the centre of our planetary system remained a discredited hypothesis for 2000 years. Surely, this should instruct us not to regard an hypothesis as necessarily erroneous or illegitimate merely because we cannot yet see how it works out : but neither can we in such a case regard it as established, unless we take somebody's word for it. Secondly, the canon says that an hypothesis is not estab- lished, unless it accounts for the phenomena so far as it professes to. But it implies a complete misunderstanding to assail a doctrine for not explaining what lies beyond its 214 LOGIC: DEDUCTIVE AND INDUCTIVE scope. Thus, it is no objection to a theory of the origin of species, that it does not explain the origin of Ufe : it does not profess to. For the same reason, it is no objection to the theory of Natural Selection, that it does not account for the variations which selection presupposes. But such objections might be perfectly fair against a general doctrine of Evolu- tion. An interesting case in Mr. WaW^ce's Darwinism (chap, x) will illustrate the importance of attending to the exact conditions of an hypothesis. He says that in those groups of "birds that need protection from enemies.- "when the male is brightly coloured and the female sits exposed on the nest, she is always less brilliant and generally of quite sober and protective hues"; and his hypothesis is. that these sober hues have been acquired or preserved by Natural Selection, because it is important to the family that the sitting bird should be inconspicuous. Now to this it might be objected that in some birds both sexes are brilliant or conspicuous ; but the answer is that the female of such species does not sit exposed on the nest; for the nests are either domed over or made in a hole ; so that the sitting bird does not need protective colouring. If it be objected, again, that some sober-coloured birds build domed nests, it may be replied that the proposition • All con- spicuously coloured birds are concealed in the nest,' is not to be con- verted simply into ' All birds that sit concealed in the nest are con- spicuously coloured.' In the cases alleged the domed nests are a protection against the weather, and the sober colouring is a general pro- tection to the bird, which inhabits an open country. It may be urged, however that jays, crows and magpies are conspicuous birds, and yet build open nests : but these are aggressive birds, not needing protection from enemies. Finally, there are cases, it must be confessed, in which the female is more brilliant than the male, and which yet have open nests ! Yes : but then the muie sits upon the eggs, and the female is stronger and more pugnacious ! Thus every objection is shown to imply some inattention to the con- ditions of the problem ; and in each case it may be said, exceptio prohat regulam-ihe exception tests the rule. (Of course, the usual translation -proves the rule." in the restricted modern senseof " prove." is absurd.) That is to say, it appears on examination ; (i) that the alleged excep- tion is not really one, and (2) that it stands in such relation to the rule as to confirm it. For, you will notice that, to all the above objections it is replied that, granting the phenomenon in question (special protec- tive colouring for the female) to be absent, the alleged cause (need of protection) is also absent ; so that the proof is. by means of the objections, extended from being one by the method of Agreement, into one by the HYPOTHESES 215 Double Method. Unfortunately.it is not always that an assailant's neglect to observe the exact conditions of the doctrine m dispute can be turned to such good account. Thirdly, an hypothesis originally intended to account for the whole of a phenomenon and failing to do so, though it cannot be established in that sense, may nevertheless contam an essential part of the explanation. Thus the Neptunian Hypothesis in Geology, was an attempt to explain the formation of the Earth's outer crust, as havmg been deposited from an universal ocean of mud. In the progress of the science other causes, seismic, fluvial and atmospheric, have been found necessary in order to complete the theory of the history of the Earth s crust • but it remains true that the stratified rocks, and some that have lost their stratified character, were originally deposited under water. Inadequacy, therefore, is not a reason for entirely rejecting an hypothesis or treating it as illegitimate. (3) Granting that the hypothetical cause is real and ade- quate, the investigation is not complete. Agreement with the facts is a very persuasive circumstance, the more so the more extensive the agreement, especially if no exceptions are known. Still if this is all that can be said in favour of an Hypothesis, it amounts to proof by the Method of Agreement only ; it does not exclude the possibility of ' plural causes ' ; and if the Hypothesis proposes a new agent that cannot be directly observed, it may be possible to invent another Hypothesis, about another imagined agent, which shall be equally plausible. According to Whewell, it is a strong mark of the truth of an Hypo- thesis when it agrees with distinct inductions concerning different classes of facts, and he calls this the •Consilience » I°.d""--' because they jump together in the unity of the Hypothesis. It is particularly convincing when this Consilience takes place easUy and naturally without necessitating the mending and ""kering of the Hypothesis; and he cites the Theory of Gravitation and he Undula- tory Theory of Light as the most conspicuous examples of such ever- vlcLrious Hypotheses. Thus, Gravitation explains the fal of bodies on the Earth, and the orbits of the planets and their satellites, .t applies to the tides, the comets, the double stars, and gives consistency to the Nebular Hypothesis, whence flow important Geological infer- 2i6 LOGIC: DEDUCTIVE AND INDUCTIVE HYPOTHESES 217 ences; and all this without any need of amendment. Nevertheless, Mill, with his rigorous sense of duty, points out, that an induction is merely a proposition concerning many facts, and that a consilience of inductions is merely a multiplication of the facts explained ; and that, therefore, if the proof is merely agreement in each case, there can be no more in the totality : the possibility of vicarious causes is not pre- cluded ; and the hypothesis may, after all, describe an accidental cir- cumstance. Whewell also laid great stress upon Prediction as a mark of a true Hypothesis. Thus, Astronomers predict eclipses, occultations, transits, long beforehand with the greatest precision ; and the prediction of the place of Neptune by sheer force of deduction is one of the most astonishing things in the history of science. Yet Mill persisted in showing that a predicted fact is only another fact, and that it is really not very extraordinary that an hypothesis that happens to agree with many known facts should also agree with some still undiscovered. And, I must say, there seems to be some illusion in the common belief in the probative force of prediction. Prediction surprises us, puts us off our guard, and renders persuasion easy ; in this it resembles the force of an epigram in rhetoric. Accordingly, cases can be produced in which erroneous Hypotheses have led to prediction ; and Whewell himself produces them. Thus, he says that the Ptolemaic theory was confirmed by its predicting eclipses and other celestial phenomena, and by leading to the construction of Tables in which the places of the heavenly bodie were given at every moment of time. Similarly, both Newton's theory of Light and the Chemical doctrine of Phlogiston led to predictions which came true. What sound method demands in the proof of an Hypo- thesis, then, is not merely that it be shown to agree with the facts, but that every other Hypothesis be excluded. This, to be sure, may be beyond our power ; there may in some cases be no such negative proof except the exhaustion of human ingenuity in the course of time. The present theory of colour has in its favour the failure of Newton's corpuscular hypothesis and of Goethe's anti-mathematical hypothesis ; but the field of conjecture remains open. On the other hand, Newton's proof that the solar system is controlled by a central force, he supported by the demonstration that a force having any other direction could not have results agreeing with Kepler's second law of the planetary motions, namely, that, as a planet moves in its orbit, the areas described by a line drawn from the sun to the planet are proportional to the times occupied in the planet's motion. When a planet is nearest to the sun, the area described by such a line is least for any given distance traversed by the planet ; and then the planet moves fastest : when the planet is furthest from the sun, the area described by such a line is greatest for an equal distance traversed ; and then the planet moves slowest. This law may be deduced from the hypothesis of a central force, but not from any other ; the proof, therefore, as Mill says, satisfies the method of Difference. Apparently, to such completeness of demonstration certain conditions are necessary : the possibilities must lie between alternatives, such as A or not-A, or amongst some definite list of cases that may be exhausted, such as equal, greater or less. He whose hypothesis cannot be brought to such a definite issue, must try to refute whatever other hypotheses are offered, and naturally he will attack first the strongest rivals. With this object in view he looks about for a " crucial instance," that is, an observation or experiment that stands like a cross (sign-post) at the parting of the ways to guide us into the right way, or, in plain words, an instance that can be explained by one hypothesis but not by another. Thus the phases of Venus, similar to those of the Moon, but con- curring with great changes of apparent size, when discovered by Galileo, presented a crucial instance in favour of the Copernican hypothesis, as against the Ptolemaic, so far at least as to prove that Venus revolved around the Sun inside the orbit of the Earth. Foucault's experiment determining the velocity of Light (cited in the last chapter) was at first intended as an experimentum crucis to decide between the corpuscular and undulatory theories ; and answered this purpose, by showing that the velocity of a beam passed through water was less than it should be by the former, but in agreement with the latter doctrine (Deschanel : §813). Perhaps experiments of this decisive character are commonest in Chemistry: chemical tests, says Herschel, "are almost universally crucial experiments." The following is abridged from Playfair [Encycl. Met., Diss. HI) : The Chemists of last century observed that metals were rendered heavier by calcination ; and there were two ways of accounting for this : either something had been added in the process, though what they could not imagine ; or, something had been driven off that was in its nature light, namely. Phlogiston. To decide between these hypotheses, Lavoisier hermetically sealed some tin in a glass retort, and weighed the whole. He then heated it ; and, when the tin was calcined, weighed the whole again, and found it the same as before. No substance, therefore, either light or heavy, had escaped. Further, \ 2i8 LOGIC: DEDUCTIVE AND INDUCTIVE when the retort was cooled and opened, the air rushed in, showing that some of the air formerly within had disappeared or lost its elasticity. On weighing the whole again, its weight was now found to have in- creased by ten grains ; so that ten grains of air had entered when it was opened. The calcined tin was then weighed separately, and proved to be exactly ten grains heavier than when it was placed in the retort ; showing that the ten grains of air that had disappeared had combined with the metal during calcination. This experiment, then, decided against Phlogiston, and led afterwards to an analysis of common air confirming Priestley's discovery of oxygen. § 4. We have now seen that an Hypothesis must, to deserve the name in Science, be verifiable and therefore definite ; and that to establish itself as a true theory, it must present some symptom of reality, and be adequate and unconditional. Thus guarded. Hypotheses seem harmless enough; but, certainly, people sometimes have a strong prejudice against them, as against a tribe of savages without government, or laws, or any decent regard for vested interests. It is well known, too, that Bacon and Newton disparaged them. But Bacon in his examples of an investigation according to his own method, is obliged after a preliminary classification of facts, to resort to an hypothesis, calling it permissio iutelledus, interpretatio inchoata or vindemiatio prima. And what Newton meant by hypotheses ?ion Jingo, seeing that he invented so many, is itself fair game for an hypothesis. At any rate, it is plain that hypotheses are essential aids to discovery: indeed, speaking generally, deliberate investigation depends wholly upon the use of them. It is true that we may sometimes observe a train of events that chances to pass before us, either when we are idle or engaged with some other inquiry, and so obtain a new glimpse of the course of nature. Or we may try experiments haphazard, and watch the results. But, even in these cases, before our new notions can be considered knowledge, they must be definitely framed in hypotheses and re- observed or experimented upon, with whatever calculations or pre- cautions may be necessary to ensure accuracy or isolation. As a rule, however, when inquiring deliberately into the cause of an event, whether in nature or in history, we first reflect upon the circumstances of the case and compare it with similar ones previously investigated HYPOTHESES 219 and so are guided by a preconception more or less definite of ' what to look for,' what the cause is likely to be, that is, by an hypothesis. Then, if our preconception is justified, or something which we observe leads to a new hypothesis, either we look for other instances to satisfy the canons of Agreement : or (if the matter admits of experiment) we endeavour, under known conditions according to the canons of Differ- ence and Variations, to reproduce the event by means of that which our hypothesis assigns as the cause; or we draw remote inferences from our hypothesis, and try to test these by the Inductive Canons. If we argue from an hypothesis and express ourselves formally, it will usually appear as the Major Premise; but this is not always the case. In extending ascertained laws to fresh cases, the Minor Premise may be an hypothesis, as in testing the chemical constitution of any doubtful substance, such as a piece of ore. Some solution or preparation, A, is generally made which (it is known) will, on the introduction of a certain agent, B, give a reaction, C, if the preparation contains a given substance, X. The major premise, then, is the law of reaction — Whenever A is X, if treated with B it is C. The minor premise is an hypothesis that the preparation contains X. An experiment then treats A with B. If C results, a probability is raised in favour of the hypothesis that A is X ; or a certainty, if we know that C results on that condition only. So important are hypotheses to science, that Whewell insists that they have often been extremely valuable even though erroneous. Of the Ptolemaic system he says, " We can hardly imagine that Astronomy could, in its outset, have made so great a progress lender any other form." It served to connect men's thoughts on the subject and to sustain their interest in working it out; by successive corrections "to save appearances," it attained at last to a descriptive sort of truth, which was of great practical utility ; it also occasioned the invention of technical terms, and, in general, digested the whole body of observations and prepared them for assimilation by a better hypo- thesis in the fulness of time. Whewell even defends the maxim that "Nature abhors a vacuum," as having formerly served to connect many facts that differ widely in their first aspect. "And in reality is it not true," he asks, "that nature does abhor a vacuum, and does all she can to avoid it ? " Let no forlorn cause despair of a champion ! Yet no one has accused Whewell of Quixotry ; and the sense of his position is that the human mind, of course, is a rather feeble affair, which can hardly begin thinking except with blunders. The progress of Science may be plausibly attributed to a process of Natural Selection : Hypotheses are produced in abundance and variety, and those unfit to bear verification are destroyed, until only the fittest survive. Wallace, a practical naturalist, if there ever was one, as well ~r«~ I W,W 220 LOGIC: DEDUCTIVE AND INDUCTIVE HYPOTHESES 221 as an eminent theorist, takes the same view as Whewell of such in- adequate conjectures. Of ' Lemuria,' a hypothetical continent in the Indian Ocean, once supposed to be traceable in the islands of Mada- gascar, Seychelles and Mauritius, its surviving fragments, and named from the Lemurs, its characteristic denizens, he says {Island Life, chap, xix.) that it was "essentially a provisional hypothesis, very useful in calling attention to a remarkable series of problems in geographical distribution [of plants and animals], but not affording the true solution of those problems." We see, then, that ' provisional hypotheses,' though erroneous, may be very useful or (as Whewell says) necessary. Hence, to be prolific of hypotheses is the first attribute of scientific genius ; the first, because without it no progress whatever can be made. And some men seem to have a marked felicity, a sort of instinctive judgment even in their guesses, as if their heads were made according to Nature. But others among the greatest, like Kepler, guess often and are often wrong before they hit upon the truth, and them- selves, like Nature, destroy many vain shoots and seedUngs of science for one that they find fit to live. If this is how the mind works in scientific inquiry (as it certainly is, with most men, in poetry, in fine art, and in the scheming of business), it is useless to repine. We should rather recognise a place for fool's hypotheses, as Darwin did for '• fool's experiments." But to complete the scientific character, there must be great patience, accuracy, and impartiality in examining and testing these conjectures, as well as great ingenuity in devising experiments to that end. It is the want of these qualities that leads to crudity and public failure and brings hypotheses into derision. Not partially and hastily to believe in one's own guesses, nor petulantly and hastily to reject them, but to consider the matter, to suspend judgment, is the moral lesson of science : difficult, distasteful, and rarely mastered. Everybody, according to his lights, makes haste to frame hypotheses, whether for scientific or private uses ; because, as Whewell says, " man is prone to become a deductive reasoner," and hypotheses, anticipating the laborious induction of highly general laws, are a short cut to deduction. There are two sides to this proneness of our nature, / a good and a bad. The good is that hypothesis and deduction have in fact been the great means of explaining or enabling us to understand the world ; so that our instinctive resort to them is a predisposition to Science. The bad is that this method encourages superficiality. Deduction is generally easier than Induction, because it is carried on far more by means of signs, whether in Mathematics or common language. To wield the higher Mathematics needs a dis- tinguished head ; but this power cannot be put into competition with the distinct and comprehensive imagination necessary to represent masses of facts for inductive analysis. For the great use of language and of all symbols in thinking, is to economise this energy of imagina- tion. Without such devices the human race could never have developed : for who can imagine the purport in denotation of a single general name ? But these devices show ' the defects of their qualities ' by often quite superseding thought and degenerating into gibberish. Whether, indeed, this is ever true of the higher Mathematics is not for me to say ; but everybody knows how true it is of common speech. § 5. The word Hypothesis is often also used for the scientific device of treating an Abstraction as, for the purposes of argu- ment, equivalent to the concrete facts. Thus, in Geometry, a line is treated as having no breadth ; in Mechanics, a bar may be supposed absolutely rigid, or a machine to work without friction ; in Economics (as we saw in the last chapter), man is sometimes regarded as actuated solely by love of gain and dislike of exertion. The results reached by such reasoning may be made applicable to the concrete facts, if allowance be made for the omitted circumstances or properties, in the several cases of lines, bars, and men ; but otherwise all con- clusions from abstract terms are limited by their definitions. Abstract reasoning, then (that is, reasoning limited by defini- tions), is often said to imply * the hypothesis ' that things exist as their names are defined, having no properties but those enumerated in their definitions. This seems, however, a needless and confusing extension of the term ; for an hypothesis proposes an agent, collocation, or law hitherto unknown ; whereas abstract reasoning proposes to exclude from consideration a good deal that is well known. There seems no reason why the latter device should not be plainly called an Abstraction. ^^^ LOGIC: DEDUCTIVE AND INDUCTIVE Such Abstractions are, of course, also necessary to Science; rtre lleTo L\e strange blunders by mistaking the character of the results : treating the results as simply tru- actu':. things, instead of as true of actual th.ngs only so fa as they are represented by the Abstractions. In addressing Thslict reasoning, therefore, to those especially .^o a e unfamiliar with scientific methods, pains shou d ^e taken to make it clear what the Abstractions are, what are the con Tequen imitations upon the argument and its conclusions a^d what corrections and allowances are necessary in orderjo make the conclusions into an adequate account of the concrete fact The greater the number, variety, and subtlety o the properties possessed by any object (such as human nature) Ae ' ater the qualifications required in the conclusions o abstrlTreasoning, before they can hold true of such an object "ciosettn^^^^^^^^ this method of Abstraction is the Mathe- JS Melhod of Limits. In his History of Scientific Meas (B II. c. 12), Whewellsays: of straight lines, and theretore ^^ ' ^ j ^^y curve. aoctrines '>^ ^^X^^- ^rZ^^Z^:,!.' cu... b/putting But we may make up a ngure 1 c y polygonal building of ,.,ether -^^^f^^tX^:^^^Zirr'Jr.. And in order ;- Portr/nd neaL to a c„„ ^:^^X^^^ and more small, more and more ""'"^™"^. ';,%i^^3; ^n^aii lines to find some mode of measurement some ^^'^t'™ "^^^^^^ j^e sides. r ""trf^ 'i:Ztt^t^s':::ST:^'-^^ equivalent to however far it be carriea ^ .,•„ ^he sides we may approach r,,<:.acnrin? the curve itselt , tor d> muiupiyi"5 . j:«-^,.^nrp» measuring uie ^u appreciable ditlerence "°'^^"%Te"cutTCis tLT^:^/!^ /Xgon; and in this ;re:s\e procX^^^^^^^ A^ion, that .What is true up to the Limit is true at the Limit.' " HYPOTHESES 223 Now, what Whewell calls the Axiom here, others might call an Hypothesis; but perhaps it is properly a Postulate. And it is just the obverse of the Postulate implied in the Method of Abstractions, namely, that ' What is true of the Abstraction is true of concrete cases the more nearly they approach the Abstraction.' What is true of the ' Economic Man ' is truer of a broker than of a farmer, of a farmer than of a labourer, of a labourer than of the artist of romance. Hence the Abstrac- tion may be called a Limit or limiting case, in the sense that it stands to concrete individuals, as a curve does to the figures made up "by putting together many short straight lines." Correspondingly, the Proper Name may be called the Limit of the class- name ; since its attributes are infinite, whereas any name whose attributes are less than infinite stands for a possible class. In short, for logical purposes, a Limit may be defined as any extreme case to which actual examples may approach without ever reaching it. And in this sense ' Method of Limits ' might be used as a term including the Method of Abstractions ; though it would be better to speak of them generically as * Methods of Approximations.' It is easy to conceive of an objector urging that such devices as the above are merely ways of avoiding the actual problems, and that they display more cunning than skill. But Science, like good sense, puts up with the best that can be had ; and, like prudence, does not reject the half-loaf. The position, that a conceivable case that can be dealt with may, under certain conditions, be substituted for one that is unworkable, is a touchstone of intelligence. To stand out for ideals that are known to be impossible, is only an excuse for doing nothing at all. In another sense, again, the whole of Science is sometimes said to be hypothetical, because it takes for granted the Uniformity of Nature ; whilst this, in its various aspects, can only be directly ascertained by us as far as our experience extends ; whereas the whole value of the principle of Uniformity consists in its furnishing a formula for the 224 LOGIC: DEDUCTIVE AND INDUCTIVE extension of our other beliefs beyond our actual experience. Transcendentalists, indeed, call it a form of Reason, just because it is presupposed in all knowledge ; and they and the Empiricists agree that to adduce material evidence for it, in its full extent, is impossible. If, then, material evidence is demanded by any one, he cannot regard the conclusions of Mathematics and physical Science as depending on what is itself unproved ; he must, with Mill, regard these conclusions as drawn " not from but according to" the axioms of Equality and Causation. That is to say, if the axioms are true, the conclusions are; the material evidence for them being the same, namely, uncontradicted experience. Now when we say, ' If Nature is uniform, Science is true ', the hypothetical character of Science appears in the form of the statement. Nevertheless, it seems undesirable to call our confidence in Nature's uniformity an ' hypothesis ' : it is incongruous to use the same term for our tentative conjectures and for our most indispensable beliefs. ' The Universal Postulate ' is a better term for the principle which, in some form or other, every generalisation takes for granted. CHAPTER XIX LAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; ANALOGY § I. Laws are classified, according to their degrees of generality, as higher and lower, though the grades may not be decisively distinguishable. First, there are Axioms or Principles, that is real, universal, self-evident propositions. They are— (i) real propositions; not, like 'The whole is greater than any of its parts,' merely definitions, or implied in definitions. (2) They are universally true of phenomena, as far as the form of their expression extends; that is, for example. Axioms concerning quantity are true of everything that is considered in its quantitative aspect, though not (of course) in its qualitative aspect. (3) They are self-evident; that is, each rests upon its own evidence (whatever that may be); they cannot be derived from one another, nor from any more general law. Some, indeed, are more general than others: the Logical Principle of Contradiction, * If A is B, it is not not-B ', is true of qualities as well as of quantities; whereas the Axioms of Mathematics apply only to quantities. The Mathematical Axioms, again, apply to Time, Space, Mental phenomena, and Matter and Energy; whereas the Law of Causation is only true of concrete events in the redistribu- tion of Matter and Energy : such, at least, is the strict limit of Causation, if we identify it with the Conservation of Energy ; although our imperfect knowledge of Life and Mind often drives us to speak of feelings, ideas, volitions, as p 226 LOGIC: DEDUCTIVE AND INDUCTIVE causes. Still, the Law of Causation cannot be derived from the Mathematical Axioms, nor these from the Logical. The kind of evidence upon which Axioms rest, or whether any evidence can be given for them, is (as before observed) a question for Metaphysics, not for Logic. Axioms are the upward limit of Logic, which, like all the Special Sciences, takes them for granted. Next to Axioms, come Primary Laws of Nature : these are of less generality than the Axioms, and are subject to the conditions of methodical proof; being universally true only of certain forces or properties of matter, or of nature under certain conditions ; so that proof of them by logical or mathematical reasoning is expected, because they depend upon the Axioms for their formal evidence. Such is the law of Gravitation, in Astronomy ; the law of Heredity, in Biology ; in Psychology, the law of Relativity. Then, there are Secondary Laws, of still less generality, resulting from a combination of primary conditions or forces in given circumstances, and therefore conceivably derivable from the laws of those conditions or forces, if we can discover them and compute their united effects. Accordingly, Secondary Laws are either— (i) Derivative, having been analysed into, and deduced from, Primary Laws; or (2) Em- pirical, those that have not yet been deduced (though from their comparatively special and complex character, it seems probable they may be, given sufficient time and ingenuity), and that meanwhile rest upon some unsatisfactory sort of induction by Agreement or Simple Enumeration. Whether laws proved only by the canon ^f Difference are to be considered Empirical, is perhaps a question : their proof derives them from the principle of Causation ; but. being of narrow scope, some more special account of them seems requisite in relation to the Primary Laws before we can call them Derivative in the technical sense. Many Secondary Laws, again, are partially or imperfectly Derivative : we can give general reasons for them, without being able to determme theoretically the precise relations of the phenomena they describe. Thus Meteorologists can explain the general conditions of all sorts of LAWS CLASSIFIED 227 weather, but have made but little progress toward predicting the actual course of it (at least, for our island) : Geologists know the general causes of mountain ranges, but not why they rise just where we find them : Economists explain the general course of a commercial crisis, but not why the great crises recur at intervals of about ten years. Derivative Laws make up the body of the exact Sciences, having been assimilated and organised ; whilst Empirical Laws are the undi- gested materials of Science. The theorems of Euclid are good examples of Derivative Laws in Mathematics ; in Astronomy, Kepler's laws and the laws of the tides ; in Physics, the laws of shadows, of perspective, of harmony ; in Biology the law of Natural Selection, and others from this ; in Economics, the laws of prices, rents, wages, interest. Empirical Laws are such as Bodes law of the planetary distances ; the laws of the expansion of different bodies by heat, and formulae expressing the electrical conductivity of each substance as a function of the temperature. Strictly speaking, 1 suppose, all the laws of chemical combination are Empirical : the law of definite proportions is found true in all cases that have been examined, except for varia- tions that may be ascribed to errors of experiment. Much the same is true in Biology ; most of the secondary laws are Empirical, except so far as structures or functions may be regarded as specialised cases in Physics or Chemistry and deducible from these Sciences. The theory of Natural Selection, however, has been the means of rendering many laws, that were once wholly Empirical, at least partially Derivative; namely, the laws of the Geographical distribution of plants and animals, and of their adaptation in organisation, form and colour, habits and instincts, to their various conditions of life. The laws that remain Empirical in Biology are of all degrees of generality, from that of the tendency to variation in size and in every character shown by all (or nearly all) species (though as to the reason of this there are promising hypotheses), down to such curious cases as that the colour of roses and carnations never varies into blue, that scarlet flowers are never sweet- scented, that bullfinches fed on hemp-seed turn black, that the young of white, yellow and dun pigeons are born almost naked (whilst others have plenty of down); and so on. A ' Fact,' in the common use of the word, is a particular Observation : it is the material of science in its rawest state. As perceived by a mind, it is, of course, never absolutely particular : for we cannot possibly perceive anything without classing it, more or less definitely, with things already known to us ; nor describe it without using connotative terms which imply a classirication of the things denoted. Still, we may 428 LOGIC: DEDUCTIVE AND INDUCTIVE consider an Observation as particular, in Comparison with a Law that includes it with numerous others in one general proposition. To turn an Observation into an Experiment or (where experiment is impracticable) to repeat it with all possible precautions and exactness, is the first stage ot scientific manufacture. Then comes the formulation of an Empirical law ; and lastly, if possible, deduction or derivation, either from higher laws previously ascertained, or from an hypothesis. However, as a word is used in various senses, we often speak of laws as 'facts': we say the law of Gravi- tation is a fact, meaning that it is real, or verifiable by observa- tions or experiments. § 2 Secondary laws may also be classified according to thdr constancy into-(i) the Invariable (as far as -^Pfnence reaches), and (2) Approximate Generalisations Of the Invariable we have given examples above. The following are Approximate Generalisations : Most comets go round the bun from East to West ; Most metals are solid at ordinary temperatures ; Most marsupials are Australasian ; Most arctic animals are white in winter ; Most cases of plague are fatal ; Most men think first of their own interests. Some of these laws are empirical, as that ' Most metals are solid at ordinary temperatures ' : at present no reason can be given for this ; nor do we know why most cases of plague are fatal. Others, how- ever are at least partially derivative, as that Most arctic animals are white ' ; for this seems to be due to the advantage of concealment in the snow ; whether, as with the bear, he better to surprise its prey, or, with the hare, to escape the notice of its enemies. But the scientific treatment of such a proposition requires that we should also explain the exceptions : if ' Most are , this in^phes that ' Some are not ' ; why not, then ? Now, if we can give reasons for all the exceptions, the Approximate Generali- Lion may be converted into a Categorical, thus : All arctic animals are white, unless (like the raven) they need no conceal- ment eitner to prey or to escape ; or unless mutual recognition LAWS CLASSIFIED 229 is more important to them than concealment (as with the musk-sheep)'. The same end of categorical statement may be gained by including the conditions on which the pheno- menon depends, thus : ' All arctic animals to whom conceal- ment is of the utmost utility are w^hite '. When Statistics are obtainable, it is proper to convert an Approxi- mate Generalisation into a proportional statement of the fact, thus : instead of ' Most attacks of plague are fatal ', we might find that in a certain country 70 per cent, were so. Then, if we found that in another country the percentage of deaths was 60, in another 40, we might discover, in the different conditions of these countries, a clue to the high rate of mortality from this disease. Indeed, even if the proportion of cases in which two facts are connected does not amount to ' Most ', yet, if any definite percentage is obtainable, the proposition has a higher scientific value than a vague ' Some ' : as if we know that 2 per cent, of the deaths in England are due to suicide, this may be compared with the rates of suicide in other countries; from which perhaps inferences may be drawn as to the causes of suicide. In one department of life, namely, Politics, there is a special advantage in true Approximate Generalisations amounting to ' Most cases '. The citizens of any State are so various in character, enlightenment, and conditions of life, that we can expect to find few propositions universally true of them : so that propositions true of the majority must be trusted as the bases of legislation. If most men are deterred from crime by the fear of punishment ; if most men will idle if they can obtain support without industry ; if most jurymen will refuse to convict of a crime for which the prescribed penalties seem to them too severe ; these are most useful truths, though there should be numerous exceptions to them all. § 3. Secondary Laws can only be trusted in ' Adjacent Cases ' ; that is, where the circumstances are similar to those in which the laws are known to be true. A Derivative Law will be true wherever the forces concerned exist in the combi- nations upon which the law depends, if there are no counter- acting conditions. Thus, that water can be pumped to about 33 feet at the sea-level, is a derivative law on this planet: is it true in Mars? That depends on 230 LOGIC: DEDUCTIVE AND INDUCTIVE whether there are in Mars bodies of a liquid similar to our water; whether there is an atmosphere there; and how great its pressure is; which will vary with its height and density. If there is no atmosphere, there can be no pumping; or if there is an atmosphere of less pressure than ours, water such as ours can only be pumped to a less height than 33 feet. Again, we know that there are arctic regions in Mars; if there are also arctic animals, are they white? That may depend upon whether there are any beasts of prey. If not, concealment seems to us of no use. An Empirical Law, being one whose conditions we do not know, the extent of its prevalence is still less ascertainable. Where it has not been actually observed to be true, we cannot trust it unless the circumstances, on the whole, resemble so closely those amongst which it has been observed, that the unknown causes, whatever they may be, are likely to prevail there. And, even then, we cannot have much confidence in it ; for there may be unknown circumstances which entirely frustrate the eftect. The first naturalist who travelled (say) from Singapore eastward by Sumatra and Java, or Borneo, and found the mammalia there similar to those of Asia, may naturally have expected the same thing in Celebes and Papua; but. if so, he was entirely disappointed; for in Papua the mammalia are marsupials like those of Australia. Thus his empirical law, 'The mammalia of the Eastern Archipelago are Asiatic,' would have failed for no apparent reason. According to Mr. Wallace, there is a reason for it, though such as could only be discovered by exten- sive researches: namely, that the sea is deep between Borneo and Celebes, so that they must have been separated for many ages ; whereas it is shallow from Borneo westward to Asia, and also southward from Papua to Australia; so that these regions, respectively, may have been recently united: and the true law is that similar mammalia belong to those tracts which at comparatively recent dates have formed parts of the same continents. A considerable lapse of time, again, may make an empirical law no longer trustworthy ; for the forces from whose combination it resulted may have ceased to operate, or to operate in the same combination ; and since we do not know what those forces were, even the knowledge that great changes have taken place in the meantime cannot enable us, after an interval, to judge whether or not the law still holds true. New stars shine in the sky and go out ; species of plants and animals become extinct ; diseases die out and fresh ones afflict mankind : all these things doubtless have their causes, but if we do not know what they are, we CO-EXISTENCE 231 have no measure of the effects, and cannot tell when or where they will happen. § 4. Secondary Laws, again, are either of Succession or of Co-existence. Those of Succession are either — (i) of direct causation, as that ' Water quenches fire ', or (more strictly) that ' Evaporation reduces temperature ' ; or (2) of the effect of a remote cause, as * Bad harvests tend to raise the price of bread ' ; or (3) of the joint effects of the same cause, as that ' Night follows day ' (from the revolution of the Earth), or the course of the seasons (from the inclination of the Earth's axis). Laws of Co-existence are of several classes, (i) One has the generality of a Primary Law, though it is proved only by Agreement, namely, * All gravitating bodies are inert '. Others, though less general than this, are of very extensive range, as that * All gases that are not decomposed by rise of temperature have the same rate of expansion ' ; and, in Botany, again, that * All monocotyledonous plants are endogenous '. These laws of Co-existence are concerned with the most fundamental properties of bodies. (2) Next come laws of the Co-existence of those properties which are comprised in the definitions of Natural Kinds. Mill distinguished between (a) classes of things that agree among themselves and differ from others only in one or a few attributes (such as ' red things ', ' musical notes ', ' car- nivorous animals', soldiers'), and (/3) classes of things that agree among themselves and differ from others in a multitude of characters : and the latter he calls Natural Kinds. These comprise the chemical elements and their pure compounds (such as water, alcohol, rock-salt, chalk), and the species of plants and animals. Clearly, each of these is constituted by the co-existence or coinherence of a multitude of properties, some of which are selected as the basis of their definitions. Thus, Gold is a metal of high specific gravity, high melting point, low chemical affinities, great ductility, yellow colour, etc. : a Horse has ' a vertebral column, mammae, a placental embryo, { 232 LOGIC: DEDUCTIVE AND INDUCTIVE four legs, a single well-developed toe in each foot provided with a hoof, a bushy tail, and callosities on the inner sides of both the fore and the hind legs ' (Huxley). Since Darwinism has obtained general acceptance, some logicians have doubted the propriety of calling the organic species 'Kinds' on the grounds that they are not, as to definiteness and permanence, on a par with the chemical elements or such compounds as water and rock- salt; that they vary extensively, and that it is only by the loss of former generations of animals that we are able to distinguish species at all. But to this it may be replied that species (so-called) are often approximately constant for immense periods of time, and may be called permanent in comparison with human generations; and that, although the leading principles of Logic are perhaps eternal truths, yet upon a detail such as this, the science may condescend to recognise a dis- tinction if it is good for (say) only 10,000 years. That if former generations of plants and animals were not lost, all distinctions of species would disappear, may be true ; but they are lost— for the most part beyond hope of recovery; and accordingly the distinction of species is still recognised; although there are cases, chiefly at the lower stages of organisation, in which so many varieties occur as to make adjacent species almost or quite indistinguishable. So far as species are recognised, then, they present a complex co-existence of qualities, which is certainly a logical problem ; and, coming more naturally under the head of Natural Kinds than any other, they must be mentioned in this place. (3) There are, again, certain coincidences of qualities not essential to any kind, and sometimes prevailing amongst many different kinds : such as ' Insects of nauseous taste have vivid (warning) colours'; ' White tom-cats with blue eyes are deaf; * White spots and patches, when they appear in domestic animals, are most frequent on the left side '. (4) Finally, there may be constancy of relative position, as of sides and angles in Geometry; and also among concrete things (at least for long periods of time), as of the planetary orbits, the apparent positions of fixed stars in the sky, the distribution of land and water on the globe, opposite seasons in opposite hemispheres. All these cases of Co-existence (except the Geometrical) present the problem of deriving them from Causation ; for there is no general Law of Co-existence from which they can CO-EXISTENCE 233 be derived ; and, indeed, if we conceive of the external world as a perpetual redistribution of matter and energy, it follows that the whole state of Nature at any instant, and therefore every Co-existence included in it, is due to Causation issuing from some earlier distribution of matter and energy. Hence, indeed, it is not likely that the problems of Co-existence as a whole will ever be solved, since the original distribution of matter is, of course, unknown. Still, starting with any given state of Nature, we may hope to explain some of the co- existences in any subsequent state. We do not, indeed, know why weight always co-exists with inertia, nor why the chemical ' elements are what they are; but it is known that "the properties of the elements are functions of their atomic weight," which (though, at present, only an empirical law) may be a clue to some deeper explanation. As to plants and animals, we know the conditions of their generation, and can trace a connection between most of their characteristics and the conditions of their life : as that teeth and stomach vary with their food, and that their colour generally varies with their habitat. Geometrical Co-existence, when it is not a matter of definition (as ' a square is a rectangle with four equal sides '), is deduced from the Definitions and Axioms : as when it is shown that in triangles the greater side is opposite the greater angle. The deductions of theorems or secondary laws, in Geometry is a type of what is desirable in the Physical Sciences : the demonstration, namely, that all the connections of phenomena, whether successive or co-existent, are conse- quences of the redistribution of matter and energy according to the principle of Causation. Coincidences of Co-existence (Group (3) ) may sometimes be deduced and sometimes not. That ' nauseous insects have vivid coloration ' comes under the general law of ' protective coloration'; as they are easily recognised and therefore avoided by insectivorous birds and other animals. But why white tom-cats with blue eyes should be deaf, is (I believe) 234 LOGIC: DEDUCTIVE AND INDUCTIVE unknown. When Co-existences cannot be derived from Causation, they can only be proved by collecting examples and trusting vaguely to the Uniformity of Nature. If no exceptions are found, we have an empirical law of considerable probability within the range of our exploration. If exceptions occur, we have at most an Approximate Generalisation, as that * Most metals are whitish ', or ' Most domestic cats are tabbies' (but this is probably the ancestral colouring). We may then resort to statistics for greater definiteness, and find that in Hampshire (say) ^o per cent, of the domestic cats are tabby. § 5. Scientific explanation consists in discovering, deducing, and assimilating the laws of phenomena. In the ordinary use of the word, explanation means the satisfying a man's under- standmg; and what may serve this purpose depends partly upon the natural soundness of his understanding, and partly on his education. Generally, what we are accustomed to seems to need no explanation, unless our curiosity is particularly directed to it. That boys climb trees and throw stones, and that men go fox-hunting, may easily pass for matters of course. If any one is so exacting as to ask the reason, there is a ready answer in the 'need of exercise.' On reflection, how- ever, this will not explain the peculiar zest of those exercises, which is something quite different from our feelings whilst swinging dumb-bells or tramping the highway. Others, more sophisticated, tell us that the civilised individual retains in his nature the instincts of his remote ancestors, and that these assert themselves at stages of his growth corresponding with ancestral periods of culture or savagery: so that if we delight to climb trees, throw stones, and hunt, it is because our forefathers once lived in trees, had no missiles but stones, and depended for a livelihood upon killing something. To some of us, again, this seems an explanation ; to others it merely gives annoyance, as a super- fluous hypothesis, the fruit of a wanton imagination and too much leisure. However, what we are not accustomed to immediately excites curio- sity. If it were exceptional to climb trees, throw stones, ride after foxes, whoever did such things would be viewed with suspicion. An eclipse, a shooting star, a solitary boulder on the heath, a strange animal, a Chinaman in the street, call for explanation; and among some nations, eclipses have been explained by supposing a dragon to EXPLANATION 235 devour the sun or moon; solitary boulders, as the missiles of a giant; and so on. Such explanations, plainly, are attempts to regard rare phenomena as similar to others that are better known; a snake havmg been seen to swallow a rabbit, a bigger one may swallow the sun^ a gfant is supposed to bear much the same relation to a boulder as a boy does to ha fa brick. When any very common thmg seems to need no explanation, it is because the several instances of its occurrence are a suflicient basis of assimilation to satisfy most of us. Still, ^'^ ^'^^^^^ for such a thing is demanded, the commonest answer has the s^me implication, namely, that assimilation or classification is ^J-^^^^ reason for it. Thus, if climbing trees is referred to the need of exer cise. it is assimilated to running, rowing, etc. ; if the customs of a savage tribe are referred to the command of its gods, they are assimilated to those things that are done at the command of chieftains. Explanation, then, is the finding of resemblance between the phenomenon in question and other phenomena. In Mathematics, the explanation of a theorem is the same as its proof, and consists in showing that it repeats, under different conditions, the definitions and axioms already assumed and the theorems already demonstrated. In Concrete Sciences, to discover the cause of a pheno- menon is to explain it; because a cause is an invariable antecedent, and therefore reminds us of, or enables us to conceive, an indefinite number of cases similar to the present one wherever the cause exists ; and, as we have seen that the discovery of the laws of nature is essentially the discovery of causes, the discovery of laws is scientific explanation. The discovery of quantitative laws is especially satisfactory, because it not only explains why an event happens at all, but why it happens just in this direction, degree, or amount ; so that (the only likeness between quantities, as such, being equality), the cause is shown to be equal not only to other causes but to its own effect ; wherefore, whether the conservation of matter and energy be universally true or not, it must sciU be an universal postulate of scientific explanation. The mere discovery of an empirical law of co-existence, as that 'white tom-cats with blue eyes are deaf, is indeed something better than an isolated fact : every general propo- 236 LOGIC: DEDUCTIVE AND INDUCTIVE sition relieves the mind of a load of facts ; and, for many people, to be able to say — ' It is alwa\ s so ' — may be enough ; but for scientific explanation we require to know the reason of it, that is, the cause. Still, if asked to explain an Axiom, we can only say, ' It is always so '. § 6. There are three modes of scientific explanation : First, the analysis of a phenomenon into the laws of its causes. The pumping of water implies (i) pressure of the air, (2) distribution of pressure in a liquid, (3) that motion takes the direction of least resis- tance. Similarly, that thunder follows forked lightning, and that the report of a gun follows the flash, are resolvable into (i) the discharge of electricity, or the explosion of gunpowder; (2) distance of the observer from the event; (3) that light travels faster than sound. The planetary orbits are analysable into the tendency of planets to fall into the sun, and their tendency to travel in a straight line. When this conception is helped out by swinging a ball round by a string, and then letting it go, to show what would happen to the earth if gravitation ceased, we see how the recognition of resemblance lies at the bottom of ex- planation. Secondly, the discovery of steps of causation between a cause and its remote effects ; the interpolation and con- catenation of causes. The maxim ' No cats no clover ' is explained by assigning the inter- mediate steps in the following series ; that the fructification of red clover depends on the visits of humble-bees, who scatter the pollen in seeking honey ; that if field-mice are numerous they destroy the humble-bees' nests ; and that (owls and weasels being exterminated by game-keepers) the destruction of field-mice depends upon the supply of cats; which, therefore, are a remote condition of the clover crop. Again, the communication of thought by speech is an example of some- thing so common that it seems to need no explanation ; yet to explain it is a long story. A thought in one man's mind is the remote cause of a similar thought in another's: Here we have (i) a thought associated with mental words; {2) a connection between these thoughts and some tracts of the brain ; (3) a connection between these tracts of the brain and the muscles of the larynx, the tongue and the lips ; (4) movements of the chest, larynx and mouth, propelling and modifying waves of air ; (5) the impinging of these air-waves upon another man's ear, and by a complex mechanism exciting the aural nerve; (6) the transfer of this excitation to certain tracts of his brain ; (7) a connection there with sounds of words and their associated thoughts. If one of these links fail, there is no communication. EXPLANATION 237 Thirdly, the Subsumption of several laws under one more general expression. Thus the tendency of bodies to fall to the Earth and the tendency of the Earth itself (with the other planets) to fall into the Sun, are sub- sumed under the general law that 'All matter gravitates.' The same law subsumes the movements of the tide. By means of the notion of specific gravity, it includes ' levitation,' or the actual rismg of some bodies, as of corks in water, of balloons, or flames in the air ; the fact being that these things do not tend to rise, but to fall like everything else ; only as the water or air weighs more in proportion to its volume than corks or balloons, the latter are pushed up. This process of Subsumption bears the same relation to Secondary Laws, that these do to particular facts. The generalisation of many particular facts (that is. a statement of that in which they agree) is a law and the generalisation of these laws (that is, again, a statement of that in which they agree) is a higher law ; and this process, upwards or downwards, is essentially the course of scientific progress. The per- fecting of any science consists in comprehending more and more of the facts within its province, and in showing that they all exemplify a smaller and smaller number of principles, which express their most profound resemblances. It can easily be shown that these three modes of explanation all consist in generalising or assimilating the phenomena. The pressure of the air, of a liquid, and motion in the direction of least resistance, are all commoner facts than pumping ; that light travels faster than sound is a commoner fact than a thunder-storm or gun-firing. Each of the laws-^ Cats kill mice,' 'Mice destroy humble-bees' nests,' 'Humble-bees fructify red clover '—is wider and expresses the resemblance of more numerous cases than the law that ' Clover depends on cats'; because each of them is less subject to further conditions. Similarly, every step in the communication of thought by language is less conditional, and therefore more general, than the completion of the process. In all the above cases, again, each law into which the phenomenon (whether pumping or conversation) is resolved, suggests a host of related resemblances : as the moditymg of air-waves by the larynx and lips suggests the various devices 238 LOGIC: DEDUCTIVE AND INDUCTIVE by which the strings and orifices of musical instruments modify the character of notes. As for Subsumption (case (3)), it consists entirely in proving the existence of an essential similarity between things in which it was formerly not observed: as that the gyrations of the moon, the M\ of apples, and the flotation of bubbles are all examples of gravitation : or that the purifying of the blood by breathing, the burning of a candle, and the rustmg of iron are all cases of oxidation : or that the colouring of the underside of a red-admiral's wings, the spots of the giraffe, the shape of a stick-caterpillar, the transparency of deep-sea animals, and coundess other cases, though superficially so different, agree in this, that they conceal and thereby protect the organism. Not any sort of likeness, however, suffices for scientific explanation: it must be 'fundamental'; or (as this is a vague expression) we may say that the only satisfactory explanation of concrete things or events, is to discover their likeness to others in respect of Causation. Hence attempts to help the understanding by familiar comparisons are often worse than useless. Any of the above examples will show that explanation, instead of making a phenomenon seem familiar, puts (as the saying is) 'quite a new face upon it.' The proneness to substitute familiarisation for radical explana- tion, is the easily besetting sin of human understanding : the most plausible of fallacies, the most attractive, the most difficult to avoid even when we are on our guard against it. § 7. The explanation of Nature (if it be admitted to consist in generalisation, or the discovery of resemblance amidst differences) can never be completed. For— (i) there are (as Mill says) facts, namely, fundamental states or processes of consciousness, which are distinct ; in other words, they do not resemble one another, and therefore cannot be generalised or subsumed under one explanation. Colour, heat, smell, sound, touch, pleasure and pain, are so different that there is one group of conditions to be sought for each ; and the laws EXPLANATION 239 of these conditions cannot be subsumed under a more general one without leaving out the very facts to be explained. A general condition of sensation, such as the stimulating of the sensory organs of a living animal, gives no account of the s/>ecia/ characters of colour, smell, e/c\ ; which are, however, the phenomena in question : and each of them has its own law. (2) When physical science is treated objectively (that is, with as little reference as possible to the fact that all pheno- mena are only known in relation to the human mind), colour, heat, smell, sound (considered as sensations) are neglected, and attention is fixed upon certain of their conditions : Ex- tension, Figure, Resistance, Weight, Motion, with their derivatives. Density, Elasticity, eU. These are called the Primary Qualities of Matter; and it is assumed that they belong to matter by itself, whether we look on or not : whilst colour, heat, sound, etc., are called Secondary Qualities, as depending entirely upon the reaction of some conscious animal. From this point of view, the world is considered in the abstract, as a perpetual redistribution of matter and energy. But, not to dwell upon the difficulty (which may be temporary) of reducing the activities of life and chemistry to mechanical principles— even if this were done, complete explanation could not be attained. For— («) as explanation is the discovery of causes, we no sooner succeed in assigning the causes of the present state of the world than we have to inquire into the causes of those causes, and again the still earlier causes, and so on to infinity. But, this being impossible, we must be content, wherever we stop, to contemplate the uncaused, that is, the unexplained ; and then all that follows is really unexplained. Besides this difficulty, however, there is another that prevents the perfecting of any theory of the abstract material world, namely (<^), that it involves more than one first principle. For we have seen that the Uniformity of Nature is not really a principle, but a merely nominal generalisation, since it cannot 240 LOGIC: DEDUCTIVE AND INDUCTIVE be definitely stated ; and, therefore, the principles of Contra- diction, Mediate Equality, and Causation remain incapable of subsumption ; nor can any one of them be reduced to another : so that they remain unexplained. (3) Another b.ir to explanation lies in the infinite character of every particular fact ; so that we may know the laws of many of its properties and yet come far short of understanding it as a whole. A lump of sandstone in the road : we may know a good deal about its specific gravity, temperature, chemical composition, geological conditions ; but if we inquire the causes of the particular modifications it exhibits of these properties, and further why it is just so big, containing so many molecules, neither more nor less, disposed in just such relations to one another as to give it this particular figure, why it lies exactly there rather than a yard off, and so forth, we shall get no explanation of all this. The causes determining each particular phenomenon are infinite, and can never be computed ; and, therefore, it can never be fully explained. § 8. Analogy is a kind of probable proof based upon imperfect similarity (as the best that can be discovered) between the data of comparison and the subject of our inference. Like Deduction and Induction, it assumes that things which are alike in some respects are also alike in others ; but it differs from them in not appealing to a definite general law assigning the essential points of resemblance upon which the argument relies. In Deductive proof, this is done by the major premise of every syllogism : if the major says that * All fat men are humourists ', and we can establish the minor, ' X is a fat man ', we have secured the essential resemblance that carries the conclusion. In Induction, the Law of Causation and its representatives, the Canons, serve the same purpose, specifying the essential marks of a cause. But, in Analogy, the resemblance relied on cannot be stated categorically. If we argue that Mars is inhabited because it resembles the datum, our Earth, (i) in being a planet, (2) neither too hot nor too cold for ANALOGY 4.1 life, (3) having an atmosphere, (4) sea and land, etc., we are not pre- pared to say that ' All planets having these characteristics are inhabited.' It is, therefore, not a deduction ; and since we do not know the original causes of life on the Earth, we certainly cannot show by induction that adequate causes exist in Mars. We rely, then, upon some such vague notion of Uniformity as that ' Things alike in some points are alike in others ' ; which, plainly, is either false or nugatory. The cogency of any proof depends upon the character and definiteness of the likeness which one phenomenon bears to another ; but Analogy trusts to the general quantity of likeness between them, in ignorance of what may be the really important likeness. If, having tried with a stone, an apple, a bullet, etc., we find that they all break an ordinary window, and thence infer that a cricket ball will do so, we do not reason by Analogy, but make instinctively a deductive extension of an induction, merely omitting the explicit generalisation, 'All missiles of a certain weight, size and solidity break windows.' But if, knowing nothing of snakes except that the viper is venomous, a child runs away from a grass-snake, he argues by Analogy; and, though his conduct is prudentially justifiable, his inference is wrong: for there is no law that 'A.ll snakes are venomous,' but only that those are venomous that have a certain structure of fang ; a point which he did not stay to examine. . Analogical argument, therefore, is only probable, and that in various degrees. (i) The greater the number and importance of the points of agreement, the more probable is the inference. (2) The greater the number and importance of the points of difference, the less probable is the inference. (3) The greater the number of unknown properties in the subject of our argument, the less the value of any inference from those that we do know. Of course the number of unknown properties can itself be estimated only by Analogy. In the case of Mars, they are probably very numerous ; and the prevalent assumption that there are intelligent beings in that planet, seems to rest less upon probability than on a curiously imaginative extension of the gregarious sentiment, and a hope that there may be conversable and ' clubable ' souls nearer than the Dog-star. CHAPTER XX PROBABILITY § I. Chance was once believed to be a distinct power in the world, disturbing the regularity of Nature ; though, accoiding to Aristotle, it was only operative in occurrences below the sphere of the moon. As, however, it is now admitted that every event in the world is due to some cause, if we can only trace the connection, whilst nevertheless the notion of Chance is still useful when rightly conceived, we have to find some other ground for it than that of a spontaneous capricious force inherent in things. Every event is a result of causes : but the multitude of forces and the variety of collocations beir^ immeasurably great, the overwhelming majority of events occurring about the same time are only related by Causation so remotely that the connection cannot be followed. Whilst my pen moves along the paper, a cab rattles down the street, bells in the neighbouring steeple chime the quarter, a girl in the next house is practising her scales, and throughout the world innumerable events are happening which may never happen together again, so that should one of them recur, we have no reason to expect any of the others. This is Chance, or chance coincidence. 1 he word coincidence is vulgarly used only for the inexplicable concurrence of in- teresting events — " quite a coincidence ! " On the other hand, many things are now happening together or coinciding, that will do so, for assignable reasons, again and again ; thousands of men are leaving the City, who leave at the same hour five days a week. But this is not chance ; it is PROBABILITY 243 causal coincidence due to the custom of business m this country, as determined by our latitude and longitude and other circum- stances No doubt the above chance coincidences— writing, cab-rattling, chimes, scales, ./..-are causally connected at some point of past time. They were predetermined by the condition of the world ten minutes ago ; and that was due to earlier con- ditions, one behind the other, even to the formation of the planet But whatever connection there may have been, we have no such knowledge of it as to be able to deduce the coincidence, or calculate its recurrence. Hence Chance is defined by Mill to be : Coincidence giving no ground to inter uniformity. However, in fact, some chance coincidences do recur ac- cording to laws of their own : I say some, but it may be all. If the world is finite, the possible combinations of its elements are exhaustible ; and, in time, whatever conditions of the world have concurred will concur again, and in the same relation to former conditions. This writing, that cab, those chimes, those scales will coincide again : the Argonautic expedition, and the Trojan war, and all our other troubles will be renewed. But, to avoid melancholy, let us consider some more manageable instance, such as the throwing of dice. Every one who has played much with dice knows (so I am told) that double sixes are sometimes thrown, and sometimes double aces. Such coincidences do not happen once and only once ; they occur again and again, and a great number of trials will show that though their recurrence has not the regularity of cause and effect, it yet has a law of its own, namely-a tendency to average regularity. In 10,000 throws there will be some number of double sixes; and the greater the number of throws, the more closely will the average recurrence of double sixes, or double aces, approximate to one in thirty-six Such a law of average recurrence is the basis of Probability. Chance being the fact of coincidence without assignable cause. Proba- bility is expectation based on the average frequency of its happening. 244 LOGIC: DEDUCTIVE AND INDUCTIVE § 2. Probability is an ambiguous term. Uusually, when we say that an event is ' probable,' we mean that it is more likely than not to happen. But, scientifically, an event is probable if our expectation of its occurrence is less than certainty, as long as the event is not impossible. Probability thus conceived is represented by a fraction. Taking i to stand for certainty, and o for impossibility, probability may be VWo' ^^ ioVo> ^^ (generally) i. The denominator, of course, represents the number of times that an event happens, and the numerator the number of times that it coincides with another event. In throwing a die, the probability of ace turning up is expressed by putting the number of throws for the denominator and the number of times that ace is thrown for the numerator ; and we may assume that the more trials we make the nearer will the resulting fraction approximate to J. Instead of speaking of the 'throwing of the die' and its ' turning up ace ' as two events, the former is often called ' the event' and the latter 'the way of its happening.' And these expressions may easily be extended to cover relations of distinct events ; as when two men shoot at a mark and we desire to represent the probability of both hitting the bull's eye together, each shot may count as an event (denominator) and the coinci- dence of ' bull's-eyes ' as the way of its happening (numerator). It is also common to speak of probability as a proportion. If the fraction expressing the probability of ace being cast is ^, the proportion of cases in which it happens is i to 5 ; or (as it is, perhaps, still more commonly put) ' the chances are 5 to i against it.' § 3. As to the grounds of probability opinions differ. According to one view the ground is subjective: probability depends, it is said, upon the quantity of our Belief in the happening of a certain event, or of its happening in a particular way. According to the other view the ground is objective, and, in fact, is nothing else than experience, which is most trust- worthy when carefully expressed in statistics. To the subjective view it rnay be objected, (a) that Belief PROBABILITY 245 cannot by itself be satisfactorily measured. Surely, no one will maintain that Belief, merely as a state of mind, always has a definite numerical value of which one is conscious, as yjo ^^ j\. Let anybody mix a number of letters in a bag, knowing nothing of them except that one of them is X, and then draw them one by one, endeavouring each time to estimate the value oi his belief that the next will be X ; can he say that his belief in the drawing of X regularly increases as the number of letters Ipft decreases ? If not, we see that {d) Belief does not uniformly correspond with the state of the facts. If in such a trial as proposed above, we really wish to draw X (as in looking for somethmg in a number of boxes), how common it is after a fewfaimres to feel quite hopeless and to say : " Oh, of course it will be in the last." For belief is subject to hope and fear, temperament, passion and prejudice, and not merely to rational considerations. And it is useless to appeal to ' the Wise Man,' the purely rational judge of probability, unless he is producible. Or, if it be said that belief is a short cut to the evaluation of experience, be- cause in fact it is the resultant of all past experience, we may reply that this is not true. For everybody knows that one striking experience, or two or three recent ones, will immensely outweigh a great number of faint or remote experiences. More- over, the experience of two men may be practically equal, whilst their beliefs upon any question greatly differ. Any two English- men have about the same experience, personal and ancestral, of the weather ; yet their beliefs in the saw that ' if it ram on St. Swithin's Day it will rain for forty days after,' may differ as confident expectation and sheer scepticism. Upon which of these beliefs shall we ground the probability of forty days rain? But {c), at any rate, if Probability is to be connected with Inductive Logic, it ought surely to rest upon the same, ground, namely— Observation. Induction, in any particular case, is not content with beliefs or opinions, but aims at probing, testing, verifying or correcting them by appealing to the facts ; and Probability has the same object and the same basis. 246 LOGIC: DEDUCTIVE AND INDUCTIVE There are, indeed, cases in which the conditions of an event are supposed to be mathematically predetermined, as in tossing a penny, tiirowing dice, dealing cards. In throwing a die, the ways of happening are six ; in tossing a penny only two, head and tail : and we usually assume that the odds with a die are fairly 5 to i against ace, whilst with a penny 'the betting is even' on head or tail. Still, this assumption rests upon another, that the die is perfectly fair, or that the head and tail of a penny are exactly alike ; and this is not true. With an ordinary die or penny, a very great number of trials would, no doubt, give an average approximating to J or J ; yet might always leave a certain excess one way or the other, which would also become more definite as the trials went on ; thus showing that the die or penny did not satisfy the mathematical hypothesis. Buffon is said to have tossed a coin 4040 times, obtaining 1992 heads and 2048 tails ; a pupil of De Morgan tossed 4092 times, obtaining 2048 heads and 2044 tails. There are other important cases in which probability is estimated and numerically expressed, although statistical evidence directly bearing upon the point in question cannot be obtained ; as in betting upon a race ; or in the prices of stocks and shares, which are supposed to represent the probability of their paying, or continuing to pay, a certain rate of interest. But the judgment of experts in such matters is certainly based upon experience ] and great pains are taken to make the evidence as definite as possible by comparing records of speed, or by financial estimates ; though something must still be allowed for reports of the condition of horses, or of the prospects of war, etc. However, where statistical evidence is obtainable, no one dreams of preferring to estimate probability by the quantity of his belief. Insurance offices, dealing with fire, shipwreck, death, accident, etc., prepare elaborate statistics of these events, and regulate their rates accordingly. Apart from statistics, at what rate ought the lives of men aged 40 to be insured, in order to leave a profit of 5 per cent, upon jQiooo PROBABILITY 247 payable at each man's death? Is 'quantity of belief a sufficient basis for doing this sum ? § 4. The ground of probability is experience, then, and, whenever possible, statistics ; which are a kind of inductions. It has indeed been urged that induction is itself based upon probability; that the subtlety, complexity and secrecy of nature are such, that we are never quite sure that we fully know even what we have observed ; and that, as for laws, the conditions of the universe at large may at any moment be completely changed; so that all imperfect inductions, in- cluding the law of Causation itself, are only probable. But, clearly, this doctrine turns upon another ambiguity in the word 'probable.' It may be used in the sense of Mess than abso- lutely certain ' : and such doubtless is the condition of all human knowledge, in comparison with the comprehensive intuition of archangels ; or it may mean ' less than certain according to our standard of certainty/ that is, in comparison with the law of Causation and its derivatives. We may suppose some one to object that " by this relative standard even empirical laws cannot be called ' only probable ' as long as we ' know no exception to them ' ; for that is all that can be said for the boasted law of Causation ; and that, accordingly, we can frame no fraction to represent their probability. That 'all swans are white' was at one time, from this point of view, not probable but certain ; though we now know it to be false. It would have been an indecorum to call it only probable as long as no other coloured swan was known ; not merely because the quantity of belief amounted to certainty, but because the number of events (seeing a swan) and thenumber of their happenings in a certai n way (being white) were equal, and therefore the evidence amounted to i or certainty." But we reply, that such an empirical law is only probable, and that the estimate of its probability must be based on the number of times that similar laws have been found liable to exceptions. White crows, though rare, are exceptions to the 248 LOGIC: DEDUCTIVE AND INDUCTIVE law that crows are black ; and it is not uncommon to find allied varieties of animals differing in colour in different localities. Had the evidence been known and duly weighed, then, it could never have seemed more than probable that ' all swans are white.' But what law, similar in rank to the law of Causation, presents any exceptions ? It ought not to be difficult to see that induction, humanly speaking, does not rest on probability ; but that the probability of concrete events (not of mere mathematical abstractions like the falling of absolutely true dice) rests on induction and, therefore, on Causation. The inductive evidence underlying an estimate of probability may be of three kinds : (a) direct statistics of the events in question ; as when we find that, at the age of 20, the average expectation of life is 39-40 years. This is an empirical law, and, if we do not know the causes of any event, we must be content with an empirical law. But (/?) if we do know the causes of an event, and the causes which may prevent its happening, and can estimate the comparative frequency of their occurring, we may deduce the probability that the effect (that is, the event in question) will occur. Or (c) we may combine these two methods, verifying each by means of the other. Now either the method (fi) or (n. Still, the two modes of procedure maybe usefully distinguished: \n deducUon xve advance from a whole to its parts, from general to special .m induction, from special (or particular) to general, from the parts to their whole. § 4. The process of Deductive Classification, or Formal Division, may be represented thus : A AB Ab ABC ABc AbC I Abe Given any class (A) to be divided. I Select one important character, attribute, or quality l^)- "^^ common to all the individuals comprehended in the class, as the basis of division [futidameiitum divisionis). 2. Proceed by Dichotomy; that is. cut the given class ^^^o two one having the selected attribute (say. B). the other not having it (b). Ihis like all formal processes, assumes the principles of Contradiction and Excluded Middle, that ' No A is both B and not-B.' and that ' Every A is'eitherBor not-B' (chap. vi. § 3); and if these principles are not true, or not applicable, the method fails. When a Class is thus subdivided, it may be called, in relation to its Subclasses, a Genus; and in relation to it. the Subclasses may be called Species : thus -Genus A, Species AB and Ab, ^^'^■ 3 Proceed gradually in the order of the importance of characters , that is. having divided the given class, subdivide on the same principle the two classes thence arising; and so again and again, step by step, until all the characters are exhausted: Divisio ne fiat per saltiim. DIVISION AND CLASSIFICATION 259 Suppose we were to attempt an exhaustive classification of things by this method, we must begin with 'All Things.' and divide them (say) into phenomenal and not-phenomenal, and then subdivide phenomena, and so on, thus : All Things Phenomenal Not-phenomenal I Extended Unextended {e.g., Pleasure and Pain) Resistant (Matter) Non-resistant (Space) Gravitating Non-gravitating Simple Compound Having subdivided ' Simple ' by all possible characters, we must then go back and similarly subdivide Not-phenomenal. Unextended, Non- resistant, Non-gravitating and Compound. Now, if we knew all possible characters, and the order of their importance, we might prepare a priori a classification of all possible things ; at least, of all things that come under the principles of Contradiction and Excluded Middle. It might, indeed, appear that many of our compartments had nothing actual answering to them; there may. for example, be nothing that is not phenomenal to some mind, or nothing that is extended and non-resistant (no vacuum), and so forth. It is true that this implies a breach of the rule, that the dividing quality be not common to the whole class; but. in fact, doubts have been, and are. seriously entertained whether these compartments are filled or not. If they are not, we have concepts representing nothing, which have perhaps been generated by the mere force of grammatical negation ; and, on the strength of these empty concepts, we have been misled into dividing by an attribute, which (being universal) cannot be a fundamentum divisionis. But though places might be empty, there would be a place for everything; for whatever did not come into some positive class, such as Gravitating, must, at any rate, fall under one of the negative classes (the 'Nots'j that would run down the right-hand side of the Table and of its sub- divisions. This is the ideal of classification. Unfortunately, however, we have to learn what characters or attributes are possible, by experience and .6o LOGIC : DEDUCTIVE AND INDUCTIVE comparison; we are far fro. Unowing ^^:i:^'-Z^ ZX^or^' the order of their importance ; nor are ^ve even c ea vvh _ P ^^ , ^^ means in this context, -hef-^ ' ^'-^f^ P^^.^^'H^nce, in classifying •causally influential,; or; -dKattve of oAe^- .."fth particular things, actual things, the inducUve ■-*°f/, .'^^tT^I^^'discovered by investiga- and sorting them accordmg to «*'«'Y'^^^"^!'/„3„,ed to. The excep- tion of their nature, must nearly '■^l^J.'^J^^'^tnr where certain tional cases, in which deduction is -^e^'y ~ °^^" ^^ ^e known, limits to the number and combination of q"^''''- ^^PP^^ mathematical as they may -J;;^-- --^'t: dS "^ of Architecture rrre itiir 'rtr^s^nd s.an.as of Hng,.h Poe^-— - fact, these things are too free, subtle and -mplex fo ^^^^ ^^^ ment : for do not the Arts grow like trees ■ J^J J ^^ree kinds mathematical; as «e may ^^ow that the e a- poss y^^ of plane triangles, four conic sections, hve re„uia § 5 The rules for /esfing a Division are as follows : , Each Sub-class, or Species, should comprise less than the Class, or Genus, to be divided. v n u^ ^ rpal one and not based This provides that the ^^^^^^^^^ ^J ^l^Leiore. .^e f^rst upon an attribute ---°" '° .'^^^^^.^ten Completely adhered to. But, rule for making a division shall ha e ^ee" co p y ^^ as in § 4. we are here met by a ogical f "; J^"PP°;,, g, into AB be divided is A, and we attempt .'« ^'vide upon the a« ^ ^^^^ .^ and Ab: is this now a 'rue division if -e do not y^ ^ ^^ ^^^ not B ? As far as our knowledge extends, w hav n^^ .^ ^^^^^ But. on the other hand, our knowledge o exhaustive; so that, althcnigh we know o^n A *^^^ exist, and we have seen that is a >o <= ^^.^ ^^ ,,,,, ,, .^ems better we do not know. In a aeauciue c division Hence, in to regard every attribute as y^os^Uejro.n^of^^^^^^ ^^^^^^^^_ the above d--- ° ^^J^^^f^J^^..^^ , ,p%ar as negative classes Non-resistant, Resistant in uu g^ r ^„ ^ttrihute^ although their real (that is, classesbased on the nega- of n attnbute)^^^^ ^^^ g^^^^ ^^^^^^ existence may be doubtful ^ut, i tnis j ^ ^^^^-^i ---'^^^-^thl dtrrb^dlvide^/' ^else we must confine comprise less than the class to ; dividing Colour into the rule to (a) thoroughly empirical divisions, as' » ^^^ ^^^ Red and Not-red, where we know that both sub ^^ ^^^^^ (6) divisions under demonstrable -"^u^^^^-^ ;t-now that it is only Tr^tb^ctr SkfntX should be e.ual to the Class to be DIVISION AND CLASSIFICATION 261 divided : the sum of the Species constitutes the Genus. This provides that the Division shall be exhaustive; which is always secured by- dichotomy, according to the principle of Excluded Middle ; because whatever is not in the positive class, must be in the negative : Red and Not-red include all colours. 3. The Sub-classes must be opposed or mutually exclusive : Species must not overlap. This again is secured by Dichotomy, according to the principle of Contradiction, provided the Division be made upon one attribute at a time. But, if we attempt to divide simultaneously upon two attributes, as ' Musicians ' upon ' nationality ' and ' method,' we get what is called a Cross-division, thus: 'German Musicians,' 'Not- German,' ' Classical,' ' Not-Classical,' for these classes may overlap, the same men sometimes appearing in two groups — Bach in ' German ' and ' Classical,' Pergolesi in 'Not-German' and 'Classical.' If, however, we divide Musicians upon these attributes successively, cross division will be avoided, thus : Musicians Classical Non-classical German Non-German German Non-German Here no Musician will be found in two classes, unless he has written works in two styles, or unless there are works whose style is undecided. Let this " unless— or unless " suggest caution in using dichotomy as a short cut to the classification of realities. 4. No Sub-class must include anything that is not comprised in the class to be divided : the Genus comprises all the Species. Do not divide Dogs into fox-terriers and dog-fish. § 6. The process of Inductive Classification may be repre- sented thus : Given any multitude of individuals to be classified : (i) Place together in groups (or in thought) those things that have in common the most, the most widely diffused and the most important qualities. (2) Connect those groups which have, as groups, the greater resemblance, and separate those that have the greater difference. (3) Demarcate, as forming higher or more general classes, those groups of groups that have important characters in 262 LOGIC: DEDUCTIVE AND INDUCTIVE common ; and, if possible, on the same principle, form those higher classes into classes higher still : that is to say, graduate the classification upwards. Whilst, in Division, the terms 'Genus' and 'Species' are entirely relative to one another and have no fixed positions in a gradation of classes, it has been usual, in Inductive Classification, to confine the term ' Species ' to classes regarded as lowest in the scale, to give the term ' Genera' to classes on the step above, and at each higher step to find some new term, such as 'Tribe,' 'Order,' 'Sub-kingdom,' 'Kingdom'; as may be seen by turning to any book on Botany or Zoology. If. having fixed our Species, we find them subdivisible, it is usual to call the Sub-species ' Varieties.' Suppose we attempt to classify by this method the objects m an ordinary sitting-room. We see at a glance carpets, mats, curtains, grates, fire-irons, coal-scuttles, chairs, sofas, tables, books, pictures, musical instruments, etc. These we may call ' Species.' Carpets and mats clearly go together ; so do chairs and sofas ; so do grates, fire- irons, and coalscuttles ; and so on. These greater groups, or higher classes, we may call 'Genera.' Putting together carpets, mats and curtains as 'warmth-fabrics'; chairs, sofas and tables as 'supports'; books, pictures and musical instruments as ' means of culture ' : these groups we mav call Orders. Sum up the whole as, from the house- wife's point of view, 'furniture.' If we then subdivide some of the species, as books into poetry, novels, travels, etc., these Sub-species may be considered ' varieties.' A Classification thus made, may be tested by the same rules as those given for testing a Division ; but if it does not stand the test, we must not infer that the classification is a bad one. If the best possible, it is good though formally imperfect : whatever faults are found must then be charged upon the 'matter,' which is traditionally perverse and intractable. If. for example, there is a hammock in the room, it must be classed not with the curtains as a warmth- fabric, but with the sofas as a support • and books and pictures may be classed as. in a peculiar sense means of culture, though all the objects in the room may have been modified and assorted with a view to gratifying and developing good taste. § 7. The difficulty of classifying natural objects is very great. It is not enough to consider their external appearance : exhaustive knowledge of their internal structure is necessary, and of the functions of every part of their structure. This is a matter of immense research, and has occupied many of the DIVISION AND CLASSIFICATION 263 greatest minds for very many years. The following is a tabular outline of the classification of the Animal Kingdom Sub-kingdom: Vertebrates Invertebrates (5 Sub-kingdoms) Sauropsida Ichthyopsida Class: Mammals Birds Reptiles Amphibia Fishes Sub-class : Placental Division : Monodelphia Implacental Didelphia Ornithodelphia I I I I I O'^DER : Quadrumana Rodentia Carnivora Ungulata Caetacea, etc. Section Pinnigrada Plantigrada Digitigrada I I ( Seals, etc. ) ( Bears, etc. ) Genus: Mustelidae Viverridae Hya^nidae Canidae Felidae (Weasels, etc.) (Civets, etc.) Lion Tiger Leopard Puma Lynx Cat, etc. Species : Variety : African Syrian Cave-lion (extinct) As there is not space enough to tabulate such a classification in full, I have developed at each step the most interesting groups : Vertebrates, Mammals, Monodelphia, Carnivora, Digi- tigrada, Felidse, Lion. Most of the other groups in each grade are also subdivisible, though some of them contain far fewer sub-classes than others. To see, however, the true character of this classification, we must consider that it is based chiefly upon knowledge of 264 LOGIC: DEDUCTIVE AND INDUCTIVE existing animals. Some extinct animals, known by then: fossilsffind places in it; for others new places have been made. But it represents, on the whole, a cross section, or cross-sections, of Nature as developing in time ; and, in order Tg ve a just view of the relations of animals, it must be seen in the light of other considerations. The older systems of this system are determined by quantity of resemblance in co-existent qualities, as the ground of their afhnity. § 8. Darwin's doctrine of the origin of species modifies he conception of natural classification in several ^^ays^ In the first pLe, if all living things are blood-relations modifi^^^^^ the course of ages according to their various conditions of life 'Affinity' must mean ' nearness of common descent ; and it seems irrational to propose a classification upon any other basis We have to consider the Animal (or the Vegetable) Kingdom as a family tree, exhibiting a long fine of ancestors, and (descended from them) all sorts of cousins, first, second third ./.., perhaps once, twice, or oftener ' removed Of course, animals in the relation of first cousins must be classed as nearer than second cousins, and so on. But, if we accept this principle, and are able to trace relationship, it may not lead to the same results as we should reach by simply relying upon the present quantity of resemblance ', unless we understand this in a very particular way For the most obvious features of an animal may have been recently acquired, as often happens with those characters which adapt an animal to its habits of life, as the wings of a bat or the fish-like shape of a dolphin ; or as in cases of 'mimicry'. Some butterflies, snakes, efc, have grown to resemble closely, in a superficial way, other butterflies and nakes from which a stricter investigation widely separates them -'and this superficial resemblance is probably a recent acquisition, for the sake of protection : the imitated butterflies DIVISION AND CLASSIFICATION 265 being nauseous, and the imitated snakes poisonous. On the other hand, ancient and important traits of structure may, in some species, have dwindled into inconspicuous survivals, or be still found only in the embryo ; so that only great know- ledge and sagacity can identify them ; yet upon ancient traits, though hidden, classification depends. The seal seems nearer allied to the porpoise than to the tiger, the shrew nearer to the mouse than to the hedgehog ; and the Tasmanian hyaena, or the Tasmanian devil, looks more like a true hyaena, or a badger, than like a kangaroo ; yet the seal is nearer akin to the tiger, the shrew to the hedgehog, and the Tasmanian carnivores are marsupial, like the kangaroo. To overcome this difficulty we must understand the resemblance upon which classification is based to include resemblance of Causation, that is, the fact itself of descent from common ancestors. In the case of organic beings, all other rules of classification are subordinate to one : trace the genealogy of every form. By this rule, however, we get a definite meaning for the phrase 'important or fundamental attribute' as determining organic classes ; namely, most ancient, or ' best serving to indicate community of origin'. Grades of classification will be determined by such fundamental characters, and may cor- respond approximately to the more general types (now mostly extinct) from which existing animals have descended. In the second place, by the hypothesis of development the fixity of species is discredited. The lowest grade of a classification is made up not of well-defined types un- changing from age to age, but of temporary species, often connected by uncertain and indistinct varieties : some of which may, in turn, if the conditions of their existence alter, undergo such changes as to produce new species. Hence, again, the notion that Kinds exist in organic nature must be greatly modified. During a given period of a few thousand years, Kinds may be recognised; because, under such conditions as now prevail in the world, that i 266 LOGIC: DEDUCTIVE AND INDUCTIVE period of time is insufficient to bring about g-^ft changes. But, if it be true that lions, tigers, and leopards have had a common ancestor, from whose type ihey have gradual y diverged, it is plain that their present distinctness results only from the death of intermediate specimens and the destruction of intermediate varieties. Could we, by the evidence o fossils, restore all the ranks of the great processions that have descended from the common ancestor, we should find nowhere a greater difference than between offspring and parents ; and the appearance of Kinds existing in nature which is so striking in a museum or zoological garden, would entirely vanish. A classification, then, as formerly observed, represents - "---'^^ of nature as developing in time : could we begm at the beg— and follow this development down the course of time, we should find no clisses, but an ever moving, changing, ^P-^^^f ' ''-"^'^'"^'^t " » It mav be represented thus ; Suppose an animal (or plant) A, extendmg over ascertain geographical area, subject to different influences and con- d ttons of climlterfood, hill and plain, wood and prairie, enemies and rivals, and undergoing modifications here and there in ^^ap ation to he varying conditions of hfe : then varieties appear. These varieties diverging more and more, become distinct Species (AB, AC, AD, AX). Some of these Species, the more widely '^>ff"^^<'' ^S^\" P^^f ""S ™m\tse' which, in turn, become Species (ABE, ABF, ADG^ADH). From these, again, arise ABFI, ABFJ , ADHK, ADHL, ADHM. Then ABE ABF and ADH are Genera (ADG being extinct) ; and the earlier types represent Families and Orders. DIVISION AND CLASSIFICATION 267 ABL ABFI ADHK ADHL ADHM If in this age a classifier appears, he finds seven living Species which can be grouped into four Genera (ABE. ABF. AC. ADH). and these again into three Families (AB, AC, AD), all forming one Order. If the fossils of ADG and AX can be found, he has two more Species, one more Genus (ADG). and one more Family (AX). For AC, which has persisted unchanged, and AX, which has become extinct, are both of them Families, each represented by only one Species. But now suppose that he could find a fossil specimen of every generation (hundreds of thousands of generations), from ABFI. etc., up to A ; then, as each generation would only differ from the preceding as offspring from parents, he would be unable at any point to distinguish a Species ; at most, he would observe a slightly marked variety. ABFI and ABFJ would grow more and more alike, until they became indis- tinguishable in ABF ; ABF and ABE would merge into AB ; AB, AC, AD and AX would merge into A. Hence, the appearance of Species is due to our taking cross-sections of time, or comparing forms that belong to periods remote from one another (like AX. ADG. and ADHK. or AD. ADH and ADHK), and this appearance of Species depends upon the destruction of ancestral intermediate forms. In the third place, the hypothesis of development modifies the logical character of classification : it no longer consists in a direct induction of co-existent characters, but is largely a deduction of these from the characters of earlier forms, together with the conditions of variation; in other words, the definition of a species must, with the progress of science, cease to be a mere empirical law of co-existence and become a derivative law of Causation. But, after all, this was already implied in the position that causation is the fundamental principle of the explanation of concrete things ; and, accord- ingly, the derivative character of species or kinds extends beyond organic nature. § 9. The classification of inorganic bodies also depends on causation. There is the physical classification into Solids, Liquids, and Gases. But these states of matter are dependent on temperature ; at least, it is known that many bodies may, at different temperatures, exist in all three states. They cannot therefore be defined as solid, liquid, or gaseous absolutely, but only within certain degrees of temperature, and therefore as dependent upon causation. Similarly, the geological classification of bodies, according to relative anti- quity (primary, secondary, tertiary, with their subdivisions), 268 LOGIC: DEDUCTIVE AND INDUCTIVE and mode of formation (igneous and aqueous), rests upon causation; and so does the chemical classification of compound bodies according to the elements that enter into them in definite proportions. Hence, only the classification of the elements themselves (amongst concrete things), at present, depends largely upon empirical Co-existence. If the elements remain irresolvable into anything simpler, the defini- tions of the co-existent characters that distinguish them must be reckoned amongst the ultimate Uniformities of Nature. But if a definite theory of their origin both generally and seve- rally, whether out of ether vortices or what-not, shall ever gain acceptance, similarity of genesis or causation will naturally be the leading consideration in classifying the chemical elements. In fact, the ultimate explanation of nature is always causation ; or, in other words, the Law of Causation is the backbone of the system of Experience. CHAPTER XXII NOMENCLATURE, DEFINITION, PREDICABLES § I. Precision of thought needs precision of language, not only for recording such thought and for communicating it to others, the two uses most frequently insisted upon, but even for forming general or abstract ideas. It is true that we can often remember with great vividness persons, things, landscapes, changes and actions of persons or things, without the aid of language (though words are often mixed with such trains of imagery), and thus may form judgment and inferences in par- ticular cases ; but for general notions, judgments and inferences not merely about this or that man, Bismarck or Garibaldi, but about all men or all Germans, we need something besides the few images we can form of them from observation or from pictures. Even in those cases where we may possess generic images, say, of ' horse ' or ' cat ' (that is, images formed, like composite photographs, by a coalescence of the images of all the horses or cats we have seen, so that their common properties stand out and their differences frustrate and cancel one another), these are useless for precise thought ; for the generic image will not correspond with the general appearance of horse or cat, unless we have had proportional experience of all varieties and have been impartially interested in all ; and, besides, what we want for general thought is not a generic image of the appear- ance of things, though it were much more definite and fairly representative than such images ever are, but a general repre- sentation of their important characters ; which may be con- nected with internal organs, such as none but an anatomist 270 LOGIC: DEDUCTIVE AND INDUCTIVE ever sees. We require a symbol connected with the general character of a thing, or quality, or process, as scientifically determined, whose representative truth may be trusted in ordinary cases, or may be verified whenever doubt arises. Such symbols are for most purposes provided by language ; Mathematics and Chemistry have their own symbols. § 2. First, then, there should be " a name for every important meaning " : (a) A Nomenclature, or system of the names of all classes of objects, adapted to the use of each science. Thus, in Geology there are names for classes of rocks and strata, in Chemistry for the elements and their compounds, in Zoology and Botany for the varieties and species of animals and plants, their genera, families and orders. To have such names, however, is not the whole aim in forming a scientific language, it is desirable that they should be systematically significant, and even elegant. Names, like other instruments, ought to be efficient, and the efficiency of names consists in conveying the most meaning with the least effort. In Botany and Zoology this result is obtained by giving to each species a composite name which includes that of the genus to which it belongs. Thus the species of Felidae given in chap. xvii. § 7, are called Felis ho (lion), Felis tigris (tiger), Felis leopardus (leopard), Felis concolor (puma), Felis lyncus (European lynx), Felis catus (wild cat). To take another illustration from the nomen- clature of Butterflies: Vanessa Atalanta (red admiral), Vanessa lo (pea- cock), Vanessa polycloros (large tortoise-shell), Vanessa urtica (small tortoise-shell), Va?iessa Antiopa (Camberwell beauty), etc. In Chemistry, again, the nomenclature is extremely efficient. Names of the simpler compounds are formed by combining the names of the elements that enter into them ; as Hydrogen Chloride, Hydrogen Sulphide, Carbon Dioxide ; and these can be given still more briefly and efficiently in symbols, as HCl, HjS, CO,. The symbolic letters are usually initials of the names of the elements: as C = Carbon, S = Sulphur; sometimes of the Latin name, when the common name is English, as Fe — - Iron. Each letter represents a fixed quantity of the element for which it stands, viz., the atomic weight. The number written below a symbol on the right-hand side shows how many atoms of the element denoted enter into a molecule of the compound. (b) A Terminology is next required, in order to describe and define the things that constitute the classes designated by the nomenclature, and to describe and explain their actions. NOMENCLATURE 271 (i) A name for every integral part of an object, as head, limb, vertebra, heart, nerve, tendon ; stalk, leaf, corolla, stamen, pistil ; plinth, frieze, etc. (ii) A name for every metaphysical part of an object (that is, for every abstract quality of it, or for a quality considered apart from the rest that constitute it), and for their degrees and modes : as extension, figure, solidity, weight ; rough, smooth, elastic, friable ; the various colours^ red, blue, yellow, in all their shades and combinations ; and so with sounds, smells, tastes, temperatures. The terms of Geometry are employed to describe the modes of figure, as angular, curved, square, elliptical ; and the terms of Arithmetic to express the degrees of weight, elasticity, temperature, pitch of sound. When other means fail, qualities are suggested by the names of things which exhibit them in a salient way : figures by such terms as amphitheatre, bowl-like, pear-shaped, egg-shaped ; colours by lias- blue, sky-blue, gentian-blue, peacock-blue ; and similarly sounds, smells and tastes. It is also important to express by short terms complex qualities, as harmony, fragrance, organisation, sex, symmetry, stratifi- cation. (iii) In the explanation of Nature we require further suitable names for processes and activities : as deduction, conver- sion, verification, addition, integration, causation, tendency, momentum, gravitation, aberration, refraction, conduction, affinity, combination, germination, respiration, attention, asso- ciation, development. There may be sometimes a difficulty in distinguishing the terms which stand for qualities from those that express activities, since all qualities imply activities. Weight, for example, implies gravitation ; and the quality heat is also a kind of motion. But the distinction aimed at lies between a quality as perceived by means of an effect upon our senses (as weight is resistance to our effort in lifting ; heat, a sensa- tion when we approach fire), and that property of a body which is con- ceived to account for its energy (as gravitation that brings a body to the ground, or physical heat that expands an iron bar or works an engine). The former class of words, expressing qualities, are chiefly used in description ; the latter class, expressing activities, are chiefly needed in explanation. They correspond respectively, like classifica- tion and explanation, with the static and dynamic aspects of Nature. The terms of ordinary language fall into the same classes as 272 LOGIC: DEDUCTIVE AND INDUCTIVE those of science : they stand for things, classes of things, parts, or quahties, or activities of things ; but they are far less precise in their signification. As long as popular thought is vague its language must be vague ; nor is it desirable too strictly to correct the language whilst the thought is incorrigible. Much of the effect of poetry and eloquence depends upon the elasticity and indirect suggestiveness of common terms. Even in reasonmg upon some subjects, it is a mistake to aim at an unattainable precision. It is better to be vaguely right than exactly wrong. In the criticism of manners, of fine art, or of literature, in politics, religion and moral philosophy, what we are anxious to say is often far from clear to ourselves ; and it is better to indi- cate our meaning approximately, or as we feel about it, than to convey a false meaning, or to lose the warmth and colour that are the life of such reflections. It is hard to decide whether most harm has been done by sophists who take a base advan- tage of the vagueness of common terms, or by honest paralo- gists (if I may use the word) who begin by deceiving themselves with a plausible definiteness of expression, and go on to pro- pagate their delusions amongst followers eager for systematic insight but ignorant of the limits of its possibility. §^3. A Definition is necessary for every scientific name (it possible). To define a name is to give a precise statement of its meaning or connotation. The name to be defined is the subject of a proposition, whose predicate is a list of the funda- mental qualities common to the things or processes which the subject denotes, and on account of possessing which qualities this name is given to them. Thus acurveis a lineofvvhich no partis straight. The momentum of a moving' body is the product of its mass and its velocity (these bemg ex- pressed in numbers of certain units). Nitrogen is a transparent colour- less gas. of specific gravity -9713. "Ot readily combining, etc A Lion may be defined as a monodelphian mammal, predatory, walkmg on its toes, of nocturnal habits, with a short rounded head and muzzle ; dental formula: Incisors 1^ . Canines I_J . premolars 1^ , molars ' ' = 30 ; four toes on the hind and five on the fore foot, 1 - I NOMENCLATURE 273 retractile claws, prickly tongue, light and muscular in build about w th a tufted tail. If anything answers to this description, it is called a hon ; if not, not : for this is the meaning of the name Definition'''?h?t ^"Tr l' ""f^ '"'^'^^ '° ^'^^ '^^ Incomplete Deiinition, that IS, a list of qualities not exhaustive, but containing enough to Identify the things denoted by the given name; as Tf we ^y that a hon is • a large tawny beast of prey with a tufted ta • Such purposes may also be served by a Description; which is tech- nically, a proposition mentioning properties sufficient to distinguish the tutZf- ';°,' '^f P-P-'- 'hat enter into the definition as If a hon is called -the monarch of the desert that figures in^the royal standard,' or .that helps the unicorn to suppon the § 4- The rules for testing a Definition are : I.— As to its Contents — (i) It must state the whole connotation of the name to be denned. (2) It must not include any quality derivative from the con- notation. A breach of this rule can do, indeed, no positive harm, but it is a depar ure from scientific economy. There is no need to state in the definition what can be derived from it; and whatever can be derived that mrniTer' "' '"^*^"'^"'^'i' demonstration, should be exhibited in Such a quality is called a Proprium. (3) It must not mention any circumstance that is not a part of the connotation, even though it be universally found in the thmgs denoted. Such a circumstance, if not derivable from the connotation, is called an Accident. That, for example, the Lion at present only inhabits the Old World IS (I presume) an accident ; if a species otherwise like a Lion were found m B azil. It would not be refused the name of Lion on the score of locality Whilst however, the rules of Logic have forbidden the inclusion of Proprmm or Accident in a Definition, in fact the definitions of fnr/H^ b"v^ r ""™"°" ^""^ attributes when characteristic Indeed, definitions of superordinate classes-Families and Orders-not infrequently give qualities as generally found in the subordinateclasses and at the same time mention exceptional cases in which they do not occur. ■' '"' 274 LOGIC: DEDUCTIVE AND INDUCTIVE II.__As to its Expression— (4) A Definition must not include the very term to be defined, nor any cognate. In defining Lion we must not repeat Mion,' nor use Meonine' ; it would elucidate nothing. (5) It must not be put in vague language. (6) It must not be in a negative form, if a positive form is obtainable. We must not be content to say that a lion is * no vegetarian,' or ' no lover of daylight.' To define a curve as a line * always changing its direction ' may be better than as ' m no part straight.' § 5. The process of determining a Definition is inseparable from classification. We saw that classification consists in dis- tributing things into groups according to their likenesses and differences, regarding as a class those individuals which have most qualities in common. In doing so we must, of course, recognise the common qualities or points of likeness ; and to enumerate these is to define the name of the class. If we discover the qualities upon which a class is based by direct observation and induction, by the same method we discover the definition of its name ; and similarly if we discover the qualities of the class by the help of both observation and deduction, as in the modern classification of plants and animals. We saw also that classification is not merely the determina- tion of isolated groups of things, but a systematic arrangement of such groups in relation to one another. Hence, again, Definitions are not independent, but relative to one another ; and, of course, in the same way as classes are relative. That is to say, as a class is placed in subordination to higher or more comprehensive groups, so the definition of its name is subordinate to that of their names ; and as a class stands in contrast with co-ordinate classes (those that are in the same degree of subordination to the same higher groups), so the definition of its name is in contrast or co-ordination with the definitions of their names. Lion is subordinate to Felis. to Digitigrade, to Carnivore and so on up NOMENCLATURE 275 to Animal; and beyond the Animal Kingdom, to Phenomenon : it is wi'th A"" r'V JZ^'J"""^' '''' ' ^"^ "^^^^ ^^^°^^Jy i^ i^ co-ordinate w h Felf; K^:\Z"''' "^^f '°"^ ""'^^ '^^'-"^ ^-- co-ordinate wi h Fehs. The definition of Lion, therefore, is subordinate to that of Fehs. and to all above it up to Phenomenon; and is co-ordinate with fl ^T"' t .""'i^ ^^^ 'P"'^"^ ^^ '^^ ^^"^^ g^^d^- This is the ground of the old method of Definition per gams et diffemitiam. The Genus being the next class above any Species, the differentia or Difference consists of the qualities which mark that Species in addition to those that mark the Genus, and which therefore distinguish it from all other Species of the same Genus. In the above definition of Lion for example, all the properties down to "light and muscular in build'' are generic that is. are possessed by the whole Genus. Felis; and the remaining four (size, colour, tufted tail, and mane in the male) are the Difference or specific properties, because in those points the Lion con- Tw7'l\'^^ °'^"' ^P""^"^ ^^ '^^' Genus. Differences may be exhibited thus : ^ Lion. Size : about 9I feet from nose to tip of tail. Colour : tawny. Tail : tufted in the male. Mane : present in the male. Tiger. About 10 feet. Warm tawny, striped with black. Tapering. Both sexes maneless. There are other differences in the shape of the skull. In defining Lion then. It would have been enough to mention the Genus and the properties making up the Difference ; because the properties of the Genus may be found by turning to the definition of the Genus : and on the principle of economy, whatever it is enough to do it is right to do To define ; by genus and difference.' then, is a point of elegance, when the genus is known ; but the only way of knowing it is to compare the individuals comprised in it and in co-ordinate genera, according to the methods of scientific classification. It may be added that, as the genus represents ancestral derivation, the predication of genus in a definition indicates the remote causes of the phenomena denoted by the name defined. And this way of defining corresponds with the method of double naming by genus and species : Felis ho, Felis tigris, etc. ; Vanessa Atalanta, Vanessa lo, etc. The so-called Genetic Definition, chiefly used in Mathematics, is a rule for constructing that which a name denotes, in such a way as to ensure Its possessing the primary attributes connected by the name itius. for a circle : Take any point and. at any constant distance from It. trace a line returning into itself. In Chemistry a genetic definition ot any compound might be given in the form of directions for the requisite synthesis of elements. 276 LOGIC: DEDUCTIVE AND INDUCTIVE § 6. The difficulties and limits of Definition must next be considered. The chief difficulty in the definition of scientific names consists in determining exactly the nature of the thmgs denoted by them, as in classifying plants and animals. If organic species are free growths, continually changing, however gradually, according as circumstances give some advantage to one form over others, we may expect to find such species branching mto varieties, which differ considerably from one another in some respects, though not enough to constitute distinct species. This is found to be the case ; and, consequently, there arises some uncertainty in collecting from all the varieties those attri- butes which are common to the species as a whole ; and, there- fore, of course, uncertainty in defining the species. The same difficulty may occur in defining a genus, on account of the extent to which some of its species differ from others, whilst having enough of the common character to deter the classifier from forming a distinct genus on their account. On the other hand, the occurrence of numerous intermediate varieties may make it difficult to distinguish genera or species at all. Even the Kingdoms of plants and animals cannot be precisely dis- criminated : sponges and other organisms seeming to belong to one as much as to the other. Now, where there is a difficulty of classification there must be a corresponding difficulty of definition. It has been proposed in such cases to substitute a Type for a Defini- tion • to select some variety of a species, or species of a genus, as exhibiting its character in an eminent degree, and to regard other groups as belonging to the same species or genus, according as they agree more with this Type than with other Types representing other species or genera. But the selection of one group as typical implies a recog- nition of its attributes as generally prevailing (though not universally) throughout the species or genus ; and to recognise these attributes and yet refuse to enumerate them in a Definition, seems to be no great gain. To enumerate the attributes of the Type as an Approximate Definition of the species or genus, true of most of the groups constituting the species or genus, answers the same purpose, is more explicit, and can mislead no one who really attends to the exposition. An Approximate Definition is, indeed, less misleading than the indication of a Type ; for the latter method seems to imply that the group which is now typical NOMENCLATURE 277 has a greater permanence or reality than its co-ordinate groups; whereas, for aught we know, one of the outside varieties or species may even now be superseding and extinguishing it. But the statement of a Definition as approximate, is an honest confession that both the definition and the classification are (like a provisional hypothesis) merely the best account we can give of the matter according to our present knowledge. § 7- The limits of Definition are twofold : (a) A name whose meaning cannot be analysed cannot be defined. This limita- tion meets us only in dealing with the names of the metaphy- sical parts or simple qualities of objects under the second requisite of a Terminology. Resistance and weight, colour and its modes, many names of sounds, tastes, smells, heat and cold— in fact, whatever stands for an unanalys- able perception, cannot be made intelligible to any one who has not had experience of the facts denoted ; they cannot be defined, but only exemplified. A sort of genetic definition may perhaps be attempted, as if we say that colour is the special sensation of the retina, or that blue is the sensation produced by a ray of light vibrating about 700.000,000,000,000 times a second ; but such expressions can give no notion of our meaning to a blind man, or to any one who has never seen a blue object. Nor can we explain what heat is like, or the smell of tobacco, to those who have never experienced them ; nor the sound of C 128 to one who knows nothing of the musical scale. If, however, we distinguish the property of an object from the sensation it excites in us, we may define any simple property as ' the power of producing the sensation ' ; the colour of a flower as the power of exciting the sensation of colour in us. Still, this gives no information to the blind nor to the colour-blind. (d) The second limit of Definition is the impossibility of exhausting infinity, which would be necessary in order to convey the meaning of the name of any individual thing or person. For, as we saw in ch. iv., if in attempting to define a proper name we stop short of infinity, our list of qualities or properties may possibly be found in two individuals, and then it becomes the definition of a class- name, or general name, however small the actual class. Hence we can only give a Description of that which a proper name denotes, enume- rating enough of its properties to distinguish it from everything else as far as our knowledge goes. Abstract names may be defined by defining the corresponding concrete: the definition of 'human nature' is the same as of 'man.' 278 LOGIC: DEDUCTIVE AND INDUCTIVE But if the corresponding concrete be a simple sensation (as blue), this being indefinable, the abstract (blueness) is also indefinable. § 8. The five Predicables (Species, Genus, Difference, Pro- prium. Accident) may best be discussed in connection with Classification and Definition; and in giving an account of Classification, most of what has to be said about them has been anticipated. Their name indeed connects them with the doctrine of Propositions ; for Predicables are terms that may be predicated, classified according to their connotative relation to the Subject of a proposition (that is, according to the relation in which their connotation stands to the connotation of the Subject) ; nevertheless, the significance of the relations of such predicates to a subject is derivative from the general doctrine of classification. For example, in the proposition 'X is Y,' Y must be one of the five sorts of Predicables in relation to X ; but of what sort, depends upon what X (the subject) is, or means. The subject of the proposition must be either a Definition, or a general Connotative Name, or a Singular Name. If X is a Definition, Y must be a Species ; for nothing but a general name can be predicated of a Definition : and, strictly speaking, it is only in relation to a Definition (as Subject) that Species can be a predicable ; when it is called Species predicabilis (i). If X is a Connotative Name, it is itself a Species {Species siihjicihilis) ; and the place of the Subject of a proposition is the usual one for Species. The Predicate, Y, may then be related to the Species in three different ways. First, it may be a Definition, exactly equivalent to the Species ; — in fact, nothing else than the Species in an explicit form, the analysis of its connotation. It seems most reasonable to regard this as a second form of the Species predicabilis. Secondly, the Predicate may be, or connote, some part only of the Definition or connotation of the Species ; and then it iseither Genus (2), or Difference (3). Thirdly, the Predicate may connote no part of the Definition, and then it is either derivable from it, being a Proprium (4), or not derivable from it, being an Accident (5). These points of doctrine will be expanded and illustrated in subsequent pages. If X is a Singular Name, deriving connotation from its constituent terms (chap, i v. § 2), as ' The present Emperor of China,' it may be treated as a Species suhjicibilis. Then that he is ' an absolute monarch,' predi- cates a Genus ; because that is a genus of ' Emperor of China,' a part of the Singular Name that gives it connotation. That he wecirs a yellow NOMENCLATURE 279 robe is a Proprium, derivable from the ceremonial of his court. That he is thirty years of age is an Accident. But if X is a Proper Name, having no connotation, Y must always be an Accident ; since there can then be no Definition of X, and therefore neither Species, Genus, Difference, nor Proprium. Hence, that ' Alphonso Schultze is a man ' is an Accidental Proposition : ' man ' is not here a Species predicabilis ; for the name might have been given to a dog or a mountain. That is what enables the proposition to convey information: it would be useless if the Proper Name implied ' humanity.' Species is most frequently used (as in Zoology) for the class denoted by a general name ; but in Logic it is often better to treat it as a general name used connotatively for the attributes possessed in common by the things denoted, and on account of which they are regarded as a class : it is sometimes called the Essence (§ 9). In this connotative sense, a Species is implicitly what the Definition is explicitly ; and therefore the two are always simply convertible. Thus, 'A plane triangle' (Species) is 'a figure enclosed by three straight lines' (Definition) : clearly we may equally say, ' A figure enclosed by three straight lines is a plane triangle.' A Genus is also commonly viewed denotatively, as a class containing smaller classes, its species; but in Logic it is, again, often better to treat it connotatively, as a name whose definition is part of the definition of a given species. A Difference is the remainder of the definition of any species after subtracting a given genus. Hence, the Genus and Difference together make up the Species; whence the method of definition per genus et differentiam (ante, § 5). It has already been mentioned, that whilst in the classificatory sciences (Botany and Zoology), the species is fixed at the lowest step of the classification (varieties not being reckoned as classes), and the genus is also fixed on the step next above it, in Logic these predicables are treated as moveable up and down the ladder : any lower class being species in relation to any higher; which higher class, wherever taken, thus becomes a genus. Lion may logically be regarded as a species of digitigrade, or mammal, or animal ; and then each of these is a genus as to lion: or, again, digitigrade may be regarded as a species of mammal, or mammal as a species of animal. The highest class, however, is never a species ; wherefore it is called a Summum Genus : and the lowest class is never a genus ; wherefore it is called an Injima Species. Between these two any step may be either species or genus, according to the relation to other classes in which it is viewed, and is then called Subaltern. The summum genus, again, may be viewed in relation to a given universe or suppositio (that is, any limited area of existence now the object of attention), or to the whole universe. If 28o LOGIC: DEDUCTIVE AND INDUCTIVE we take the animal kingdom as our suppositio, Animal is the summum genus; but if we take the whole universe, 'All things' is the summum genus. " Porphyry's tree " is used to illustrate this doctrine. It begins with a summum genus, ' Substance,' and descends by adding differences, step by step, to the infima species, 'Man.' It also illustrates Division by Dichotomy. CORPOREAL INCORPOREAt ANIMATE INANIMATE SENSIBLE INSENSIBLE RATIONAL IRRATIONAL Socrates Plato , Anslolle Beginning with 'Substance,' as summum genus, and adding the differ- ence ' Corporeal,' we frame the species ' Body.' Taking 'Body' as the genus and adding the difference ' Animate,' we frame the species ' Living Body ; ' and so on till ' Man ' is reached ; which being infima species, is only subdivisible into Individuals. But it should be noted that the division of Man into individuals involves a change of principle: it is a division of the denotation, not an increase of the connota- tion as in the earlier steps. Only one side of each dichotomy is followed out : if the other side had been taken Incorporeal Substance would be ' Spirit' ; which might be similarly subdivided. Genus and Species, then, have a double relation. In denotation the Genus includes the Species, in connotation the Species includes the NOMENCLATURE 281 Genus. Hence the doctrine that by increasing the connotation of a name you decrease its denotation : if, for example, to the definition of lion you add ' mhabiting Africa,' Asiatic lions are no longer denoted by It. On the other hand, if you use a name to denote objects that it did not formerly apply to, some of the connotation must be dropped • If, for example, the name • lion ' is used to include 'tigers.' the tufted tail, mane and colour can no longer be part of the meaning of the word ; smce tigers have not these properties. This doctrine is logically or formally true, but it may not always be true in tact. It is logically true ; because, wherever we add to the con- notation of a name, it is possible that some things to which it formerly applied are now excluded from its denotation, though we may not know of any such things. Still, as a matter of fact, an object may be discovered to have a property previously unknown, and this property may be fundamental and co-extensive with the denotation of its name or even more widely prevalent. The discovery that the whale is a mammal did not limit the class ' whale ' ; nor did the discovery that lions, dogs, wolves, etc., walk upon their toes, affect the application of any of these names. Similarly, the extension of a name to things not previously denoted by it. may not in fact alter its definition ; for the extension may be made on the very ground that the things now first denoted by it have been found to have the properties enumerated in its definition, as when the name 'mammal' was applied to whales, dolphins, etc. U, however. ' mammal ' had been formerly understood to apply only to land animals, so that its definition included (at least, popularly) the quality of 'living on the land,' this part of the connotation was of course lost when the denotation came to include certain aquatic animals. ^ A Proprium is an attribute derived from the definition : being either (a) implied in it. or deducible from it. as 'having its three angles equal to two right angles' may be proved from the definition of a triangle • or (b) causally dependent on it. as being ' dangerous to flocks ' results from the nature of a wolf, and as ' moving in an ellipse ' results from the nature of a planet in its relation to the sun. An Accident is a property accompanying the defining attributes without being deducible from them. The word suggests that such a property is merely ■ accidental,' or there ' by chance ' ; but, of course, it is not regarded in that way. Proprium and Accident bear the same relation to one another as Derivative and Empirical Laws : both Accidents and Empirical Laws present problems, the solution of which consists in reducing them respectively, to Propria and Derivative Laws. In fact, the predication of a Proprium is a Derivative Law, and the predication of an Accident IS an Empirical Law. Thus the colour of animals was once regarded as 282 LOGIC: DEDUCTIVE AND INDUCTIVE an Accident for which no reason could be given ; but now the colour of animals is regarded as an effect of their nature and habits, the chief cause of it being the advantage of concealment ; whilst in other cases, as among brightly coloured insects and snakes, the cause seems to be the advantage of advertising their own noxiousness. If such reasoning is sound, colour is a Proprium (and if so. it cannot logi- cally be included in a Definition, but it is better to be judicious than formal). . If the colour of animals is a Proprium. we must recognise a distmction between Inseparable and Separable Propria, according as they do, or do not, always accompany the essence: for mankind is regarded as one species ; but each colour, white, black or yellow, is separable from it under different climatic conditions: whilst tigers are everywhere coloured and striped in much the same way ; so that we may consider their colouring as inseparable, in spite of exceptional specimens black or white. . The same distinction may be drawn between Accidents. ' Inhabiting Asia ' is an Inseparable Accident of tiger, but a Separable Accident of lion. Even the occasional characteristics and occupations of individuals are sometimes called Separable Accidents of the species; as, of Man, being colour-blind, carpentering, or running. A Proprium in the original signification of the term {'iSiop) was peculiar to a Species, never found with any other, and was therefore convertible with the Subject; but this restriction is no longer insisted on. ■ -.r u i § 9. Any predication of a Genus, Difference or Definition, is a Verbal, Analytic, or Essential proposition: and any predication of a Proprium or Accident, is a Real, Synthetic, or Accidental proposition (chap. v. § 6). A Proposition is called Verbal or Analytic when the predicate is a part, or the whole, of the meaning of the subject; and of course, the subject being species, a genus or difference is part, and a definition is the whole, of its meaning or connotation. Hence such a proposition has also been called explicative. Again, a proposition is called Real or Synthetic when the predicate is no part of the meaning of the subject; and, the subject being species, a proprium or accident is no part of its meaning or connotation. Hence such a proposition has been called ampliative. As to Essential and Accidental, these terms are derived from the doctrine of Realism. Realists maintain that the Essence of a thing, or that which makes a thing to be what (or of what kind) it is, also makes everything else of the same kind to be what it is. The Essence, they say, is not proper to each thing or separately inherent in it, but is an •Universal' common to all things of that kind. Some hold that the universal nature of things of any kind is an Idea existing apart from them in the intelligible world, a rather shy corner, invisible to mortal NOMENCLATURE 283 eye and only accessible to thought ; whence they are called noumena : that only the Idea is truly real, and that the things (say, men, lions, bedsteads and cities) which appear to us in sense-perception, and which therefore are called phenomena, only exist by participating in. or imitating, the idea of each kind of them. The standard of this school bears the legend Ufiiversalia ante rem. But others think that the Universal does not exist apart from particular things, but is their present Essence; gives them actuality as individual substances; "informs" them, or is their formal cause, and makes them to be what they are of their kind according to the definition: the universal lion is in all lions, and is not merely similar, but identical in all; for thus the Universal Reason thinks and energises in Nature. This school inscribes upon its banners, Universalia in re. To define anything, then, is to discover its Essence, whether tran- scendent or immanent; and to predicate the definition, or any part of it (genus or difference), is to enounce an essential proposition. But a proprium, being no part of a definition, though it always goes along with it, does not show what a thing is ; nor of course does an accident ; so that to predicate either of these is to enounce an accidental proposition. Another school of Metaphysicians denies the existence of Universal Ideas or Forms ; the real things, according to them, are individuals ; which, so far as any of them resemble one another, are regarded as forming classes; and the only Universal is the class-name, which is applied universally in the same sense. Hence, they are called Nominalists. The sense in which the name is applied, is derived, they say, from a comparison of the individuals, and by abstraction of the properties they have in common ; and thus the definition is formed. Universalia post rem is their motto. Some Nominalists, however, hold that, though Universals do not exist in nature, they do in our minds, as Abstract Ideas or Concepts ; and that to define a term is to analyse the Concept it stands for; whence, these philosophers are called Conceptualists. Such questions belong to Metaphysics and Psychology rather than to Logic ; and I have only given a commonplace account of a subject upon every point of which there is much difference of opinion. § 10. The doctrine of the Predicaments, or Categories, is so inter- woven with the history of speculation and especially of Logic that, though its vitality is exhausted, it can hardly be passed over unmen- tioned. The Predicaments of Aristotle are the heads of a classification of terms as possible predicates of a particular thing or individual. Hamilton {Logic : Lect. xi.) has given a classification of them; which, if it cannot be found in Aristotle, is an aid to the memory, and may be thrown into a table thus {cf. Bain : Logic, App. C.) : 284 LOGIC: DEDUCTIVE AND INDUCTIVE Substance ovffla (I) -Quantity TTOffOU {2) [Attribute] -Quality TTOIOV (3) -Relation irpdff TL (4) rWhere -When irov (5) irdre (6) pAction TTOie^V (7) [Modes of Relation] _^ "^ LPassion irdax^iv (8) pPosture Keiadai (9) LHabit h,€iv (lO) Taking a particular thing or individual, as 'Socrates,' this is Substance in the proper sense of the word, and can never be a predicate, but is the subject of all predicates. We may assert of him (i) Substance in the secondary sense (species or genus) that he is a man or an animal ; (2) Quantity, of such a height or weight ; (3) Quality, fair or dark ; (4) Relation, shorter or taller than Xanthippe ; (5) Where, at Athens ; (6) When, two thousand and odd years ago; (7) Action, that he questions or exercises ; (8) Passion, that he is answered or condemned ; (9) Posture, that he sits or stands ; (10) Habit, that he is clothed or armed. Thus illustrated {Categoric: c. 4), the Predicaments seem to be a list of topics, generally useful for the analysis and description of an individual, but wanting in the scientific qualities of rational arrange- ment, derivation and limitation. Why are there just these heads, and just so many ? It has been suggested that they were determined by grammatical forms : for Substance is expressed by a substantive ; Quantity, Quality and Relation are adjectival; Where and When, adverbial ; and the remaining four are verbal. It is true that the parts of speech were not systematically discriminated until some years after Aristotle's time; but, as they existed, they may have unconsciously influenced his selection and arrangement of the Predicaments. Where a principle is so obscure one feels glad of any clue to it {cf. Grote's Aristotle, c. 3, and Zeller's .^Ws/o//^, c. 6). But whatever the origin and original meaning of the Predicaments, they were for a long time regarded as a classification of things ; and it is in this sense that Mill criticises them {Logic : Bk. I. c 3). If, however, the Predicaments are heads of a classification of terms predicable, we may expect to find some connection with the Pre- dicables ; and, in fact, secondary Substances are species and genus; whilst the remaining nine forms are generally accidents. But, again, we may expect some agreement between them and the fundamental forms of predication {ante, chap. i. § 5, and chap. ii. § 4) : Substance, whether as the foundation of attributes, or as genus and species, implies the predication of coinherence, which is one mode of Co-existence. Quantity is predicated as equality (or inequality) a mode of Likeness ; NOMENCLATURE 285 and the other mode of Likeness is involved in the predication of Quality. Relation, indeed, is the abstract of all predication, and ought not to appear in a list along with special forms of itself. ' Where ' is position, or Co-existence in space ; and ' When ' is position in time, or Succession. Action and Passion are the most interesting aspect of Causation. Posture and Habit are complex modes of Co-existence, but too specialised to have any philosophic value. Now, 1 do not pretend that this is what Aristotle meant and was trying to say : but if Like- ness, Co-existence, Succession and Causation are fundamental forms of predication, a good mind in analysing the fact of predication is likely to happen upon them in one set of words or another. By Kant the word Category has been appropriated to the highest forms of judgment, such as Unity, Reality, Substance and Cause, under which the Understanding reduces phenomena to order and thereby constitutes Nature. This change of meaning has not been made without a certain continuity of thought ; for forms of judgment are modes of predication. But, besides altering the list of Categories and greatly improving it, Kant has brought forward under an old title a doctrine so original and suggestive that it has extensively influenced the subsequent history of Philosophy. At the same time, and pro- bably as a result of the vogue of the Kantian philosophy, the word ' category' has been vulgarised as a synonym for ' class,' just as ' pre- dicament ' long ago passed from Scholastic Logic into common use as a synonym for 'plight.' A minister is said to be ' in a predicament,' or to fall under the ' category of impostors.' CHAPTER XXIII DEFINITION OF COMMON TERMS § I. Ordinary words may need definition, if in the course of exposition or argument their meaning is liable to be mistaken. Definition should not be regarded as giving the sense of the word for all occasions of its use. It is an operation of great delicacy. Fixity of meaning in the use of single words is contrary to the genius of the common vocabulary; since each word, whilst having a certain predominant character, must be used with many shades of significance, in order to express the different thoughts and feelings of multitudes of men in endlessly diversified situations ; and its force, when- ever it is used, is qualified by the other words with which it is connected in a sentence, by its place in the construction of the sentence, by the emphasis, or by the pitch of its pronunciation compared with the other words. Clearly, the requisite of a scientific language, *that every word shall have one meaning well defined,' is too exacting for popular language; because tlie other chief requisite of scientific language cannot be complied with, 'that there be no important meaning without a name.' 'Important mean- ings,' or what seem such, are too numerous to be thus provided for ; and new ones are constantly arising, as each of us pursues his business or his pleasure, his meditations or the excursions of his fancy. It is impossible to have a separate term for each meaning: and, therefore, the terms we have must admit of variable application. An attempt to introduce new words is generally disgusting. DEFINITION OF COMMON TERMS 287 Few men have mastered the uses of half the words already to be found in our classics. Much more would be lost than gained by doubling the dictionary. It is true that, at certain stages in the growth of a people, a need may be widely felt for the adoption of new words : such, in our own case, was the period of the Tudors and early Stuarts. Many fresh words, chiefly from the Latin, then appeared in books, were often received with reprobation and derision, sometimes disappeared again, sometimes established their footing in the language. See The Art of Eiiglish Poetry (ascribed to Puttenham), Book III. chap. 4, and Ben Jonson's Poetaster, Act v. sc. i. Good judges did not know whether a word was really called for : even Shakespeare thought ' remuneration ' and ' accommo- date ' ridiculous. But such national exigencies rarely arise • and in our own time great authors distinguish themselves by the plastic power with which they make common words convey uncommon meanings. Fluid, however, as the ordinary language is and ought to be, it may be necessary for the sake of clear exposition, or to steady the course of an argument, to avoid either sophistry or unintentional confusion, that words should be defined and discriminated ; and we must discuss the means of doing so. § 2. Scientific method is applicable, with some qualifications, to the definition of ordinary words. Classification is involved in any problem of definition : at least, if our object is to find a meaning that shall be generally acceptable and intelligible. No doubt two disputants may, for their own satisfaction, adopt any arbitrary definition of a word important in their contro- versy ; or any one may define a word as he pleases, at the risk of being misunderstood, provided he has no fraudulent in- tention. But in exposition or argument addressed to the public, where words are used in some of their ordinary senses, it should be recognised that the meaning of each one involves that of many others. For language has grown with the human mind, as representing its knowledge of the world : this know- ledge consists of the resemblances and differences of things 288 LOGIC: DEDUCTIVE AND INDUCTIVE and activities, that is, of classes and causes ; and as there is such order in the world, so there must be in language: language, therefore, embodies an irregular classification of things with their attributes and relations according to our knowledge and beliefs. The best attempt (known to me) to carry out this view is contained in Roget's Thesaurus^ which is a classification of English words according to their meaning : founded, as the author tells us, on the models of Zoology and Botany. Popular language, indeed, having grown up with a predominantly practical purpose, represents a very imperfect classification philoso- phically considered. Things, or aspects, or processes of things, that have excited little interest, have often gone unnamed ; so that scientific discoverers are obliged, for scientific purposes, to invent thousands of new names. Strong interests, on the other hand, give such a colour to words that, where they enter, it is difficult to find any indifferent expres- sions. Consistency being much prized, though often the part of a block- head, inconsistency implies not merely the absence of the supposed virtue, but a positive vice : Beauty being attractive and ngline'is the reverse, if we invent a word for that which is neither, ' plainness,' it at once becomes tinged with the ugly, In short, we love beauty and morality so much as to be almost incapable of signifying their absence without expressing aversion. Again, the erroneous theories of mankind have often found their way into popular speech, and their terms have remained there long after the rejection of the beliefs they embodied : as — lunatic, augury, divination, spell, exorcism : though, to be sure, such words may often be turned to good account, besides the interest of preserving their original sense. Language is a record as well as an index. Language, then, being essentially classificatory, any attempt to ascertain the meaning of a word, far from neglecting its relations to others, should be directed toward elucidating them. Every word belongs to a group, and this group to some other larger group. Groups are sometimes formed by derivation, at least so far as their differences are marked merely by inflections, as ihort, shorter, shorten, shortly : but, for the most part, are a conflux of words from many different sources. Repose, depose, suppose, impose, propose, are not nearly connected in meaning ; but are severally allied in sense much more closely with words philologically remote. Thus repose is allied with rest, sleep, tranquillity ; disturbance, unrest, tumult: whilst depose is, in DEFINITION OF COMMON TERMS 289 fcTTnd 'if '"',,:"* """"'"""■ '"""■«• *''"""«■• '■"'""■ confirm, cstab- hsh. and m another sense, with ««„,««„/. «,w, /.ot,, ct GrouDS denotd " '""^ resemblance in character of the things Words, accordingly, stand related to one another, for the most part, though very irregularly, as genus, species, and co-ordinate species. coIrfinftltvHh' ' ^'""'' r ''"^■' "^ ^P^^"^ °f "• "'°"«'' "°' --ctly (reposeofmind , r /'"?"''=■•• """^-^''-V with a mental differentia As this illustration suggests, synonyms are species or v;,riP(,P= ttmTeTu^tlttr/tr '^ '"^^'^^ - '''- -"o^discri" T.^Z T , "'^ ^"""'"^ '"<'^"'"S • f"' which there may or ^huL -*'■ "^ ^>"°"y"'s : but, if we attend to the ways ir^ wh.ch they are actually used, perhaps none of them can claim To i a Senus m relation to the rest. If not. we must resort to a'ompound term for the genus, such as • absence of some sort of difference Then « ts absence of difference in quantity ; sa.e.uss is of^n absence of difference m quality, though the usage is not strict: likeness siMv and nsemMance^n their actual use, perhaps, cannot be diSiminated unless kkeness be the more concrete, siJanty the more abs7rait bui ^ey may all be used compatibly with the recognition of morro; le absence of difference of ongin, a continuity of existence, with so much sameness from moment to moment as is compatible with changTsIn the course of nature; so that egg, caterpillar, chrysalis, butterfly may be Identical for the run of an individual life, in spite of differences inTdrat;' '"' ''"'"'"'^•^' ^^ '^"'>' ^^ ^ ^^"""S tha't all the dme ,ie: Co-ordinate Species, when positive, have the least contrariety but ont^ra^es Th°''" '"k"''"''^ "^^^''^"^' contradictories and'fuUe contraries. These may be regarded as either co-ordinate genera or the .LnfrTr T ''''''' ''"""' ^"'^ '^ ^ "^e^'i^-e ^"d contradictory hen aclnay implying an end in view), motion (limited to matter) Z'- turbance (implying changes from a state of calm), tunuM. ./f a i' co- ordinate species of «<,/-„/<,„, and are therefore co-ordinate opp;shes or contraries, of the species of repose. pposites, or As for correlative words, like Master and Slave. Husband and Wife, ele It may seem far-fetched to compare them with the sexes of the ^ame species of plants or animals ; but there is this resemblance between the 290 LOGIC: DEDUCTIVE AND INDUCTIVE two cases, that sexual names are correlative, as ' lioness.' and that one sex of a species, like a correlative name, cannot be defined without implying the other; for if a distinctive attribute of one sex be men- tioned. as the lion's mane, it is implied that the other wants it. and apart from this implication the species is not defined ; just as the definition of ' master ' implies a ' slave ' to obey. Common words, whilst less precise than the terms of a scientific nomenclature, differ from them also in this, that the same word may occur in different genera. Thus, sleep is a species of repose as above, but it is also a species of unconsciousness, with co-ordinate species swoon, hypnotic state, etc. In fact, every word stands under as many distinct genera, at least, as there are simple or indefinable qualities to be enumerated in its definition. § 3. But besides being partly similar to a scientific nomen- clature, ordinary language is, of course, partly a terminology for describing things according to their qualities and structure. Such are all the names of colours, sounds, tastes, contrasts of tem- perature, of hardness, of pleasantness ; in short, all descriptive adjectives, and al^. names for the parts and processes of things. Any word connoting a quality may be used to describe many very different things, as long as they agree in this quality. This is the generality of a word (sometimes said to make it, or its meaning, universal, chap. xxii. § 9), or its general applicability. But we must observe, that the quality connoted by a word, and treated as always the same quality, is often only analogically the same Take the word great : we speak of a great storm, a great man, a great book ; but great is in each case not only relative, implying small, and leaving open the possibility that what we call great is still smaller than something else of its kind, but it is also predicated with reference to some quality or qualities which may be very different in the several cases of its application. If the book is prized for wisdom, or for imagination, its greatness lies in that quality; if the man is dis- tinguished for influence, or for courage, his greatness is of that nature ; if the storm is remarkable for violence, or for duration, its greatness depends on that fact. The word great, therefore, is not used for these things in the same sense, but only analogically and elliptically. Similarly with good, pure, free, strong, rich, and so on. 'Rest' has not the same meaning in respect of a stone and of an animal, nor • strong ' in respect of thought and muscle, nor ' sweet ' in respect of sugar and music. But here we come to the border between literal and DEFINITION OF COMMON TERMS 29,- A Jin 1 y ''*^"''"™ "^e may become literal. 4r; r/esS T„7:oi;:fetb''r "' -'-''''■ -- ^-^^^ scape, or in defining^n/ spedrte" m t'^" "r^"' " ' '^"''■ doctrine, that anvconnrf.fP,h T' ^'"^ '^ '^^ «™se of the it maya lea t be co^s[dl^^t^™"''"'°'«™'^^^'"''^^°^"°i^'«^sals: to sa];, thaTln^bj^cf ; tl (who, to fully comprehend" mu'cas.ivTt"„r^''' '° ' 'f"""'"^ represents a cLsist^eteTheTrof t^:;- " ^^"" ^ °^-=' mlLs '™"" °' "''"« " <''^«""'- "'-y "« g-ded by the following (I) Find the usage of good modern authors • that is las ,h. define a word explicitly), consider what in ^■arous relations th'' """^^ words; and observe the quahtS in 1 h T 'f:"'^'"^"^ '""^ "PPo^ite in which they differ rom' htrLno ed bvth f '™°''' '^"''' '"^ If civilisation is to be defin.H i r ^ ^ contraries and opposites. civihsed, of barCus and : sa™a« • T f"'?' ^'''"''' °' ^"''- civiiised peoples and ^J^:'^:^:^^:::;^:^'^^"''' exercise worth attempting. If poetrv is fn h! i a , " ""' typical examples of wh'at g'ood crii:: 'rec gnL s poeTrv Z^'' "'"^ them with examples of literary prose oratarv l^ ^' ""P"^ determined the characteristics of elch t.nH i, '""":""• "^"°g them opposite one another in parable coumn vvf "'"" '° "'^"^^ by this method a few impor.Lt wo ds freanenti ''' '"'' '° '^^^"^ sation will find his head tL cleareTt ,''rd''rvircZTbv thr^'^^' much information which mpv Ko "" ^^i^' collect by the way itself, should he everfind one ' " ^"'""''^ '^^" "'^ '^^^-'i™ pr^l"ma; re":horl:d^li': "^ '''"''' '^ ^-'^^ ^--. 'he ;-« (that^, .appX^o S°;^t'e^;,r suir;^!^!:^^ :rm:r:;nrse^er r ditrrzr r'°^^ -- -^ '"" -- these en nrrlin.. '"^ . ^^^^^f "^la of poetry by a comparison of it with d^::ence uTon it?ir: ^ ^^l'^,-'-^ o^en e^^s genus and • cricket bat • h f T : , • '"'er-penetrate,' ■tuning-fork,' insS^or' frh::^^drriX"°TndXtvt rst rr' covered, it is well to state it/..^„«. ., „p,ZZ ''""'"°" ''' "''■ (4) In defining any term we should avoid encroaching upon the meaning of any of the co-ordinate terms; for else their usefuCsst 2^2 LOGIC: DEDUCTIVE AND INDUCTIVE lessened : as by making ' law ' include ' custom.' or ' wealth ' include 'labour' or * culture.' . (5) If two or more terms happen to be exactly synonymous, it may be possible (and, if so. it is a service to the language) to divert one of them to any neighbouring meaning that has no determinate expression^ Thus. Wordsworth and Coleridge, at the beginning of this century, took great pains to distinguish between Imagination and Fancy, which at that time had become in common usage practically equivalent ; and they sought to limit ' imagination ' to an order of poetic effect, which (they said) had prevailed during the Elizabethan age, but had been almost lost during the Gallo-classic, and which it was their mission to restore. Co-ordinate terms often tend to coalesce and become synonymous, or one almost supersedes the other, to the consequent impoverishment of our speech. At present proposition (that something is the fact) has almost driven out proposal (that it is desirable to co-operate in some course of action). Even good writers and speakers, by their own practice, encourage this confusion : they submit to Parlia- ment certain ' propositions ' (proposals for legislation), or even make ' a proposition of marriage.' Definition should counteract such a tendency. (6) We must avoid the temptation to extend the denotation of a word so far as to diminish or destroy its connotation ; or to increase its connotation so much as to render it no longer applicable to things which it formerly denoted : we should neither unduly generalise, nor unduly specialise, a term. Is it desirable to define education so as to include the ' lessons of experience'; or is it better to restrict it as implying a personal educator ? If any word implies blame or praise, we are apt to extend it to everything we hate or approve. But co^'ard cannot be so defined as to include all bullies, nor noble so as to include every honest man, without some loss in distinctness of thought. The same impulses make us specialise words; for, if two words express approval, we wish to apply both to whatever we admire and to refuse both to whatever displeases us. Thus, a man may resolve to call no one great who is not good : greatness, according to him, connotes goodness: whence it follows that (say) Napoleon I. was not great. Another man is disgusted with greatness : according to him, good and great are mutually exclusive classes, sheep and goats, as in Gray's wretched clench : " Beneath the good how far, yet far above the great." In fact, however, ' good ' and ' great ' are descriptive terms, sometimes applicable to the same object, sometimes to different: but 'great' is the wider term and applicable to goodness itself and also to badness ; whereas by making ' great ' connote goodness it becomes the narrower term. And, as we have seen (§ 3), such epithets may be applicable to objects on account of different qualities : good s not predicated on the same ground of a man and of a horse. (7) In defining any word, it is desirable to bear in mind its derivation, DEFINITION OF COMMON TERMS 293 and to preserve the connection of meaning with its origin • unless there are preponderant reasons for diverting it. grounded on our need of the other wordT; T''"' """' ^""^ '""^ '^'^'^^ ^^^^^^y ^f finig a'; 00 The vuta ^^"^%P"fPf ^- I^ i^ better to lean to the cla sical • ^he^otnal'r "^" ^' ' ^"^'^^^^^^•' 'i-P-tinent.' -aggravating,' qualities, and each ^^^1^:^^:!^^^:;'--^ '^^Z bTblrismTT'^^/t '^"^^ '-' '' ^^^^ -^'-' civili-fiorand some tS h on7 ^ " '"'^ '' '''^'^'^ ^^^^^^^^^ ^^ '^ P-try. must be stirH '' '"1 'T'^'' ^"^ ^''""'y "^^'^'^'^ ^hat the metre aTmLsteT O^^^^^^^^^ rhythm is as the essence of poe^r;:^^^^ re t^^^^^^^^^^^^^ intensity of this mood is requisite. We also hear that poetry hof such a nature that the enjoyment of it is an end in itself ;lut as it s not maintained that poetry must be wholly impersuasive or unL uctive there seems to be no means of deciding what amount or prom nence of per uasion or instruction would transfer the work to the re'fon o o atory or science. Such cases make the method of defining bv the aid of a type really useful: the difficulty can hardly be got over withom pointing to typical examples of each meaning, and admitting th" there may be many divergences and unclassifiable instances on the border between allied meanings. L.uiuer § 5- As science began from common knowledge, the terms of the common vocabulary have often been adopted into the s lences, and many are still found there : such as weight, mass work, attraction, repulsion, diffusion, reflection, absorption' base, salt, and so forth. ' In the more exact sciences, the vague popular associations with such words IS hardly any inconvenience; since those who are addicted to such studies do not expect to master them without undergoing special discipline ; and, having precisely defined the terms, they acquire the habit of thinking with them according to their assigned significance in those investigations to which they are appropriate. It is in the Social Sciences, especially Economics and Ethics, that the use of popular terminology is at once unavoidable and prejudicial. For the suWect- matters. industry and the conduct of life, are every man's business" and accordingly, have always been discussed with a consciousness of their 294 LOGIC: DEDUCTIVE AND INDUCTIVE direct practical bearing upon public and private interests, and therefore in the common language, in order that everybody may as far as possible benefit by whatever light can be thrown upon them. It is true that Astronomy, Mechanics and Chemistry are of incalculable importance to industry, and to public and private interests : still their application to practice is generally in the hands of specialists (navigators or dyers), who may undergo the requisite special training in proportion as their share in any process requires an appreciation of its scientific grounds. But the saying, that 'what is everybody's business is nobody's,' re- ceives melancholy illustration from the popular attitude toward the Science of Wealth and Industry. Is there not another saying that *a man knows his own business best ' ? He looks, perhaps, into a work on Economics and sees that it is all about Prices, Money, Rent, Wages, Profits. Now, he has received and paid Money all his life, and either received or paid Rent, Wages and Profits: how, then, can things so familiar need any explanation ? He may often say with much truth, that he has made more money than the author. It has been justly observed, however, that nearly all uninstructed and traditionary opinions upon these subjects are curiously wrong. They are not merely erroneous, but perverse and absurd. The obtaining of instruction, however, has been hindered by the very means adopted to facilitate it, the use of common language in a technical sense ; for without special discipline in the use of technicalities, the special meaning of the terms employed will often be confused with the vague meanings that they have in ordinary conversation ; and if their divergence from ordinary usage is observed, it is likely enough to give annoyance, or to raise a laugh at the apparent ignorance of the ' theorist ' who wrote the book. The almost uniform practice of Economists and Moralists, however, shows that, in their judgment, the good derived from writing in the common vocabulary outweighs the evil; though it is sometimes manifest that they themselves have been misled by extra-scientific meanings. To reduce the evil as much as possible, the following precautions seem reasonable: (i) To try to find and adopt the central meaning of the word (say Rent or Money) in its current or traditionary applications ; so as to lessen in the greater number of cases the jar of conflicting associations. But if the central popular meaning does not correspond with the scientific conception to be expressed, it may be better to invent a new term. (2) To define the term with sufficient accuracy to secure its clear and consistent use for scientific purposes. DEFINITION OF COMMON TERMS 295 (3) When a popular term has to be used in a sense that departs from the ordinary one in such a way as to incur the danger of misunderstanding, to qualify it by some adjunct or '' interpretation-clause." It must be confessed that the first of these rules is not always adhered to; and. m the progress of a science, as subtler and more abstract relations are discovered amongst the facts, the meaning of a term may have to be modified and shifted further and further from its popular use. The term -Rent,' for example, is used by economists in such a sense, that they have to begin the discussion of the facts it denotes bv explaining that it does not imply any actual payment by one man o another. Here, for most readers, the meaning they are accustomed to, seems already to have entirely disappeared ; but worse follows • and we ought, therefore, to pity the sorrows of a plain man of common sense who sits down to study Economics in a railway carriage. Difficulties may, however, be largely overcome by qualifying the term m Its various relations, as produce-rents, ground-rents, customary rents, and so forth. (C/. Dr. Keynes' Scope and Method of Political Economy, chap. 5.) ^ omicai § 6. Definitions affect the cogency of arguments in many ways, whether we use popular or scientific language. If the definitions of our terms are vague, or are badly abstracted from the facts denoted, of course, all arguments involving these terms are inconclusive. There can be no confidence in reasonmg with such terms ; since, if they are vague, there is nothmg to protect us from ambiguity ; or, if their meaning has been badly abstracted, we may be led into absurdity— as if ' impudence ' be defined in such a way as to confound it with honesty. Again, it is by Definitions that we can best distinguish between \^erbal and Real Propositions. AVhether a term predicated is implied in the definition of the subject, or adds something to its meaning, deserves our constant attention. We often persuade ourselves that statements are profound and important, when, in fact, they are mere verbal propositions. "It is just to give every man his due"; ''the greater good ought to be preferred to the less " ; such dicta sound well- indeed, too well ! lor 'a man's due ' means nothing else than 296 LOGIC: DEDUCTIVE AND INDUCTIVE what it is just to give him ; and ' the greater good ' means the one that ought to be preferred : these, therefore, are Truisms. The investigation of a definition may be a very valuable service to thought ; but, once found, there is no merit in repeating it. To put forward verbal or analytic propositions, or truisms, as information (except, of course, in actually explaining terms to pupils), shows that we are not thinking what we say ; for else we must become aware of our own emptiness. Every step forward in knowledge is expressed in a Real or Synthetic Pro- position ; and it is only by means of such propositions that information can be given (except as to the meaning of words) or that an argument or train of reasoning can make any progress. Opposed to a truism is a Contradiction in Terms ; that is, the denying of a subject something which it connotes (or which belongs to its definition), or the affirming of it something whose absence it connotes (or which is excluded by its definition). A Verbal Proposition is necessarily true, because it is tautologous ; a Contradiction in Terms is necessarily false, because it is inconsistent. Yet, as a rhetorical artifice, or figure, it may be effective : that * the slave is not bound to obey his master' may be a way of saying that there ought to be no slaves ; that * property is theft,' is an uncompromising assertion of the communistic ideal. Similarly a Truism may have rhetorical value : that * a Negro is a man ' has often been a timely reminder, or even that "a man's a man." It is only when we fall into such contradiction or tautology by lapse of thought, by not fully understanding our own words, that it becomes absurd. Real Propositions comprise the predication of Propria and Accidentia. Accidentia, implying (as we have seen) a sort of empirical law, can only be established by direct induction. But propria are deduced from (or rather by means of) the Definition with the help of real propositions, and this is what is called ' arguing from a Definition.' Thus, if increasing capacity for co-operation is a specific character of Civilisationj DEFINITION OF COMMON TERMS 297 great wealth may be considered as a proprium of civilised as compared with barbarous nations. For co-operation is made most effectual by the division of labour, and that this is the chief condition of producing wealth is a real proposition, established both inductively and deductively. Such arguments from Definitions concerning concrete facts and causation of course, require verification by comparing the conclusion with the facts. The verification of this example is easy, if we do not let ourselves be misled in estimating the wealth of barbarians by the ostentatious " pearl and gold " of kings and nobles where 99 per cent, of the people live in penury and servitude 1 he wealth of civilisation is not only great but diffused, and in Its diffusion its greatness must be estimated. To argue from a Definition may be a process of several degrees of complexity. The simplest case is the establishment of a proprium as the direct consequence of some connoted attribute, as in the above example. If the definition has been correctly abstracted from the particulars, the particulars have the attributes summarised in the definition ; and, therefore they have whatever can be shown to follow from those attributes But It frequently happens that the argument rests partly on the qualities connoted by the class name and partly on many other tacts. In Geometry, the proof of a theorem depends not only upon the definnton of the figure or figures directly concerned, but also uLn one or more axioms and upon propria or constructions already established Thus^ m Euclid's Fifth Proposition, the proof that L angles a. he base of an isosceles triangle are equal, depends not on] on the equality of the opposite sides, but upon this together with the con strucuon that shows how from .he greater of two lines a part may be cut off equal to the less, the proof (or assumption) that triangles that can bl concen-ed to coincide are equal, and the a..iom that if equals be Taken from equals the remainders are equal. Similarly, in Biology Tf colourmg favourable to concealment is a proprium of carnivorous animals, .t .s not deducible merely from their predatory characte or any other attribute entering into the definition of any spedes I them, but from their predatory character together with the cause summarised ,n the phrase ■ Natural Selection'; that is. competition fo a livelihood, and the destruction of those that labour under anv d s 298 LOGIC: DEDUCTIVE AND INDUCTIVE advantages, of which conspicuous colouring would be one. The par- ticular colouration of any given species, again, can only be deduced by further considering its habitat (desert, jungle or snow-field) : a circum- stance lying wholly outside the definition of the species. The validity of an argument based partly or wholly on a Definition depends, in the first place, on the existence of things corresponding with the Definition — that is, having the properties connoted by the name defined. If there are no such things as isosceles triangles, Euclid's Fifth Proposition is only formally true, like a theorem concerning the fourth dimension of space : merely consistent with his other assump- tions. But if there are any triangles only approximately isosceles, the proof applies to them, making allowance for their concrete imperfection : the nearer their sides approach straight- ness and equality the more nearly equal will the opposite angles be. Again, as to the existence of things corresponding with terms defined. Dr. Venn has pointed out that ' existence ' may be understood in several senses : (i) merely for the Reason, like the pure genera and species of Porphyry's tree ; the sole condition of whose being is logical consis- tency: or (2) for the Imagination, like the giants and magicians of romance, the heroes of tragedy and the fairies of popular superstition, whose properties may be discussed and verified by appeal to the right documents and authorities (poems and ballads) : or (3) for Perception, like plants, animals, stones and stars. We may argue, therefore, from the definition of a fairy, or a demigod, or a dragon, and deduce various consequences without absurdity, if we are content with poetic consis- tency and the authority of myths and romances as the test of truth. When, however, we pass into the region of concrete objects, whose properties are causes, and not merely determinations of space (as in Geometry), we meet with another condition of the validity of any argument depending on a Definition : there must not only be objects corresponding to the definition ; but there must be no other causes counteracting those qualities on whose agency our argument relies. Thus, though we may infer from the quality of co-operation connoted by civilisation, that a civilised country will be a wealthy one, this may not be found true of such a country recently devastated by war or DEFINITION OF COMMON TERMS 299 other calamity. Nor can co-operation always triumph over d sadvantageous circumstances. Scandinavia is so poor in the g.fe of nature that are favourable to industry, that it is not wealthy ,„ spUe of civilisation : still, it is far wealthier than i would be m the hands of a barbarous people. In short, while argumg from a Definition, we can only infer the teJe.cy of ZCr '^'T'''"''"' '""'"'^^^ '■" " ■' *e unqualified reahsafon of such a tendency must depend upon the Absence of counteracting causes. As soon as we leave the region of pure conceptions and make any attempt to bring our specula- tions hometo the actual phenomena of nature or of human ibligltLn "'°" "'"■"^' "'"""^ '^'^•=°"*^^^" ""--«-g CHAPTER XXIV FALLACIES § I. A Fallacy is any failure to fulfil the conditions of Proof. If we neglect or mistake the conditions of proof unintentionally, whether in our private meditations or in addressing others, it is a Paralogism : but if we endeavour to pass off upon others evidence or argument which we know or suspect to be unsound, it is a Sophism. Fallacies, whether paralogisms or sophisms, may be divided into two classes : (a) the Formal, or those that can be shown to conflict with one or more of the truths of Logic, whether Deductive or Inductive ; as if we attempt to prove an universal affirmative in the Third Figure ; or to argue that, as the average expectation of life for males at the age of 20 is 39J years, therefore Alcibiades, being 20 years of age, will die when he is 39i; (^0 the Material, or those that cannot be clearly exhibked as transgressions of any logical principle, but are due to hasty or superficial inquiry or confused reasonmg ; as in adopting premises on insufficient authority, or without examining the facts ; or in mistaking the point to be proved. § 2. Formal Fallacies of Deduction and Induction are, a\\ of them, breaches of the rule ' not to go beyond the evidence.' As a detailed account of them would be little else than a repetition of most of the foregoing chapters, it may suffice to recall some of the places at which it is easiest to go astray. (I) It is not uncommon to mistake the Contrary for the Contradictory, ^s— A is not taller than B, .'. he is shorter. FALLACIES 301 (2) To convert ^. or O. simply, as- All Money is Wealth .-. All Wealth is Money, or-Some Wealth is not Money .-. Some Money is not Wealth. In both these cases. Wealth, though undistributed in the convertend. IS distributed in the converse. (3) To attempt to syllogise with two premises containing four terms, as The Papuans are savages ; The Javanese are neighbours of the Papuans : .-. The Javanese are savages. Such an argument is excluded by the definition of a Syllogism, and presents no formal evidence whatever. We should naturally assume that any man who advanced it merely meant to raise some probability that ' neighbourhood is a sign of community of ideas and customs ' But. if so, he should have been more explicit. There would, of course, be the same failure of connection, if a fourth term were introduced in the conclusion, instead of in the premises. (4) To distribute in the conclusion a term that was undistributed in the premises (an error essentially the same as (2) above), i.e.. Illicit process of the major or minor term, as— Every rational agent is accountable ; Brutes are not rational agents : .-. Brutes are not accountable. In this example (from Whately), an illegitimate mood of Fig. I the major term, ' accountable/ has suffered the illicit process ; since, in the premise, it is predicate of an affirmative proposition and, therefore undistributed; but, in the conclusion, of a negative proposition and' therefore, distributed. The fact that nearly everybody would accept the conclusion as true, of course, might lead them to overlook the inconclusiveness of the formal proof. Again, All men are two-handed ; All two-handed animals are cooking animals : .-. All cooking animals are men. Here we have Bramantip concluding in A. ; and there is, formally an illicit process of the minor ; though the conclusion is true ; and the evidence, such as it is, is materially adequate. (Of course, ' two-handed.' being a peculiar Differentia, is nugatory as a middle term, and may be cut out of both premises ; but ' cooking ' is a Proprium peculiar to^he species Man; so that these terms might be related in U.,All men aye all cookers; whence, by conversion, All cookers are men.) (5) To omit to distribute the middle term in one or the other premise as — All verbal propositions are self-evident ; All axioms are self-evident : .'. All axioms are verbal propositions. This is an illegitimate mood in Fig. II. ; in which, to give any con- 3o: LOGIC: DEDUCTIVE AND INDUCTIVE elusion, one premise must be negative. It may serve as a formal illustration of Undistributed Middle; though, as both premises are verbal propositions, it is materially not syllogistic at all, but an error of classification ; a confounding of co-ordinate species by assuming their identity because they have the generic attribute in common. (6) To simply convert a hypothetical proposition, as — If trade is free, it prospers ; .-. If trade prospers, it is free. Clearly, this is similar to the simple conversion of the categorical A. ; since it takes for granted that the antecedent is co-extensive with the consequent, or (in other words) that the freedom of trade is the sole condition of, or (at least) inseparable from, its prosperity. The same assumption is made if, in a hypothetical syllogism, we try to ground an inference on the affirmation of the consequent or denial of the antecedent, as — If trade is free, it prospers: It does prosper ; .'. It is free. It is not free ; .-. It does not prosper. Neither of these arguments is formally good : nor, of course, is either of them materially valid, if it be possible for trade to prosper in spite of protective tariffs. An important example of this fallacy is the prevalent notion, that if the conclusion of an argument is true the premises must be all right ; or, that if the premises are false the conclusion must be erroneous. For, plainly, that — If the premises are true, the conclusion is true, is a hypothetical proposition ; and we argue justly— The premises are true ; .'. The conclusion is true ; or. The conclusion is false ; .-. The premises are false. This is valid for every argument that is formally correct ; but that we cannot trust the premises on the strength of the conclusion, nor reject the conclusion because the premises are absurd, the following example will show : All who square the circle are great mathematicians ; Newton squared the circle: .-. Newton was a great mathematician. Here our conclusion is, no doubt, true ; but the premises are intoler- able. If. then, to-day the inferences of our favourite orator are very much to' our taste, we had better not for that reason embrace his premises without examining them. Another day, in circumstances slightly different, they may have other, less innocent results. FALLACIES 3^3 How the taking of Contraries for Contradictories may vitiate Dis- ih:ri^'Srer"' "^^^-^-^^^ '- '- -^^^-^^y^^^^n^^^ § 3. Formal Fallacies of Induction consist in supposing or inferring Causation without attempting to prove it or in pretending to prove it without satisfying the Canons of observation and experiment : as— as^'.l^whvT ^^^f""^^^^ ->'^hing that is not a concrete event: Z reZJ' 7 T '^" '^"'^ °"^y ^" °"^ P^^^^- ^"^^ should give he reason . for this expression includes, besides evidence of causation the principles of formal deduction, logical and mathematical (2) To argue, as if on Inductive grounds, concerning the cause of the Universe as a whole. This may be called the fallacy of transcenden inference . since the Canons are only applicable to instances of evem uniiuT ""''"' ' '"'' ''""^^ ^'^' '''''' ^^^^ ^^h-h ^^ - it^ n~ (3) To mistake co-existent phenomena for cause and effect • as when a man. wearing an amulet and escaping shipwreck, regards the amulefas the cause of his escape. To prove his point, he must either get aga" into exactly the same circumstances without his amulet, and then be drovvned -according to the method of Difference ; or, shi king the onl TITJ T '"'.'"""^^ "P "^^' "^^^^ ^^^^~^- h^ n-^t show (a) that all who are shipwrecked and escape wear amulets, and (b) thai their cases agree in nothing else; and (.). by the Joint Method ha al who are shipwrecked without amulets are drowned. And ev;n if ht evidence, according to Agreement, seemed satisfactory in a,I these points. It would still be fallacious to trust to it as proof of direc causa Tthir •: Ts^'r V"" ^'" "^^^.^^^ ^^^^--^^ ^^ never Tuf^:-::; tor this ^ It IS only by experiment in prepared circumstances that we can confidently trace sequence and the transfer of energy dpLnT ;' '^^ '^'^^""^ ^''°' °^ "^i^'^king causal connection for in- dependent co-existence : as if anyone regards it as merely a curious coincidence that great rivers generally flow past great towns In thi case, however, the evidence of connection does not depend me eW upon direct Induction. ^ merely (4) Post hoc ergo propter hoc: to accept the mere sequence of pheno- caTse :r T?"" °'^^^ "P^^^^'- ^^ P^^^'^"^ ^^^^ ^h' phenomena Le cause and effect, or connected by causation. This is a very natural error: for although, the antecedents of a phenomenon being nume ous mos of them cannot be the cause, yet it is among them that the cause must be sought. Indeed, if there is neither time nor opportunity for analysis, it may seem better to accept any antecedent as a cause (or at ■least, as a sign) of an important event than to go without any guide / .^^ 304 LOGIC: DEDUCTIVE AND INDUCTIVE And. accordingly, the vast and complicated learning of omens, augury, horoscopy and prophetic dreams, relies upon this maxim ; for whatever the origin of such superstitions, a single coincidence in their favour trium- phantlv confirms them. It is the besetting delusion of everybody who has wishes or prejudices, that is. of all of us at some time or other; for then we are ready to believe without evidence. And. plainly, the fallacy consists in judging off-hand, without any attempt, either by deductive or inductive methods, to eliminate the irrelevant ante- cedents; which, however, may include all the most striking and specious. . V (5) To regard the Joint-Effects (whether simultaneous or successive) of a common cause as standing in the direct relation of cause and effect Probablv no one supposes that the falling of the mercury in his thermometer is the cause of the neighbouring lakes freezing. True, it is the antecedent, and (within a narrow range of experience) may be the invariable antecedent of the frost; but. besides that the two events are so unequal, everv one is aware that there is another antecedent, the fall of temperature, which causes both. Yet in many cases, the same kind of mistake is made from not remembering that, to justify indue- tively our belief in a cause, the instances compared must agree, or differ, in one circumstance only (besides the effect). The flowmg tide is an antecedent of the ebbing tide ; it is invariably so. and is equal to it • but it is not the cause of it : other circumstances are present ; and the moon, chieflv, is the cause of both flow and ebb. In several in- stances, States that have grown outrageously luxurious have declined in power that luxury caused the downfall may seem obvious, and capable of furnishing a moral lesson to the young. Hence other important circumstances are overlooked, such as the institution of slavery, the corruption and rapacity of officials and tax-gatherers, an army too power- ful for discipline ; any or all of which may be present, and sufficient to explain both the luxury and the ruin. (6) To mistake one condition of a phenomenon for the whole cause. To speak of an indispensable condition of any phenomenon as the cause of it may be a mere conventional abbreviation ; and in this way such a mode of expression is common not only in popular but also in scientific discussion. Thus we say that a temperature of 33° F ^^ ^ cause ot the melting of ice; although that ice melts at 33 F. ^^^\ ^^''^^' depend upon something in the nature of water ; for every solid has its ow^ melting-point. As long. then, as we remember that; cause, used in this sense, is only a convenient abbreviation, no harm is done ; but. if we forget it. fallacy may result ; as when a man says that the cause of a financial crisis was the raising of the rate of discount, neglecting the other conditions of the market ; whereas, in some circumstances a rise of the Bank-rate may increase public confidence and prevent a crisis. FALLACIES 305 cause or an indispensabL condition of ?J u ^ '"■*"'" ^"'e-«!ent is a tion. If, ..erefoL, it is^ rpr:„rl'aT— : '"'^-'"-''«- either experiment directly uoon th^ r.th "'^.'*°'^ '^ause, we must Method of Residues and 'd d^ctit reto^ni^r'"""^' " ^^'°^' '° *^ without showing, where such Zt.? ^' """^ """«•« be content cause and the gi:;„phen^rn'n~u"a;^ •"^^""^' ''" "^« ^"^»-'' eff2t,TratX:ntit%Trrrnno°' ' ''^ -"- ^^ ">« -"o'e mistakes of private conduct and of leZZTrT ""''''' =^" ""^ temporary lassitude by a stimuIan^a„Tst^an::.h:^•'^ '' ^ ^° ^"" lish a new industry by protective dnl IT ''™'' ■ '° ^^'^b- rest of the country'; to gag the press and" '''^■•^''>'J-P°-rish the into conspiracy ; to build ^nalm^ house and" th""^ "' ^i^-'-'ed into the parish, raise the rates ar^H H^ '^"'^''^ *'^='<^' P^^Pe" /»i x„ J J ' ^"" discourage industrv (8) To demand greater exactness in the estimate n> than a given subject admits of In ,h ^"™^'« °f causes or effects Sociology, PsycLlogy,Tis°tften ^ZZlZt^ ^T ' '''°'°^^' the conditions of a given phenomenon^a fbeln ^1 ""f '"' *"' "" Its consequences have been traced. The causes of th"' "' *"' "" Revolution have been carefully investigated and still' ^""^^ ^I'"* whether they have all been discovered or whether h -"^ ™^^ '^""'^ importance has been rightly determTneH K ! ^"' =°'"Pa'-ative reasonable to treat that even, °^'^™'"^'^ ' t""' " would be very un- totle observes n h s s'lv hL a oT'T"','"' ""-'^"'gible. 'Aris- degree of precision is o be exoec ed ' T^''^ """'^ '"'°-^ ""at trovertists, being sufficient duca fd TndTat "TT ■ "^"^^' ~"- do not comment superciliously upo' the IT ' 'r""^ ^"^ P'^^' demonstration where it is of course roUaL^r^ °' mathematical Jse rrt^rrenr^fTm'iter"" '" "-^ ^^ ^" --""'«-" tions of forces and, tre efo'rfor m H^fi"''^"'''""''^ ^°^ "^" <^°'"''i"^- although we often sayThrNaLr'f p ""^ °' "'^ ^^f-'' Thus, cause of his downfall ve the effe. u-'"^" expedition was the conditions. Had ^^'Il^sVoT^lZru^^:: TadT ^""^ '"*- exceptionally mild, had the Prussians InH a .: *^ """'^'' ^^^ him, the eve'nt might have bfen y"; d^fferett uTs "V^ ^^^'"^' liberties of modern Europe to the Iv.„r f ./ J^* '° *''^<=« '^e powers of perception are so uneq al .o thtsutl^tro^", '"'r^' °" m experimental science there is time iT > T "^""■^' "'*' ^^n between what we treat as a cause and tLe el r"'" "'''"''' '° °'=^" such cases the -ictly unconai.i:n:"lt S^brrctli^^ '" (10) To neglect the negative conditions to which a cau^.r t When we say that water boils at .xa» F., we meaf.. prrd^'thrpC u > 3o6 LOGIC : DEDUCTIVE AND INDUCTIVE s„.e be not greater that, that of the ^--^X^:XX:;^^^e for under a greater P^««="^f J'^'^^ ™'" "° temperature. Irt the usual whilst under less pressure .tbo.ls ^' ^ 1°-^^^;'^P^3 ,,„ed • disturbing,' statement of a la« of causation, what are somet.m ^^^ frustrating.' ■counteracting' --—■=;'■ .f.f; ;.ement of such — ^^a^m^t^^ro^^ ;^^^^^^^^ favourable, or in the absence of contrary forces. ^^.^ ^^ ^^^^^ ,„) It is needless to repeat "^'-^'^^^^f^^^'^^eglect of a possible fallacies that beset -ducfve proof , su h as^;;^^, »,^ ^„„,,i,,d ; the plurality of causes where the ^""^^ the chief errors to extension of empirical laws beyond adjacent cases ^ application of .hich the estimate of analogies -"^ P "^^'^The r liance'^upon direct the principles of classification are hab e^ and th ^^^^^^^ ^^ ^^^^ Induction where the aid of deduction may ^^^^^^.^^ observation «>^ere experiment m^^^^^ .T^ls on°«>-' -"'°^' '*^'= that may be avoided b> aanerin^ "1 'f There remain many ways in which arguments fall 9 4- inere icn. j thouah they cannot short of a tolerable standard of proof, thougn y i„ 'h.™.n,isJ! o, i. .h. conclu.i.n, o, ,„ .b. a„empt .0 connea a conclu.ion .i* -h. P«- ^|,,^, rT^ Now the premises of a souna argumc J lid deductions, or valid inductions, or J^"-^-;^;- ^ ^r nxioms In an unsound argument, then, wtiose uons or ^''•o'" ;^ /" ^^^^^ deduction or induction, re:^L::Vayr uce'd to logical rules; and its fa.lure f the eore a ogical fallacy' such as we have already dis- cussed U follow: that an extra-logical fallacy of the prem.se must lie in what cannot be reduced to rules of evidence, that is, bad observations or f2rZ"c.n only be fallacious if (2) As to the conclusion, this can umy / FALLACIES 3^^ !r! T'" /=°"''"^'°" has been substituted for that which was to have been proved. (3) Fallacies in the connection between premises and conchision, if all the propositions are distinctly and explicitly stated, become manifest upon applying the rules of Logic. Fallacies, therefore, which are not thus manifest, and so are extra-logical, must depend upon some sort of slurring confusion, or ambiguity of thought or speech /A .l ^"'Tff ^''"''''' °^ Observation, Mill distinguishes (r) those of Non-observation, where either instances of the presence or absence of the phenomenon under investigation or else some of the circumstances constituting it or attending upon >t, though important to the induction, are overlooked These errors are implied in the Formal Fallacies of Induction already treated of in § 3 (paragraphs (3) to (7)). Mill's class (2) comprises fallacies of Malobservation Mal- observation may be due to obtuseness or slowness of percep- tion ; and It IS one advantage of the physical sciences as means of education, that the training involved in studying them tends to cure these defects. But the occasion of error upon which Mill most insists .s our proneness to substitute a hasty inference for a iust representation of the fact before us; as when a yachtsman, all agog for marvels, sees a line of porpoises and takes them for the sea-serpent. Every one knovvs what it is to mistake a stranger for a friend, a leaf for a sparrow, one word for another (X persisted in reading Unsertesen as untersetzen). The wonder is that we are not oftener wrong • considering how small a part present sensation has in percen' tion, and how much of every object observed is supplied by a sort of automatic judgment. You see something brown, which your perceptive mechanism classes with the appearance of a cow at such a distance; and instantly all the other properties of a cow are supplied from the resources of former experience • but on getting nearer, it turns out to be a log of wood It is some protection against such errors to know that we are laiMMBliaiaMMIifliHIil 3o8 LOGIC: DEDUCTIVE AND INDUCTIVE subject to them ; and the Logician fulfils his duty in warning us accordingly. But the matter belongs essentially to Psy- chology ; and whoever wishes to pursue it will find a thorough explanation in Prof. Sully's volume on Illusions. Another error is the accumulation of useless, irrelevant observations, from which no proof of the point at issue can be derived. It has been said that an important part of an induc- tive inquirer's equipment consists in knowing what to observe. The study of any science doubtless educates this power by showing us what observations have been effective in smiilar cases : but something depends upon genius. Observation is generally guided by hypotheses : he makes the right observa- tions who can frame the right hypotheses ; whilst another over- looks things, or sees them all awry, because he is confused and perverted by wishes, prejudices or other false preconceptions ; and still another gropes about blindly, noting this and docket- ing that to no purpose, because he has no hypothesis, or one so vague and ill conceived that it sheds no light upon his path. § 6. The second kind of extra-logical Fallacy lying in the premises, consists in offering as evidence some verbal jingle or assertion which is entirely baseless : it is generally known as petitio prhicipii, or begging the question. The question may be begged in three ways:— (i) there are what Mill calls Fallacies a priori, mere assertions, pretending to be self- evident, and often sincerely accepted as such by the author and some infatuated disciples, but in which the cold-blooded spectator sees either no sense at all, or palpable falsity. These sham axioms are (grievous to confess) not uncommon in the writings of the greatest philosophers. There are thousands of them ; and probably every one is familiar with the following examples : That circular motion is the most perfect; That every body strives toward its natural place ; That like cures like ; That every bane has its antidote; That the soul is especially active and intelligent in dreams; That pleasure is nothing but relief from pain ; That the good, the beautiful and the true are inseparable; That, in trade, whatever is somewhere gained is somewhere lost; That only in agriculture does nature assist man ; That a man may do what he will with his own ; That some FALLACIES 309 men are naturally born to rule and others to obey. Now some of these doctrines are specious enough ; whilst as to others, how they could ever nave been entertained arouses a wonder that can only be allayed by a lengthy historical and psychological disquisition. (2) Verbal propositions offered as proof of some matter of fact. These have, indeed, one attribute of Axioms: they are self-evident to any one who knows the language ; but as they only dissect the meaning of words, nothing but the meaning of words can be inferred from them If anything further is arrived at, it must be by the help of real propositions. How common is such an argument as this: 'Lying IS wrong, because it is vicious '-the implied major premise being that • what IS vicious is wrong.' Now if anybody hesitates whether to be a liar or not. good reasons can be given him for abstaining ; but the above argument only shows that lying is called wrong ; and this the impending liar already knew. The argument, therefore, must be supplemented by a further premise, that 'what is called wrong in English is most probably something that ought to be avoided ' : but this is a real proposition, which to a foreigner might seem to need a vast amount of evidence. So let us hope there is some shorter and more cosmopolitan way of restraining the moral plunger. Still, such arguments, though bad Logic, often have a rhetorical force : to call lying not only wrong but vicious, may be dissuasive by accumulating associations of shame and Ignominy. Definitions, being the most important of verbal propositions (since they imply the possibility of as many other verbal propositions as there are defining attributes and combinations of them), need to be watched with especial care. If two disputants define the same word in different ways, with each of the different attributes included in their several definitions they may bring in a fresh set of real propositions as to the agency or normal connection of that attribute. Hence their conclusions about the things denoted by the word defined, diverge in all directions and to any extent. And it is generally felt that a man who is allowed o define his terms as he pleases, may prove anything to those who through ignorance or inadvertence, grant that the things that those terms stand for have the attributes that figure in his definitions. (3) Circulus in demonstrando, the pretence of giving a reason for an assertion, whilst in fact only repeating the assertion itself— generally in other words. In such cases the original proposition is, perhaps, really regarded as self-evident, but by force of habit a man says ' because ' ; and then after vainly fumbling in his empty pocket for the coin of reason, the same 3,0 LOGIC: DEDUCTIVE AND INDUCTIVE ■ Hve., event ^-^TZ:s^^:^^^^ P^e-e.stL; nomena. and this implies a u^"^ , • operation which can only have ^enpo.:b...the^-^^^^^^^^^^^ ^^ ^^P^_^^_ capable of transforming .t O^' ^g^m . ^j^^^^id not imply because it is urong to shed blood. But, plainly ^^^^ bloodshed, the unlawfulness of this could be notfung ^^amst more serious any matter is, *« --^'XiteKe s^h wholesome to reason thoroughly about it, or to content ""^sehes assertions. How many • arguments ' are superfluou! §, The Fallacy of surreptitious conclusion (/.§-«<^r g ?w he was a good judge of paintings and indulgent to his wife. ' To h^. 4s^ Falfacies'belongs the arg.nnen,.,,. a.i '-""«""■ J*;-^^^ insists In showing not that a certain proposition is true, but that cX ought to accept it in consistency with his Cher opinions^ Thu . l"""ry parish the cost of education ought to be paid out °"^eja^^- ImLsI have said that there can be no sound economy, unless local you, atleast, navesaici iiiau I R„t whether this is a fallacy expenses are defrayed from local funds. But whe her tni y fnconsistency^ In the latter case, the argument is quite fair, whatever -S^mi,-':::=^^^^^^^^^^^ :-me.u.is favourable same ma> ^^^^^^^ ^ ^^ honour among thieves, there is no ffc ^ t^e^ -ral Lul is franUly repudiated. The argument from MLLACIES 311 authority is often brought under this head: 'such is the opinion of Aristotle.' Ahhough this does not establish the truth of any proposition, it may be fairly urged as a reason for not hastily adopting a contrary conclusion : that is, of course, if the subject under discussion be one as to which Aristotle (or whoever the authority may be) had materials for forming a judgment. A negative use of this fallacy is very common. Some general doctrine, such as Positivism, Transcendentalism, Utilitarianism, or Darwinism, is held in common by a group of men ; who, however, all judge inde- pendently, and therefore are likely to differ in details. An opponent exhibits their differences of opinion, and thereupon pretends to have refuted the theory they agree in supporting. This is an argumentum ad scholam, and pushes too far the demand for consistency. But in fact it recoils upon the Sophist ; for there is no sense in quoting men against one another, unless both (or all) are acknowledged to speak with the authority of learning and judgment, and therefore the general doctrine which they hold in common is the more confirmed. This, in fact, is an example of the paralogism of ' proving too much ' ; when a disputant is so eager to refute an opponent as to lay down, or imply, principles from which an easy inference destroys his own position. To appeal to a principle of greater sweep than the occasion requires may easily open the way to this pitfall : as if a man should urge that ' all men are liars,' as the premise of an argument designed to show that another's assertion is less credible than his own. A common form of ignoratio elenchi is that which Whately called the ' fallacy of objections ' : it consists in insisting upon all the considerations against any doctrine or proposal, without any attempt to weigh them against the considerations in its favour ; amongst which should be reckoned all the considerations that tell against the alternative doctrines or proposals. Incontestable demonstration can rarely be expected even in science, outside of the Mathematics ; and in practical affairs, as Butler says, ' probability is the very guide of life ' ; so that any conclusion depends upon the balance of evidence, and to allow weight to only a part of it is an evasion of the right issue. § 8. Fallacies in the connection of premises and con- clusion that cannot be detected by reducing the arguments to syllogistic form, must depend upon some juggling with language to disguise their incoherence. They may be gener- ally described as Fallacies of Ambiguity, whether they turn upon the use of the same word in different senses, or upon eUipsis. Thus it may be argued that all works written in a classical language are classical, and that, therefore, the History of Philosophy by ^i^sm mmmamitUB^MKtaM 312 LOGIC: DEDUCTIVE AND INDUCTIVE Diogenes Laertius. being written in Greek, is a classic. Such ambi- guities aie sometimes serious enough; sometimes are httle better than jokes. For jokes, as Whately observes, are often fallacies ; and con- sidered as a propoedeutic to the art of sophistry, punning deserves the ignominy that has overtaken it. / \ > ^- / Fallacies of ellipsis usually go by learned names, as ; (i) a auto secundum quid ad dictum simpliciter. It has been argued that smce. according to Ricardo. the value of goods depends solely upon the quantity of labour necessary to produce them, the labourers who are employed upon (say) cotton cloth ought to receive as wages the whole price derived from its sale, leaving nothing for interest upon capital. Ricardo. however, explains that by ' the quantity of labour necessary to produce goods ' he means not only what is immediately applied to them but also the labour bestowed upon the implements and buildings with which the immediate labour is assisted. Now these buildings and implements are capital, the labour which produced them was paid for and it was far enough from Ricardo's mind to suppose that the capital which assists present labour upon (say) cotton cloth has no claim to remuneration out of the price of it. In this argument, then, the word labour in the premise is used secundum quid, that is. with the suppressed qualification of including past as well as present labour ; but in the inference labour is used simpliciter to mean present labour only. (2) A dicto secundum quid ad dictum secundum altevum quid. It may be urged that, since the tax on tea is uniform, therefore all consumers contribute equally to the revenue for their enjoyment of it. tJut written out fairly this argument runs thus: Since tea is taxed uniformly .d per lb., all consumers pay equally for their enjoyment of it whatever quality they use. These qualifications introduced, nobody can be deceived. n j / 77 ^v, U) A dicto simpliciter ad dictum secundum quid, also called Jallacia accidentis. Thus : To take interest upon aloan is perfectly just therefore. I do right to exact it from my own father in distress. The popular answer to this sort of blunder is that ' circumstances alter cases. We commit this error in supposing that what is true of the average is likely to be true of each case ; as if one should say : ' The offices are ready to insure my house against fire at a rate per annum which will leave them heavy losers unless it lasts a hundred years; so. as we are told not to take long views of life, I shall not insure.' The Fallacy of Division and Composition consists in suggesting, or assuming, that what is true of things severally denoted by a term is true of them taken together. That every man is mortal is generally admitted, but we cannot infer that, therefore, the human race will become extinct. That the remote prospects of the race are tragic may be plausibly argued, but not from that premise. ^ . . . ,. .. . Chan<^ing the Premises is a fallacy usually placed in this division . FALLACIES 313 although, instead of disguising different meanings under similar words, it generally consists in using words or phrases ostensibly differing, as if they were equivalent : those addressed being expected to renounce their right to reduce the argument to strict forms of proof, as needless pedantry in dealing with an author so palpably straightforward. If an orator says — ' Napoleon conquered Europe ; in other words, he murdered five millions of his fellow creatures ' — and is allowed to go on, he may infer from the latter of these propositions many things which the former of them would hardly have covered. This is a sort of hyperbole, and there is a corresponding meiosis. as : ' Mill admits that the Syllogism is useful ' ; when, in fact, that is Mill's contention. It may be supposed that, if a man is fool enough to be imposed upon by such transparent colours, it serves him right; but this harsh judgment will not be urged by any one who knows and considers the weaker brethren. § 9. The above classification of Fallacies is a rearrangement of the classifications adopted by Whately and Mill. But Fallacies resemble other spontaneous natural growths in not submitting to precise and definite classification. The same blunders, looked at from different points of view, may seem to belong to different groups. Thus, the example given above to illustrate fallacia accidentis, ' that, since it is just to take interest, it is right to exact it from one's ow^n father,' may also be regarded ^s petitio principii, if w^e consider the unconditional statement of the premise— 'to take interest upon a loan is perfectly just ' ; for, surely, this is only conditionally true. Or, again, the first example given of simple ambiguity — * that whatever is wTitten in a classical language is classical, etc.\ may, if we attend merely to the major premise, be [rta'.ed as a bad generalisation, an undue extension of an inference, founded upon a simple enumeration of the first few Greek and Latin works that one happened to remember. It must also be acknowledged that genuine wild fallacies, roaming the jungle of controversy, are not so easily detected or evaded as specimens seem to be when exhibited in a Logician's collection ; where one surveys them without fear, like a child at a menagerie. To assume the succinct mode of statement that is most convenient for refutation, is not the natural habit of these things. But to give reality to his account of fallacies If f 314 LOGIC: DEDUCTIVE AND INDUCTIVE an author needs a large space, that he may quote no inconsider- able part of literature ancient and modern. As to the means of avoiding fallacies, a general increase of sincerity and candour amongst mankind may be freely recommended. With more honesty there would be fewer bad arguments ; but there is such a thing as well-meaning mca- pacity that gets unaffectedly fogged in converting A., and regards the refractoriness of O., as more than flesh and blood can endure. Mere indulgence in figurative language, again, is a besetting snare. "One of the fathers, in great severity, calltd poesy vimim dccmonum,'' says Bacon : himself too fanciful for a philosopher. Surely, to use a simile for the discovery of truth is like studying beauty in the bowl of a spoon. The study of the natural Sciences trains and confirms the mind in a habit of good reasoning, which is the surest preservative against i)arulogism, as long as the terms in use are, like those of science, well defined ; and where they are ill defined, so that it is necessary to guard against ambiguity, a thorough training in politics or metaphysics may be useful. Logic seems to me (I must confess) to serve, to some extent, both these purposes. The conduct of business, or experience, a sufficient time being granted, is indeed the best teacher, but also the most severe and expen-ive. I n the seventeenth century some of the greatest philosophers wrote de ititellectiis emen- datione ; and if their successors have given over this very practical inquiry, the cause of its abandonment is not success and satiety but despair. Perhaps the right mind is not to be made by instruction, but can only be bred. This is a slow process, and meanwhile the rogue of a sophist may count on a steady supply of dupes to amuse the tedium of many an age. FINIS. QUESTIONS TU folloiiing questions are chiefly taken from public examination papers : Civil Service [S] . Oxford [OJ , and Cambridge [C] . I. TERMS. ETC. 1. What is a Term? Explain and illustrate the chief divisions of Terms. What is meant by the Connotation of a Term ? Illus- trate. [S] 2. " The connotation and denotation of terms vary inversely." Ex- amine this assertion, explaining carefully the limits within which it is true, if at all. [S] 3. Exemplify the false reasoning arising from the confusion of Con- trary and Contradictory Terms. [S] 4. Discuss the claims of the doctrine of Terms to be included in a Logical System. Distinguish between a General and an Abstract Term. [S] 5. Explain and illustrate what is meant by the Denotation and Conno- tation of a Term. What terms have both, and what have one only ? [S] 6. Distinguish between Abstract and Concrete Names. To which of these classes belong (a) adjectives, {b) names of states of con- sciousness ? Are any abstract names connotative ? [S] 7. Distinguish between {a) Proper and Singular Terms, {b) Negative and Privative, {c) Absolute and Relative. Illustrate. 8. What connection is there between the Connotation and the Relativity of Names ? 9. Examine the logical relations between the following pairs of terms : {a) happy and happiness ; {b) happy and unhappy ; {c) ' the jury- man ' and ' the jury ' ; (d) parent and offspring. Explain the technical words used in your answer. [C] 10. Distinguish between name; part of speech; term: and illustrate by reference to the following— use, useful, usefully. [C] 11. Describe the nature of Collective terms ; examining in particular any difticulties in distinguishing between these and general or abstract terms. [C] 3i6 LOGIC: DEDUCTIVE AND INDUCTIVE 12. Distinguish between positive, negative, and privative names. Of what kind are the following, and why — parallel, alien, idle, un- happy ? What ambiguity is there in the use of such a term as "not- white"? [C] II. PROPOSITIONS AND IMMEDIATE INFERENCE 13. What is meant by (i) the Conversion, and (2) the Contraposition of a proposition ? Apply these processes, as far as admissible, to the following : — {a) All invertebrates have cold blood. (h) Some cold-blooded animals are not invertebrates. (c) No wingless birds are songsters. {d) Some winged birds are not songsters. What can you infer from (a) and (6) jointly, and what from {c) and {d) jointly ? [S] 14. " The author actually supposes that, because Professor Fawcett denies that all wealth is money, he denies that all money is wealth. " Analyse the differences of opinion implied in the above passage. [S] 15. Take any universal affirmative proposition ; convert it by obversion (contraposition) ; attach the negative particle to the predicate, and again convert. Interpret the result exactly, and say whether it is or is not equivalent to the original proposition. [S] 16. What information about the term "solid body" can we derive from the proposition, "No bodies which are not solids are crystals"? [S] 17. Discuss the proposal to treat all propositions as affirmative. 18. Convert the proposition "A is probably B." What information does the proposition give us concerning B ? [S] ig. Show in how many ways you can deny the following assertions : All cathedral towns are all cities ; Canterbury is the Metropolitan see. [S] 20. Explain the nature of a hypothetical (or conditional) proposition. What do you consider the radical difference between it and a categorical ? [S] 21. What is the function of the copula f In what different manners has it been treated ? [S] 22. Convert "A killed C unjustly": "All Knowledge is probably useful " ; " The exception proves the rule " ; " Birds of a feather flock together." [S] 23. What is modality? How are modals treated by {a) formal logic and ip) by the theory of induction ? [S] QUESTIONS 317 24. What is the subject of an impersonal proposition ? Give reasons for your answer. [S] 25. Is a categorical proposition sufficiently described as referring a thmg or things to a class ? [S] 26. Enumerate the cases in which the truth or falsity of one proposition may be formally inferred from the truth or falsity of another Illustrate these cases, and give to each its technical name [S] 27. Illustrate the relation of Immediate Inferences to the Laws of Thought. 28. Explain what is meant by {a) Symbolic Logic ; {h) the Logic of Relatives. Describe some method of representing propositions by means of diagrams ; and indicate how far any particular theory of the import of propositions is involved in such representation. 29. Explain the exact nature of the relation between two Contradictory propositions; and define Conversion by Contraposition, deter- mining what kind of propositions admit of such conversion Give the contradictory and the contrapositive of each of the following propositions :— {a) All equilateral triangles are equiangular ; {b) No vertebrate animal has jaws opening sideways ; (c) Wherever A and B are both present, either C or D is also present. [S] 30. Define Obversion and Inversion, and apply these processes also to the above three propositions. 31. Propositions can be understood either in extension or in intension Explain this, and discuss the relative value of the two interore tations. [S] ^ 32. Distinguish between real and verbal propositions; and explain the importance of the distinction. ZZ- Illustrate the process called ' change of Relation.' III. SYLLOGISM AND MEDIATE INFERENCE 34 What is a Syllogism ? Find, without reference to the mnemonic verses, in what different ways it is possible to prove syllogistically the conclusion No S is P; and show the equivalence between these different ways. [S] 35. From what points of view can the syllogism be regarded (i) as being, (2) as not being, a petitio principii ? [S] Ze. What are the figures of syllogism ? For what kind of arguments are they severally a dapted ? [S] Z7- What is meant by Mood and Figure? How can the validity of a Mood be tested ? Should there be four Figures or three ? [S] 3i8 LOGIC: DEDUCTIVE AND INDUCTIVE 38. Construct syllogisms in Camenes, Datisi and Baroco, and reduce them to the corresponding moods of the first figure. 3Q. Explain the meaning of " ostensive " and "indirect" Reduction. Show that any Mood of the second Figure may be reduced in either way. 40. Show that A. cannot be proved except in the First Figure. Express the following reasoning in as many syllogistic figures as you can : Some theorists cannot be trusted, for they are unwise. [S] 41. Discuss the possibility of reducing the argument a fortiori to the syllogistic form. [S] 42. Can a false conclusion be reached through true premises, or a true conclusion through false premises? Give reason for your answer. [S] 43. Can we under any circumstances infer a relation between X and Z from the premises— Some Y's are X's Some Y's are Z's? [S] 44. fake an apparent syllogism subject to the fallacy of negative pre- mises, and inquire whether you can correct the reasoning by converting one or both of the premises into the affirmative form. [S] 45. Enumerate the faults to which a syllogism is liable, giving instances of each. [S] 46._State any Enthymeme, and expand it into (i) a Syllogism, (2) an NEpicheirem^tJTa Sorites; and give in each case the technical mime^the Mood or Order that results. 47. Stat^y^y Disjunctive. -Syllogism, and change it (i) into a Hypo- thfetical, (2) into a Categorical ; and discuss the loss or gain, in cogency or significance, involved in this process. 48. Can the Syllogism be treated as merely a consequence of the " Laws of Thought " ? If not, why not ; and what else does it imply ? 49. Prove that with three given propositions (of the forms A., E.. I., O.) it is never possible to construct more than one valid syllogism. 50. Distinguish between a Constructive and a Destructive Hypothetical Syllogism ; and show how one may be reduced to the other. [C] IV. INDUCTION, ETC. ^1 51. What constitutes a Valid Induction ? Distinguish it from a legiti- mate hypothesis. [S] 52. Is it possible to form true universal propositions about facts if we have not actually observed all the individuals designated by the subject of the proposition ? If so, how ? [S] QUESTIONS 3»9 53 "Perfect induction is demonstrative and • syllogistic ; imperfect induction is neither." Explain the difference between perfect and imperfect induction, and examine the truth of this asser- tion. [S] 54. Why is it that one should not regard night as the cause, nor even as a universal condition of day ? Explain "cause" and condition. [S] 55. What do you understand by an experiment ? Can you say how many experiments are required to establish (i) a fact, (2) a law of nature ? 56. How would you define antecedent, cause, effect, consequent ? [S] 57- England is the richest country in the world, and has a gold currency. Russia and India, in proportion to population, are poor countries and have little or no gold currency. How far are such kind of facts logically sufficient to prove that a gold currency is the cause of a nation's wealth ? [S] 58. A man having been shot through the heart immediately falls dead Investigate the logical value of such a fact as proving that all men shot through the heart will fall dead. [S] 59 Explain the process of induction called the Method of Difference, and give some new instances of its application. How is it related to the Method of Concomitant Variations ? What is the Major Premise implied in all these methods ? [S] 60. Explain the logical cogency of experiments in the search for physical causes. [S] 61 . If the effects of A B C D are fully expressed by a b c d . and those of B / C D by b c d, what inductive inference can be drawn and on what- y principle ? State the canon according to which it is drawn. [S] ^^" 62. Compare the advantage of observation and experiment as means of gaining data for Reasoning. [S] 63. Compare the cogency of different Inductive Methods, showing the kind of evidence each requires, and the principle on which it is based. [S] 64. Compare the Canons of Agreement and Difference (i) as to the difficulty of fitting them with actual " Instances, " and (2) as to their conclusiveness. 65. Describe what is meant by residual phenomena, and estimate their value in inductive science. [SJ 66. What is the argument from Analogy ? How does it differ from (a) Induction, {b) Metaphorical argument ? [S] 67. What are the various senses in which the word Analogy has been used ? Distinguish, giving instances, between good and bad analogies. [S] 68. How do you distinguish between what Mill calls the Geometrical, Physical and Historical Methods ? 320 LOGIC: DEDUCTIVE AND INDUCTIVE 69 70. 71- 72. 73 74- 75- What is meant by a doctrine being unverifiable ? If a conclusion reached by deduction does not agree with the facts, where must we look for error ? There are certain cases in which failure of verification is fatal to a theory and other cases in which it is of comparatively little cogency. How would you distinguish between these classes of cases ? [S] Taking the "evolution," or any other proposed hypothesis, how should one proceed {a) to show whether it satisfies the conditions of a legitimate hypothesis sufficiently to entitle it to investigation, and (b) to test it with a view to its acceptance or rejection as a truth of science ? [S] What do you mean by saying that "a phenomenon has been satisfactorily explained " ? Explain and illustrate the Historical Method of Sociological inquiry. [S] What is the relation of the theory of Probability to Logic ? [S] Explain and discuss the doctrine that Induction is based upon the Theory of Probability. [S] 76. Explain the nature and use of Classification, the means to, and tests of, its successful performance. [S] 77. What is Definition and what is its use ? Mention various difficulties that occur in the process, and show how they are to be met. [S] 78 Propose rules for a good Division and a good Definition and exemplify the breach of them. [S] 79. Examine the validity of the idea of Real Kinds. [O] 80. What kind of words are indefinable, and why ? When do we define by negation and by example ? [S] 81. Distinguish between the province and aims of classification and (logical) division. Illustrate. [S] 82. What is an infima species or species specialissima? Compare the use of the terms genus and species in Logic with that which is common in speaking of animals or plants. [S] 83. How far does the formation of Definitions and Classifications constitute the end of Science ? [S] 84. Examine the methodological relations between Definition, Classifi- cation and Nomenclature. [S] 85. Give instances of " Differentia," "Property," "Inseparable Acci- dent " ; and examine, with reference to your instances, how far it is possible to distinguish them. [S] QUESTIONS V. MISCELLANEOUS. 321 88 89. 100. " People can reason without the help of Logic." Why is this not a sufficient objection to the study? In your answer show dis- tinctly why Logic should be studied. [S] What is the meaning of the assertion that Logic is concerned with the form, and not with the matter, of thought ? [S] " Neither by deductive nor inductive reasoning can we add a tittle to our implicit knowledge." (Jevons.) Explain and criticise. [S] What is the logical foundation of the indirect method or rediictio ad ahsurdiun ? Is it applicable to non-mathematical subjects ? [S] On what grounds do we believe in the reality of a historical event ? [SJ • " Facts are familiar theories." Explain and discuss this. [O] Wherein lies the difficulty of proving a negative ? [OJ Can any limits be assigned to the possible unification of the sciences '> Are the results of inductive inference necessarily certain ? [O] - / *^' The method of deductive science is hypothetical. Explain and discuss. [O] I 7,^1^^ ^ ^H^\ "The uniformity of Nature can never be more than a working hypothesis. ' ' Explain and criticise. "Without speculation there is no good and original observation " Why ? [O] Can the provinces of induction and deduction be kept separate ? How far is the relation of logical dependence identical with that of causation ? [O] State in syllogistic form (mood and figure) the following argu- ments : — [a) As polygamy is in many countries legal, we may infer the variability of the moral standard. {b) If gold is wealth, to export it diminishes the national resources. {c) If all good people are happy, unhappiness is an indication of vice. {d) One may be sure of the benefits of inuring young children to cold, from the strength exhibited by all men and women thus treated in infancy. {e) Where there is no law, there is no injustice. (/) " Dissimulation is but a faint kind of policy or wisdom ; for it asketh a strong wit and a strong heart to know when to tell the truth, and to do it ; therefore it is the weaker sort of politicians that are the greatest dissemblers." (Bacon.) {g) Money being a barren product, it is contrary to nature to X OLA^ Cw- 322 LOGIC : DEDUCTIVE AND INDUCTIVE make it reproduce itself. Usury, therefore, is unnatural, and, being unnatural, is unjustifiable. (h) The study of mathematics is essential to a complete course of education, because it induces a habit of close and regular reasoning. [S] y^Toi. Explain and illustrate the following terms :—Subalternans, Vera Causa, Plurality of Causes, Law of Nature, Empirical Law, Summiim Genus, Predicament, A rbor Porphyriana, Axiom, Universe of discourse {suppositio), Antinomy, Dilemma, Realism, Dichotomy. ~lo2. Is there any distinction and, if so, what, between a complete Description and an Explanation ? [C] 103. On what principles have Fallacies been classified ? To what extent do you think a satisfactory classification of Fallacies possible ? [C] 104. Examine how far conceptions of Persistence and of Invariable Concomitance of Properties are involved in the methodolo- gical application of the conception of Cause. Inquire whether the two following propositions can be reconciled with one another : (a) The same conjunction of antecedents is invariably followed by the same consequent ; {h) We never find the same concurrence of phenomena a second time. [C] 105. Using the term Logic in a wide sense so as to include Methodology, inquire how far a Logic of Observation is possible, and show in what it will consist. [C] 106. What is Proof ? ' -^^ Explain and cjiscuss the following dicta: — (a) Qui nimium prohdt, nihil prohat : {h) A bad proof is worse than no proof; (c) The exception proves the rule; {d) Negatives cannot be proved. [C] Examine how far the rules of immediate and syllogistic inference are modified by differences of interpretation of the categorical proposition in respect to the existence of the subject. [S] " An effect is but the sum of all the partial causes, the concurrence of which constitutes its existence." " The cause of an event is its invariable and unconditional ante- cedent." Explain and compare these two theories of causation. Does either alone exhaust the scientific conception of cause ? [S] Under what logical conditions are statistical inferences authorised, and what is the nature of their conclusions ? [S] no. Distinguish between Psychology, Metaphysics, and Logic; and discuss briefly their mutual relations. [S] III. All processes of inference in which the ultimate premises are parti- cular cases are equally induction. Induction is an inverse deduction. Explain and contrast these two theories of the relation of induc- tion to deduction. [S] 109. ^ > QUESTIONS 323 112. What are the Fallacies specially incident to Induction ?-or to the application of the theory of Probabilities ? [S] What is meant by the personal error (or persojial equation) in observa- tion ? Discuss its importance in different branches of know- ledge. [S] Define and illustrate .—Paralogism, ignoratio elenchi, faUacia acci- dentis. argumentum ad verecundiam, illicit process, undistributed middle. 113 14. Printed by Ballantyne Hanson ^^ Co. London ^ Edinburgh. By GRANT ALLEN. Demy 8vo, cloth, 20s. net, THE EVOLUTION OF THE IDEA OF GOD: AN ENQUIRY INTO THE ORIGINS OF RELIGIONS. SOME PRESS OPINIONS. AZt'irf.t^{ fv'''V''^'-T''^^^ sympathetic spirit in which Mr. Allen treats a delicate and complex subject should have kindly con- nhonftr "" ^^""V '•'^°"' ^'^^ '^""'y °f "^'^"'s beliefs and guesses nf^^Vf iTTi^^'^^'^PP^^^ A book which is the oStcome of careful scholarly research." c.n^tJ^'"''^'^''^™^- ^°°^' *^^ outcome of twenty years of thought trihnHnnrrth^'l"'"'^' IS Certainly one of the most important con- r s Pi?^^^^ ^ ^'\\7V^ '^'^ ^^""^^" "^^"d ^^'i^h the last decade nas given us. . . . We have no space to trace further the unfcldin? of these suggestive Ideas, which are developed and illustrated with work^ mT An^''''""'^" "I ^'°^^ °^ ^^•■'°"^ P^'-P^^^^- The present uork Mr Allen says, is but a sketch which wdl be fil'ed m and amplified if the public is sufficiently interested - suc^essfulT Mr '?!?." °^ '^^ "^°'' ambitious and net the least successful of Mr. Aliens works. ... It is needless to say that the book IS clever, showing marks of wide reading, ingenuity, and a rPnl^n r^'f^''"""''^-^^' '^^ ^''^^^' ^^^ ^^at it altracts by^tl e very reason that the writer is cumbered with few doubts or misgivings as o he soundness of his theories The true student of the sub- ject will profit much by Mr. Grant Allen's erudition and his cri.icisnis of the work of his predecessors." '^i^mb int^rL^* 5* ^^''^L«'"theZ)«//j.lAz//._" A work of extraordinary interest and sugges ion. ... It is on the whole a worthy treatmem Sinf i™"!f"'''^^ interesting subject, a book for the intelligen general reader, one of the books that bristle with thealvvavsplau fble and frequently convincing, reason why." " ^ ^"^'"^'" T^e Scotsman.—" It will be understood by every one thit thp subject Mr. Allen has chosen would be handle7by him n a thoroughly scientific manner, and in absolute independence of aU Geological theories. ... The writer has collected an immense tT.^ f °^I^''' ^'-'^""^ ^'^ '^^ development of religion, andTi^s pm o tt wfn 1'' "' "" "^of interesting way. I he mSre educated par of the world is prepared for a work like this, and we have no doub it will be read by many with the deepest interest." GRANT RICHARDS, 9 HENRIETTA STREET, COVENT GARDEN, W.C. I By EDWARD CLODD. Second Edition. Crown 8vo, cloth, 5s. net. PIONEERS OF EVOLUTION FROM THALES TO HUXLEY. WITH AN INTERMEDIATE CHAPTER ON THE CAUSES OF ARREST OF THE MOVEMENT. With Photogravure Portraits of Charles Darwin, Prof. Huxley. Mr. A. R. Wallace, and Mr. Herbert Spencer. SOME PRESS OPINIONS. The Times.—'' We are always glad to meet Mr. Edward Clodd. He is never dull ; he is always well informed, and he says what he has toTay whh clearness and incision. . . . The interest intensifies as Mr Clodd attempts to show the part really played in the growth of he doctrine of evolution by men like Wallace. Darwin, Huxley, and Soencer. Mr. Clodd clears away prevalent misconceptions as to ^h? work of hese modern pioneer^. Especially does he give to Mr. S^ncer the credit which is his due. but which ^^^ often mistakenly award^ to Darwin. Mr. Clodd does not seek m the least to lov^er Darwin from the lofty pedestal which he rightly occupies ; he only seeks to show precisely why he deserves to occupy such a position. We comn.end?he book to those who want to know what evoUuron really means ; but they should be warned beforehand that they have to tackle strong meat." 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