I i J^u.^J / 28957 BAXTER, PRINTER, OXFORD. PREFACE. Whatever variety of opinion may exist as to the absolute merits of Aldrich's Logic, there are many considerations which recommend a new edition of that work, as by far the most convenient mode of supplying an acknowledged deficiency in the studies of the University. The majority of Teachers will probably agree with me in regarding the dry skeleton of a Latin Manual as better adapted to the discipline of beginners than any of the more elegant, but somewhat diluted Essays of the present day : to which must be added the consideration, that Latin is the original language of many of the technicalities of the subject, which cannot be so conveniently learned through the medium of a translation. But among the Latin Compendia, that of Aldrich has long reigned almost exclusively in Oxford ; nor would it be easy to select any rival manual of such decided superiority as to counterbalance the evils neces- sarily attendant on all violent changes in a long- established system. Deficient as the work unde- b VI PREFACE. niably is in many of the prominent features of the Scholastic Logic, its very deficiencies render it in some respects preferable to a more faithful expo- nent. The criticism of the present age has con- tributed much towards a more just appreciation of the merits of the mediaeval Philosophy ; but he must be a bold champion of reaction who would advocate the complete disinterment of the Logic of the Schools. Who would desire now to oppress the Student with the heavy burden of modals, or to bewilder him with the mysteries of Suppositio, Ampliatio, Restriction and the whole farrago of the Parva Logicalia? Omissions of this character may, with equal probability and more charity, be attributed to the sound judgment of the University, than to the decline of the Professorial System and the incompetency of College Tutors % On the other hand, it must be confessed that there is much to be added to this or any other Compendium, to enable it to meet the demands of the existing University Examinations. This will at once be admitted by all who have had any recent practice in tuition ; it may be easily ascer- tained by any who will take the trouble of com- paring the contents of the book with those of any of the present examination-papers. To this deficiency, the increasing study of the original writings of Aristotle has not a little contributed. But the transition from the bare text of Aldrich to ^ See Edinburgh Keview, No. 115. p. 195. PREFACE. Vll that of Aristotle is far too abrupt to be beneficial to the Student. Occasionally indeed he may recognise an old friend in a new dress ; but the difference of language, order, and manner of treatment will conceal from the unpractised eye most of the passages in which his Latin successors have attempted any thing more than a bare translation of the words of the Stagirite. In this respect, it is hoped that the numerous references to, and quotations from, the Oiganon, which will be found in the following pages, will contribute in some degree towards a most important object, — the clear discrimination between those portions of the system w^iich belong to the original work of Aristotle, and those for which we are indebted to subsequent Logicians. For a like rea- son, in my references to the latter, I have occa- sionally endeavoured to furnish some information as to the author and the period of the innovation. Nothing is more strongly to be reprehended than the slovenly practice of referring in general terms to the Logic of the Schoolmen ; as if every individual of that body had written a distinct treatise on the subject, or as if those who have were a race of harmonious commentators, whose labours exhibit a supernatural uniformity, such as tradition narrates of the translators of the Septuagint. What would be thought of a reference in general terms to the doctrine of the Greek Philosophers ? Yet Aristotle scarcely departed more widely from Plato, than b2 Vm PREFACE. did Abelard from William of Champeaux, or Occam from Scotus. In some cases it is indis- pensable to the right understanding of doctrines and modes of expression, to know when and by whom they were first introduced into Logic. If, for example, as in the treatment of the Predicables and of Definition, we find language held neither by Aristotle nor by Porphyry, expressly insisted on by one sect of the Schoolmen, and as expressly repudiated by another, there can be no doubt what views, whether right or wrong in themselves, must be adopted as a necessary basis for the inter- pretation of that language. Of my own very imperfect acquaintance with the post-Aristotelian Logicians, I am well aware. But when the alternative lies between the postponement of the present work to an almost indefinite period, and the attempting it from such resources as I can at present command, the necessity that has long been felt for something of the kind, will, I trust, be allowed as some apology for the deficiencies of the execution. One other point remains to be noticed. In com- menting, whether for explanation or correction, on the language of a manual so brief as that of Aldrich, there is no tutor but must have felt the difiiculty of attaining the happy medium between dogmatic assumption on the one hand and prohx discussion on the other. It is possible so to bewilder a pupil with premises that he shall utterly lose sight of the PREFACE. IX conclusion : it is possible so to overwhelm him with assertion^ as to leave him no choice but th^t of blind submission to the ipse dixit of his tutor or the ipse scripsit of his text-book. The same difficulty meets the editor. In controverting the positions of a work which for more than a century and a half has enjoyed the sanction of the University, somewhat more of the verecunde dissentio is becoming than can always be comprised within the necessary limits of a foot-note. The further discussion of such points in an Appendix has in some instances unavoidably produced a certain amount of repetition. This however, though injurious to the form of the work, will, it is hoped, not render it the less serviceable to that not in- considerable class of students oig ouls 7 gig XsyovTsg l^ixvo6[ji.sQot. A few passages omitted in recent editions of the Compendium have been restored in the present. This, however, has been done but sparingly. An account of the Arbor Porphyriana has been trans- ferred to the first chapter from its original place in the Penus Logica, The obvious utility of the insertion will, it is hoped, warrant the liberty in this single instance taken with the text. The references to Aristotle have been adapted to the Oxford reprint of Bekker's text. In Germany, a custom seems to be gaining ground of referring to the pages of the Berlin edition, but that work has not been sufficiently circulated X PREFACE. here to make the example convenient to follow. Of the Isagoge of Porphyry, Buhle's edition has been used. With the Greek Commentators, my chief acquaintance has been made through the medium of the Berlin Scholia collected by Brandis, to which, as the most accessible edition, reference has been made. Boethius is quoted from the Basel edition of 1570. The other quotations will in most instances speak for themselves. To the present edition is prefixed an Intro- duction, containing a short historical account of logical writers^ ancient and modern, which, though necessarily cursory and incomplete, will, it is hoped, be found more satisfactory than the notices which can be gathered from most English works of a similar character. In this sketch I have derived considerable assistance from the valuable Essay of M. St. Hilaire. Mr. Blakey's elaborate History of Logic has been occasionally consulted ; but his principle of classification and examination is too different from mine to enable me to make much use of his labours. My critical views of Logic are briefly exhibited in the second part of the Intro- duction, and have been pubhshed at greater length in a separate work. Some apology is perhaps needed for the references to this work which will be found in the following pages, especially in the earlier portion. But I have long been of opinion that Logic, as generally taught, requires constant illustration from Pyschology, and that the earlier PREFACE. XI part of Aldrich's text in particular is especially liable to be misunderstood without some such assistance as it was one principal aim of the Prolegomena Logica to supply. My obligations in the present work, as in that, to the writings of Kant, of M. Cousin, and of Sir William Hamilton, require special acknowledgment; to these works must be added here the logical works of Professor Trendelenburg, Waitz's excellent edition of the Organon, and Biese's " Philosophic des Aristo- teles/' INTRODUCTION. PART I. HISTORICAL. Although the writings of Aristotle are the source from History of which the science of Logic is principally derived, it is Logic remarkable that there is no single name sanctioned by the Stagirite himself, under which can be comprehended either the whole collection of treatises known by the name of the Organon, or the whole subject of which they treat. Aoyix^, as the name of an art or science, is not to be found in his works, and the cognate terms, Xoyixos and KoyiKoog, are used in a very different sense from that which has subsequently been given to them^ The J"/^ zl^-'^-^ logical syllogism of Aristotle is opposed sometimes to the analytical, sometimes to the physical, sometimes to the demonstrative syllogism ; and signifies a ])rocess of reasoning from general principles of probability, as distinguished from one of which the principles are elicited by special contemplation of a given object or notion ^\ It is therefore opposed, alike to the demon- strative reasoning, in which necessary truths are resolved into the axiomatic principles on which they depend, and to that by which physical phenomena are referred to general laws of nature. The first use of the term Logic, as the name of a science, is probably later than Aristotle, and to be re- =^ Cf. Anal. Post. i. 22. 10. i. 24. 11. ii. 8. 3. Top. i. 14. 1. Phi/s. iii. 3. 2. ^ See Gassendi, Logicce Proccvunm xn'it. Biese, Philosophie dcs Arislotelcs, vol. i. p. 133. Waitz, Organon, vol. ii. p. 353. Trendelenburg, Elimcnia, p. 47. XIV INTRODUCTION. ferred to Zeiio the Stoic. The division of Philosophy into Logic, Physics, and Ethics, probably originated with this Philosopher^ and the use of the name Logic in Cicero is principally in relation to the Stoical doctrines'^. For the application of the term to the contents of the Aristotelian Organon, the Greek commentators upon Aristotle are our earliest extant authority. Alexander of Aphrodisias, the oldest of these whose works have come down to us% speaks of ^ Xoyix^ xai a-uWoyia-TiJcvj TrgotyfLocTelu as containing under it aToSejxrixi^, SiaAsxriJc^, TTsigota-TixYji and (j-o(Pk7tikv) ^ Here, while Dialectic retains its Aristotelian sense. Logic is extended so as to include the syllogistic theory in general, and its particular appli- cations to necessary and probable matter. A similar extension of Dialectic is found in the commentaries of David the Armenian s; and Philoponus uses both terms as synonymous, and in the same extent^. <= Laert. vii. 39. Plutarch, De Plac. Phil. i. 1. This division is some- times attributed to Plato. (Cf. Cicero, Quasi. Acad. i. 19. De Fin. i. 22. Euseb. PrcBp.Evan.-sx. 1. Augustin, De Civ. Dei, viii.4.) But none of the three names occur in any of the extant Platonic writings ; and a different division of sciences into cognitive and practical is intimated by Plato himself, Polit. p. 258. Indeed the state of philosophy in Plato's day would hardly allow of the Stoical division being made. Cf. Van Heusde, Initia Phil. Platon. p. 41. 117. Aristotle's supposed adoption of the same threefold classification is still more questionable ; being founded on a misinterpretation of Topics, i. 14. 4. and at variance, as well with the earliest commentary on that passage, as with Aristotle's constant use of the word KojikSs, and with his Avell-known division of theoretical Philo- sophy into Physics, Mathematics, and Theology. ^ Tusc. Qucest. iv. 33. Cf. Trendelenburg, Elementa, p. 47. e The Paraphrase on the Ethics, attributed to his predecessor Andronicus Rhodius, is spmious. Its real author is probably HeUodorus Prusensis. See Sainte-Croix, Examen Critique des Anciens Histoires d' Alexandre le Grand, p. 524. f Scholia, p. 141. a. 19. The testimony of Boethius {In Top. Cic. p. 766.) would seem to refer this usage of the word to the elder Peripatetics, but we must reject hit? reference to Aristotle. ? Scholia, p. 18. a. 34. Waitz, vol. ii. p. 437. h Scholia,^, 143. a. 4. INTRODUCTION. XV Two names sanctioned by Aristotle are applicable to Names parts, but to parts only, of the Organon. These are Aristotle. Analytic and Dialectic. The former term is applied by Analytic. Aristotle to the four books which treat of the syllogism and of demonstration^, and appears to denote the reso- lution of the reasoning process into its scientific forms. This w^ord is the most nearly synonymous with the modern Logic of any used by Aristotle himself; but it embraces the process of Reasoning. only, to the exclusion of Conception^and Judgment^. Dialectic is a word pro- Dialectic, bably invented by Plato ^, though afterwards applied to the works of earlier philosophers, e.g. Zeno the Eleatic. In its Platonic sense it denoted the highest of all sciences ; that which takes cognisance of the eternal and immutable, of being in general and its attributes, and thus has insight into the universal principles upon which all other knowledge is dependent". It thus corresponds in matter, though different in form, with the first Philosophy or Theology of Aristotle, afterwards called Metaphysics. The name Dialectic had reference • Galen {de libris propriis, ch. II.) says that the title Analytica is not Aiistotelian ; the Prior Analytics being called by their author ircpi avWo- yia-fiov, and the Posterior, Trept airoSel^ecos. This testimony is accepted by M. St. Hilaire, Memoire. p. 42. But the name ayaXvriKct occurs too frequently in Aristotle's own writings to warrant this view, unless we suppose (which is very improbable) that all the references have been interpolated by a later hand. Cf. Waitz, vol. i. p. 367. The distinction, however, between Prior and Posterior Analytics is not recognised by Aristotle, and we may perhaps conjecture that the name avaXvTiKo. was given by him to the entire four books, each dirision being also distin- guished by its own title, as mentioned by Galen. ^ Q>i. An. Pr. i. 33. 2. Toi/s yeyii/rjfxevovs avWoyidfiovs ayoAvoi/xey eis ra wpoiipTjfjLeua o-x^Maro. Cf. Trendelenburg, Elementa, p. 47. Waitz, vol. i. p. 36b. The analytical method of inquiry, attributed to Plato by Laertius, iii. 24.is his method of division, exemplified especially in the Sophistes and Politicus; though he does not give it the name of analysis. 1 See PhcBdrus, p. 266. Laert. iii. 24. Cousin's Plato, vol. vi. p. 450. "> Phcedrus, p. 276. SojMst. p. 253. Repitb. vi. p. 510 sqq. vii. p. 021. 534. Cf. Van Heusde, Initio, p. 247. XVI INTRODUCTION. to the colloquial form, which, whether in solitary medi- tation, or in conversation with others, Plato regarded as the true method of eliciting and communicating know- ledge"; a view intimately connected with his doctrine of ideas, and with the theory which placed all knowledge in reminiscence. The Dialectic of Aristotle holds a far lower position, being merely the act^^of ^disputing by;. question; of attacking and defending a given thesis, from principles of mere probability, such as the opinions of men in general, or of the majority, or of certain eminent authorities. The Dialectical Syllogism is thus the same as the Logical; and the names Logic and Dialectic, if used solely in conformity with Aristotle's authority, would correspond, not to the Organon as a whole, but only to the two last treatises, the Topics and Sophistic Refutation s°. Hisory of Thus much may suffice, as regards the origin and use Science. ^^ ^^^ name Logic and the cognate terais. More im- portant is the inquiry, to w^hat extent the science itself, as exhibited in Aristotle, is indebted to the labours of previous philosophers. Dialectic, the thing though pro- bably not the name, is regarded, on the authority of Zeno the Aristotle, as the invention of Zeno the Eleatic^. By this is probably only meant that Zeno was the first to employe dialogue as the medium of philosophical instruction ; his predecessors of the same school, Xenophanes and Parmenides, having communicated their doctrines in verse. The dialectic method was afterwards exten- sively used by different schools, and for different pur- poses, which ultimately obtained distinctive names. n ThecEt. p. 189. Soph. p. 2C3. Phcedrus, p. 275. Protag. p. 329. o Top. i. 1. 2. P Laert. ix. 25. But in another passage (iii. 48.) he quotes Aristotle, as attributing the first written dialogues to Alexamenus of Styra. See Athenaeus, xi. 102. Eleatic. INTRODUCTION. XVll Aristotle enumerates four different kinds of reasoning, to which the colloquial form (to ^laXsysa-Qon) was applied, \6yoi StSacrxaXixo/, dioiXsKTixol, TtsipaarriKol, and spKyTixoii. The first are demonstrative reasonings, from the proper and axiomatic principles of a given subject. The second, or dialectic reasonings in the Aristotelian sense of the term, are those derived from general principles of proba- bility, such as the opinions of the majority of mankind, or of philosophers. The third are only a special appli- cation of probable reasonings to expose the ignorance , of pretenders in science '". The fourth are fallacious reasonings, from apparent but not real probabilities. In a subsequent passage, he distinguishes between egiariKol and jo^jiCTTixo/ ; the former being such as employ fallacy merely for a display of skill ; the latter, for pecuniary profit. Hence he defines (ro^Krrixr) as x^rii/.ccTKrTix.Y} tic, Sctto (ro(plu5 (pctivo[ji.svYi^\ These distinctions however will be of comparatively late origin ; after the various applications of the original method of Zeno had rendered specific names necessary. The eristic or sophistic was, as might naturally be The So- expected, the earliest of these special developments of the dialectic method. The arguments of Zeno himself had no small affinity to sophistry ; and the state of philosophy at that period was such as naturally to promote further advance in the same direction. The conflicting opinions of the three great pre-Socratic schools, the Ionian, the Pythagorean, and the Eleatic ; the one-sided and exclusive character of their principles, q Soph. Elench. 2. 1. >■ Kritik des dialektischcn Scheins, Kant, Kritik der r. V. p. G4. Kant is unjust to the ancient dialectic, when he describes it as a sophistical art of giving illusion the appearance of truth. The tentative use of dialectic very nearly corresponded with his own. =• Soph. Elench. It. 1, 5. XVlll INTRODUCTION. combined with the universality of their aims, and the consequent failure of each in the attempt to resolve diffi- culties beyond their respective provinces — all this could hardly fail to produce a spirit of scepticism, which should end in denying the possibility of attaining to truth at all*. Such w^as the purpose of the eristic method of the Sophists. They employed it chiefly to enforce their leading dogma of the unreality of all knowledge, specu- lative or practical. Accordingly, they endeavoured, by ingenious applications of the dialectic mode of reasoning, to involve those with whom they disputed in self-con- tradictions and absurdities ; and thus to shew that, what- ever principles we start from, paradox and inconsistency will be the invariable result. At a later period, the eristic method was adopted and pursued to a consider- able extent by Euclid of Megara, and his successors Eubulides, Diodorus Cronus, Alexinus, and Stilpo. Socrates. On the other hand, the method of Socrates partook largely of the Trsj^ao-rtjcrj, or tentative, which Aristotle describes as follows, r} yag Trsigaa-TiKY) ka-n SiaXsjcTtxij ri§ koc) $scogel ou rov slhoTu ocWoi rov uyvoomru xolI '7rgoiCJog dlxonog; FOP. Uavroog S^ttou'^. A reasoning of this kind has no place in a system of Formal Logic. That science recognises no inference that is not necessitated by the laws of thought; whereas in instances like the above, it is obvious that the premises may be true, and yet the conclusion false ^. Or two specimens may be found, both complying with the above form, one of which shall carry conviction to every reasonable man, while the other is utterly worthless. Its moral force may thus vary " from the highest moral certainty to the very lowest presumption*"." Its logical value is zero. Socratic Xhe Definition of Socrates has also more of a material Definition. than a logical character. He continually distinguishes between the essence and the qualities of a thing, and insists on determining what a thing is, rather than what it resembles^ ; a distinction afterwards repudiated by his disciple Antisthenes, w^ho denied the possibility of real definition. But Definition, as treated by Socrates, is a contribution, not to Logic, but to Metaphysics. It does not analyse by the laws of pure thought the contents of a given notion ; but endeavours to penetrate the real essence of things^. The same may in some degree be said of the Aristotelian treatment of Definition in the Posterior Analytics. ^ Gorgias, p. 460. e Of which the above example is adduced as a specimen by Boethius, Opera, p. 600. f Butler, Introduction to Analogy. g Cf. Goryias, p. 448. ThecBt. p, 146. ^ Cf. Fries, System der Logik, §. 3. For specimens of the Socratic Definition and the Dialectic Method, see the inquiries into the nature of piety, justice, msdom, &c. Xen. Mem. iv. 6.; of holiness, Plato, Euthy- phron, p. 6. ; of virtue, Meno, p. 72. INTRODUCTION. XXI From the position constantly assigned to Socrates in Plato. be Platonic Dialogues, it is impossible to determine "rith any accuracy how much of the doctrines and nethods advocated in those writings is due to the master, md how much has been added by his disciple. From j he express testimony of Aristotle, however, we may !onclude that Socrates did not, like Plato, maintain the xistence of ideas separate from the sensible phenomena , )f the world^; and consequently, that the exaltation of dialectic from its tentative use to the rank of the science )f absolute being, a view intimately connected with the deal theory, is due to Plato rather than to Socrates. To lato also probably belong in a great degree the methods )f (Tuvaywy^ and 5ia/^eo-ij, mentioned in the Phaedrus as the wo principal parts of Dialectic, and illustrated at some ength in the Sophistes and the Politicus''. The former onsists in the collection of a number of scattered bjects, in reference to one idea, with a view to definition; he latter in a gradual dichotomy, by means of contrary r contradictory members, so as to ascertain as accurately s possible the number of subordinate species contained nder each genus. It is the careful performance of this rocess, proceeding gradually through the intermediate lasses to the lowest, that especially distinguishes the rue dialectic method from the eristic ^ These pro- esses, for which Plato was perhaps in some degree in- ebted to the Eleatic and Megaric Philosophy "', may be Metaph. xii, 4. 5. 'AAA.' 6 jxkv '2,uiKp6.rT]S to kuOSaov ov x^picrra iirolei ou5e ovs Spifffiovs' 01 S' 6x<^P'^<^''> '^^■^ '''^ TOiavra rwv ovtuu iScas ■trpocrrjydpeva'au, " Phcedrus, p. 205. 277. Soph. p. 218. Polit. p. 2G2. Phileb. p. 16. ' Phileb. p. ] 7. With this may be compared Bacon's aphorism on the nportancG of axiomata media. Nov. Org. 1. i. aph. 19. Bacon indeed, iph. 105.) intimates that his own method was perhaps anticipated by lato, and this hint has been developed at greater length by Coleridge 1 his Treatise on Method. But the accuracy of the parallel may be uestioned. Cf. Stallbaum, Prolegomena in Philebum, p. 16. XXll INTRODUCTION. regarded as the precursors of the Aristotelian doctrine of searching for definitions by the two opposite methods, afterwards known as those of Division and Induction^. j In Plato we find also the analysis of the Proposition, with the noun and the verb as its constituent elements ; the union of the two being necessary to every assertion. Aiavoia and >^oyog correspond to each other as the 6 s37»3Tiljj), a title afterw^ards given to the Arabian Averroes. The school of Greek Commentators extends to the latter part of the sixth century : the principal writers, after Other Alexander, are Themistius, Ammonius, David the tators. Armenian, Simplicius, and Philoponus. The only important addition to the matter of logical Poriihyry. science emanated from the Neo-Platonic school. The elo-aywyij or Introduction to the Categories, written by Porphyry in the third century, is the original source of the fivefold classification of the Predicables, adopted by most subsequent Logicians. Whether this classification is an improvement on, or consistent with, the Aristote- lian doctrine, admits of considerable question*. * St. Hilaire, Memoire, vol. ii. p. 123, 14:5. b Gralen, in point of time, is a few years earlier than Alexander, but no important commentary of his is extant. Of the numerous logical writings attributed to him, there remains only a small treatise, Trepi tS>v irapa t)]v k4^i.v (To^KTixaTOiv^ the genuineness of which is questionable ; to which may be added the Elcraywyf) AiaXcKTiK^ recently discovered and published by M. Mynas. Neither is of any great logical value. Galen's invention of the fourth figure of Syllogism (attributed to him by Averroes) is doubtful. See below, p. 7o. note x. <= See below, p, 23. note q. XXV INTRODUCTION. Greek Abridg- meuts. Joannes Dama- scenus. Photius. Psellus. Blemmi- das. Pachy- meres. Leo Ma- gentinus. Georgius Trape- zantius. The Greek Abridgments of Aristotle, though in point of chronology they extend below the scholastic period, are in matter rather connected with the preceding series of Commentators. While the Scholastic Logic began in the extreme west of Europe, the Greek Logicians oi this class belong entirely to the extreme east, or to Asia. John of Damascus, in the early part of the eighth century, made a brief analysis of the Isagoge of Porphyry and of the Categories, and is remarkable as one of the first who applied Logic to Theology. Photius. the learned and turbulent Patriarch of Constantinople in the ninth century, was the author of abridgments of the Categories and the De Interpretation e. Michael Psellus the younger, in the eleventh century, composed a Synopsis of the Categories and of Porphyry's Intro- duction'^. The most remarkable work of this kind is the Epitome Logica of Nicephorus Blemmidas, written in the thirteenth century, which has been quoted as containing the earliest instance of that system of logical mnemonics which the schoolmen afterwards brought to such per- fection^. The list of Greek Logicians closes with the names of George Pachymeres of Constantinople, author of an abridgment of the Isagoge and the Categories; and of Leo Magentinus, Metropolitan of Mytilene, author of an Exegesis of the De Interpretatione, principally taken from Ammonius, and of Commentaries, some of which are still unpublished. To this list, some have added the name of George of Trebizond ; but he, though a Greek by birth, is better known as a resident at Rome, and, as an author, by his Latin translations and abridg- ments of Aristotle. His name is rather connected with ^ The Synopsis of the Organou attributed to Pselhis is probably spimous, ^ See St. Hilaire, Memoire, vol. ii p. 160. It may be questioned whether the Latin Logicians are indebted to the Greek in this respect. See Sir W. Hamilton's Discussions, p. 126, 6ol *, and below, p. 81. IiNTRODUCTION. XXVU a different phase of philosophy, with the Platonic and Aristotelian controversies in the time of Pope Nicholas V. The progress of Logic among the Latins presents in Latin Lo- one respect a contrast to that among the Greeks. With the latter, the age of abridgments and distinct treatises followed that of commentaries ; with the former, it preceded. The earliest work of a logical character in Latin is the abridgment of Aristotle's Topics by Cicero ; Cicero. the object of which, however, is rather rhetorical than dialectical. This treatise, which was written from memory, differs in many respects considerably from the original. After Cicero, we find nothing but a few allusions to the subject in Quintilian and Aulus Gellius', till we come to the short account of the doctrine of the De Interpretatione and the Prior Analytics, written in the second century by Apuleius. This occurs in the Apuleius. third book of his treatise De Dogmate Platonis ; and the singular error of attributing the syllogistic theory to Plato has caused the genuineness of this book to be questioned^. The only other logical writings in Latin Augustine, before Boethius, are the two works attributed to St. Augustine ; the one, an abridgment of the Categories, now generally allowed to be spurious, but probably written about the same period ; the other, an unfinished treatise called Principia Dialectica, the commencement of an essay on language with a view to disputation. To these must be added the singular allegory of Mar- cianus Capella, on the Marriage of Mercury and Philo- Capella. logy ; a medley of prose and verse, composed probably towards the end of the fifth century. The Seven Liberal Arts, afterwards so celebrated as forming the Trivium, and Quadrivium, or Encyclopaedia of the middle ages appear in the following order. Grammar, Dialectic, ^ See St. Hilaire, Memoire, vol. ii. p. 165. 8 Hildebraud, De Apuleii Sc7'iptis, p. xliv. XX VI 11 INTRODUCTION. Rhetoric, Geometry, Arithmetic, Astronomy, and Music ^. Dialectic is represented as a female of a sour counte- nance, holding in her left hand a serpent, aud in her right a hook baited with sundry formulae. She discloses her wisdom by a brief abstract of the Isagoge of Por- phyry and of the first three treatises of Aristotle. This is followed by an account of hypothetical syllogisms ; and the lady is about to proceed to an exposition of sophisms, when she is interrupted and very summarily dismissed by Minerva. Boethius. Boethius, in the sixth century, is the only commentator proper among the Latins. He has left a considerable number of valuable logical works, viz. two commentaries on the Isagoge of Porphyry, one on the Categories, two on the De Interpretatione, and translations of the other parts of the Organon ; besides original treatises on the Categorical and Hypothetical Syllogism, on Division, on Definition, and on Topical Differences ; together with a commentary on the Topics of Cicero. His works are of great importance in the history of Logic. They form the connecting link between the Greek and Scholastic writings, and were, with those of Augustine and Capella, the principal authority of subsequent generations, at a time when the Greek la,nguage was but little cultivated, and when the original fountains of logical science were consequently inaccessible. Cassiodo- Contemporary with Boethius was Cassiodorus the h M. St. Hilaire has committed an oversight in citing the di\ision of the Seven Liberal Arts from the Dialectic of Augustine. No such di%ision occurs there ; though one nearly the same is found in his second Book De Oydine, ch. 13. M. Haureau {de la Philosophie Scholastique, vol. i. p. 21.) attributes the invention of this classification to CapeUa, which is hardly reconcileable with the above reference. The Seven Liberal Arts were afterwards exhibited in the following mnemonic : " Crram. loquitur, Dia, vera docet, Rket. verba colorat, Mus. canit, Ar. numerat, Geo. pouderat, Ast. colit astra." INTRODUCTION. XXIX Senator, the author of a Treatise on the Seven Liberal Arts. His Dialectic contains a brief analysis of the Isagoge of Porphyry and the Organon of Aristotle, with additions, a considerable portion being borrowed from Apuleius and Boethius. His analysis of the Organon does not include the Sophistic Refutations, but contains a separate chapter De Faralogismis, which treats of purely logical fallacies. The arrangement of the work is by no means methodical, and extraneous matters are introduced which properly belong to Rhetoric. The body of Arabian Commentators derive their ap- The pellation from the language in which they wrote : their coramen- places of residence were various, and none of them tators. within the limits of Arabia. In fact, the Arabian lite- rature did not arise till after the conquests of the suc- cessors of Mahomet had extended the Saracen empire far beyond the boundaries of their original country. Like the latter Greek Logicians, the Arabians contributed little original matter to the science; their principal works being either translations, made sometimes from the Greek but more frequently from the earlier Syriac versions, or abridgments and commentaries. Of these the most important are the logical abridgments of Aviceiina and Algazel, and especially the voluminous translations and commentaries of Averroes. A Latin Averroes. version of the translations of Averroes, made from a Hebrew one, was the principal source from which the earlier Schoolmen derived their knowledge of all the writings of Aristotle, except his logical works, which had been translated by Boethius. This barbarous ver- sion continued in use even after a more accurate trans- lation from the original Greek had been made by William of Moerbecke, under the direction of Thomas Aquinas. The merits of Averroes as a commentator have been variously estimated. Ludovicus Vivos speaks XXX INTRODUCTION. of him with great contempt. " Nomen est commentatoris iiactus, homo qui in Aristotele enairando nihil minus explicat quam eura ipsum quern suscipit declarandum." With this may be contrasted the eulogy of Keckermann. " Nemo tarn veterum interpretum videri potest proximus Aristotelis menti atque hie Arabs." The modern critic will probably take a middle course between the two. While his commentaries may be pronounced somewhat prolix, and inferior in elucidating the text of Aristotle to those of the Greeks, particularly of his rival commentator Alexander ; his general view of the Organon and its parts has much of the clearness which distinguishes the abridg- ments of Avicenna and Algazel'." The principal material added by the Arabians to the text of Aristotle is the celebrated distinction between first and second intentions. This is found in the Epitome of the Categories by Averroes. It has also been traced to Avicenna''. To the Arabians also are probably owing some of the distinguishing features, though certainly not the origin, of the Scholastic Realism. The The period at which the Scholastic Philosophy may be men. ^^^^ ^^ have commenced, is a point of considerable dis- Scholastic pute. It cannot, like various Greek schools of philosophy, sophy ^® traced to a single founder; but was the gradual result of a collection of various doctrines and methods of teach- ing. Some have traced it up to John of Damascus, and even to St. Augustine ^ Some commence with John Scotus Erigena in the ninth century, some with the nominalism of Koscelin in the eleventh""; while by others it has been brought down, at least as far as Theology is concerned, as low as the thirteenth century, the era of • St. Hilaire, Memoire, vol. ii. p. 191. ^ See Smiglecii Logica, Disp. ii. Qu. 2. ' Brucker, vol. iii. p. 716. '" Hallara, Literature of Europe, vol. i. p. 13. INTRODUCTION. XXXI Albevtus Magnus and Thomas Aquinas". The name of Schoolmen appears to have been taken from the teachers of the cathedral and conventual schools established by Charlemagne and his successors, and was eventually applied to all who, whether professedly teachers or not, adopted in their writings the method and matter which finally formed the course of education in these and similar establishments. The distinguishing feature of Scholas- ticism, the union of a theological matter with a dialectical method, is found at least as early as the writings of Lanfranc in the eleventh century. Commencing from this point. Scholasticism may be divided into three periods, 1. Its infancy, extending from the eleventh to the middle of the thirteenth century. 2. Its prime, from the latter period to the middle of the fifteenth. 3. Its decline, extending to the end of the sixteenth century °. The Logic of the Schoolmen is a phrase frequently Scholastic employed, and often very inaccurately. It is incorrect ° to apply this name to the various applications of the syllogistic method, in Theology, in Metaphysics, in Phj^sics, or in Psychology. These are merely treatises on their proper subjects, with a somewhat more osten- tatious display of logical art than has been usual at other periods. But the applications of Logic to reason- ings on this or that branch of material science have nothing in them which is more peculiarly the property of the Schoolmen than of any other reasoners. The Logica uteris is one and the same to all generations of men ; all who reason soundly, reason consciously or unconsciously by logical laws, and the open display of the instrument in use does not make it a distinct in- " Hampden, Bampton Lectures, p. 72. " Cousin, Ouvrages d'Ahelard, Introduction, p. Ixv. XXXll INTRODUCTION. strumeiit from that which others employ in a more concealed manner. A historical account of the Scholastic Logic ought therefore to confine itself to commentaries and treatises expressly on the science ; and the scholastic contri- butions to the matter of Logic should be confined to such additions to the Aristotelian text as have been incorporated into the Logica docens. In this respect the Schoolmen did much to fix the technical terms of the science, particularly in respect of the relation of thought to language. Most of the distinctions of the different uses and significations of words are due to them ; — distinctions, however, carried to an useless and wearisome minuteness in the grammatical subtleties of the parva logicalia. They also contributed considerably to that which is most wanting in Aristotle, an exact conception of the nature and oflice of Logic ; though their definitions were not always consistent with the rest of their treatment; the text of Aristotle being seldom modified to suit the theory of the science. But the most remarkable contribution of this period is to be found in that singular system of logical mnemonics by which, from the time of Petrus Hispanus, nearly all the forms and processes of Logic might be learned by rote and performed almost mechanically, by the aid of a memorial word or line. The controversy between the Realists and the Nominalists, though introduced into the pages of professedly logical treatises, cannot be regarded as an accession to the science. Its real bearings on the text of Aristotle and Porphyry were not seen by the disputants on either side^; and the controversy, as conducted by them, must be regarded as a metaphysical excrescence, introduced out of its place in a logical system. p See p. 24, note r, and Appendix, note A. INTRODUCTION. XXXlll The earliest scholastic writings on Logic proper are Abelard. those of Abelard, the greater part of which have recently been published for the first time by M. Cousin. They consist of glosses on the original and translated works of Boethius, a fragment on Genera and Species, and a distinct treatise called Dialectica'^. The glosses are of little value, but the Dialectica is one of the most im- portant monuments of the scholastic philosophy. At first sight it appears to be a commentary; but, though the titles of the work follow Aristotle, Porphyry, and Boethius, it is in many respects an original and in- dependent treatise ^ It appears clearly from these relics that Aristotle was only known in the twelfth century through the translations and commentaries of Boethius. Contemporary with Abelard was Gilbert de la Porree, Gilbert de , r« T» • • • • /. -I • 1 1^ Porree. whose bex Frincipia^ an expansion oi the six last categories cursorily treated by Aristotle, was adopted in most of the scholastic logical treatises down to the sixteenth century ^ Towards the end of the twelfth century w^e come John of to a work of great importance in the history and philosophy of the scholastic Logic, the Metalogicus of John of Salisbury. The work purports to be a defence of Logic, under which is included Grammar and Rhetoric, against a sciolist of the day, to whom he gives the name of Cornificius'. It contains an interesting account of the author's own preparation for dialectic q A theological treatise called Sic el Non is contained in the same volume. ■■ Cousin, Introduction, p. xxiii. s Haureau, Philosophle Scholastiqve, vol. i. p. 298. t This name, M. Haureau explains as follows. " Cornifex, Cornificius, signifiera ' celui qui fait des cornes.' Mais de quelles cornes peut-il etre ici question ? Sans doubt de ces cornua dispvtationis dont parle encore Ciceron; ce qu'on appelle, en logique, les cornes d'un dilemme. A ce compte, nos Cornificiens auraient ete d'aigres disputeui's, des logiciens aceres, d'intraitables sophistes." Philosophic Scholastique, p, 344. XXXIV INTRODUCTION. Studies, notices of the origin of Logic, and a good analysis of the Organon with criticisms. Among other points, it is worthy of notice that he considers the Aristotelian doctrine of the predicables, given in the Topics, to be preferable to the common account, derived from Porphyry. He highly praises Abelard ; and his testimony is the more valuable, as he himself appears to incline to the doctrines of the Realists". Petrus In the second period of Scholasticism, contemporary * with Albertus Magnus and Thomas Aquinas, is Petrus Hispanus, raised to the papal chair as John XXT. He died in 1277. His Summulce Logicales may be regarded as the earliest scholastic treatise on Logic which professes to be any thing more than an abridgment of or commentary on portions of the Organon. But this work is especially remarkable, as introducing for the first time the memorial verses which form so striking a feature of the Logic of the Schoolmen. Nearly the whole of the ordinary logical mnemonics occur in this treatise, which appears to have had no predecessor, except perhaps the imperfect syllo- gistic mnemonic attributed to Blemmidas, which, even if genuine, was probably unknown to the Author'. The 1 St. Hilaire, vol. ii. p. 215. His opinions in this respect however ai-e douhtful. See Haureau, vol. i. p. 354. * In the first edition, I mentioned the Summulce Logicales as a translation from the Greek of Psellus, This charge has heen made by Keckennann and Buhle ; and the two works certainly correspond ahnost to a word. But from a communication with which I have been favoured by Sir William Hamilton, I am inclined to think that the reverse is the truth ; that the Greek work is in reahty translated from the Latin ; and of course in that case falsely attributed to Psellus. The author of the Summulge appears to have had very httle knowledge of Greek ; and in the only mnemonic which occurs in the Greek sjoiopsis {5ov\ov/xeyaL IXidSes irapvacriov iKTp4xov(ri) , the diphthong would hardly have occmred to an original -vsiiter ; though a natural substitute for the Purpurea Iliace Amabimus EdentuU of the Latin Logicians. Indeed, the name of Psellus appears to have been given on conjectm-e by the editor, Ehinger. Some remarks on this point will be found in the Discussions on Philosophy, by Sir W. Hamilton, p. 126. [See also the 2d Edition of the same work, p. 67J .] INTRODUCTION. XXXV last treatise of the Sunimiilaey, called Purva Logicaliay contains sundry additions to the text of Aristotle, in the form of dissertations on supposition ampliatio, restrictio, ex- pordhle propositions, and other subtleties, more ingenious than useful, and belonging rather to Grammar than to Logic. To these are added notices of some popular sohpisms, worthy of Eubulides or Chrysippus ; which are curious, as shewing that the Scholastic Logic, like the Aristotelian, had its eristic predecessors, whose names the reviving literature of the period has not rescued from oblivion. We now come to the two chief names in the Scholastic Albertus philosophy, Albert of Cologne, surnamed the Great, ^^""^' and his pupil, Thomas Aquinas, known as the Angelic Doctor. These have been called the Plato and Aristotle of Scholasticism ; and, as regards the Theology of the Schools, there is some truth in the comparison. The master was the first to combine into a system of the unconnected reasonings which formed the beginnings of the School Philosophy. The disciple carried out that system in detail, and elaborated its minutest parts ^. As a commentator, Albert was the main instrument in introducing the writings of Aristotle into the Schools; his laborious expositions, however, have been frequently corrupted by Platonic and Arabian glosses ^ His logical works are comprised in commentaries on the Organon, and treatises on Universals and on Definition. Aquinas Aquinas. has left also commentaries on the Hermeneia and Posterior Analytics ; and some independent logical y^. treatises ; the principal one being " Summa totius vJ^ y The original edition of the Summulae is di\ided into two parts ; the abridgment of the Organon and the Parva Logicalia. Subsequent Editors subdivide it into seven treatises. See Haui'eau, vol. ii. p. 241. ^ Encyclopaedia Metropolitana, art. Aquinas, (by Bishop Hampden,) p. 796. * See Haureau, vol. ii. p. 10. ^ XXXVl INTRODUCTION. Logicae," which contains an abstract of the Isagoge of Porphyry and of the first four treatises of the Organon. The Topics and Sophistic Refutations are omitted in this work ; but the latter form the basis of a sejDarate treatise on the Fallacies. He has likewise written Opuscula on Demonstration, on Modals, on the four Opposed Terms, on Genus and Accident, and on the Nature of the Syllogism. The directly logical writings of Aquinas do not materially differ from Aristotle. Logic, however, is defined as scientia rationalis, and the three operations of the reason are brought within its province. Some of the mnemonic formulae occur here, as in Hispanus. Duns John Duns Scotus, the Subtle Doctor, flourished at Scotus. ^i^g g^j Q^ ^^ thirteenth and the beginning of the four- teenth century. He has commented on the Isagoge of Porphyry, under the title of De Universalibtis, and on the several parts of the Organon. In common with Aquinas, he held Logic to be a science ; but maintains that its object is not the three operations of the reason, but the Syllogism^. His commentaries bear out his cognomen; consisting for the most part of minute dis- tinctions, suggested by the text of his author, with argu- ments on both sides precisely stated, and distinctions drawn to the extreme of subtlety. Scotus, like Aquinas, was a Realist, and the more consistent of the two. He held that the universal existed in the individual, not really, as his predecessor had taught, but formally". Hence the rival sects of Thomists and Scotists, the latter of whom ultimately adopted the name of Formalists. Both agreed, however, in opposition to Nominalism. Occam. From the school of Scotus, however, arose the great reviver of Nominalism, William Occam, the Invincible *» Scotus de Univ. Qu. 3. Smiglecii Logica, Disp. ii. Qu. 1. <= On this distinction, see Haureau, vol. ii. p. 335. INTRODUCTION. XXXVU Doctor, the ablest writer in Logic whom the Schools have produced. His doctrine, like that of Abelard, was really Conceptualisrn*^. The Summa totius Logicce of Occam is the most valuable contribution of the middle ages to the Logica docens. If we do not subscribe to the hyperbole of his editor, Mark of Beneventum, w^ho, borrowing from the well-known eulogy of Plato, declares that if the Gods used Logic, it would be the Logic of Occam, we may fairly allow, with M. St. Hilaire, that it is the clearest and most original of the works of that period. Occam, like Petrus Hispanus, departs from the ordinary arrangement of treating consecutively the Isa- goge of Porphyry and the several books of the Organon. He commences with the different divisions of terms, of which his account is much more complete than that of the Summulce Logicales, He then proceeds to the pre- dicables, introduced by a defence of the nominalist view of universals, then to definition, division, and the cate- gories, and concludes the first part with an account of the supposition of terms. The second part treats of propositions, and the third of syllogisms and fallacies. Between Scotus and Occam comes in order of time Raymond the most eccentric genius of the scholastic period, Ray- ^' mond Lully. He is principally known as the author of the Ars Magna, by which he professed to teach a man ignorant even of letters the whole encyclopaedia in the course of three months. This work is nominally logical, but has little in common with the Aristotelian Logic, being principally a mechanical contrivance for connect- ing different philosophical terms with each other®. But in his Dialectica, Lully condescends to follow the beaten track, and has composed a clear and concise ^ See Cousin, Abelard, Introduction, p. civ. *^ St. Hilaire, Memoire, vol. ii. p. 225. d XXXVlll INTRODUCTION. Later School men. synopsis of Logic, framed principally on that of Petnis Hispanus^ The writings of Occam, as well as those of Scotus, con- tributed especially to raise Logic to the rank of a distinct science, independent of its applied uses^. But they approached it from opposite sides. The principles of Occam, developed by modern philosophy, would lead us to the Logic of Kant: those of Scotus, almost to the Logic of Hegel. The science of the former would acquire a clear and distinct object in the province of Thought : that of the latter would gradually absorb all else, as coextensive with Being. Occam is the last great name among the Schoolmen : the triumph of Nominalism involved the downfall of the principal applications of Bmidan. the scholastic method. Buridan, his disciple, the reputed author of the sophism called Asinus Buridani^, deve- loped the doctrines of Nominalism to a still further extent, but has the character of having pushed to an extreme point the subtleties distinctive of the scho- lastic system. Another philosopher of the same period, Walter Burley, is the author of some commentaries on the Logic of Aristotle, and deserves mention as the first compiler of a history of philosophy. This work is entitled, de vita et morihus philosophorum, and forms a biographical history of philosophy from Thales to Seneca'. f An account of Lully's system will be found in Keckermann, Prceeognita, ii. 2. 39. and in Gassendi de Origine Logicce, c. 8. See also Hallam, Literature of Europe, vol. i. p. 310. s Cf. Haureau, vol. ii. p. 310. 425. 447 sqq. St. Hilaii-e, vol. ii. p. 226. M. Haureau appears to regard Scotus as the author of the distinction between the logica docens and utens ; which is not the case. Cf. Aquinas, in iv. Metaph. Lect. 4. Indeed, it is substantially contained in the SiaKeKTiK^ X'*'P^5 irpay/xdrwu and iv xp^^^^i- irpayixdrwv of the Greek Inter- preters. h See Hamilton on Eeid, p. 238. ' Brucker, vol. iii. p. 856. Burley appears to have held a middle course between Nominalism and Realism. See Ham-eau, vol. ii. p. 476. Burley. INTRODUCTION. XXXIX The reaction against the Scholastic Logic began in Early Re- the fifteenth century. Laurentius Valla, Rodolphus Agricola, and Ludovicus Vives, successively attacked the system in 1440, 1516^, and 1531. Their attacks were directed, partly against the Latinity, partly against the matter of the School Logic. The additions proposed by these reformers are chiefly rhetorical innovations from Cicero and Quintilian. A more formidable assault was made in 1543 by Ramus, Ramus. who not only devoted a special work to the criticism of Aristotle^, but, adopting the dialectical and rhetorical innovations of the earlier reformers, composed a new system of Logic in opposition to the Aristotelian. He complains of the want of a definition of Logic in Aristotle, and treats it himself as the Art of Disser- tation ; its principal parts being Invention and Judgment. These he investigates at length in his Dialecticce In- stitutiones and Scliolce Dialecticce, and in his Dia- lectique, the earliest work on the subject in the French language. Invention he treats chiefly rhetorically, giving an account of arguments artificial and inartificial, and loci for establishing them. Argument in Ramus denotes any term of a question, not, as in Cicero, the middle. Of Judgment he admits three degrees, Axiom, (proposition,) Syllogism, and Method. In the earlier editions of his Dialectic he admits the three Aristotelian figures, but afterwards rejects the third. Each figure has six moods, two general (universal), two special (parti- cular), and two proper (singular). Method he divides into Methodus Doctrince, and Methodus Prudentice. He rejects, as extralogical, the Categories, the Hermeneia, i Agricola died in 1485. His three books De Inventione Dialectica were a posthumous work, first published in an imperfect form at Louvain in 1516. ^ Aristotelicee Animadversiones, a title also given to the Scholce Dialecticce. The two works must not be confounded together. d2 xl INTRODUCTION. Melanch- thon. and the Examination of Fallacies. Ramus, as may be seen even from the above cursory notice, introduced many needless alterations in the language of Logic, In his logical innovations, he is partly indebted to Rodolphus Agricola and Joannes Sturmius ; and, for some of his attacks on the Aristotelians, to Valla and Vives\ On the other hand, the Aristotelian Logic, purified of many of its scholastic accessions, was defended and taught by Melanchthon. The earlier editions of his Erotemata Dialectica preceded the attacks of Ramus": but in 1547 he published a new edition, in the intro- duction to which he says, " Ego veram, incorruptam, nativam Dialecticen, qualem et ab Aristotele et aliquot ejus non insulsis interpretibus, ut ab Alexandro Aphro- disiensi et Boethio accepimus, prsedico. . . . Etsi multi Aristotelicos libros vituperant, et tanquam tabulas dis- persas fractse navis esse dicunt, tamen, si quid ego judicare possum, affirmo eos Dialecticen recte tradere, et ab iis, qui liberali doctrina exculti sunt, intelligi posse." Melanchthon however agrees with Ramus, in considering Logic as an Art. " Dialectica," he says, "est ars seu via recte, ordine, et perspicue docendi ; quod fit recte definiendo, dividendo, argumenta vera connectendo, et male cohserentia seu falsa retexendo et refutando." Under their united sanction, this became the prevailing doctrine of Logicians. The authority of Melanchthon established the Aristotelian Logic in the Protestant schools of Germany and Holland, and in Britain. At a later period, a conciliation was attempted between this Later system and that of Ramus. Burgersdyck, in 1626, Logicians, classes the Logicians of his day in three schools, the 1 For a fuller account of Kamus and his system, see Waddington- Kastus, Be Petri Rami Vita, Scriptis, Philosojjhia, Paris, 1848. ra Keckermann Prescognita, Tr. ii. c. v. INTRODUCTION. xli Aristotelians, the Ramists, and the mixed school repre- sented by Keckermann, Aristotelian in matter, Ramist in method". These were called Philippo-Ramists, or Semi-Ramists ; and were rejected by the genuine dis- ciples of Ramus, as Pseudo-Ramists. Among the English Ramists of the seventeenth century, the most learned and important as a Logician is George Downame, Downame. Bishop of Derry, author of a Commentary on the Dia- lectic of Ramus ; but the name most interesting to the general reader is that of John Milton, who published Milton. in 1672, two years before his death, a small volume entitled, " Artis Logicae Plenior Institutio ad Petri Rami Methodum concinnata." It would be impossible to give any thing like a complete history, or even a list, of the host of logical wTiters of the sixteenth and subsequent centuries. A brief account of most of them, down to his own time, will be found in the Prcecognita of Keckermann, published in 1603. A cursory account of the modern schools is all that my present limits will allow. Of the great schools of modern philosophy, down to Modern the time of Kant, it is remarkable, that, though we have ^ no treatise on Logic from the hand of any of the leaders and representatives of the several sects, we find in every case a work of the kind supplied and adapted to their fundamental principles by one or more of their most eminent followers. Bacon, Descartes, and Locke have left no logical writings, and Leibnitz only a few frag- ments. To call the Novum Organum^ or the Discours de la Methode^, or the Conduct of the Understanding, a " Of these, Sanderson says, " Invehimtur ipsi palam in Eameos, lau- dant Peripateticos : sed tamen in Systematibus suis Logicis Ramei magis sunt quam Peripatetici." ° The RegulcB ad directionem inyenii, a posthumous work of Descartes, is sometimes called his Logic. See Hallam, Literature of Europe, vol. ii. p. 454 ; Franck, Histoire de la Logique, p. 250. But Descartes in this work Xlii INTRODUCTION. treatise on Logic, is simply to assume for the Aristotelian Logic a purpose never contemplated by Aristotle or his followers, and then to classify under the same head works pursuing this supposed end by totally diiferent means. To entitle any work to be classed as the Logic of this or that school, it is at least necessary that it should, in common with the Aristotelian Logic, adhere to the syllogistic method, whatever modifications or additions it may derive from the particular school of its author. Li this point of view, the Baconian school may be represented by the Logics of Hobbes and Gassendi; the Cartesian, by those of Clauberg and Arnauld; that of Locke, by Le Clerc and 'S GravesandeP; that of Leibnitz, by Wolf, Baumgarten, and his editor Meyer. Hobbes. The Logic of Hobbes was the natural result of the utilitarian spirit predominant in the method of Bacon. The results, indeed, which Hobbes deduced, would pro- bably in many points have been rejected by his master; but the indirect influence of Bacon is manifest through- out. The end of knowledge, according to Hobbes, is power, and the scope of all speculation is the perform- ance of some action, or thing to be done. In this we recognise the echo of the words of Bacon, " Meta scien- expressly rejects the rules and forms of Logic, as useless for the discovery of truth, and mentions in one place (rule 13.) the only point in which his system has any thing in common with the dialecticians. In fact, this work, though fuller, is in principle the same as the Discours de la Methode. P The sensationalist school of France, professing to be an oflfshoot of that of Locke, has produced more than one treatise nominally on Logic ; the principal ones being those of Condillac and Destutt de Tracy. But these have nothing in common with the Aristotelian system. Condillac regards Logic as an art of thinking, but thought is identified with sensation, and the process of reasoning is nothing but the analysis of our sensations by means of language. Hence his declaration, tout I'art de raisonner se reduit a I'art de Men parler. In the system of De Tracy, Logic is the science of the characteristics and causes of truth and error in the combination of our ideas. His work is strictly psychological, examining, on the extreme sensationalist hypothesis, into the formation of ideas and their different modes of combination. INTRODUCTION. xHu tiarum vera et legitima non alia est quara ut dotetur vita humaiia novis inventis et copiis''." Reasoning, accord- ing to Hobbes, is computation, the adding and sub- tracting of our thoughts and of their signs. A pro- position is but the addition of two names, and a syllogism the adding together of three. In a proposition, two names are so coupled together, that he that speaks conceives both to be names of the same thing ; from whence it follows that truth and falsehood consist only in speech, and that the first truths were arbitrarily made by those who first imposed names on things. A full criticism of this doctrine would exceed my present limits. I can only observe that the main error of Hobbes does not lie, as is sometimes said, in his theory of notions, but in that of judgments. He has overlooked the fact, that apprehension is primarily the analysis of judg- ment, not judgment the synthesis of apprehensions. The Baconian influence is also manifest in Gassendi, Gassendi. the friend of Hobbes and the antagonist of Descartes. Like Hobbes, he describes reasoning as a computation, and he anticipates Condillac in tracing all knowledge to sensation. He adopts the fourfold division of Logic, into Apprehension, Judgment, Reasoning, and Method, which had virtually been invented by Ramus and accepted by the Semi-Ramists, and which was shortly afterwards adopted by the Port Royal Logic. He admits two figures only of Syllogism, an affirmative and a negative, (answering to the affirmative and nega- tive moods of the first figure in Aristotle ;) and it is worthy of remark, that in the order of the premises, he returns to the arrangement of the Greek Logicians, (the reverse ^ Nov. Org. P. 1. Apli. 81. In the same spirit Socrates, according to Xenophon, fxexpt tov w^eAt/U*"' irdura Koi avrhs (rweTr€(TK6ir€i kuI avvSie^'pei roh (Tvvovffiv. Mem. iv. 7. On the influence of Bacon on Hobbes, see Morell, Hist, of Modern Philosophy, vol. i. p. 86. Xliv INTRODUCTION. of tha? of the Latins,) and places the minor before the major. His theory of reduction, by which he brings every syllogism ostensively to his two figures, contains some curious blunders. Clauberg. Clauberg, called by Wolf optimus omnium eonfessione Cartesii interpres"^ , published his Logica Vetus et Nova in 1654. It contains more of Cartesianism even than the Port Royal Logic, and is divided into four parts, Logica Geiietica, Logica Analytica, Hermeneutica Genetica, and Heimeneutica Analytica, The two last parts are a series of rules for interpreting and criticising the writings of others. The second treats of methods of teaching, and the qualifications for a good teacher and learner. The first, or Logic proper, is interspersed with numerous psychological precepts, chiefly taken from the Discours de la Methode of Descartes. Many of his examples are also taken from the Cartesian philosophy. His rules for induction are fuller than in the old Logic, and those of syllogism shorter. Port Eoyal The Port Royal Logic, or Art of Thinking, is con- sidered as the Logic par excellence of the Cartesian school. This work has been attributed to several authors ; but is now generally allowed to have been written by x4rnauld, assisted by Nicole. The first edition appeared in 1662. In addition to the logical merits of this work', the elegance and simplicity of its style contributed immensely to spread and popularize doctrines which had hitherto been reserved for the study of the learned in the dry formulas of the schools *. The authors, however, must be admitted to have sacrificed in some degree scientific accuracy to popularity ; and r Ontologia, §. 7. * For an account of the scientific merits of the Port Eoyal Logic, see the Introduction to Mr. Baynes's Translation, p. xxix. ' St. Hilaire, vol. ii. p. 271. INTRODUCTION. xlv in their attempt to convey miscellaneous instruction in logical examples, they have unfortunately given their high authority to the support of that spurious utili- tarianism which has so often defaced the simplicity of logical science. Father Buffier is also entitled to honourable mention Buffier. among the French Logicians. In his Priyicipes du Raisonnement, the rules of the syllogism are reduced to a single principle, that which is in the co7itained is in the containing. This formula, an important step towards the true law of syllogism, the Principle of Identity, is perhaps originally due to Leibnitz". Buffier has had the good fortune to receive high praise from two very opposite quarters, and on very different grounds. He has been celebrated, on the one hand, as one of the earliest who attempted to found philosophy on certain primary truths, given in certain primary sentiments or feelings ; and, on the other hand, as having advanced some important steps in the direction of the sensa- tionalism of Condillac\ Le Clerc, (Joannes Clericus,) the friend and disciple Le Clerc. of Locke, published his Logic in 1692, three years after the first edition of Locke's Essay, of which he had previously seen the Epitome. This work is principally based on the views of Locke, with some additions from the Port Royal Logic, and the Recherche de la Verite of Malebranche. The fourth book, on Argumentation, does not materially differ from the Aristotelian view ; though, like Locke, he has not a high opinion of the syllogism, and considers it to be mainly an instrument of disputation. He adds a chapter on the Socratic method of discussion, which he considers more valuable « See. St. Hilaire, vol. ii. p. 274. ^ See Hamilton on Eeid, p. 786. and Destutt-Tracy, -E/emens d' Ideologic, P. iii. p. 130. Xlvi INTRODUCTION. than the Aristotelian syllogism. The Logic and Meta- 'S Grave- phvsics of 'S Gravesande, published in 1736, is highly sande. praised by M. St. Hilaire, as simplifying with great clearness the ancient Logic, in connection with the principles of Locke. The doctrines of Locke, modified by Cartesianism, had also considerable influence on the Watts. Logic of Watts, in which a somewhat incongruous union of Logic, Metaphysics, Psychology, and Educational Pre- cepts is put forth as the Art of using Reason well in our inquiries after truth, and the communication of it to others. Equally vague in its conception and unsystematic in its Bentham. contents is the fragment on Logic by Jeremy Bentham. According to his definition. Logic is " the art which has for its object or end in view, the giving, to the best advantage, direction to the human mind, and thence to the human frame, in its pursuit of any object or purpose to the attainment of which it is capable of being applied." In the same spirit as Hobbes, he considers Logic from the utilitarian point of view, as a means to the augment- ation of happiness. But the treatise, except as regards some severe and by no means just criticisms of San- derson, has little in common with the Aristotelian system. A more just and philosophical view of Logic will be Kirwan. found in the works of another English writer. Dr. Kirwan, whose " Logic, an Essay on the elements, principles, and different modes of Reasoning," was published in 1807. Dr. Kirwan deserves honourable mention as one who has profited by, without servilely following, the teaching of Locke. While adopting much that is valuable in the writings of Locke and his successors, particularly Berkeley and Condillac, he has ably defended the Aristotelian Logic against the depreciating criticisms of Locke and his followers. He has however taken too narrow a view of the field of Logic, in confining it to the single process of Argumentation, in which, as well as in INTRODUCTION. xlvii his definition of it as both a Science and an Art, he has been followed by Archbishop Whately ; while, on the other hand, his treatment of the argumentative process contains much which from the formal point of view must be condemned as extralogical. The most important work on Logic from the school Wolf. of Leibnitz is the Philosophia Rationalis of Wolf, first published in 1728. Wolf is regarded by Kant as the representative of the dogmatic philosophy. Philosophy with Wolf is the science of things possible, so far as they are possible, and contains three principal branches. Theology, Psychology, and Physics. The criterion of the possible is the principle of contradiction. Whatever is not contradictory is possible". Logic directs the mind in the knowledge of all being ; its principles being drawn on the one side from Ontology, on the other from Psychology. The Logica Docens is defined by Wolf as a Practical Science ; the Logica Utens as an Art; the former being acquired by teaching, the latter by practice. The details of Wolf's Logic are principally Aristotelian, with one or two ingenious but perverse refinements. Thus, he reduces subaltern opposition to a syllogism with an identical minor premise, and all immediate consequences to abridged hypothetical syl- logisms. Induction he regards, like Archbishop Whately, as a s3dlogism with the major premise suppressed. Wolf is also the author of a smaller Logic in German, of which there is a good English translation, published in 1770. To the same school as Wolf belong Baumgarten and Baum- Meyer. Baumgarten is highly praised by Kant for his Meyer! concentration of the Wolfian system. An annotated copy of Meyer's Logic is the foundation of that of Kant himselfy. '^ On this criterion, see Hamilton on Reid, p. 377. y See the Preface to Rosenkranz's edition of Kant's Logic. Xlviii INTRODUCTION. Lambert. Lambert, whose Neues Organon appeared in 1764, may be regarded as uniting in a great measure the doctrines of the antagonist schools of Locke and Leibnitz, and as the precursor of the Critique of Kant. His system is divided into four principal parts, contributing conjointly to the investigation and communication of truth : Dianoiology, or the doctrine of the laws and power of the understanding in thought ; Alethiology, or the doctrine of truth as opposed to error; Semiotic, or the doctrine of signs and their influence to the know- ledge of truth ; and Phenomenology, or the doctrine of false appearances and the means of avoiding them. In his first part, he principally follows Wolf, but differs from him in his view of the Syllogistic figures ; the three last figures being regarded as resting on inde- pendent axioms, coordinate with the dictum de omni et nullo. These axioms are distinguished as dictum de diverse, dictum de exemplo, and dictum de reciproco. In his second part, which treats of simple and complex notions, and of truth and error, Lambert acknowledges his obligations to Locke. Li the third, the theory of language and its relation to thought is treated with considerable fulness. The fourth part, which treats of appearance as distinguished from reality, has more of a metaphysical and psychological than of a logical character, with some mixture of physiology. Ploucquet. Another German Logician who deserves mention, not so much for the importance as for the eccentricity of his views, is Godfrey Ploucquet of Tubingen, a con- temporary of Lambert's, the author in 1768 of a " Me- thodus calculandi in Logicis," afterwards included with other writings in his " Commentationes Philosophicae selectiores," published in 1781. Ploucquet's work is re- markable as an attempt to exhibit the reasonings of Logic in the form of an algebraical calculus, an attempt recently INTRODUCTION. xllX carried out to a greater extent by the " Neue Darstellung der Logik" of Drobisch, and in the logical writings of Professors De Morgan and Boole. A severe criticism of the principle of Ploucquet's Calculus will be found in Hegel's Logic, vol. ii. p. 143. The geometrical illus- trations of the syllogism by Euler and Lambert are not of sufficient importance to require a separate notice. An account of these, as well as of Ploucquet's system, is given in the Appendix to Professor De Morgan's " Formal Logic," p. 323. Kant has done more for logical science than any Kant, philosopher since Aristotle; partly in his distinct treatise on the subject, and still more in the exact examination of the forms and functions and limits of thought which runs through the Critique of Pure Reason. To Kant is owing, what has been so long needed, a definition of Logic, which secures for it a distinct and positive field of inquiry, as the Science of the Necessary Laws of Thought. Kant also did great service in banishing to a separate region, under the name of Applied Logic, the psychological precepts which his predecessors, especially the Cartesians, had incorporated with the body of the science, and giving thereby to formal thought its proper position as the object of Pure Logic. His demonstration that an universal material criterion of truth is not only impossible, but self-con- tradictory % has furnished us with the principle of a more liberal and enlightened appreciation of the real character and value of formal thinking than can be supplied by the whole previous history of philosophy. At the same time, it must be admitted that the logical system of Kant is chargeable with one serious deficiency, which has been prominently shewn in the subsequent * Logik, Einleitmig, vii. 1 INTRODUCTION. history of the science. He divorces altogether his d priori science from all connection with the psycho- logical phenomena of consciousness, from all examination of the actual characteristics of any determinate operation of thought^ These matters he rejects as empirical; but without such empiricism, Logic and all pure science is impossible. It is matter of each man's personal experi- ence that he actually thinks; and, without examination of the phenomena of special acts of thought, it is impossible to ascertain the necessary laws of thought in general^. Logic and Psychology thus necessarily form portions of one and the same philosophical course, and, without a knowledge of the latter, it is impossible to have any sound criticism or accurate estimate of the former. Later The writings of Kant have had immense influence on LoSSns. *^^ subsequent Logic of Germany. It is true that the two greatest of his immediate successors, Fichte and Schelling, have produced no direct logical work ; and have openly expressed their low estimate of the sciences But a host of able writers have notwithstanding arisen, as numerous as the Logicians of the sixteenth and seven- teenth centuries, to promulgate, to correct, or to oppose the Kantian Logic. Some of these, as HofFbauer and Kiesewetter, adhere for the most part to the Kantian limits. Others, as Krug and Fries, are mainly Kantian, though they have materially enriched the science from their own resources ; and the latter has especially noticed the want of a psychological relation, as the main defect * See Kritik der r. V. p. 58, 276. ed. Eosenkranz. ^ Cf. Cousin, Lemons sur Kant, p. 180. c FicMe, in his " Vorlesungen ueber das Verhaltniss der Logik zur Philosophie," altogether repudiates the ordinary Logic to make way for a transcendental system, and complains that this was not sufficiently done by Kant. Schelling in his " Bruno" holds the same view. " Welche Hoff- nung zur Philosophie fiir den, welcher sie in der Logik sucht ? Keine." INTRODUCTION. ll of Kant's system. The most eminent name among the strictly formal Logicians since Kant is Herbart ; but both he and his disciple Drobisch have pushed to an extreme Kant's error in an exclusively a priori view of the science. On the other hand, the Logic of Hegel reconstructs from Hegel. the opposite side the metaphysical fabric which Kant had overthrown. After the Kantian Critique, it was impossible to bring a philosophy of the Absolute within the received compass of Jiuman thought : there remained only the attempt to expand thought to the immensity of the object, by a gigantic scheme of Intel- lectual Pantheism, in which the personal consciousness and its limits should be absorbed in the processes of the one Infinite Mind. Such is the fundamental principle of the Logic of Hegel, a Logic constructed, not in obe- dience to, but in defiance of, the laws of thought, which are held to be valid only for the finite understanding dealing with finite objects; the philosophy of the infinite being based on their abrogation. It is not easy to give in a short compass an account of Hegel's Logic, which shall be intelligible to an English reader. If we were to describe it as an attempt to develope a Philosophy of Being in general, by repro- ducing the Divine Thought in the act of Creation, we might support the view by sufficient quotations from the work ; but it would convey an erroneous impression to one who did not bear in mind the total suppression of personality, divine as well as human, in the Hegelian philosophy. It may perhaps be better characterized as an illegitimate expansion of the fundamental principle of the Cartesian philosophy, modified in some degree by the Kantian. " Cogito, ergo sum" is true within the limits of the personal consciousness. I exist only in so far as I am conscious of my existence ; and I am conscious Hi INTRODUCTION. only as being affected in this or that determinate manner. Within these limits Thought and Being are identical, and every modification of the one is a modification of the other. But if the same principle is to be accepted in its Hegelian extent, 1 must commence by ascending from my per- sonal consciousness to a supposed Universal Thought, identical with Being in general. Here personality dis- appears altogether ; and the problem is, to deduce from the identity of Thought and Being in general, the several identical determinations of the one and the other. Such a process is not thought but its negation. If the Uni- verse had one consciousness, the system might be possible ; for Thought and Being are identical only in and through consciousness. But such universal con- sciousness could not be my consciousness ; and thus the Hegelian assumption cannot be grasped by any act of human thought. On the other hand, thought without consciousness is inconceivable ; since it implies a ne- gation of the one essential characteristic under which all thought is presented to the human mind. The logical notion which is not a function of my own personal thought, is a mere empty abstraction, inconceivable by reason; and the system deduced from it is incompatible with those regulative truths that are above reason. Vulgar Rationalism subjects belief to thought; it has been reserved for Transcendental Philosophy to subject it to the annihilation of thought. Speculative philosophy has had three great periods, each of which has been consummated by a critical system of which Formal Logic has been a constituent portion. The Eleatic and Platonic metaphysics found their consummation in Aristotle ; the Scholastic Philo- sophy in Occam; that of the seventeenth and eighteenth centuries in Kant. But from the Kantian philosophy has arisen another phase of speculation, not less dogmatic INTRODUCTION. liii in its positions, not less extravagant in its aims, not less unstable in its foundations. A criticism which shall sift thoroughly the pretensions of this philosophy, it remains for the present generation to accomplish. PART II. CRITICAL. " That Logic," says Kant, " has even from the earliest /<-'^-^< times advanced in the sure course of a science, is manifest ^^ ii^"' from the fact that since Aristotle it has taken no back- '^""-!Z— / ward step." " It is worthy of remark however," he con- ^^ ' ' tinues, " that it has also up to this time been able to take no step forward, and thus to al] appearance seems i to be concluded and perfected." This remark is true as regards what Aristotle did ; but on the other hand, as regards what Aristotle left undone, it is no less true that the whole subsequent history of the science exhibits scarcely any thing but the ebb and flow of unsettled opinion. The master left behind him a collection of writings; and to the substance of that collection his \ disciples have, for the most part, faithfully adhered ; but he left no definition of the science on which he wrote, and no principle for determining its boundaries ; and these accordingly have been matter of controversy ever since. Clitomachus compared the Logic of his day to the j^^^^--*-*^^**' moon, which never ceases waxing and waning". The ^^ €Z-^ /(^<^■ Melanchthon. ' Bentham. t Burgersdyck, Sanderson, Aldrich. INTRODUCTION. Iv Let US endeavour to disentangle some of the confusion in which the reader may be involved by this multitude of definitions. Logic was divided by the Schoolmen into the Logica docens and the Logica uteris, and the same division had been made before by the Greek Com- mentators, under the title of Logic without and with application to things'". The former denotes Logic in its theoretical character, as concerned merely with the laws and forms of thought; the latter is the practical appli- cation of thought to this or that object matter. The discrepancies in the definition of Logic, as Science or Art, may partly be traced to a confusion between these two. The Logica docens is properly a Science and not an<^ u<-^^* c^c:^^^^ ^ Art. It is not correct to say, as has frequently been •^'-**^^ ' <^^^-^ said or implied by modern Logicians, that every Science is an Art, because all knowledge admits of a practical application. "The truth is," says Bentham, "that how- soever clearly distinguishable in idea, the two objects, Art and Science, in themselves are not, in any instance, found separate. In no place is any thing to he done, but in the same place there is something to he known; in no place is anj' thing to l)e known, but in the same place there is something to be done." The terms thus extended are too vague to be of any value, and tend to " " Intelligendum est tamen quod Logica dupliciter consideratur. Uno modo in quantum est docens, et sic ex necessariis et propriis principiis procedit ad necessarias conclusiones, et sic est scientia. Alio modo in quantum utimur ea applicando earn ad ilia in quibus est usus, et sic non est ex propriis, sed ex communibus ; nee sic est scientia." Scotus, super Univ Porph. Qu. 1. "Est Logica docens, quae tradit praecepta, quibus docetur quid, quomodo faciendum : utens vero est, quae ex praeceptis eflficit opera ipsis conformia, sicut cum artifex ex praeceptis artis eflficit opera artis." Smiglecii Logica, Disp. ii. Qu. vi. For the parallel distinction between Logic without and wdth application to things, (x^pis TrpayixdrMUy crvfifiifiaCofifurf ro7s irpdyixaaiv, iv xP'h^^'- ''"^ yvfxvacrla trpayfidTCDV,) see Ammonius, Prooem. in Categ. Philoponus, Prooom. in Anal. Prior. e 2 Ivi INTRODUCTION. confuse rather than to distinguish. Science is not Art, though scientific knowledge may be the basis of artistic. A Science admits of a practical employment under certain conditions; but it does not become an Art until those conditions are complied with, and it may exist as a Science without them. The ordinary distinction between the man of theory and the man of practice is a proof of this. A man may have a scientific knowledge of music, and yet have no power of playing on any instrument. He may be acquainted with the principles of perspective, without any skill in the use of the pencil. He may know the mathematical principles of Optics, and yet be sadly at a loss if required to make a pair of spectacles. He may have studied the anatomy of the human frame, and yet be unable to perform a surgical operation. He may talk like a Curius, and live like a Bacchanal. And in like manner, he may be familiar with Barbara, Celarent, and Barali'pton, but in practice be a weak and inconclusive reasoner. On the other hand, he may possess Art without Science, that is to say, he may have considerable dexterity in the practice of any operation, without being able to give a clear account of the principles on which it is conducted. Science is no more Art because the man of science may become an artist, than a boy is a man because he may grow up into one. Nay, far less so; for the boy becomes a man in the course of nature, without any effort of his own ; while the man of theory may remain a man of theory all his life, without ever learning to apply his knowledge to practice. '^ /c^c<^?y/,^ When we are asked. What is Logic? it is clearly '/^-^^^f ^^^^--^^^QQ^^l^ What is the object of which books on Logic treat. No treatise on Logic can give all its practical applications. It can at best select only a few speci- mens, and these by way of example, not as an essential INTRODUCTION. Ivii part of the theory. But it professes to give, and is bound to give, the entire principles of reasoning, or rather of thinking in general, even though it illustrates its teaching by no other examples than algebraical symbols. A treatise on Logic is not designed primarily to give men facility in the practice of reasoning, any more than a treatise on Optics is intended to improve their sight ; and it would be as correct for a writer on the mathematical principles of Optics to entitle his work, Optics, or the art of improving defective vision," as it is for a writer on the principles of Logic to adopt for his title, " Logic, or the art of reasoning." Yet we do not therefore deny that a knowledge of Optics is useful in making spectacles, nor that a knowledge of Logic is valuable in the practice of reasoning. Art, in the strict sense of the term, is acquired by practice, Science by study". A man who has learnt to reason accurately by practice in special cases, without a knowledge of the laws of the syllogism, has the art of reasoning, but not the science. He who knows the theory, but does not practise it, has the science of reasoning, but not the art. The Logic to be found in treatises on the subject, i. e. the Logica docens^ is thus clearly a science and not an art ; for it is gained by study and not by exercise. But there is a further ^\^-, ^^ o^iZi.iUZ^ tinction between speculative and practical science, sJic d^<'/^f-^iZic. according as the knowledge which it conveys is con- ^^dJ^a^AA / •"^ See Wolf, Philosophia Ratlonalis, Proleg . §. 10. " Omnis Logica utens est habitus, qui proprio exercitio comparatur, minima autem discendo acquiritur, adeoque at ipsa docai'i nequit. Quamobrem, cum Logica omnis sit vel docans vel utens, neque euim prsetar regularum notitiam atque habitum aas ad praxin transfarandi tertium concipi potest; sola Logica artificialis docans ea est qu*. doceri adeoque in numerum disci- plinarum philosophicarum referri potest. Atque ideo quoqua Logicam definivimus per sciantiam, minime autem per artem vel habitum in genera, quod genus convenit Logicse utenti." Iviii INTRODUCTION. sidered as an end in itself, or only as a means to be applied to some further purpose''. And here again, Logicians of eminence, who are agreed as to the genus of Logic, are at issue as to its species. Granted that Logic is a science, is it speculative or practical ? Wolf, the ablest of the German writers on Logic before Kant, while distinguishing accurately between Science and Art, regards Logic as belonging to the practical, not to the speculative sciences, the knowledge which it fur- nishes being subservient to the discipline of the mind ' /^.t./^*--^^^ ^^^ ^^ acquisition of further truths. Accordingly fa.t^s'ua^ /fi^'^^^^^^Q defines Logic as " Scientia dirigendi facultatem cog- noscitivam in cognoscenda veritate^" On the other r^^^-T'^'^^^^ hand, Kant, who defines Logic as " the Science of the ^e^Uc^^L^^^-^' necessary laws of the Understanding and the Reason," considers and treats it as speculative"*, and the same view is well maintained by the excellent French trans- lator of the Organon, M. St. Hilaire, whose language may be quoted as an accurate and admirably expressed statement of the true purpose of Logic and the spirit in which it should be studied. " Sans la logique, I'esprit de I'homme pent admirablement agir, admirablement raisonner; mais sans elle, il ne se connait pas tout entier : il ignore I'une de ses parties les plus belles et les plus fecondes. La logique la lui fait connaitre. Voila son utilite: elle ne pent pas en avoir d'autre^." , CZ<-^^^(^jr£y^-^ That this latter is the true view is manifest, as soon as y^^'v^^ we distinguish accurately between the essential con- • ,t:^L^eC.^^^t£^'aZl ^ Arist. Metaph. A minor, c. 1. 'OpOws S' ex^i Kcd rh KaK^lffOai t^v (piKo- <^< " ^ /fc^^ ■£^<^^^-'^^4ro(plav iirt.ffT'fiixTjv rrjs aXTjOeias, ©euprjTiKrjs fihv yhp Te\os oA^^eta, irpo/CTtKTjs „^,t^_/ ^ ,{^2^3=wX/ ^ Philosophia Rationalis, §.61. This was also the opinion of Occam and W, i^^'^ ^ ^^^^^Lt^thers. See -^ *^^^-^ entirely conversant about languat/e ; adding, " If any process of reasoning pTa «-♦/ i^ ^a~t can take place in the mind, without any employment f language, orally or mentally, (a metaphysical question which I shall not here discuss,) such a process does not come within the province of the science here treated of." That language in its most extended sense, i. e. some system of signs, verbal or other, is essential not merely to the communication, but to the formation of thought, appears to be proved by universal expe- rience and by the character of conceptions as distinguished from in- tuitions. But notwithstanding this, language must be regarded only as the secondary and accidental object of Logic, which is primarily conversant about the laws of thought, not about the instrument by which it is formed or communicated. And if any process of human thought were possible without language, (which Archbishop Whately appears to consider as at least conceivably true,) the laws of such a process would, equally with any other, be matters of logical investigation. On the question of the relation of language to thought, see Prolegomena Logica, p. 15. <■ Edinhiirgh Review, No. 115, p. 206. reprinted in his Discussions, p. 135. y Ixii INTRODUCTION. elusive, by the immense majority even of the Peripatetic dialecticians ; and not a single reason has been alleged by Dr. Whately to induce us to waver in our belief, that the laws of thought ^ and not the laws of reasoning, con- stitute the adequate object of the science." " The error," continues Sir W. Hamilton, " would be of comparatively little consequence, did it not induce a perfunctory consideration of the laws of those faculties of thought; these being viewed as only subsidiary to the process of reasoning." Of the truth of this charge there can be no question. A student might read through nearly every one of the popular treatises on Logic, without finding the slightest hint of the fact, that in the processes of conception and judgment, as well as in that of reasoning, there is a distinction to be made between the form of the thought and the matter, the former being equally in all three processes accurately and completely determinable by logical rules ; the latter being equally in all three beyond the domain of the science. A thought may violate its own laws, and thus virtually destroy itself; or it may be perfectly consistent with itself, but at variance with the facts of experience. The result in the one case is a product logically ille- gitimate, or the unthinkable i in the other the empirically illegitimate, or unreal. In both cases alike the mind is supposed to be already in possession of the necessary data for thinking at all. Where there is a material deficiency in the conditions preliminary to an act of thought, we cannot be said to think logically or illogically; for we cannot attempt to think at all. Thus, if we are told to conceive objects which have never been presented in their proper experience, a colour for instance which we have never seen, or a scent which we have never smelt; or if we are required to form a judgment, other than iden- INTRODUCTION. Ixui tical, with less than two concepts, or a syllogism with less than two premises, we are in the position of a builder without materials, who can neither obey nor disobey the rules of architecture. In every art or science, in every inquiry speculative or practical, the existence of the objects of inquiry is presupposed. The astronomer is not required to create the heavens, nor the grammarian to supply rules of speech to the mute fishes, nor the logician to analyse the laws of thought where no act of thought can be attempted. Thought is representative ; its primary materials are /2 l^^czi^ c/<^ presentations, either of the external or the internal sense, r" '^^ '^f *' '^r In the product of any act of thought, it is necessary to ^^^»„.w^^ . distinguish between the matter and the forrfi. The former is all that is given out of and prior to the thinking act; the latter is all that is conveyed in and by the act itself". To conception are given attributes ; to judgment are given concepts ; to reasoning are given judgments. By the act of conceiving, the attributes are thought as representing one or more objects ; by the act of judging, the concepts are thought as related to one or more common objects; by the act of reasoning, the judgments are thought as necessitating another judgment as their consequence. The thinking process itself may also be distinguished ai'^'-^Uirt as material or formal. It is formal when the matter 7' given is sufficient for the completion of the product, without any other addition than what is communicated in the act of thought itself. It is material when the data are insufficient and the mind has consequently to go out of the thinking act to obtain additional materials. If, for example, having given to me the attributes A, B, C, 8 Cf. Hoffbauer, Logik, §.11. " Materie des Denkens sind Vorstellungen, aus welchen Gedanken erzeugt werden konnen, und die Form des Denkens ist die Art und Weise, wie dieses geschieht." Ixiv INTRODUCTION. I can think those attributes as coexisting in an object, without appealing to experience to discover what objects actually possess them, this is formal conceiving. If, having given to me the concepts P and Q, I can pro- nounce "P is Q," or *'P is not Q," without a similar appeal, this is formal judging. If, having given to me the judgments " W is X," " Y is Z," I can elicit a con- clusion from them alone, this is formal reasoning. The term experience is here used in a wide sense, for all accidental knowledge, all that is not part and parcel of the thinking act itself. '^^^ca^-^lIi-j/C^- One condition of formal conceiving is, that the attri- '^c-^Cc^^ . ^ butes given must not contradict one another. There is no contradiction between the notions of a horse's body and a man's head. A centaur therefore is as ■ conceivable as a man or a horse, whether such a creature exists in nature or not. But if we try to conceive a surface both black and white in the same portion, the attempt to individualize the attributes by applying them to an object shews at once their incom- patibility. Such a combination of attributes is incapable of representing any possible object. Hence we have a law of thought, or condition of logical possibility; namely, that whatever is contradictory is inconceivable. This is the well-known Principle of Contradiction, the most general expression of which is, " nothing can be A and not A," or "no object can be conceived under contra- dictory attributes." J;!:^l_f:7*'^ '^ Another law of thought may be derived from the fact J ' . that all thought is representative of possible objects of I intuition^. Hence, whatever limits our constitution im- poses a 'priori on the presentations of intuition, the same limits hold good of the representations of thought. Now ^ On the meaning of the term intuition, as distinguished from thought, see below, p. 2, notes o and d. 'i fit^^-i^ciCu^ m-'f*^ INTRODUCTION. Ixv intuition is possible only under the condition of limit- ation by differences. An object of intuition, as such, possesses definite characteristics, by Tvhich it is marked off and distinguished from all others : otherwise it would not be an object, but the universe of all objects. In the act of conception, therefore, when we regard certain given attributes as constituting an object, we conceive it as thereby limited and separated from all other objects, as being itself o^ndi nothing else. The indefinite ideas, therefore, corresponding to the general terms, Thing, Object, Being in general, are not concepts, as con- taining no distinctive attributes; and the general object denoted by such terms is inconceivable. This law of thought is expressed by the Principle of Identity, " Every A is A," or " Every object of thought is con- ceived as itself." Attributes which comply with these law^s are logicallynL Ci.^ f^/'^^ ^^ conceivable; but for an act of material conception, or ^ - ^/ rather of conception combined wdth perception or / / memory, more than this is required. A centaur, as has before been observed, is logically as conceivable as a horse ; and, as mere thoughts, one is as legitimate as the other. But the senses or other evidence must further assure me of the reality of the objects, before I can think of either horse or centaur as having any existence out of my imagination. This assurance is not the result of a law of thought, but of a fact of perception. Hence as a general rule : all imaginary objects are conceived as such formally ; all real objects are conceived as such materially, that is to say, not by an act of pure con- ception, but by uniting that act with the presence or remembrance of other sources of information. Formal judging is possible, affirmatively, whenever^w^^^^t^-^' one of the given concepts is contained in the other ;/^^^^^^;;2^ negatively, whenever one of them contradicts the other. u-iiUiXZ. Ixvi INTRODUCTION. If the concepts P and Q have no attributes in common or contradicting each other, I cannot determine whether they coexist in any object without an appeal to expe- rience ; but if Q contains the attributes O, P, I can by a law of thought alone determine that all Q is P, or if Q contain an attribute contradictory of P, I can in like manner determine that no Q is P. The Laws of Identity and Contradiction are here again called into operation. Hence as a general rule: all analytical judging is formal; all synthetical judging is material. Formal reasoning is possible when the given judgments are connected by a middle terra under such conditions of quantity and quality that the mere act of thought necessarily elicits the conclusion. If any addition to the data is required, the consequence is material. Purely formal mediate reasoning or syllogism is de- pendent on the same laws as formal judging, the Law of Identity governing the affirmative categorical syllo- gism and the Law of Contradiction the negative^; while J". ^ the subordinate Law of Excluded Middle is called into J; operation in the immediate inferences of Opposition and Conversion^ A single example must suffice. In a syllogism in Barbara we reason in this form. " All A is [some] B, all C is [some] A, therefore all C is [some] B." The law which determines the conclusion is, that whatever is identical with a portion of A is identical with a portion of that which is identical with all A. Here is again the Principle of Identity. "Every portion of a concept is identical with itself." The other forms of syllogism may easily be analysed in the same manner. " Hypothetical and Disjunctive judgments and reasonings are omitted, as being either extralogical or reducible to Categorical form. See this question discussed in the Appendix, Note I. J See Prolegomena Logica, p. 200. INTRODUCTION. Ixvii The critical province of Logic is coextensive with the v^*^ /^HceJ^ constructive. As the logician can form concepts, judg- f"^ ments, reasonings, in a certain manner from certain data, so he is competent to examine all that is or pro- fesses to be formed in like manner from like data. To distinguish the apparent from the real is the purpose of logical criticism "": that which presents no false ap- pearance is beyond its field. If a thought professes to be based solely on formal grounds, to be guaranteed as legitimate by the laws of thought alone. Logic is competent to examine and decide upon its pretensions. If it professes to rest in any degree on extralogical foundations, on a sensible experience for example, or on suppressed premises. Logic neither accepts nor rejects its claims to a material validity, but dismisses it to be tried before another tribunal. Accordingly, when Logic is defined to be the science of the laws of formal thinking, or the science of the laws of thought as thought, (not as modified by experience,) it follows that it can adequately determine the cone eiv ability of an object, the truth or falsehood of an analytical judgment, or the validity of Q> professedly formal reo^^onmg, in which the given premises are stated as the complete conditions of the conclusion. On the other hand, it cannot determine the real existence of an object, the truth or falsehood of a synthetical judg- ment, or the validity of a reasoning professedly material, in which the premises are given as a part only of the conditions of the conclusion. Formal thinking can be called into operation by itself. Material thinking can only operate in conjunction with an act of perception or memory J and the laws of thought alone are no guarantee ^ Arist. Soph. Elench. c. 11. 'H 70^ ireipaaTiKri icrri SiaKcKTiKT} ris koI dewpel oil Thv elSdra aWa rhv ayvoovvra koX irpocriroiovfxeuou. 'O ixeu oZv Karh rh irpayfjLa d^wpcov to Koiua 5ia\e/CTtKds, 6 Se tovto tpaiyofxevus iroiwu (T0(f>l(rTlK6s. Ixviii INTRODUCTION. for the trustworthiness of the concomitant process. It is of course open to any innovator to attempt to extend the boundaries of the science by material additions ; but he does so in the teeth of Kant's demonstration, that a criterion of material truth is not only impossible, but self-contradictory. In attempting to enlarge the field of Logic, he only makes it impossible to assign to it any definite field whatever. If a single intruder is admitted from the province of material knowledge, no barrier can be devised which shall not with equal facility • A S^^^ access to all. e/--^^:Ca^^/. ^"^ ^^^ grouud objcctious may be taken against the ^lu^s^-«^^^^fe^ Logic is to investigate the laws under which the subject ^^^ifif'--^ 4--^-^^ / thinks; the purpose of the Baconian Logic is to inves-^V*^ cr&y^C'^, ^( tigate the laws under which the phenomena of the object f~^ ^ ^ ^^:a^^ take place"". They are thus respectively occupied with *- i^«^'^<«^'^<^'^/ * the two opposite poles of human knowledge, the ego and ^^^//^^2T^ ^ the non ego. The questions of the former are to be an- ^^^.,^,^.*>^V^^ ^ swered by an examination of the internal consciousness ; Ce^^^i^*>--^-€j- ^ ch the questions of the latter by an examination of external ^^'^^"''^ /^/^ nature. The two systems are thus diametrically opposed y^ ''^^^j/*^'^^'^' .. to each other in their objects. In the second place : the^^^ '"^ ' Aristotelian laws are laws of thought as it ought to he, . ^ ^<.^<^ The Baconian laws are laws of nature as it is, Thev- ^cr-^.>^ > former are principles resting upon their own evidence ;/j-'^^--/^-«^^. certain ct priori as laws, whether actually complied with or not; approving themselves to consciousness the instant they are enunciated; and irreversible in thought, because thought itself is under their control. The latter are laws resting upon the evidence of the facts to which they relate ; valid only in so far as they are actually complied with ; and ceasing to be laws at all, the instant that an ex- ception to them is discovered. And, however universally true in nature, they are always reversible in thought; for prior to their discovery we had no reason to think of them at all, and afterwards we have only to discard an adventitious knowledge. The two systems are thus dis- tinct in their evidence; the opposite of the one being the mentally inconceivable, that of the other the physically impossible. In the third place: in the applications of the Aristotelian Logic we proceed from the law to the facts, constructing types of reasoning according to given prin- ™ See Sir W. Hamilton, Beid's Works, p. 712. f IXX INTRODUCTION. eiples, and accepting or rejecting all actual cases, ac- cording as they do or do not exemplify the law. In the applications of the Baconian Logic we proceed from the facts to the law, accepting as genuine all that actually occurs, and rejecting every law that does not account for the facts. The two systems are thus opposed in their methods. 'Cc^<^i^ /- 1^. e^^ On account of these differences, the fundamental z»^ c^yjiJ^rtT^^po^^^P^^o^^ of the two systems cannot be expressed gxi:_<,, /t. 6fc„ i^ tjie same terms without ambiguity. Law in the : .,_^.^ «*^ ^^^^r'^^Aristotelian system implies a consciousness of obli- ^^^^^ /^^j^5^-^^^:gation, which exists whether realised or not in practice. '■ Law in the Baconian system means an uniform se- ^ quence, which exists only as it is realised in practice. In the field of nature, the conceptions of cause and effect imply no more than the antecedent and consequent phe- nomenon. In the field of thought, the cause is the con- sciously productive self, the effects, the thoughts which by its own power and under its own laws it produces. Necessity in the one case denotes what invariably is ; in the other, what cannot but be thought. In short, there is hardly a term in the one which can be transferred to the other, except by analogy. In all that is phenomenal, the facts of the philosophy of matter can only be applied by imperfect analogy to the philosophy of mind. In all that is real, the facts of the philosophy of mind can only by imperfect analogy be made use of in the philosophy of matter. The Aristotelian Logic, like Mathematics and Moral Philosophy, is constructed a priori from con- ceptions; and its principles and conclusions are pri- marily true of the conceptions, secondarily only of actual objects, on the supposition that they conform to the conceived model. The type of perfect reasoning is the same, though there may not be such a thing as a perfect reasoner in the world ; just as the standard of morality INTRODUCTION. Ixxi is the same, though no man is morally perfect, and as the demonstrations of Geometry hold good of conceived figures, though such figures in their mathematical exact- ness are never met with in practice. On the other hand, the Baconian Logic, like the subordinate branches of physical science, is constructed a posteriori from the observed uniformities of nature ; and its principles and conclusions are true primarily of the facts as they exist in nature, secondarily only of our conceptions, so far as they are accurate representations of the facts. Hence the truth of the system entirely depends on the real exist- ence of the objects of which it treats ; and the whole fabric would fall to the ground if the objects were anni- hilated or their constitution reversed. Hence too, a conception not in accordance with facts is worse than useless : if it is not the representation of nature as it is, it cannot claim to be accepted as the representation of nature as it should be. An error of this sort becomes serious in its con-7yi< c^ "' < i^v^^ sequences. It is a great mistake to treat various defi- ^^ <^ * r/^^ c^ nitions of Logic as mere matters of opinion, in which'T^^ ,^02.-^ each person is at liberty to expand or contract the f^i^^ /^a^e^ boundaries of the science according to his own leading conception. The whole province of the practice of reasoning may be affected by an error in its theory. For example. A writer who treats the Organon of Aristotle and the Organon of Bacon as parts of the same system is in consistency obliged to regard the so-called laws of thought as being in reality laws of external nature"; n Thus Mr. Mill {Logic, vol. i. p. 235.) obsenes : " So long as what were termed Universals were regarded as a peculiar kind of substances, having an objective existence distinct fiom the individual objects classed under them, the dictum de omni conveyed an important meaning ; because it expressed the intercommunity of nature, which it was necessary upon that theory that we should suppose to exist between those general sub- stances and the particular substances which were subordinated to them. JXXII INTRODUCTION. and the same obligation extends to all cognate branches of knowledge. Hence the laws of physical causation are introduced without modification into the moral and intellectual world ; and, instead of an ideal science of man as he ought to think or act, we are presented with an empirical science of the observed relations between thoughts or actions as they actually take place. Thus in the place of a system of Ethics based upon the theory of a free will as it ought to be determined by moral obli- gations, is substituted Ethology, or the science of the actual phenomena of habits formed by a necessary agent under the laws of an invariable causation °. And in con- sistency, as a part of the same system, we ought also to be presented with an a posteriori science of Geometry, based upon the measurement of figured bodies as actually found in nature. This alone is needed to furnish the consummation, and at the same time the reductio ad absurdum, of the whole system?. That every thing predicable of the universal was predicahle of the various individuals contained under it, was then no identical proposition, but a statement of what was conceived as a fundamental law of the universe." o The reader need scarcely be reminded, that this is Mr. Mill's actual conception of Ethology as the Exact Science of Human Nature. See his Logic, B. VI. Chap. V. P This indeed is almost implied in the conception of M. Comte, who regards it as the principal office of Mathematics to furnish a substitute for the measuring rod. To quote his own words. " Nous devons regarder comme suffisamment constatee rimpossibilite de determiner, en les me- surant directement, la plupart des grandeurs que nous desirous connaitre. C'est ce fait general qui necessite la formation de la science mathematique. Car, renongant, dans presque tous les cas, a la mesm^e immediate des grandeurs, I'esprit humain a du chercher a les determiner indii'ectement, et c'est ainsi qu'il a ete conduit a la creation des mathematiques." Oours de Philosophie Positive, t. i. p. 123. With this may be contrasted the language of Plato, Rep, vii. p. 527. Aeyovffi [xiv irov /xdXa yeXoias re Kol auayKaiws' ws yap irpaTTOvres re Kal irpd^ews 'ducKa irduras rovs \6yous ■7roiovfj.evoi Xeyovcrii rerpaywvi^eiv re koI irapareCveip Kal Trpo(rTideuai, Kal Tavra ovtcc (pB eyy 6 fievoi' rb S' eCTt ttov irav rh fidOrf/xa yucixreais %veKa eirmr)- SevS/xei/ou. INTRODUCTION. Ixxiii On the above grounds, we are justified in rejecting Mr. Mill's definition of Logic as too wide for scientific accuracy, as that of Archbishop Whately is too narrow for scientific completeness. Between these two, the views of Kant, which have been substantially adopted in the preceding pages, hold an intermediate position, and one which promises more effectually than either to secure for the science what it has long needed, an exact de- finition and a systematic treatment. In accordance with these views, the conception of Logic which has been taken as the basis of the present work is that of the Science of the Laws of Pure or Formal Thinking, or, in thejlanguage of Sir William Hamilton % "the Science of the Laws of Thought as Thought." q Reid's Works, p. 698. 9ir^ ARTIS LOGICS RUDIMENTA. I ARTIS LOGICS RUDIMENTA. CAP. I. De Terminis Simplicibus, §. 1. Mentis operationes in universum tres sunt*. 1. Simplex Apprehensio. 2. Judicium, 3. Discursus^. ^ Mentis operationes tres sunt. More correctly : the products of pure thought are three, the Concept, the Judgment, and the Syllogism. Whether these are to be referred to three distinct operations of mind, is a psychological, not a logical question. At any rate, the three operations must be regarded as a merely logical division, invented as a convenient mode of classifying the products of thought, which are the proper objects of Logic. Cf. Herbart, Psychologie als Wissenschaft, Th. ii. §. 119. ^ " Sicut dicit Philosophus in tertio de Anima, duplex est operatio intellectus, Una quidem, quae dicitur indivisibilium intelligentia, per quam scilicet apprehendit essentiam unius- cujusque rei in se ipsa. Alia est operatio intellectus, scilicet componentis et dividentis. Additur autem et tertia operatio, scilicet ratiocinandi, secundum quod ratio procedit a notis ad inquisitionem ignotorum. Harum autem operationum prima ordinatur ad secundam : quia non potest esse compositio et B Z ARTIS LOGICS 1. Simplex Apprehensio, est nudus rei con- ceptus intellectivus ''^ similis quodammodo per- ceptioni sensitivse '^ ; sicut enim Imago rei est in divisio, nisi simplicium apprehensorum. Secunda vero ordi- natur ad tertiam : quia videlicet oportet quod ex aliquo vero cognito, cui intellectus assentiat, procedatur ad certitudinem accipiendam de aliquibus ignotis. Cum autem Logica dicatur rationalis scientia, necesse est quod ejus consideratio versetur circa ea, quae pertinent ad tres prsedictas operationes rationis." Aquinas in Periherm. Lect. 1. Cf. Opusc. xlviii. Tract, de Syll. cap. 1. The passage alluded to by Aquinas is De An. iii. 6. 1. Tj fxev ovv tS)V dbiaipercov vo-qaris iv tovtois iv€p\ a ovk eari to yj/ev8os' iv ois de TO yj/'evbos Koi to d\r}6€s, crvvdeaLS tls rjdr] vor]fj.a.T(ov cocTrep iv ovTcov. 'AbialpeTa are either dpiBpS) or eiSet. Metaph. ix. 1. 4. The latter only are vorjTa, the former alo-di]Td. Cf. Anal. Post. i. 24. 11. <= Simple Apprehension, in the only sense in which it can have any connection with Logic, is an operation of Thought, and is more properly called Conception. It is necessary to distinguish Thought, which is representative, and whose immediate object is an universal notion, gained by comparison and indifferently applicable to many individuals, from the various intuitive faculties, which are presentative, and whose immediate object is an individual thing, act, or state of mind, existing without or within ourselves. This distinction is properly psychological, but must be carefully borne in mind in reference to the logical character of Thought. A fuller explanation is given in Prolegomena Logica, Chap. I. ^ Among various intuitive faculties, it is necessary to dis- tinguish between Sensation, Perception, and Imagination. The two former are distinguished by Stewart, Outlines of Moral Philosophy, §. 15. " Sensation expresses merely that change in the state of the mind which is produced by an impression upon an organ of sense ; of which change we can conceive the mind to be conscious without any knowledge of external objects. The word Perception expresses the knowledge we obtain, by means of our sensations, of the qualities of matter." # RUDIMENTA. d oculo, ita Idea in animo ^ : estque Incomplexa vel Complexa, Apprehensio simplex Incomplexa, est unius ob- jecti, ut calami, vel etiam plurium, confuse ; ut calami, manus, &c. Complexa, plurium, sed cum ordine quodam et respectu ; ut calami in manu\ And so M. Royer Collard, Jouffroy's Reid, vol. iii. p. 329. " II y a dans I'operation du toucher sensation et perception tout ensemble : changement d etat ou modification interieure, c'est la sensation : connaissance d'un objet exterieur, c'est la perception." This distinction originated with Eeid : by earlier writers Perception was used Avidely, as coextensive with Consciousness in general. See Hamilton's Reid, p. 870. Imagination is properly the consciousness of an image in the mind resembling an absent object of intuition. The image, like the object which it represents, is individual. By the earlier writers, logical and psychological, this and other pro- cesses of intuition are confounded with those of thought. Thus Gassendi, from w^hom Aldrich has borrowed, treats Imagiiiation, Simple Apprehension, Conception, Notion, and Intellection, as identical, and employed in the formation of images, ideas, concejjts, or phantasms of things. e Idea. In the later and post-Cartesian sense of the word; in which sense, it is defined by Locke, " whatsoever is the object of the understanding, when a man thinks." For the history of this word, see Sir W. Hamilton, Edinburgh Review, No. 99. p. 18-2. ^ Confuse. This confuted apprehension of many objects is in truth only a succession of single apprehensions : thus in the example, we have two apprehensions, first of calami, and then of manus. Aldrich's distinction between incomplex and com- plex Apprehension is inaccurate, and depends merely on an accident of language. In respect of thought, it is indifferent whether we express the same notion in many words, as an animal with the head of a man and the body of a horse, or in one word, as Centaur. Complex Apprehension should properly b2 4 ARTIS LOGICS 2. Judicium, est quo mens non solum percipit duo objecta, sed, quasi pro tribunal! sedens, ex- presse apud se pronuntiat, ilia inter se convenire aut dissidere^ Arist. de Est enim Judicium aliud Affirmativum, quod Int. i. 3. vocatur etiam Compositio^ ; aliud Negativum, quod et Divisio, Porro, tam particula Est, quae affirmando con- venientiam exprimit^ quam Non-Est, quae negando Dissidium, appellatur Copula; (sicut et Gram- matica Conjunctiones Disjunctivas habet ;) at que hanc sub determinatione cognoscendo differt Judi- cium ab Apprehensione complexa. E. g. Si quis dixerit Triangulum cequilaterum be applied only to the apprehension of the proposition, (the \ oratio perfecta, — Aquinas, Opusc. xlviii. de Int. c. 3.) as dis- tinguished from that of a term or an imperfect sentence. e Percipit duo ohjecta. This expression is only accurate in the earlier and wider sense of perceives = is conscious of. The elements united in the logical judgment proper are general notions, the objects of Conception. With this explanation, Aldrich's definition is tolerably accurate as regards the logical judgment, formed by the union of two concepts repre- sented each by its separate sign in language. But this must not be confounded with the psychological judgment, which takes place in every act of consciousness. The latter is a conviction of the presence of the object of consciousness, either internally in the mind or externally in space. This | judgment does not require the aid of language, and to it.' Aldrich's definition is not applicable. Cf. Cousin, Cours de Philosophie, le9on 23. Hamilton on Eeid, p. 243, 375. Prolegomena Logica, p. 53. ^ Compositio— (ru»/^eo-ty. Divisio — biaipca-is. See de Int. i. 3. i RUDIMENTA. O esse cBquiangulmn, possum Apprehensione Simplici incomplexa intelligere quid sibi velint singula Orationis hujus vocabula^ complexa vero quid tota sibi velit Oratio': Quin et ipsius Naturae \\\mme^ .Ai^ ^/n^ ^/^ intelligo. Duo quaelibet objecta vel inter se con-^^^*^ ^^^-^ venire, vel non convenire, et proinde altera Copu- larum esse jungenda : Nondum tamen feci judi- cium donee Copulam determinaverim, i. e. apud meipsum statu erim haec Duo Objecta, Triangulum cequilaterum, et Triangulum ceqiiianguliim, hac Copula Est, non autem altera Non-Est, oportere conjungi. 3. Discursus^, est motus sive progressus mentis ' Conception, the Apprehension of Logic, implies consi- derably more than the mere understanding of the meaning of words or sentences. A word or sentence may be intel- ligible when the notion signified is inconceivable. Conception consists in an uniUj of representation, i. e. in the power of forming a mental image of the several attributes given in any ' word or combination of words. It is thus imagination relatively to a concept. Cf. Hamilton on Reid, p. 377. Pro- legomena Logica, p. 24. J Ipsius Natur(e lumine. This so-called U()ht of nature is in truth one of the laws of thought, commonly known as the Principle of Excluded Middle. {Frincipium exclusi medii inter duo contradictoria.) ^ " Additur tertia operatio qure est discursus, ab uno com- posite vel diviso ad aliud : hoc tamen fit per argumenta- tionem. Est autem argumentatio oratio significativa discursus rationis ab uno cognito ad aliud incognitum, vel a magis cognito ad minus cognitum. Sunt autem argumentationis quatuor species, scilicet syllogismus, enthymema, inductio, et exemplum." Aquinas, Opusc. xlviii. Tract, de Syll. cap. 1. The definition is too wide, being applicable to the immediate 6 ARTIS LOGICS ab uno Judicio ad aliud ; quod et Ratiocinium dicitur; et significatur Copula Illativa, qualis est Ergo, aut alia similis. v. g. Qui est extra fortunce potestatem est beatus. Sapiens est extra fortunce potestatem. Ergo, Sapiens est beatus. Singulis operationibus sui accidunt defectus^ inferences of Opposition and Conversion, as well as to the mediate by Argumentation. In all there is a progress from one judgment to another. Disciirsus is more properly the progress from two connected judgments, to a third resulting from their connection. Cf. Port Eoyal Logic, In trod. " On appelle raisonner Taction de notre esprit, par laquelle il forme un jugement de plusieurs autres," Of this division of the operations of the mind, Sir W. Hamilton has observed, that " it never was proposed as a psychological distribution of the cognitive faculties in general : but only as a logical distribution of that section of them which we denominate discursive, as those alone which are proximately concerned in the process of reasoning." Reid's Works, p. 242, 692. Hence Aristotle's division, which is psychological, w^ll not exactly correspond. The nearest ap- proach to Simple Al^prehension is ri rav dBimperav vorjais; but vorja-ts is variously used, and in its widest sense will embrace all the logical operations, and even cpavraala, which belongs rather to the perceptive soul. See de Anima, iii. 3. 8. Judgment will correspond nearly to the vwoXrjyj/is of de An. iii. 3. 7. (Cf. Trendelenburg Arist. de Anima, p. 469.) The latter term however is inapplicable to the cognition of axiomatic truths. Discursus answers to didvoia and XoyLo-fMos, the former term being applied both to the faculty and its operation. But there is much uncertainty in the use of all the above terms, Cf. Biese, vol. i. p. 89, 327. Hamilton's Eeid, p. 768. 1 The service supposed to be performed by Logic in relation to these three defects is more fully and clearly stated by Burgersdyck Inst. Log. 1. ii. c. 1. "Mens nostra qua- RUDIMENTA. 7 Apprehensioni, Indistinctio ; Judicio^ Falsitas ; Discursui, Mendosa Collectio, Quae cum Sapi- entes animadverterent, et opportuna illis remedia excogitassent, prsecepta sua in unum compegere ; druplici defectu laborat, cum occupata est in investiganda rerum cognitione : vel enim non assequitur propositae rei essentiam, sed circa illius accidentia solum hseret ac sensi- biles notas; vel essentiam rei confuse tantum concipit, et ratione minime distincta ; vel in dubiis non reperit quid statuat, aut etiam statuit quod falsum est; vel denique non servat ordinem in commentando, qui cum natura rerum consentit. Hisce quatuor malis opponit Logica totidem remedia. Definitio exhibet menti essentiam rerum : divisio efficit cognitionem distinctam : syllogismus tollit animi incertitudinem et errorem circa themata complexa: methodus ara^lav sive confusionem." Hence it appears that falsity of judgment simply was not regarded as remediable by Logic, but only falsity in relation to the syllogism, i. e. so far as it depends on the assumed truth or falsity of other judgments. But the above statement requires considerable limitation. Every process of thought is liable to a formal defect, as violating its own laws, and to a material defect, as inconsistent with experience. Thus a concept may be obscure or indis- tinct formally, as implying attributes which cannot be thought in conjunction, as when its different parts contradict one another: a judgment may be formally false, for the same reason : and a reasoning may be formally inconsequent, as transgressing the laws of the syllogism. In all these cases the fault may be detected by Logic. On the other hand, a concept may be materially obscure or indistinct, as containing attributes which we have never met with in our own expe- rience : a judgment may be materially false, as being at variance with facts : a reasoning may be materially incon- sequent, as not warranted by the laws or analogies of nature. Li all these cases, the fault can only be detected and reme- died by experience. Cf. Prolegomena Logica, p. 238. 8 ARTIS LOGICS eorumque Scientiam dixere Logicam, sive Artem Rationis'^. Est igitur Logica, Ars instrumentalis dirigens mentem in cognitione rerum° : ej usque partes tres *^ Logicam. " Logica dicta est dno rov \6yov. Aoyos duplex est Aristoteli, 6 ea-a koX 6 e|a) X6yo9, id est, sermo internus et externus. Sermonem internum vocat t6v iv rfj yj/vxTj \6yop, id est, sermonem qui in anima est: Plutarchus, Damascenus, aliique appellant \6yov ivbidderov id est sermonem intus con- ceptum ; et externum, \6yov rrpofpopiKov, id est, sermonem foras prolatum, sive pronunciatum. Aoyos ivdidderos sive internus, nihil est aliud quam ratio sive cogitatio, hoc est, actio mentis res objectas earumque nomina concipientis. Mens enim non solum res ipsas concipit atque intelligit, sed et idonea vocabula excogitat ad conceptus suos aliis indicandos atque expHcandos : atque ita quodammodo in seipsa loquitur. Ao'yos- irpot^opiKos atque externus, est sermonis interni cogitationumque interpres, atque (ut Damascenus loquitur, lib. 2. de Orth. fid. cap. 21.) ayyekos rov vorjuaros, id est, nuiicius cogitationis. Ab utroque sermone appellata est Logica, (utrumque enim regit ac format) sed ab interno, quem nihil aliud esse diximus quam mentis rationem sive cogitationem, praecipue nuncupatur; f jf^- ab externo sermone, sive ab oratione, tantum secundario. Ij«.#^t** ' ^pliogica enim regit cogitationes animi nostri per se; orationem non per se, (hoc enim Grammaticse convenit) sed eatenus tantum, quatenus rationis nostrae sive cogitationum interpres est." Burgersdicii Inst. Log. 1. i. c. 1. Cf. Arist. Anal. Post. I. 10. 6. Ov Trpbs Tov €^ci) \6yov rj dnodeL^is, dXkd. rrpos top iv rfj "^vXTly inel ov8e (rvWoyiapos. 'Aei yap earLV evo-rrjvaL irpos rov e^co \6yov, dWd npos rov ecra \6yov ovk dei. ^ Est igitur Logica. This definition is more fully given by Burgersdyck, List. Log. 1. i. c. 1. ''Logica est ars conficiens instrumenta, Usque intellectum dirigens in cognitione rerum. Logica docens dicitur quae prsecepta tradit ; utens, qu£e prseceptis utitur. Officium Logicae docentis, est tradere prsecepta et Kiodum efficiendi instrumenta, quibus mens dirigitur in cog- RUDIMENTA. y sunt, pro operation ibus mentis quas dirigit. 1. De Simplici Apprehensione, 2. De Judicio. 3. De Discursii, §. 2. QuoNiAM vero, inter docendum et dispu- tandum, neque res aliqua, neque conceptus, cui subjacet, commode in medium afferri potest ; ne- cesse est vicaria utriusque signa substituere, quorum nitione rerum, instrumentorumqiie naturam describere. In- strumenta Logica sunt quatuor, definitio, divisio, syllogismus et methodus. Officium Logicas utentis, est instrumenta, cum opus est, efficere, iisque mentem dirigere, ne in quserenda rerum cognitione hallucinetur." From this it appears that the knowledfje of things was regarded by this school as only the remote object of the Logica utens, as applied to this or that matter, and hence not to be gained from any logical treatise. Thus the distinction insisted upon by some critics between in cognitione and in cognitionem, is of no value ; both being merely verbal variations in expressing the same view. This definition of Logic as an art arose from the dialec- tical and rhetorical innovations introduced by tlie reformers of Logic in the latter part of the fifteenth century, and was adopted universally by Ramus and his followers, as well as by the Peripatetico-Ramists of the school of Keckermann, and afterwards by the Cartesians. Among the earlier philo- sophers, the Peripatetics considered Logic to be neither art nor science, but an instrument. The Stoics regarded it as a science, in which they were followed by the Schoolmen. Subsequently, in the schools of Wolf and Kant, Logic again obtained the name of Science, though the former regarded it as a practical, the latter, more correctly, as a speculative science. Cf. Zabarella de Natura Logicce, lib. i. Smiglecii Logica, Disp. 11. Qu. V. Sir W. Hamilton, Edinburgh Review, No. 115, p. 203. 10 ARTIS LOGICS usum idbneum docendo, Logica mentem una ad bene operandum instruit. Hujusmodi signa apud homines recepta, sunt Voces: Nam Vox est signum rei vel conceptus" Deint.i.s. ex iustituto vicariumP*. et in significando^ primo quidem declarat conceptum, deinde supponit pro Ye\ Dico autem ex instituto, quia soni inarticu- ° Primarily of the conception, secondarily of the thing. Cf. de Int. i. 2. Kal wanep ovbe ypafx^ara nao-t to. avra, ovbk (pavai al avrai- hv jxevroL ravra (Tr)p.eia 7rpa)T(os ravra ivacn TraBrjjiaTa rrjs "^X^^f Koi hv ravra o^oLOiiiaraf irpayfiara fjbrj ravra. On the distinction between ar)p,eiov and Sp-olcopa, see Waitz, vol. i. p. 3'24. ^ ^^^^at Aldrich calls simply Vox, is called by Aristotle (fxovri a-rjfiavrLKT], and by Boethius and Petrus Hispanus, Vox signlficativa ad placitum. In the latter case, Vox is extended to the gram- matical word ; in the former, it is limited to what may be called the Vox Logica. Logic differs from Grammar, in considering language simply as the interpretation of thought, (the ipfirjveia of Aristotle,) not as in any way expressive of the passions or the will. Logic therefore solely regards words as the signs of an operation of the reason, and hence its simplest words are the noun and the verb, which alone are per se signs of conceptions. Syncategorems, being not significative but consignificative, are excluded from Logic, but recognised by Grammar. So Aristotle, in the De Interpretatione, treats only of the noun and the verb. In the Poetics, ch. 20. he adds the cf}a)va\ aaijixoi, the conjunction and the article. Cf. Harris, Hermes, ch. iii. On the distinction betw^een the logical and the grammatical proposition, some good remarks will be found in Du Marsais, Principes de Grammaire, p. 321. 1 Supponit pro re. The supposition (as it was called) of a term being posterior to its signification. The doctrine of the supposition of terms, which is not found in Aristotle, is one of the subtleties of the parva logicalla, a scholastic addition to the Organon, rather grammatical than logical. Suppositio was defined to be " Acceptio termini substantivi pro aliquo ;" RUDIMENTA. 11 lati, vocesque quas Natura sponte suggerit^ extra artem censentur. Jam, quae simplicem Apprehensionem exprimit. Vox Simplex e^t \ quae Judicium, Complexa" ; quae Discursum, Decomplexa. Nam argumentum omne resolvitur in tres Propositiones, sive sententias, et propositio omnis complectitur voces, non semper numero, sed sensu semper tres ; 1. Siihjectum, thus the term liomo, naturally applicable to men of all generations, is, in the proposition homo currit, accidentally limited to existing individuals. In this case it was said, in not very classical Latin, "homo supponit pro praesentibus." For further information on the various kinds of supposition, the curious reader may examine Sanderson's Logic, b. ii. ch. 2. ' Vox complexa {(jicovT) o-v^Tveiikcyiievr)) in Aristotle signifies a compound word ; his example is cTraicTpoKeXrjs, of which each part has a meaning in composition. Vox simplex {diArj) where the parts have no meaning. The later meaning oivox complexa properly corresponds to Aristotle's X0709 (Oratio), and is not limited, as by Aldrich, to the Fropositlon (oratio enunciativa). Thus Petrus Hispanus : " Vocum significativarum ad placitum alia complexa, ut oratio, alia incomplexa, ut nomen et ver- bum. Orationum perfectarum alia indicativa, ut liomo currit; alia imperativa, ut Petre fac ignem ; alia optativa, ut utinam esset bonus clericus ; alia subjunctiva, ut si veneris ad me daho tibi eqiium ; alia deprecativa, ut miserere mei Deus. Harum autem orationum, sola indicativa oratio dicitur esse propo- sitio." Sum. Log. Tract. 1. Cf. Boeth. de Syll. Cat. p. 582. With regard to the vox decomplexa; as 'koyos is defined by Aristotle as a species of ^001/77, and syllogism as a species of \6yoi, the latter may without error be called vox. But the distinction is unnecessary; the syllogism, as far as apprehension is concerned, being only three several propositions. The con- nexion between them is not a matter of apprehension, but of 12 ARTIS LOGIC/E sive de quo aliud dicitur. 2. Prcedicatum, sive id quod dicitur. 3. Copulam, quae utrisque media intercedit'. Nam Subjectum et Praedicatum quoad sensum semper extrema sunt, et vocantur ideo Termini Propositionis. Atque hinc adeo vulgo dicitur Pars prima Logicse versari circa Terminos simplices, i. e. voces simplices, Apprehensionem simplicem exprimentes* : secunda circa Propositionem, sive Vocem com- plexam, quae Judicium exprimit : tertia vero circa Syllogismum, sive Vocem decomplexam, qua Argu- mentatio sive Discursus exprimitur. ^ The Latin Logicians distinguish between propositions secundi adjacentis, in which the copula and predicate form one, word, e. g. " Homo currit," and propositions tertii adjacentis, '] in which they are separated, e. g. " Homo est animaL" The * distinction originates with Aristotle, see De Int. 10. 3. But Aristotle does not maintain that propositions of the former kind are to be resolved into the latter. On the contrary, the early part of the De Interpretatione is adapted exclusively to propositions secundi adjacentis; and in order to make it ap- plicable to such propositions as " Homo est animal," we must consider the copula and predicate as equivalent to a single verb \ * In Aldrich's limitation of the terms. Vox simplex, Vox categorematica, and Terminus simplex, are synonymous : syn- categorems not being voces (logicse) at all. But in this usage he is not always consistent. * In De Int. 1. 4. it seems at first sight as if \evKhv alone was a prjixa. That this is not the case is clear from Poetics, 20. 9. rh (x\v yhp &vdpuiros ^ \evKhu ov (TTjfiaii/ei rh ttSts, rh 5e fiaSi^ci ^ fie^dSiKe irpocrariiJ.aivei rh fxev rhv napSvTa xp^^ov rh Se rhu irap^XrjXvdSTa. In fact, \evK6y, by a common Greek Idiom, is equivalent to X^vkSv eVrt. RUDIMENT A. 13 §. 3. Prima igitur pars Logicae versatur circa De int. eh. Terminos Simplices^ ; i. e. ejusmodi voces, quae solitariae in propositione praedicari vel subjici pos- sunt ; et vocantur ideo Categoremat'iccB, ut homo, lapis^. Quaedam etiam Vocabula sunt tantum Syncategoremata, sive compartes Subjecti aut Prag- dicati, ut omnis, nullus ; Quaedam etiaui mixta ^, ut semper, i. e. omni tempore ; nemo, i. e. nullus homo ; Currit, i. e. est currens ; quo etiam modo verbum omne Grammaticum resolvi potest. Verbum igitur Logicum (nempe purum) praeter Copulam nullum est : caetera ex participio et copula coalescunt". " Aristotle's Simjde terms, {opoi, eU ovs diaXverai fj irpoTaa-is,) or, as others call them, categorematic ivords, are the noun as subject, and the verb as predicate, " homo currit.'" The oblique cases of the noun and past or future tenses of the verb are not simple terms, being only nroiaeis ovofxaros or prjiiaros. The noun and verb are tlius the only two parts of speech re- cognised by Logic. See Boethius, In trod, ad Syll. p. 561. and Petr. Hisp. Tract. I. But it would be more accurate to say that Logic analyses language on a different principle, and hence does not recognise the grammatical parts of speech at all. The logical proposition should be of the form tertii adjacentis, and its predicate forms a part of the gram- matical verb. Cf. Prolegomena Logica, p. 274. " The terms categorematic and syncategorematic are not Aris- totelian, though the distinction is of course implied in his theory of the Proposition. YLarqyoprjyia in Aristotle means a predicable, e. g. de Int. 11. 4. Cf. Trendelenburg, Elementa, §. 3. Waitz, vol. i. p. 267. y Mixta. This is clearly a cross division. Every mixed word must, of course, be categorematic or syncategorematic. ^ The copula has an apparent resemblance to the gram- 14 ARTIS LOGICS Deint.2.1.' Nomen Logicum, est Terminus simplex sine /tempore significativus^ Nam ex antedictis. Ter- minus simplex idem valet atque Vox articulata et recta, et ex instituto significans : siquidem exclusse sunt voces inarticulatae, quasque natura sponte suggerit ; voces autem obliquae sunt Syncatego- remata. Multse sunt Nominis Divisiones ; quorum tres^ sufficiunt hujus loci instituto ; sed ob multiplicem earum usum, quinque alias adjungam. Deint.7.1. 1. Nomcn singular e, est quod rem unam et solam significat, ut Socrates: Commune, quod plura, et eorum singula significare potest, ut homo, matical verb, as being tbe only part of a logical proposition capable of personal inflection. But inflection is one of the accidents, not one of the essentials of a verb, and belongs to particular, not to universal grammar. The essence of a gi'ammatical verb lies in its signification, being a combination of an attribute and an assertion. Cf. Stoddart, Universal Grammar, p. 121. Latham, English Language, p. 461. The copula must of course not be confounded with the verb est, which predicates existence, as " Homo est." The whole question is ably treated by Pacius on de Int. ch. 3. Cf. Biese, PhilosopJiie des Aristoteles, vol. i. p. 95. ^ Nomen. — Arist. de Int. 2. 1. ovofia jxev ovv earl (pcovr} aijfiavTiKTj Kara avvdfjKrjv avev xpovov. Sine tempore, as opposed to the verb, the other simple term, t6 irpocra-r^^xaivov xpovov. '■'Currit,'" e. g. in addition to its principal notion of running, signifies as an adjunct the present time, (see Ammonius, Scholia, p. 105. b. 29.) This distinction is lost when we resolve the verb into copula and predicate. ^ Tres, i. e. the three employed in his definition of pra- dicabile, viz. those into singular and common, univocal and equivocal, first and second intention. RUDIMENTA. 15 [2. Transcendens, quod solis omnibusque veris Entibus convenit, ut ens, res, aliqidd, uniim, verum, honum\ S iipertr ansae ndens, quod omnibus etiam fictis, ut imagmabile, cogitabile : Non-transcendens, omne aliud nomen.] 3. Finitum, est cui abest particula non: Infi-Deims nitum^, cui praefigitur, ut non homo, i. e. omnia praeter hominem : unde particula non, dicitur in- Jinitans. 4. Positivitm% est quod significat rem quasi prae- sentem : Privativum, quod dicit absentiam rei a subjecto capaci : Negativum, quod ab incapaci. ; Sic homo est vox positiva ; videns dicitur de homine positive ; cceciis de homine privative ; ccecus, seu potius non videns, de lapide negative, 5. Univocum\ est cujus una significatio aeque Cat. i. : <^ These are usually called the six transcendents, and are regarded as predicable of the several categories analogously, not univocally. '^Infinitum. So translated by Boethius. It should be Mic?e- 1 finitum; see Hamilton on Reid, p. 685. The translation is censured by Vives, de Caus. Corr. Art. lib. 3. *" In these divisions there is much clumsiness and self- repetition. The distinction between positive and privative nouns is repeated below, under the four opposita. Negative nouns have no business here at all, being opposed, not to positive, but to affirmative, and belonging to another kind of opposition, the contradictory. Belatives also form another member of the same fourfold division ; and Rcpugnants include all the four opposita, and other nouns to boot. ^ Univocum {univocatum) — a-vvcawfxov: (Bquivocwn, {cequivo- catum) — ofMoovvfiov. 'O/xooi/u/xa Xeyerat 2)1/ ouo^a yiovov koivov, 6 8e Kara rovuojxa Xdyo? rrjs ova-ias erepos, olov ((oov o re avdpcoTTOs kol to / 16 ARTIS LOGICS convenit multis, ut homo : Mquivoctim, cujus ^/ diversser ut Gallus : Analogum, cujus una inae- qualiter ut fes, [Vox ipsa dicitur Univocum Uni- vocaiis : res significata Univocum Univocatum, et sic de caeteris.] 6. Absolutum^, est cujus tota significatio spectat yey pa^nxevov. '2vva>vvfJi,a de Aeyerai a>v to re ovoyia kolvov koL 6 Kara Tovi/ofxa Xoyos Ti]S ovaias 6 avros, oiov ^aov o re at/dpcoiros kolL 6 ^ovs. (Cat. ch. 1.) Analogous nouns are but one out of many species of equivocal, belonging to the cequivoca consilio, (diro biavoias,) of the Greek interpreters ; to which are opposed the cequivoca casu, (dno rvxns-) See Scholia, p. 42, a. 37, 47, Boethius in Prsedicamenta, lib. 1. p. 117. (Cf. Arist. Eth. Nic. i. 4. 12.) The o-wawfia of Aristotle must be distinguished from the modern synonyms, which answer to the 7vo\v6iWjjia of Speusippus, (Schol. p. 43. a. 31.) and the muUivoca of Boethius, and are defined by the latter, " quorum plura nomina, una definitio est." Swwi/u/xa was used in this sense by the Stoics, and the same sense may also be found in Aristotle, Ehet. iii. 2. 7. and perhaps Top. viii. 13. 2. s It is not easy to distinguish accurately the two divisions of terms into absolute and connotative, abstract and con- crete, respectively. The following attempt is made with some doubt as to its success. In the second chapter of the Categories, Aristotle divides all ovra into four classes. Uni- versal Substances, Singular Substances, Universal Attributes, and Singular Attributes. Substances of both kinds exist i^er se; attributes can only exist in substances. Hence the scholastic distinction between Subjects of Predication and Subjects of Inhesion. The universal substances are pre- dicable of the singular, as genera and species of individuals. " Socrates is a man." In this case the individual is a subject of predication. Attributes are not in their original state predicable of substances. Whiteness exists in snow; but we cannot say, " Snow is whiteness." Here, then, the subject is not one of predication, but of inhesion. But, by an act of the RUDIMENTA. 17 rem per se sump tarn, [ut Justitia : Connotativum, quod eandem quasi alteri nexam^ ut Justus,'] , Concretum, quod rem quasi sua natura liberam, sed jam implicitam subjecto, ut Justus: Abstractum, quod rem quasi sua natura nexam, sed jam subjecto mind, an attribute may be so connected with a subject as to become predicable of it as a differentia, property, or accident ; e. g. "snow is white." Predicates thus formed from attributes are called connotative, being said to signify primarily the attribute, and to connote or signify secondarily (Trpoa-arjfialveiv) the subject of inhesion. Hence a connotative term may be defined, " One which primarily signifies an attribute, secondarily a subject." Whereas the original universals, whether substances or at-^ tributes, as " man," or " whiteness," were called absolute. Again, by an act of the mind, the terms signifying substances, may be conceived in the form of attributes, so as to be no longer predicable of the individuals ; thus " homo " becomes "humanitas." All such terms, not predicable of singular substances, whether primarily attributes, as " whiteness," or secondarily conceived as attributes, as " humanity," are called abstract terms ; all that are predicable of the individuals, whether primarily, as "homo," or secondarily, as " white," are concrete. Hence the two divisions are distinct in principle, though some of the members of each cross. For example : Homo is concrete and absolute, albus concrete and conno- tative, albedo abstract and absolute ; but no abstract term is connotative. The above account differs considerably from that given by Mr. Mill, Logic, b. i. chap. 2. He inverts the phraseology, describing the attribute instead of the subject as connoted, and extends connotative terms, so as to include all concrete general names. This is in some respects an improvement on the scholastic distinction, but it must not be confounded with it. The materials of the present note are chiefly from Occam, Logic, p. i. chap. 5, 10. It must be admitted, however, that there is some licence in the use of the word connotative. 18 ARTIS LOGICS Cat. 1. 5. exemptam, ut Justitia, [Denique, si Concretum sola termination e diversum sit ab Abstracto, ut Justus a justitia, hoc Denominans dicitur, illud Denominatwum, Subjectum vero Denominatum^, Cat. 8. 27. Denominalivis accensentur aliquando Derwativa ilia, quae vel solam nominis Analogiam, vel solam rei vim, non utramque retinent, ut Studiosus studii et virtutis, Sed ista verius Conjugata sunt\ Connotativum quoque dicitur de nominibus quorum conceptus se mutuo ingrediuntur, ut Poter et Filius : nam et ilia opponuntur absolutis ; sed vocantur proprio nomine Relativa.] 7. Convenientia, sunt qu^ possunt de eodem simul dici, ut doctus et plus : Repug?iantia, sive ^ Tlapavvixa Se Xe-yerai oaa aTrd tlvos biacfiepoirra rfj iTTaxrei ttjv Kara Tovvofxa Trpocrtjyopiav e-)(ei, olov aTro Trjs ypaixp.aTiKrjs 6 ypafip-ariKos Koi ano Trjs dvbpcias 6 avSpelos. Cat. i. 5. The word 7rapct)vvp.a is translated by Boethius denominativa. It should have been denoininata. From the same authority denominatives have been limited by the Schoolmen to concrete adjectives, pre- dicable of a subject possessing the abstract attribute. Cf. Aquinas, Opusc. xlviii. Tract. S. cap. 1. The limitation is not warranted by Aristotle, and is expressly rejected by his Greek Commentators. See Simplicius, Scholia, p. 43. b. 5. rSiv 8e 7rapa>vvp,cov av e'ir), (prjalv 6 Ilop(f)vpLos, koi to. TrarpcovufxiKa Kal to. CrVyKpLTLKO. KoX TU VTTepOeTlKO. KOi TO. VirOKOpiCTTlKa.. i Studiosus is used in Scholastic Latin as a translation of the Greek airovdalos into the two senses of " diligent" and "virtuous." In the former, it is a denominative from studium. In the latter, not, as is observed by Aristotle, Cat. 8. 27. The name conjugata is more properly applied to derivatives from the same primitive, as sapiens, sapienter, sapientia; the ava-Toixa of Aristotle. Cf. Arist. Top. il 9, 1. Cic. Top. c. 3. _ RUDIMENTA. 19 Opposita, quae non possunt, ut album et ni- grumK [Oppositio'' incomplexa, sive terminorum simpli- Cat. lo. i. cium, est omnino quadruplex : L Relativa, inter terminos relatives, ut Patrem et Filiiim, 2. Con- traria, inter contrarios, i. e. absolutes se mutuo pellentes ex subjecto alter utrius capaci, ut album et nigrum. 3. Privativa, inter privativum et posi- tivum, ut videntem et ccecum, 4. Contradictoria, inter positivum et negativum, intellige finitum et infinitum, ut hominem et non-hominem, Hasc est op- positionum maxima, quia nullum admittit medium ; neque Participationis, quale est fuscum respectu Cat. lo. 8. albi et nigri ; neque Abnegationis, quale est lapis inter videntem et coicum^, Relativa contra, omnium ^ Repugnantia should not be considered as synonymous with opposita. There are many repugnants which are not included under any of Aristotle's four modes of opposition ; e. g. red and blue are repugnant, but not opposed. ^ Aeyerai de erepov irepa avTiKela-daL rerpaxcdS, 77 o)S to. Trpos ri, fj 6)S TO, evavTia rj cos (rreprja-LS Ka\ e^is, /} o)s KaTdy 0)? Se ra Kara (TTcprjcnv Koi e^iu, oloj> tvcJAottjs koL 6\lns, o)s Se KUTa- (jiaais KOL drrocpao-LS, olov KddrjTai ov Kd6r)Tai. Cat. 3 0. 1. Cf. Metaph. iv. 10. Contraries are the two most opposite qualities of the same class of subjects, e. g. black and white, as colours of bodies; virtue and vice, as habits of the soul. Cf. Cat. 11.5. * Medium Participationis. i. e. no object can be conceived as both A and not-A. This law of thought is called the Prin- ciple of Contradiction. Medium Abnegationis, i. e. no object can be conceived as neither A nor not-A. This law of thought is called the Principle of Excluded Middle. See above, p. 5. note j. c2 ? 20 ARTIS LOGICiE minima; nam Relata non sunt opposita, nisi ad idem sumantur.] 8. Nomen"" Primce intentionis, est Vox in com- ™ " Oi the first intention,'" says Hobbes, " are the names of . things, a man, stone, &c. of the second are the names of names / and speeches, as universal, -particular, genus, species, syllogism,! and the like." Except that the language is too much adapted to the ultra nominalism of the author, this passage exactly ex- presses the true distinction. A first intention or notion is a con- ception under which the mind regards things, whether facts of external or of internal perception. Thus the individual Socrates is regarded by the mind as man, animal, body, substance. All these are first intentions. And a mental state may be successively regarded as a smell, a sensation, a fact of consciousness. These again ar-e first intentions. A second intention or notion is a conception under which the mind regards its first intentions as related to each other. Thus the relation of animal to man^ and of man to animal, is expressed in the second intention genus or species. First intentions, as conceptions of things, are predicable of the individuals conceived under them. Thus we may say, " Socrates is man, animal, &c." Second intentions are not so predicable : we cannot say, " Socrates is species, genus, &c." Hence when we are told that a predicable is commune, univocum, secundcB intentionis, it is not meant that all universals are in themselves second intentions ; but that every predicate viewed in relation to its subject may he comprehended under one of Porphyry's five classes af pre- dicables; all which are second intentions. So when Genus is said to be predicable of Species, it is not meant that we can predicate the one second intention of the other, so as to say, " Species is Genus ;" but that the first intention " animal" is predicable of the first intention " man ;" the relation of the one to the other being expressed by the second intentions " genus" and " species." For this reason Logic was said to treat oi second intentions applied to first. See Aquinas, Opusc. Ivi. Scotus, Sup. Univ. Qu. 3. Zarabella, De Natura Logicse, lib. i. cap. 19. ^ RUDIMENTA. 21 muni usu posita. Secundce, Vox artis, quam ex communi sermone sumptam Philosophia recudit denuo et moderatur. §. 4. Vox Singularis, dicitur alio nomine Indi- mduum, ej usque significatum Unum numero : neque enim singulare est quicquid Unum dici potest; sed multa, quae sunt invicem similia, eatenus Unum censentur. Vocantur enim uno eodemque nomine ; quod ipsa Vocis definitio'' non patitur, nisi in illis reip^a sit, vel saltem concipi possit, una aliqua eademque Natura, quae huic nomini respondeat. Talem reperit intellectus, dum plura contem- plando ahstraliiV ab eorum differentiis; i. e. spectat The distinction between first and second intentions is generally considered as of Arabian origin. Scotus, however, (Sup. Univ. Qu. 3.) attributes it to Boethius, whose extant writings do not confirm the statement. It is found in Averroes, Epitome de Predicamentis ad fin. For scholastic expositions, see Aquinas, Opusc. xlviii. Tract. 1. cap. 1. in 1 Sent. Dist. 2. Qu. 1. Art. 3. Scotus, in 1 Sent. Dist. 23. In Univ. Qu. 11. Occam, Logic, P. i. cap. ] 1. A good account of the formation of second intentions is given by Burgersdyck, Imt. Log. lib. i. cap. 2. Aldrich's definition, which is ex- tremely vague though not positively erroneous, was probably suggested by Crakanthorpe, who in his Prooemium calls second intentions Voces Artis LogiccB. It is scarcely necessary to add, that the explanation of Abp. Whately is altogether erroneous. ° Vocis dejinitio. Since Vox is " signum rei vel conceptus,'" not rerum vel conceptuum. ° Ahstrahit. i. e. abstracts its attention from the distinctive features of the objects presented. The terms abstract and abstraction have been used in various applications ; retaining 22 ARTIS LOGIC.E in rebus ea tantum quae conveniunt, neglectis omnibus quibus dissident ; adeoque fundamentum however in all the primary signification of witlidrawing the attention from one portion of certain phenomena given in combination to fix it on the rest. In this sense Geometrical Magnitudes are called by Aristotle to. e^ dcfiaipecrecos, {An. Post. I. 18. 1.); because the Geometer considers only the properties of the figure, separating them from those of the material in which it is found. (See An. Post. I. 5. 6. Metaph. x. 3. 7.) On similar grounds is formed the scholastic distinction of abstract and concrete terms ; since in the former the attribute is considered apart from the subject in which it is perceived by the senses : e. g. sight presents to us only alba; the mind forms the conception albedo. And so Universals are gained by abstraction, i. e. by separating the phenomena in which a given group of individuals resemble each other from those in which they differ. For this reason Locke calls all universals abstract ideas ; a phrase etymologically allowable, but liable to be confounded with the scholastic use of the word abstract in a different sense. For this reason it is better to adhere to the term universals ; which has at the same time the advantage of leaving the Logician, as such, uncommitted to any metaphysical hypothesis as to their nature ; since the Realist may interpret Universal Substances, the Nominalist, Universal Names, the Couceptualist, Universal Notions. Generalization, which some modern writers distinguish from Abstraction, is pi'operly a species of abstraction ; viz. the divest- ing the presentations of consciousness of the conditions of existence in space and time, which are characteristic of indi- viduals. This is done by the aid of signs, verbal or other, which are at first signs of individual objects, and subsequently of general notions. Other abstractions may exist without gene- ralization ; but these are not processes of thought, but of per- ception, internal or external. Thus, to fix the eye or ear on a particular sight or sound exclusively, is in the widest sense an abstraction, but not a generalization. The psychological RUDIMENTA. 23 omne discriminis, praeter numerum, eximit. Quare naturam sic abstractam, cum sit omni singulorum differentiae superstes, concipi par est, non ut in singulis diversam, sed ut in omnibus eandem ; adeoque Universale quiddam sive Ens unum in '. muUisj ej usque signum idoneum eril,' Nomen j commune, Univocum, Secundce intentioms,m\o verbo, / Prcedicabile^ , sive Vox apta praedicari, i. e. Univoce dici de multis. §. 5. Pr^dicabilium"^ capita, constitui et controversies concerning abstraction cannot be discussed here. See Prolegomena Logica, p. 25. p " Prsedicabile (Grasce KaTrjyopovfxevov) et universale, etsi reipsa non differant, (omne enim universale prsedicari potest, et omne prsedicabile debet esse universale,) ratione tamen diversa sunt. Nam universale, quatenus universale est, prsB- dicatur de inferioribus, in qupestione qua quseritur quid sint : at prsedicabile, quatenus est prasdicabile, prasdicatur etiam de coordinatis, idque in qusestione qua qureritur qualia sint. Itaque, cum quinque sint prsedicabilia, tantum duo tamen universalia sunt, genus et species. Nam differentia, proprium, et accidens, quatenus talia sunt, non sunt universalia, sed tantum quatenus sunt genera aut species eorum qu^e sub illis continentur. Ex. gr. Sensus est proprium animalis ; sed non est universale, quatenus ut proprium de animali praedicatur, sed quatenus praedicatur de visu, auditu et cseteris sensibus, ut genus." Burgersdicii Inst. Log. 1. i. c. x. The addition of uyiivocum, secundce intentionis is supei'fluous. The latter has been explained in a former note. The former, though a necessary result of the abstraction here described, is not a necessai7 part of the notion of a predicable. Indeed, other Logicians distinguish between (Equivocal, univocal, and denomi-j native predication. See Sanderson, 1. i. c. 6. "^ The five Heads of Predicables are an addition to the 24 ARTIS LOGIC.E definiri possunt ad hunc modum. Quicquid in multis reperiri potest, vel est tota eorum essentia, vel ejus pars, vel cum essentia conjunctum '. Quare Universalia vel (quod eodem redit) Prae- dicabilia sunt quinque, et non plura ; videlicet. Genus, Species, Differentia, Proprium, Accidens, Aristotelian Logic, taken from the Isagoge or Introduction to the Categories by Porphyry, written in the third century. Aristotle's doctrine, as far as it can be gathered from the Topics, differs from that of Porphyry in several points; as does the latter from the view adopted by Aldrich. ^ Quicquid in multis, &c. These definitions are taken from Albertus Magnus, (de Praedicab. Tract. 11. cap. 1.) and were generally adopted by the Kealists, in the form of introduction to, or commentary on, the Definitions given by Porphyry. The Nominalists, on the other hand, expressly denied that any predicable was of the essence of the individual. See Occam, Logica, p. i. cap. 20, 21. To discuss the full bear- ings of this controversy would exceed the limits of a note. It will be sufficient to observe, that a considerable portion of the language adopted by Aldrich is not even intelligible, except on reaUstic principles ; and that whenever the same language is adopted by a Nominalist, he is inevitably involved in inconsistencies and self-contradictions. The same is in some degree true of the original exposition of Porphyry, though the latter professes to leave the question of Nomi- nalism and Realism open. But the question of the existence of universals a j^cifte rei is metaphysical, not logical, and no theory on this point ought to influence the language of Logic. The rules of Logic are primarily regulative of thoughts; and equally so, whatever opinion we may hold concerning the essence of things. For this reason, it is necessary to alter nearly the whole of Aldrich 's language, in speaking of the logical predicables. On the realist point of view, see further. Appendix, note k. RUDIMENTA. 25 Nam ] . Genus y est quod prasdicatur de pluribus Porph. ut eorum essentiae pars materialis sive communis ; ut animal^. 2. Differentia, quae ut essentiae pars formalis sive discretiva ; ut rationale. 3. _ Species , ^^^s-^- ^- ' -f"— '17,20. quae ut tota essentia ; ut homo. 4. Proprium, quod ut essentiae junctum necessario ; ut risibile. b. Accidens, quod ut essentiae junctum contin- genter ; ut album, nigrum, sedere\ ^ " Genus speciebus materia est. Nam sicut ?es, accepta forma, transit in statuam, ita genus, accepta differentia, transit in speciem." Boethius de dtvisione. But as logicians, we are not warranted in introducing any portion of the essence of things, but only of concepts or general notions. The whole essence of a concept is the sum of the attributes which it comprehends, and this can only be fully declared by its dejinition, not, as Aldrich says, by species. The Genus or material part of two given concepts, (to speak of the material or formal part of a single concept is nonsense,) is the sum of those attributes which are common to both ; as the difference or formal part is composed of those attributes which are peculiar to each. Thus, if there be given three concepts, containing respectively the attributes, ah, ac, he, a is the genus of the first compared with the second, h and c the respective differences. But if the first is compared with the third, h becomes the common genus, a and c the respective differences. In this, the only tenable logical point of view, there can be no such thing as an absolute genus or difference. ^-Necessario — Contingenter. This distinction is based on the supposition that certain attributes are necessarily con- nected with others, from which they flow, as effect from cause. Thus risibility was described in the scholastic philo- sophy as necessarily flowing from rationality, in the same manner as having the angles at the base equal to each other necessarily results from the equality of two sides in an 26 ARTIS LOGICiE Patet hinc P. De iis did Prcedicabile quibus inest Universale. Genusque adeo, quod est plu- isag.2. 11. rium essentiarum vel specierum pars communis, de specie differentihus, h. e. de diversis speciebus quas ingreditur, dici ; ut animal de homine et hruto. Speciem vero, de numero differentihus, h. e. de diversis individuis, quorum singula habent essen- tiam speciei vocabulo significatam ; sic homo de Socrate et Plaione dicitur, et de omnibus^ quibus natura inest humana. Reliqua vero Prasdicabilia, (prout inferius patebit) eadem de causa, tam de specie quam numero difFerentibus dicuntur. Et N. B. ex recepto more loquendi. Genus et Speciem prcedicari in (i. e. respondere qusestioni Top. iv. 2. factae per) Quid"" ; DifFerentiam in Qualequid; Isag.2. 13. 10.5.11.5. isosceles triangle. But this theory, originally borrowed from ' * the mathematics, is not true of any succession of physical phenomena. As a matter of fact, we experience that certain events are invariably conjoined, but there is not, as in mathe- matical demonstrations, any necessity that they must be so. Invariable succession, in fact, is the highest positive notion of causality to Avhich we can attain in the case of sensible phenomena, though this limitation does not include the moral causality of which we are conscious in volition. Neces- sity, however, in any sense is untenable as a logical criterion of property, since it presupposes an acquaintance with the laws of any given physical phenomena, of which the Logician as such knows nothing. A better logical distinction between property and accident is that given by Aristotle, of the con- vertible and 7ion convertible attribute. See Apj)endix, note A. •^ Pr(sdicatur in Quid ; i. e. is expressed by a noun substan- tive : in Quale; by an adjective. See Aquinas, Opusc. xlviii. cap. 2. (Of. Abelard, De Oen. et Sp. p. 528. ed. Cousin.) That RUDIMENTA. 27 Proprium et Accidens in Quale, Unde facile est conficere vulgatas Praedicabilium definitiones. Nam Genus definitur, Prcedicahile quod prcedicatur de pluribus specie differ entibus in Quid, Differentia, isag. 2. 8. quod de pluribus specie vel numero differentlhus in Quale quid &c. "" isag. 3.17. Patet 2". Genus esse Totum quiddam. nempe Arist. ,. Metaph. Logicum, sive in modo loquendi; quatenus con- iv.25.8,3. tmet (1. e. prsedicationis ambitu complectitur) species tanquam partes sui subjectivas, Speciem the distinctions of substance, quality, and the other categories, are founded on grammatical grounds, is shewn by Trendelen- burg, Excerpta, §.3. The reader of Locke must not confound this distinction with that between substances and modes; Essay, b. ii. ch. 12. (Cf. Descartes, Princ. i. 48. Port-Eoyal Logic, p. 1. ch. 2.) A quality is predicated in quid of another quality, as well as a substance of a substance ; e. g. " Prudence is a virtue." Cf. Pacius on Top. i. §. 3. Port-Royal Logic, part i. ch. 7. The distinction between Qualequid and Quale is not warranted by Porphyry. According to him, Differentia, Pro- prium, and Accidens are all predicated, eV rco ottoIov tI iv yap rjbecov evia (jivaei alperd, to. d' ivavria TovTcov, TO. be fiera^v. Dichotomy by contradiction, which Aristotle censures, had been a favourite method with Plato, as it after- wards was with Ramus and his followers. See Hamilton's Reid, p. 689. Cf Trend. Elem. §. 68. Erlauterungen, p. 106. But none of the above methods of division can be regarded as a strictly formal process of thought. Any concept A is RUDIMENTA. 37 arctius significent) quam Divisum. Nam Totum a:op. vi. est majus partibus singulis. 2. Dividentia con- ' junctim plus minusve ne contineant quam Divisum. Nam Totum est aequale partibus universis. 3. Mem- bra Divisionis sint opposita, (i. e. in se invicem ne contineantur :) nam sine distinctione frustra est partitio. §. 8. DivisiONEM excipit"" (quae per Metapho- potentially divisible into A which is B, and A which is not B; and experience alone can determine whether either of these members includes under it really existing individuals or not. Logically, the division of animal into mortal and immortal is as good as that into rational and irrational. But this division is not strictly formal ; for B, the dividing attribute, not being part of the comprehension of A, has to be sought for out of the mere act of thought, after A has been given. This has been observed by Hoffbauer and Fries, who hence rightly maintain, against Kant, that even dichotomy by contradiction . is not an act of formal thinking. Cf. Hoffbauer, Logik, §. 138. Fries System der Logik, §. 92. The only strictly formal process of this kind is that distinguished as Determination, which consists in the reunion of a genus and difference previously elicited by analysis from a given concept. Formal Division thus presupposes Defi- nition. See Drobisch, Neue Darstellung der Logik, §. 17, 29, 30. " Excipit. The reason of this order is given by x\belard : " Quoniam vero divisiones definitionibus naturaliter priores sunt, quippe ex ipsis constitutionis suse originem ducunt, in ipso quoque tractatu divisiones merito priorem locum obtine- bunt, definitiones vero posteriorem." Dialectica, ed. Cousin. p. 450. This is true in a material point of view ; the matter of a definition being sometimes gained by division. But formally, the reverse order is preferable ; a formal division or determination being only possible after definition. See the last note. 38 ARTIS LOGICS ram quoque dicitur) Definiiio ; cujus est, assignare conceptus et voces, quibus ea, quae ab invicem distincta volumus, velut agrorum fines, ex limitibus suis dignoscantur. Quas cum definitis notiora esse debeant magisque obvia, Definitio vulgo dicitur Top.i.5.L Oratio explicativa definiti. Oratio (inquam) ut a nomine distinguatur ; Explicativa quoque, nam et nomen exprimit. An. Post. Definitio alia, Nominalis est, quae vocis signifi- II. 7. 5. . . cationem aperit ; alia, Realis, quae rei"" naturam. ° Rei, i. e. of an universal notion existing in the mind ; with- out entering on the question whether there exists any external universal nature corresponding to it. Since all such notions are represented by words, a real, or more correctly speaking a notional, definition, will at the same time unfold the meaning of 'tEe^vord by wliich the given notion is represented. Still ; the two kinds of definition must not be confounded. A real ■ definition has primarily for its object to analyse a complex j notion into its component parts. Words are employed \ secondarily, though unavoidably, as signs, both of the whole ; notion, and of the simpler notions of which it is composed, j sBut the object of nominal definition is to determine of what! hotion, simple or complex, a given word is the sign. The I notion may be abeady known, more or less clearly, by means of other signs, though we were not aware of its connexion with the word in question. A different distinction between nominal and real definition is given by Leibnitz, Nouveaux Essais, 1. iii. c. 3. If this account of real definition is correct, it will follow that the same notion admits of only one definition; since the same notion cannot be a combination of more than one group of attributes. And nothing can be more clear than Aristotle's testimony on these points, nothing more positive than his repudiation of the so-called accidental and physical definitions. (Cf. Top. vi. 4, 2. vi. 14, 5. i. 8. 2, 3. Metaph. vi. RUDIMENTA. 39 Realis iterum vel Accidentalis, sive Descriptio, quae definite accidentia (puta causas, efFectus^ propri- etates aliaque id genus) assign at ; vel Essentialis, quae partes essentiae constitutivas. Essentialis denique, vel Metaphysica sive Logica'', quae Genus 11, 15.) Nevertheless, on the strength of a misunderstood passage in the De Anima, (i. 1, 16.) the threefold division of real definition has been fathered on the Stagirite. For a fuller account of Aristotle's doctrine, see Appendix, note C. Before quitting this subject, it may be observed, that Logicians have perpetually confounded the thing or notion within the mind with the things or individuals without, i Thus Abp. Whately observes, that Logic is concerned with nominal definitions only ; because all that is requisite for the purposes of reasoning is, that a word shall not be used in different senses ; a real definition of any thing belongs to the science or system which is employed about that thing. On the contrary, Logic is concerned with real or notional definitions only: its object being to produce distinctness in concepts, which are the things of Logic. Nominal definitions belong to the grammars or dictionaries of particular languages. Even Kant (Logik, §. 106.) has not quite avoided this confusion. ° Metaphysica sive Logica. On this point the two great sects of the Schoolmen were at issue. The Realists, following the Arabians, divided Logic into two parts ; one, which treated of the essence of incomplex notions and things by definition; the other, of the truth of propositions as determined by argumentation. To this latter the greater part of the Aristo- telian Logic was regarded as belonging. The former was supposed to have formed a lost portion of the ancient science. The Nominalists, on the other hand, and more correctly, main- tained that to investigate the essences of things belonged to the province of Metaphysics ; the Logician, as such, assigning no actual definitions, but borrowing them as mere examples from the science to which they properly belong. As autho- rities for the two views, compare Albert, de Prsedicab. Tract, i. chap. 5, 6. with Occam, Logic, part i. chap. 26. 40 ARTIS LOGICiE et DifFerentiam ; vel Physical, quae partes Essentiae physicas, i. e. realiter distinctas : nam Genus et Differentia sola mente distinguuntur. E. g. Definitur homo Nominaliter'^, qui ex humo. p Physical definition is rejected by Aristotle, (Metaph. vi. 11.) on the ground that the physical parts are not parts of the species, but of the individuals. Aldrich's expression, " partes essenticB physicas," cannot be tolerated, unless we regard univer- sal notions as not merely real substances, but corporeal. In the example given by Aldrich, the so-called Physical definition may be regarded as merely an indirect mode of expressing the same notion that the Metaphysical definition expresses directly. It is thus merely an accidental variation of lan- guage, easily reduced to the direct form, and is so regarded by Albert, de Prsed. Tract, i. chap. 6. and by Occam, pt. i. eh. 26. In all other cases it is no definition at all. 1 Most Logicians reckon two principal methods of nominal definition: 1. by a synonymous term, e. g. " ensis est gladius :" 2. by Etymology, as ■ in Aldrich's example. The former is in fact translation, it being indifferent whether the synonyms belong to the same language or not ; the latter will in many cases be no definition at all ; a large number of words having quite lost their etymological meaning. Neither of these methods is countenanced by Aiistotle ; see Appendix, note C. The former may be traced to the Greek Commentators ; see Alexander, in Metaph. p. 442. ed. Bonitz. The latter is an innovation borrowed from the Rhetoricians, by whom it was called Notatio. See Cicero, Top. ch. 8. " In Mathematics, and in all strict Sciences," says Abp. Whately, " the Nominal and the Eeal Definition exactly coin- cide; the meaning of the word, and the nature of the thing, being exactly the same.'" This remark is based on Locke ; j (Essay, b. iii. c. 3. §. 18.) but it confounds the Heal EssenceV of Locke, i. e. the unknown constitution of each individual \ with the Logical Essence or contents of a general notion. Cf ' Zabarello Be Methodis, 1. i. p. 159. RUDIMENTA. 41 Accidentaliter\ Animal bipes implume. Metaphy- sice% Animal rationale. Physice, Ens naturale constans corpore organico et anima rationali. Bonae Definitionis leges potissimum tres sunt. 1 . Definitio sit adsequata definite : alias non Top. vi. explicat definitum. Quae enim angustior est, explicat tantum partem, cum definitum sit totum ; quae laxior, explicat totum, cum definitum sit tantum pars. 2. Ut per se clarior* sit et notior Top.vi.4. 2, 7. ^ Accidental definition is composed of genus and one or more properties. Accidents properly so called are expressly- rejected as useless in definition by Porphyry, Isag. 3. 15. and by Boetbius, Opera, p. 3, though admitted by some subsequent authorities. Hence animal risibile would be a better example than Aldrich's animal bipes implume. But the majority of Logicians have very properly regarded accidental definition, in any form, as no definition, but merely description. It does not analyse the contents of a notion, but enumerates marks by which one individual may be distinguished from each other. The same notion can have but one definition ; the same indi- 1 vidual may have many descriptions. Cf. Albert. 1. c. Occam, ' pt. i. ch. 27. Wyttenbach. Pracept. Log. p. iii. c. v. §. 14. Drobisch, §. 104. 8 Metaphysical definition, the only proper definition in the strict sense of the term, being by genus and differentia, (or more correctly by genus and differentim ; see Top. i. 8, 3. and supra, p. 24, note s.) it wdll follow, that all definable notions must be species. Hence summa genera, which have no differentiae, and individuals, which are distinguished only by accidents, are not definable. See Arist. Metaph. iv. 3, 6. (where for els read ov, supported by two Mss. and by Alexander, Schol. p. 693, a. 8.) vi. 15. 2. The supposed difference on this point between Aristotle and Locke, or rather Descartes, may be reduced to a verbal question. See Appendix, note C. * Per se clarior ; i. e. composed of parts greater in extension 42 ARTIS LOGICiE definito : alias non explicat omnino. Dico tamen per se, quia pei' accidens potest minus intelligi Top. VI. 2. quod notius est sua natura. 3. Ut justo vocum fop.vi.2. propriarum'' numero absolvatur : nam ex Meta- * phoris oritur ambiguitas, ex nimia brevitate obscu- ritas, ex prolixitate confusio. j than the definitum, though less in comprehension ; as are the I genus and differentia, as compared with the species. For the i more universal notions are yvcopLfxarepa cpvaei, though individuals ! and lower species are yvcopifxarepa r)[juv. See An. Post. i. 2. 5. I '^op. vi. 4. 7, 9. 1 " Vocum jwopriarum ; i. e. words in common use, called in Ai.-^Jii.^. the Ehetoric, (iii. 2, 2.) Kvpia ovopLara, i. e. sanctioned by popular use; "quern penes arbitrium est et jus et norma loquendi." Cf. Poet. 21. 5. Xeyo) he Kvpiov pev cp ;(;pa)i/rat eKaaroi. In the Topics, (vi. 2. 4.) they are called established names, {Keipem ovopara.^ RUDIMENTA. 43 CAP. II. De Propositione Categorica pura, §. 1. Secunda Pars Logicse agit de PropositioneH sive Enuntiatione ; quod est signum secundae ope-1 rationis Intellectus, sive Judicium verbis expres- sum. Quare, ad Propositionem legitimam requiritur. 1. Quoad vocem, ut sit Or alio affirmans^ e;^/Deint.5.]. negans, quae est ejus essentia. 2. Quoad sensum, ut verum vel falsum significet, Be intA.s. (id scil. quod res est, vel secus, dicat,) quod essen- * " Sed cum disseramus de Oratione, cujus variae species sunt, est una inter has ad propositum potissima, quae pronun- ciabilis appellatur, absolutam sententiam comprehendens, sola ex omnibus veritati aut falsitati obnoxia : quam vocat Sergius effatum, Varro proloquium, Cicero enunciatum, Grseci protasin tum axioma; familiarius tamen dUceiuY propositio.'" Apuleius de Dogm. Platonis, lib. iii. He has not distinguished between dnocpavais and Trpdracrts, — the former of which is rendered by Boethius emmciatio, the latter propositio. See Trendelenburg, Elem. §. 2. " 'A7r6^f contra ; sic Jit conversio tota. Conversion by contraposition, which is not employed by Aristotle, is given by Boethius in his first book, De Syllogismo Categorico. He is followed by Petrus Hispanus, who first gives the mnemonic, as above. It should be ob- served, that the old Logicians, following Boethius, main- tain, that in conversion by contraposition, as well as in the others, the quality should remain unchanged. Con- sequently the converse of "All A is B" is "All not B is not A," and of " Some A is not B," " Some not B is not not A." It is simpler, however, to convert A into E and O into I, (" No not B is A ;" " Some not B is A,") as is done by Wallis and Abp. Whately; and before Boethius by Apuleius and Capella, who notice tlie conversion, but do not give it a name. The principle of this conversion may be found in Aristotle, Top. ii. 8. 1. though he does not employ it for logical purposes. 60 ARTIS LOGlCiE Nam 1. sit vera E% puta Nullum A est B : Ergo (cum uterque terminus distribuatur) quodvis A difFert a quovis B. Ergo vicissim ; Ergo Nullum B est A. 2. Sit vera I : Ergo falsa est ejus Con- tradictoria E : Ergo et contradictorise simpliciter conversa : Ergo quae conversae contradicit, (i. e. expositae simpliciter conversa,) est vera. 3. Sit vera E. Ergo et ejus simpliciter conversa : Ergo et conversae subalternata : quae est expositae con- versa per accidens. 4. Sit vera A ; Ergo et ejus *= Sit vera E. This is the proof given by Theophrastus and Eudemus. (Alexander, SchoUa, p. 148. b. 29.) Aristotle proves it by the method called cKdeans, i. e. by the exhibition of an individual instance, (jKriOevat, exponere sensui ; whence a syllogism with singular premises is called syllogismus eocpo- sitorius.) Thus, No A is B, therefore No B is A, for if not, Some individual B, say C, is A. Then C is both A and B, and therefore it will not be true that No A is B ; which was the original proposition, i^ristotle does not assume the con- version of I to prove that of E, which would be arguing in a circle. For a fuller account, see Hamilton on Eeid, p. 696. Alexander himself offers a third proof by syllogism in the first figure. No A is B, therefore No B is A ; for suppose " Some B is A," and " No A is B," .*. Some B is not B. Having proved the conversion of E, those of A and I will follow from it. " All A is B, therefore Some B is A ;" or else No B is A, and therefore (by conversion) No A is B ; whereas we assumed All A is B. And again. Some A is B, therefore Some B is A ; or else No B is A, and therefore No A is B. For these proofs, the only assumption necessary is the principle of contradiction. But proof of any kind is super- fluous. Conversion and other immediate inferences are necessary results of the laws of thought, equally evident and more direct than the mediate inferences by syllogism. Neither process is dependent on the other. ^ RUDIMENTA. 61 subalternata : Ergo et subalternatae simpliciter con versa : quae est expositae per Accidens^. Ceterae Conversiones% cum sint partim ambiguae, d In Conversion, as in Opposition, Singular Propositions have been neglected by Aldrich. Concerning these, the following extract from Wallis may assist the learner. " Pro- positio Singularis, (sive Affirmativa sive Negativa,) cum semper Universalis sit, observat leges aliarum Universalium. Puta, Virgilius est Poeta ; ergo Aliquis Poeta est Virgilius. Item, Virgilius non est Grmcus ; ergo Nullus Grcecorum est Virgilius. Atque in aUis similiter. " Si autem Convertendee proposition is Prcedicatum sit Indivi- dmim, (quodcunque habuerit Subjectum,) Convertentis Suhjectum (quippe quod fuerat Convertendce Prcedicatum) Individuum erit ; propterea et Propositio Convertens (siqua sit) necessario erit Singularis, adeoque Universalis.''' See also Reid's Works, ed. Hamilton, p. 697. ® C(Bter(B conversiones. For the benefit of the curious, we quote the following : " Tres igitur sunt famosae apud Logicos conversionis species. Dico famosae, quoniam nonnulli mo- derni invenerunt duas alias conversionis species, quarum una est conversio propositionum nullius quantitatis, ut exclusivae et reduplicativae. Nam sic convertitur exclusiva ; tantum homo est rationalis, omne rationale est homo : reduplicativa autem sic convertitur : homo in quantum homo est rationalis, rationale est homo in quantum homo. Item propositionum modalium, ut hominem esse album est possibile, ergo pos- sibile est hominem esse album. Item alii imaginati sunt duas alias species. Prima est quando mutatur qualitas et non quantitas, ut hie ; omnis homo est animal, omne animal non est homo. Secunda est quando mutatur quantitas et qualitas, ut hie ; omnis homo est animal, aliquod animal non est homo. Verum quia hujusmodi conversiones non sunt in usu, nee nobis deserviunt pro reductione syllogismorum, ideo immorabimur circa primam et secundam speciem, tangentes breviter de tertia, omnibus aliis relictis." Javellus, de Pro- positione, cap. ii. 62 ARTIS LOGICiE partim falsae, partim ad praecepta Syllogismorum in utiles, in Logica negliguntur^ ' Is the converse an inference from the exposita, or, as Whately says, the same judgment in another form? This was an early point of dispute among the Schoohnen. See Albert, in Anal. Pr. Tract, i. cap. 8. Aristotle clearly considers it an inference; otherwise it would be absured to prove it. Eeid, in his Account of Aristotle's Logic, defines it as an inference, and the definition is accepted by his learned Editor. Kant, too, regards both conversion and opposition as syllogisms of the understanding, the new judgment being always different in form, though not in matter, from the old. As regards con- version per accidens, the exposita is clearly not identical wdth the converse ; as it cannot be substituted for it, but may be false, while the converse is true. But on the new system of Sir W. Hamilton, the predicate being quantified, and the proposition reduced to an equation between the terms, it is better to consider the converted proposition as identical with the exposita. RUDIMENTA. 63 CAP. III. De Syllogismo Categorico pura, §. 1. Tertia pars Logicae agit de Argumento'' sive Syllogismo, quod est signum tertiae opera- tionis intellectiis : nempe Discursus, vel Ratioci- nium Propositionibus expressum. Quare, cum Discursus^ sit progressus mentis ab uno judicio ad aliud^ perspicuum est in eo requiri 1. Aliquid unde discursus ordiatur. 2. Aliud quo perveniat. 3. Ea sic ab invicem pendere, ut unum ex alio, et alius vi innotescat ; secus enim, unum post aliud cognoscere, est tantum saepe judicare. Jam^ ex quo aliud cognoscendum est, ipsum Anal. Post. certe praecognosci debet ; et proinde quasi sine discursu notum, antecedere, poni, prcemitti : et ex eo reliquum concliidi, colligi, inferri et seqtd dicitur. Est autem duplex consequentia : 1. Materialis ; quando ex Antecedente Conse- quens infertur, sola vi Terminorum% quae est * Argument is not properly synonymous with syllogism, but with the middle term only. See Ed. Rev. No. 115. p. 218. ^ See before, p. 5. note k. ^ The force of the terms leads to a conclusion by suggesting to the mind certain additional truths concerning the things spoken of, which are not given in the premises. But this additional knowledge is clearly extralogical. See Appendix, note D. The m.atter of the syllogism is all that is given to and out of the act of reasoning : the form is what is conveyed 64 ARTIS LOGICS Argumenti materia: ut. Homo est animaL Ergo est vivens. 2. F or malts ; quando infertur propter ipsum colligendi modum, quae est argumenti forma; vX, B est A, C est B. Ergo C est A, Mutatis terminis et servata eorum disposition e, Materialis plerumque fallit, Formalis semper obtinet : et proinde haec solum in Logica spectatur, ilia, tan- quam mutabilis et lubrica, negligitur. Anal. Pr. Hisce iutellectis, opinor satis constare quo sensu Top.i.1.2. definiatur Syllogismus ; ^ Oratio in qua positis qui- in and by the act itself. The former is expressed in the terms of which the reasoning is composed, and which vary in every different act of thought; the latter appears in the relation in which those terms are thought to one another, as constituting premises which necessitate a conclusion. This remains within certain fixed limits in every different act of thought. The same principle of distinction may be applied to discern between the matter and form of concepts and judgments. The logical forms of the syllogism are exhibited in mood and figure, as those of the proposition in quality and quantity. Cf. Burgersdyck. Inst. Log. 1. ii. c. 6. " Forma syllogismi est apta trium propositionum dispositio ad conclusionem ex praemissis necessario colligendum. Haec aptitudo posita est in figura et modo." A distinction slightly varying from the above will be found in Crakanthorpe, Logica, 1. iii. c. 13. and another in Kant, Logik, §. 59. The latter has been censured by Krug, Logik, §. 72. d Arist. Anal. Pr. i. I. 6. SuXXoyior/xos be eVrt \6yos iv a TeOevTOiV TLpav erepov Ti rav Keijievcov e^ dvdyKrjs (TVfx^aivei ra ravra eivai. See also, Top- i. 1. 2. The latter definition is translated by Aulus Gellius, xv. 26. " Oratio in qua, consensis quibusdam et concessis, aliud quid, quam quae concessa sunt, per ea, quae concessa sunt, necessario conficitur." The word concessis RUDIMENTA. 65 busdam atque concessis, necesse est aliud evenire prwter^et propter ea quce posita sunt atque con- \ cessa, I §. 2. MuLTiE sunt ejus species; sed una tantum praesentis instituti ; nempe Categoricus simplex, i. e. qui constat tribus Propositionibus de inesse". E quibus duas priores sunt Antecedens, tertia Consequens; quae extra Syllogismum spectata (scil. quamdiu haeret in incerto) Prohlema\ etAnai. Pr. Qucestio^ dicitur ; in Syllogismo autem (nempe l 26. i*. post fidem factam) Conclusio, Quaestionis duoiLi". i. sunt extrema, Subjectum et Prasdicatum ; quorum de Convenientia vel Dissidio inquiritur, ope termini is too limited ; being strictly true only of the topical syllogism. Of. Trendelenburg, Elementa, §.21. On the charge of petitio ■principii, sometimes brought against the syllogism, see Ap- pendix, note E. ® i. e. pure Categoricals. ^ To yap avTO yevei Trpo^Xrjixa kol Xripfia kol 6}xo\6yqpLa kol crvfi' Trepao-jxa Koi d^ico/xa* navra yap TTporaaeis rfj cr)(e(T€L Tr)v 8ia(f)opau exovra' npoTidepevov yap els Se'i^iv ois pr] yvoopipov tt p 6 ^Xrj pa KaXeirat, Xap^avopevov de els aXkov del^cv Xrjppa Ka\ opoXoyqpa' a^iatpa be orav akrjdes fj koi e^ eavrov yvatpipov, dedeiypevov 8e av pire pacr pa. Alexander, Schol. p. 150, b. 40. This accords with the sense of Trpo^Xrjpa in Anal. Pr. i. 4. 15. i. 26. 1. The dialectical use of the term in disputation is not very different. Cf. Topics, i. 4. I, 3. i. 11. 1. Schol. p. 256, a. 14. 8 Qucestio ; to Cn^ovpevov, Anal. Post. ii. 1. 1. which term, however, has a more extensive application than is here assigned ; for two of the Qucestiones Scibiles, an sit and quid sit, cannot in all cases be determined syllogistically. See An. Post. ii. 3. and Appendix, note C. F 66 ARTIS LOGICS alicujus tertii ; idque propter Canones sequentes% in quibus vis omnis Syllogistica fundatur. 1. Quae conveniunt in uno aliquo eodemque tertio, ea conveniunt inter se. ^ These Canons are an attempt to reduce all the three figures of syllogism directly to a single principle ; the dictum de omni et nullo of Aristotle, which was universally adopted by the scholastic Logicians, being directly applicable to the first figure only. This reduction, so long as the predicate of propositions has no expressed quantity, is illegitimate; the terms not being equal, but contained one within another, as is denoted by the names major and minor. Hence, as applied to the first figure, the word conveniunt has to express, at one and the same time, the relation of a gi^eater to a less, and of a less to a gi-eater, — of a predicate to a subject, and of 1 a subject to a predicate. In the system of Sir W. Hamilton, sby assigning a quantity to the predicate, the terms of every proposition are equal in extent; and the Canons become legitimate representatives of the syllogism; but in this case they are only narrower statements of the true syllogistic laws ; which are given in the Principles of Identity and Contra- diction. (Every A is A; No A is not A.) These, with the Principle of Excluded Middle, (Every thing is either A or not A,) are the highest and most exact statements of the Necessary Laws of Thought. Cf. Prolegomena Logica, p. 2'23. Wallis mentions the Canons as recent innovations in Logic. " Nonnulli autem Logici, (nostri seculi aut superioris,) post- habita veterum probatione per Dictum de Omni et de Nullo, aliud substituunt illius loco Postulatum ; nimirum, Quce con- veniunt in eodem tertio conveniunt inter se. Inst. Log. 1. iii. c. 5. Cf. Bacon. Nov. Org. 1. ii. aph. 27. Melanchthon {Erotemata, p. 172.) mentions them as adopted by a sect of Logicians in his day. The earliest wi'iter to whom I have found them is Eodolphus Agricola, De Inv. Dial. i. 2. He describes at con- siderable length the office of the middle term as a measure of equality or inequality. RUDIMENTA. 67 2. Quorum unum convenit, alterum differt uni et eideixi tertio, ea difFerunt inter se. / 3. Quae non conveniunt in uno aliquo eodemque / tertio, ea non conveniunt inter se. Sunto enim A et C, nee assignari possit ejusmodi tertium. Ergo nihil babent commune ; Ergo non conveniunt inter se. 4. Quorum neutri inest quod non sit in alio, ea\ non difFerunt inter se'. , 5. Quae non probantur convenire in uno aliquo j eodemque tertio, ea non probantur convenire inter 1 se. Dubitari enim potest utrum detur ejusmodi tertium, et dubitatio ista non toUitur. 6. De quibus non probatur, convenire unum eidem alicui tertio cui alterum differt, ea non probantur difFerre inter se. Dubitari enim potest, utrum detur ejusmodi tertium, h. e. utrum alterutri insit quod non est in reliquo ; et dubitatio ista non tollitur^. * The third and fourth Canons relate to conditions under which no syllogism can exist. " Two things, which have not a point in common, are totally distinct." " Two things, which have not a point of difference, are undistinguishable." But if there is no such point, there is no middle term, and therefore I no syllogism. ^ The fifth and sixth Canons relate to conditions under I which no syllogism does exist. "If no point has been ! assigned, whether of agreement or difference." But if so, I there is no syllogism. I Hence these four cannot be called Canons of syllogism. j They may be useful, however, for examining the illogical j positions of an opponent. f2 68 ART IS LOGICJ£ §. 3. Ex sex hisce Principiis Syllogismi struc- tura sic deducitur. Anal. Pr. 1. In oiiini Syllogismo sunt tres, et tres tantum, termini. Nam Syllogismus^ omnis probat aliquam conclusionem : Et in ilia sunt duo tantum extrema : Et ilia neque convenire, neque difFerre probatur, sine uno, unoque tantum, tertio. Anai.Pr.i. Jam, Prasdicatum Quaestionis dici solet majus 1.6.1.1.5.7. extremum^ , major terminus; Subjectum Quaestionis, Anai.Fr. I. minor : Terminus vero tertius, cui quaestionis 38.8.1.4.3. . ^ 1.5.1.1.6.1. extrema comparantur, Aristoteli Argumentum, vulgo Medium'^: Nam Praedicatum Quaestionis plerumque amplius est Medio ; hoc minori. ^ Aristotle adopts an inverse method ; first examining the structure and stating the laws of each separate figm-e of syllogism, in An. Pr. i. ch. 4, 5, 6. and afterwards enumerating, as the result of the examination, the general laws applicable to all, in An. Pr. i. 23 sqq. On the respective merits of the two methods, see Pacius on An. Pr. i. 4. Reid, ed. Hamilton, p. 700. ^ Majus extremum ; to yt-el^ov aKpov, (also to TrpwTov, An. Pr. i. 31. 2.) minus; t6 eXaTTov, (also to eaxaTov, An. Pr. ii. 8. 3.) Terminus, 6pos, for the various meanings of which, see Waitz, vol. i. p. 370. Major term; fielCcovopos: minor; eXarrcoj/ opos, An. Pr. i. 5. 7. The definitions of the major and minor t^rms given in the text are condemned by Pacius, (on An. Pr. i. 7.) as inapplicable to the indirect moods. Aristotle gives a separate definition of the three terms in each figure. But the indirect moods may, without loss, be dispensed w^ith. An account of various theories of the distinction between the major and minor term will be found in Sir W. Hamilton's Discussions^ 2d Ed. p. 670. Aldrich's prcsdicatum qucestionis corresponds to the distinction maintained by Alexander and Averroes. " More correctly, " Aristoteli medium, Ciceroni aliisque argu- mentumS' See Ed. Rev. No. 115. p. 218. The nearest Greek \ I RUDIMENTA. 69 2. In omni Sylloffismo sunt tres, et tres tan turn, Anai.Pr.i. . . M Ti/r T 23.5.1.25. propositiones. Duae praemissae", in quibus Medium 8. i. 32. 8. cum extremis seorsim conferatur, (nempe Major, Auai. Pr. in qu^ cum majori; Minor, in qua cum minori ;) una Conclusio, in qua extrema invicem commit- tantur. N.B. ]. Quod Major dici solet simpliciter Pro- positio ; M'mor , Assumption . 2. Quod Medium non ingreditur conclusionem, alias idem per idem pro- baretur : adeoque non essent tres termini. 3. Ancipiti medio nihil conficitur. Neque enim/^nai. Pr. afFertur in hoc casuunum aliquod idemque tertium. Soph. . . Elench. vel in quo extrema conveniant, vel cui unum con- 4.1. veniat, alterum difFerat. 4. Medium non distributum'^ est anceps. Esto^^aLPr. ^ I. 24. 1. equivalent to argumentum is ttiVti?, which, however, as em- ployed by Aristotle, is a rhetorical, not a logical term, llie r-K'^ U k.»^ origin of Aldrich's blunder it is difficult to conjecture. ^j>. dy^Civ's { i,^*.^ /*> "' ° Major premise ; rj irpos tw fxelCovi aKpto irporao-ts. Minor premise ; rj irpbs t(o eXdrrovi aKpco Trporao-is. Conclusion ; crvfiTre- paa-fia, which also signifies minor term, Anal. Pr. ii. 14. The premise is not, properly speaking, called 6pos by Aristotle. In J such expressions as KadoXov ovtcov twv opcov, (Anal. Pr. i. 5. 2.) I there is an ellipsis of npos t6v erepov, and the phrase means I strictly, that one term is predicated universally of the other, / i. e. of the whole of the other. p As by Cicero, de Invent, i. 37. Fortunatianus, Rhet. lib. ii. Cassiodorus, de Art. ac Disc. ch. 2. Boethius, de Syll. Hyp. p. 614. The terms are of Rhetorical origin. Quintilian calls the major premise, Intentio; Inst. Orat. v. 14. The conclusion is called complexio ; a term also applied by Cicero to the Dilemma ; de Inv. i. 29. ** Distribution is not an Aristotelian term. It forms part of 70 ARTIS LOGlCiE enim B terminus communis in b et /3 divisibilis ; Ergo h et 13 sunt opposita : et tamen vera dicitur Aliquod B. est b et Aliquod B est 13, Quare aliquod B est Medium anceps. 5. Quare Medium in praemissis semel ad mini- mum distribui debet ; sufficit tamen, si vel semel distribuatur. Nam 1. ad probandum A est C, conveniat C alicui B, et A omni ; Ergo eidem alicui B : Ergo affertur unum aliquod idemque tertium &c. 2. ad probandum A non est C, conveniat C alicui B, et A differat omni ; Ergo eidem alicui B : Ergo affertur &;c. 6. Processus ab extremo non distributo in praemissis, ad idem distributum in conclusione, vitiosus est. Nam ex aliquo non sequitur omne, Esto enim verum quod aliquod ; Ergo potest esse verum quod aliquod non ; (nam Subcontrariae possunt esse simul verae ;) Ergo de aliquo potest affirmari quod non de omni. Esto rursus verum what the Schoolmen call parva logicalia ; a kind of appendix to analyses of the Organon ; containing matters, some evolved from, though not distinctly treated of by Aristotle, others com- plete innovations, more properly belonging to Grammar than to Logic. The greater part of these first appear in Petrus Hispanus. See Summulce Logicales, Tr. 7. The syllogistic rules concerning distribution are of course implied in Aristotle's account of each figure, though not enunciated separately as common to all. Thus, to say that the major premise in fig. 1. must be universal, or one premise in fig. 2, negative, is equivalent to a rule for distributing the middle term. The particular conclusion in fig. 3. in like manner forbids an illicit process of the minor term. RUDIMENTA. 71 quod aliquod non : Ergo potest esse verum quod aliquod : Ergo de aliquo potest negari quod non de omni. 7. Prsemissis negantibus nihil probatur : Affer- Anal. Pr. I 24 1 tur enim tertium cui utrumque extremum difFert ; * ' ' non autem cui vel utrumque conveniat, vel unum conveniat, alterum differat. 8. Si praemissarum altera sit negativa, erit etiam Conclusio. Nam praemissarum reliqua est affirma- tiva : Ergo extremorum unum difFert medio, alte- rum convenit : Ergo extrema difFerunt inter se : Ergo conclusio est negativa. 9. Contra, si Conclusio sit neerativa, erit etiam Anai. Pr. 1 . XT TrY» . 1.24.4. altera praemissarum. Nam extrema diiierunt mter se : Ergo eorum unum convenit medio, alterum difFert : Ergo praemissarum altera affirmat, reliqua negat. 10. Praemissis particularibus nihil probatur. Nam Anai. Pr. praemissarum altera affirmat : Ergo in ilia medium non distribuitur : Ergo distribui debet in reliqua : Ergo ilia est negativa in qua medium praedicatur : Ergo conclusio negativa : Ergo praedicatum ejus distribuitur, quod in praemissis non est distri- butum ; Fuit enim vel affirmativae terminus alter, vel subjectum negativae ; horum vero nuUus distri- buitur. 11. Si praemissarum altera particularis sit, con-Auai. Pr. clusio quoque particularis est. Sit enim 1. Prae- missarum altera particularis affirmativa ; Ergo in ilia nee extremum suum nee medium distribuitur : 72 ARTIS LOGlCiE Ergo medium distribuitur in reliqua, quae etiam Universalis est, sitque 1. Affirmativa : Ergo in ilia medium subjicitur, et extremum medio attributum non distribuitur : Ergo neutrum extremorum dis- tribuitur in praemissis : Ergo neutrum in con- clusione : Ergo conclusio particularis affirmativa est. Sit 2. Negativa : Ergo conclusio negativa : sed debet habere extremum non distributum : Ergo particularis negativa est. Sit 2. Pragmissarum altera particularis negativa : Ergo Reliqua Universalis affirmativa: Ergo in prae- missis duo tantum termini distribuuntur : Ergo Conclusio habet extremum non distributum : Ergo cum negativa sit, erit etiam particularis. An.Pr. I. 12. Quod si CoHclusio'' particularis sit, non necesse est praemissarum alteram particularem esse. Fieri enim potest, ut instituto meo sufficiat subalternata, quando subalternans potuit inferri. Et cum illae sint simul verae, liberum est utramvis inferre. Quanquam stricte loquendo, Argumentatio non est accurata ; nam Subalternatae Veritas non immediate deducitur ex praemissis, sed ex sub- altern ante. r This rule is given by Aristotle, not with reference to the subaltern moods, but to the third figure, in which two uni- versal premises only warrant a particular conclusion. An inverse rule of inference holds with regard to truth and falsehood : two true pi'emises necessitate a true conclusion ; but the truth of the conclusion does not guarantee that of the premises. Cf, An, Pr. ii. 2. 1. i RUDIMENTA. 73 Syllogismi generales regulas complectitur hoc Tetrastichon^ Distribuas medium ; nee quartus terminus adsit. Utraque nee praemissa negans^ nee particularis. Sectetur partem Conclusio deteriorem. Et non distribuat, nisi cum praemissa, negetve. §. 4. SuPEREST per hasce regulas inquirere, quot modis componi possunt tres Propositiones de inesse, ut Syllogismum conficiant. Qua in inquisitione duo I spectanda sunt. 1. Modus \ sive legitima determinatio Pro- ^ The earliest form of this mnemonic is that given by Petrus Hispanus : Partibus ex puris sequitnr nil, sive negatis. Si qua prdeit partis, sequitur conclusio partis. Si qua negata praeit, conclusio sitque negata. Lex generalis erit, medium concludere nescit. * Mood (rpoTToy) is not in this sense an Aristotelian expres- sion, (unless possibly in An. Pr. i. 28. 14?) ; but it is found in his Greek commentators. See Alexander, Schol. p. 1 50, b. 3. Aristotle in the same sense employs tttoxtis, An. Pr. i. 26. 1. He does not adopt an arithmetical calculation of possible moods distinct from considerations of figure, but shews, in each figure separately, what combinations of propositions are admissible, and what not. It may be observed, that the earliest scholastic Logicians do not consider Mood as com- posed of three propositions, but of the two premises only. Thus Petrus Hispanus defines " ordinatio duarum proposi- tionum in debita qualitate et quantitate;" so Aquinas, in Opusc. xlviii. de Syll. ch. 4. In this case the number of possible moods is only sixteen. This computation is preferable to Aldrich's, because sim- pler; but neither has any logical value. The legitimate 74 ARTIS LOGICS positionum secundum Quantitatem et Qualita- tem. 2. Figura, sive legitima dispositio Medii cum partibus Qusestionis. Modi sunt in universum 64. Nam, ut supra ostensum est, ad Syllogismum faciunt Propositiones tantum quatuor A. E. I. O. Quare concipi potest Quadruplex tantum Major in Syllogismo ; cuilibet vero Majori quadruplex tantum Minor adjimgi; unde 16. paria praemissarum : et singulis praemissis quadruplex tantum Conclusio ; unde 64. Modi Syllogismorum. AAA. AAE. AAI. AAO. *AEA. AEE. AEI. AEO. *AIA. AIE. AIL AIO. *AOA. AOE. AOL AOO. EAA. EAE. EAL EAO. *EEA. EEE. EEL EEO. *EIA. EIE. EIL EIO. *EOA. EOE. EOL EOO. lAA. lAE. lAL lAO. *IEA. TEE. lEL lEO. *IIA. HE. in. 110. *IOA. lOE. lOI. 100. OAA. OAE. OAL OAO. *OEA. OEE. OEI. OEO. *OIA. OIE. OIL 010. *00A. OOE. OOL 000. Ex his excluduntur sedecim per Regulam 7. determination ought to be such as the laws of Logic require ; not one which arises from a mere arithmetical calculation. ^ On logical grounds, there are eight valid combinations of M premises; viz. AA. AE. AI. AO. EA. EI. lA. QA . The con- clusion, being determined by the premises, cannot properly be reckoned as an independent element in the combinations. Cf. Fries, System der Logik, §.57. RUDIMENTA. 75 propter prsemissas negantes, viz. EEA. EEE. EEL EEO. *EOA. EOE. EOI. EOO. *OEA. OEE. OEI. OEO. *00A. OOE. 001. 000. Duodecim per Reg. 10. propter prsemissis particulares, viz. IIA. HE. III. 110. *IOA. lOE. lOI. 100. *OIA. OIE. OIL 010. Duodecim per Reg. 8. quia praemissarum altera negat, sed non Conclusio, viz. AEA. AEI. AOA. AOL *EAA. EAL EIA. EIL *IEA. lEL *OAA. OAI. Octo per Reg. 11. quia praemissarum altera particularis est, sed non Con- clusion viz. AIA. AIE. AOE. *EIE. *IAA. lAE. *IEE. *OAE. Denique quatuor per Reg. 9. quia Conclusio negativa est sed neutra praemissarum, viz. AAE. AAO. AIO. *IAO. Excluduntur igitur in universum Modi 52 = 16 + 12 + 12 + 8 + 4. e quibus multi contra plures regulas peccant, quamvis una tantum notetur. Supersunt (64 — 52 = ) 12 Modi ad Syllogismum utiles, viz. AAA. AAI. AEE. AEO. AIL AOO. *EAE. EAO. EIO. *IAL lEO^ *0A0. §. 5. FiGURiE'' Syllogismorum sunt 4. Nam " lEO has been condemned ever since the days of x'^puleius, /• ;^ ' as far as the second and third figures are concerned. It was sometimes allowed in the first, as the indirect mood Frisesmo, but should not have been retained by Aldrich, who does not recognise the indirect moods. With a direct conclusion, it ' manifestly produces an illicit process of the nmjor term4^j.,,,^v4-Y " ^ FigurcB, a-xnixaTa, An. Pr. i. 4. 15. "Figuras syllogismoruffiT"^ quae dicuntur (Apuleius 'formulas' vocat), ab Aristotele ap- pellatas esse Jul. Pacius putat, quia figuris geometricis ad- 76 ARTIS LOGICS Medium, quod cum utroque extreme comparatur, vel 1. subjicitur majori et tribuitur minori, et fit scriptis syllogismi ab eo illustrati sint. Equidem banc vocem non tam a geometricis petitam quam de ipso ordine termi- norum accipiendam putaverim, quern (rxvH-a appellari licebit, etiam si de geometricis figuris non cogitetur : sic enim supra commemoravimus ra crxwara ttjs Kanryopias (Metaph. V. 2. 1.), TO o'xVH'fi T^s- Ideas (Metapb. vi. 3. 2.), ra o-xVfJ-aTa tt]s Xe^ecoy (Poet. ]9. 7.), a-xvi^d TV drjfioKparias (Polit. vi. 4. 5.)." Waitz, vol. i. p. 384. On tbe otber band, Sir W. Hamilton, in a very interesting paper in tbe second edition of bis Discussions, p. 666. maintains tbe opinion of Pacius, and proposes a re- storation of tbe Aristotelian diagrams. Tbis dissertation contains a fund of valuable matter on tbe bistory and pbi- losopby of Logic, wbicb will well repay a careful perusal. Aristotle acknowledges only tbree figures ; looking ratber to tbe extension of tbe middle term, as compared with tbe otber two, tban to its position in tbe two premises. In tbis point of view tbere are only tbree figures possible ; for tbe relative extensions of tbe major and minor terms being given, the middle can only have tbree positions ; between tbe otber two, as in tbe first figure; greater tban both, as in tbe second ; or less tban both, as in tbe third. See Trendelen- burg, Elem. §. 28. Waitz on Anal. Pr. i. 23. 7. The invention of the fourth figure is attributed by Averroes (on Anal. Pr. i. 8.) to Galen. The latter may possibly have first called the five moods by that name, but they were known at a much earlier period as indirect moods of the first figure. An in- direct mood is one in which we do not infer tbe immediate conclusion, but its converse. Consequently, the predicate of the conclusion, which in a direct mood is the major term, is in an indirect one tbe minor. Tbe five indirect moods of the first figure were called Baralip, Celantes, Dabitis, Fapesmo, Frisesmo. The three first are clearly Barbara, Celarent, Darii, with the conclusions converted. With regard to the two last, tbe process is a little more intricate. They have negative minor premises, and thus offend against a RUDIMENTA. 77 \jigura prima; vel 2. tribuitur utrique, et fit secunda; vel 3. subjicitur utrique, et fit tertia; vel 4. tribuitur majori et subjicitur minori, et fit quarto. Quae omnia sequenti Schemate declarantur. Dispositio trium terminorum, scilicet majoris A, medii B. minoris C in Figura, 1. 2. 3. 4. B. A. A. B. B.A. A.B. C.B. C.B. B.C. B.C. C.A. C.A. C.A. C. A. Quare quselibet Figura excludit adhuc sex modos^ Nempe special rule of the first figure ; but this is checked by a counterbalancing transgression. For by simply converting 0, we alter the distribution of the terms, so as to avoid an illicit process. T^ius, All B is A (fap) No C is B (esm) Therefore Some A is not C (o) Where to infer " Some C is not A," would involve an illicit process of the major term. Some B is A (fris) No C is B (esm) Therefore Some A is not C (o) Where to infer " Some C is not A," would involve an illicit process of the major term. The invention of these indirect moods is attributed to Theophrastus ; not, however, on the authority of Apuleius, as asserted by M. St. Hilaire, but on that of Alexander, Schol. p. 153, a. 47. But they were clearly recognised by Aristotle; the last two in Anaf. Pr. i. 7. 1. the first three in Anal. Pr. ii. 1. 2. The passage in Apuleius does not refer to the indirect, but to the indefinite, syllogism. y Certain moods, not excluded by the general rules of syllogism, are rejected in some one figure, by what are called 78 ARTIS LOGIC.E 1. Propter Medium non distributum. Prima duos lAI. OAO. Secunda quatuor AAA. AAI. AIL lAI. Quarta duos AIL AOO. 2. Propter processum majoris illicitum. Prima quatuor AEE. AEO. AOO. lEO. Secunda duos lEO. OAO. Tertia quatuor AEE. AEO. AOO. lEO. Quarta duos lEO. OAO. 3. Propter processum minoris illicitum. Tertia duos AAA. EAE. Quarta duos AAA. EAE. Supersunt Modi certo et necessario concludentes 24. sex in qualibet Figura. I. bkr Omne B est A bk Omne C est B : Ergo rk Omne C est A. the special rules of that figure. These special rules are given as follows by Petrus Hispanus. 1 1. Minore existente negativa nihil sequitur. ^^ * 12. Maj ore existente particulari nihil sequitur. 1. Maj ore existente particulari nihil sequitur. Fig. 3. ■ 3. Ex puris affirmativis nihil sequitur. \3. In secunda figura semper concluditur negative. f 1. Minore existente negativa nihil sequitur. °* ' Is. In tertia figura conclusio debet esse particularis. These rules are all to be found in An. Pr. i. ch. 4, 5, 6. Of the fourth figure three special rules have been framed ; viz. 1. '* Quando major est affirmativa, minor semper est uni- versalis." Q. " Quando minor est affirmativa, conclusio est semper particularis." 3. " In modis negativis, majorem universalem esse oportet." ^ RUDIMENTA. 79 cE Nullum B est A /A Omne C est B : Ergo rEnt Nullum C est A. dA Omne B est A rl Aliquod C est B : Ergo I Aliquod C est A. /E Nullum B est A rl Aliquod C est B : Ergo Aliquod C non est A. A Omne B est A A Omne C est B : Ergo 1 Aliquod C est A. E Nullum B est A A Omne C est B : Ergo O Aliquod C non est A. 11. cEs Nullum A est B A Omne C est B : Ergo rE Nullum C est A. cAm Omne A est B Es Nullum C est B : Ergo trEs Nullum C est A. 80 ARTIS LOGIC.E /E. Nullum A est B ^I Aliquod C est B : Ergo nO , Aliquod C non est A. bAr Omne A est B O^ Aliquod C non est B : Ergo O Aliquod C non est A. E Nullum A est B A Omne C est B : Ergo O Aliquod C non est A. A Omne A est B E Nullum C est B: Ergo O Aliquod C non est A. III. dAr Omne B est A A^ Omne B est C : Ergo tl Aliquod C est A. /E/ Nullum B est A Ap Omne B est C : Ergo tOn Aliquod C non est A. dls Aliquod B est A Am Omne B est C : Ergo Is Aliquod C est A. I RUDIMENTA. 81 bOk Aliquod B non est A Ar Omne B est C : Ergo dO Aliquod C non est A. d\t Omne B est A Is Aliquod B est C : Erga I Aliquod C est A. fEr Nullum B est A Is Aliquod B est C : Ergx> On Aliquod C non est A. IV. brAm Omne A est B An Omne B est C : Ergo tip Aliquod C est A. cAm Omne A est B Ew Nullum B est C: Ergo E5 Nullum C est A. d\m Aliquod A est B Ar Omne B est C : Ergo \s Aliquod C est A. /E5 Nullum A est B Ap Omne B est C : Ergo O Aliquod C non est A. G 82 ARTIS LOG1C.E frEs Nullum A est B Is Aliquod B est C : Ergo On Aliquod C non est A. A Omne A est B E Nullum B est C: Ergo O Aliquod C non est A. Barbara ^ Celarent, Darii, Ferioque, prioris : Cesare, Camestres, Festino, Bar oka, secundae : « Tertia, Darapti, Disamis, Datisi, Felapton, Bokardo, Ferison, habet : Quarta insuper addit Bramantip, Camenes, Dimaris, Fesapo, Fresison : ^ Barbara, Celarent, &c. This mnemonic first appears in the SummuliB Logicales of Petrus Hispanus, (see on p. 48.) But in his version the fourth figure is omitted, and its moods given as indirect moods of fig. 1 . This earliest edition of these celebrated lines runs thus : Barbara, Celarent, Darii, Ferio, Baralipet, Celantes, Dabitis, Fapesmo, Frisesmo, deinde Cesare, Camestres, Festino, Baroco, Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison. Several other versions are found in later writers. A Greek mnemonic of the same kind is inserted in editions of the Organon preceding that of Pacius. (See Buhle's Aristotle, vol. ii. p. 628.) It runs thus : Fig. 1. ypdjiixaTa — eypayj/e — ypacpldi — rexyiKos. Fig. 2. eypay^e — Kare;(e — perpicv — a)(o\ov. Fig. 3. anaa-L — adevapos — laaKis — (fiepto-ros — aa-TnSi — ofxakos. This mnemonic is attributed by M. St. Hilaire to Nicephorus Blemmidas ; but Sir W. Hamilton, in a note appended to the second edition of his Discussions, p. 669, has shewn that the Greek mnemonic is in all probability only an imperfect attempt at conversion into Greek of the Latin memorial of Hispanus. RUDIMENTA. 83 Quinque Suhalterni, totidem Generalibus orti, Nomen habent nullum, nee, si bene colligis, usum. §. 6. Atque omnes quidem 24. eatenus con- cludere, quod *in iis convenientia vel dissidium extremorum certo atque necessavio colligatur, ex Principio primo et secundo abunde constat. Quod aliter demonstrat Aristoteles ad hunc modum. Statuit primo Theorema, quod Scholastici vocant Anai.Pr.i. Dictum de Omni et Nullo'', scil. " Quod praedicatur * Aeyofiev be to Kara navros narqyopelaOaL, orav fXTjdev rj Xa^clv tS>p rov vTTOKei^evov, KaG" ov Bdrepov ov Xex^rjcreTar kol to kuto firjbevos coaavTcos, An. Pr. i. 1. 8. The same principle is implied in the first antipredicamental rule, Categ. 3. 1. oo-a KaTo. rov kott]- yopovfievov Xeyerai ivdvTa Kol KaTO. tov VTroKCifievov pr]6f)aeTai. Indeed, Aldrich's version is more nearly a translation of the latter than of the Dictum properly so called. Cf. Petr. Hisp. Tract, iv. *' Dici de omni est, quando nihil est sumere sub subjecto, de quo non dicatur prsedicatum, Dici de nullo est, quando nihil est sumere sub subjecto a quo non removeatur praedicatum." The Dictum de Omni et Nullo is most improperly called a Theorem. This term in Aristotle is synonymous with Cn'^H-^y and means a proposition, the truth of which is to be inquired into, not one laid down as an axiom. See Topics, i. 11. 1. Alexander, Scholia, p. 259, a. 38. The dictum is directly applicable only to the first figure, which- is considered by Aristotle as the type of all syllogisms, and to which the others have to be reduced, as a necessary test of their validity. In this he is followed by Kant, Logik, §. 69. Other Logicians enunciate distinct axioms for the second and third figures. This has been done by Lambert, Neues Organon, part i. ch. 4 §. 232. but he is far from happy in his enunciation of the dicta. We may state them as follows, in a somewhat improved form. g2 84 ARTIS LOGICi*: " Universaliter de alio, (i. e. de termino distribute,) '' sive affirmative, sive negative, praedicatur similiter " de omnibus sub eo contentis." Principle of second figure. Dictum de Diverso. If a certain attribute can be predicated (affirmatively or negatively) of every member of a class, any subject, of which it cannot be so predicated, does not belong to the class. Principles of third figure. I. Dictum de Exemplo. If a certain attribute can be affirmed of any portion of the members of a class, it is not incompatible with the distinctive attributes of that class. II. Dictum de Exeepto. If a certain attribute can be denied of any portion of the members of a class, it is not inseparable from the distinctive attributes of that class. The natural use of the second figure, according to Lambert, is for the discovery and proof of the differences of things : that of the third, for the discovery and proof of examples and exceptions. Concerning Lambert's imaginary principle of the fourth figure, see p. 9 1 , note n. Lambert's principles are criticised by Krug, Logik, §. 109. According to Sir W. Hamilton, {Discussions, 2^d Ed. p. 666.) " it was Melanchthon who first excogitated, as he thought, the various principles on which proceed the various syllogistic figures." The following may be gathered from his Erotemata Dialectices. Principle of first figure, Posito genere, necesse est speciem poni. Principle of second figure. Remoto genere, removetur species. Principle of third figure. Posita specie, necesse est genus poni, sed particulariter. There is a third manner of treating the syllogistic figures ; viz. by regarding them as all equally direct applications of one and the same principle. This has been attempted by Aldrich and others in the Canons ; (see p. 66.) but inaccm-ately. The three ultimate Laws of Thought are the Principles of Identity, of Contradiction, and of Excluded Middle. These ai'e directly applicable to all the syllogistic figures alike. RUDIMENTA. 85 Admisso hoc Theoremate (quod axioma sponte perspicuum est) constat una, modos quatuor priores in prima certo atque necessario concludere. Nam eorum major ostendit majus extremum prse- dicari de medio distributo ; et minor, minus ex- tremum sub medio contineri. Quare, Modi quatuor praedicti nihilo penitus indigent quo necessitas conclusionis appareat, praeter ea quae in praemissis posita sunt ; et proinde quatuor illi sunt prae caeteris evidentes. Nam caeteri omnes aiiquo vel aliquibus egent, quae, utcunque per praemissas necessaria, in Syllogismo tamen non exprimuntur. Quare illos Aristoteles Anai.Pr.i. perf ectos^, \io^ imperf ect OS di\c\t\ SchoXdi^Wci direct os. Other general principles, but less accurate, have been given by the Port-Eoyal Logic, part iii. ch. 10. by Buffier, Principes du Haisonnement, Let. vi. vii. and by Euler, Lettres a uns Prin- cesse d'Allcmagne, p. ii. 1. 36. ed. Cournot. For a criticism of the Port-Royal principle, cf. Duval-Jouve, Logique, p. 306. ^ TeXeiov (xeu ovv koKo) (TvXkoyicrfibv tuv firjdevos aXXov npoadeo^evov irapa to. etXrjfxixeva Trpos to (PavTJvai to dvayKoiov, dTeXrj 6e top npocr- beopevov fj evos y nX^ioucov, a eaTi, pev avayKoia dia tcov vnoKeipeuoiv opcBf, ov prjv (iXrjTTTai Sta TrpoTaaecov, Anal. Pr. i. 1. 7. With Aristotle, the " dictum de omni et nuUo" is the principle of all syllogism ; and the conversions, &c. required by the im- perfect syllogisms, must be performed before their conclusions are admitted as valid. The direct and indirect syllogisms of the Schoolmen must not be confounded with the perfect and imperfect of Aristotle. An indirect syllogism is one in which the minor term is the predicate, the major the subject of the conclusion. See Aquinas, Opusc. xlviii. de Syll. cap. 8. Scotus, super lib. I. Anal. Prior, QusBst. xxii. sqq. Occam, Logica, p. iii. cap. 6. Of these in- direct moods, five were admitted in the first figure, two in 7.3 86 ARTIS LOGICS et mdirectos vocant : quia per illos ad conclusio/nem, velut ad scopum, recta itur ; per reliquos eodem perveniri potest, prius tamen alio deflectendum est. An. Pr. I. Perfici" igitur et revocari at que reduci dicimus 1. 23. i. indirectos, cum per modum aliquem directum illationis suae vim demonstrant. Et definitur Reductio^, imperfecti Modi in perfectum mutatio, quo necessitas illationis fiat ex inevidenti evidens. Fiet autem, quando evidenter (h. e. in prima) ostenditur conclusionem vi prasmissarum vel 1. An. Pr. I. talem esse ; vel 2. aliam esse non posse. Unde Reductio est vel osteiisiva vel ad impossihile^, the second, (by converting the conclusions of Cesare and Camestres,) three in the third, (by converting the conclusions of Darapti, Disamis, and Datisi.) Cf. Anal. Pr. i. 7. ii. 1. Of these, the five in the first figure are the most important, being sometimes regarded as a fourth figure. See p. 75, note x. The perfect and imperfect moods of Aristotle are sometimes called immediate and ynediate. Cf. Aquinas, Op. xlviii. cap. 1. Occam, Log. p. iii. cap. 2. Boethius calls them indem^onstrahle and demonstrable. ^ Perjici, — TeXeiovadai, iiiLTeKetaOai; {jekelaxris OCCUrs An. Pr. i. 25. 8.) Reduci, dvdyeaOat, (never dndyeo-Oai:) oste)isively, deiKTiKws. ^ Reductio. The value of Keduction in Logic will depend : on the principle adopted as the basis of the syllogism. In the systems of Aristotle and Kant, whose principles ai-e im- mediately applicable only to the first figure, reduction is necessary. In the system of Lambert, in which each figure rests on a separate axiom, reduction is impossible ; the process being then the destruction of one distinct reasoning, and the substitution of another. By reducing the laws of thought to their simplest form, in which they are applicable to all syllogisms directly, reduction is superfluous. « Reductio ad impossihile. This phrase, though sanQtioned RUDIMENTA. 87 Utriusque praxin pro Modis nominatis decent ipsa Modorum nomina a Scholasticis in hiinc finem conficta. Nam in iis tres vocales sunt totidem propositiones Syllogismi sua quantitate et qualitate signatae. Consonae initiales B. C. D. F. notant modum primae, ad quem sit Reductio. S. P. propositionem, quam vocalis proxime ante- cedens designate esse in Reductione convertendam : S simpliciter ; P per accidens. M transponendas esse praemissas. K reductionem fieri per impos- sible, i. e. pro praemissa, cujus symbolo adhaeret^ sumendam esse Conclusionis contradictoriam *. Quibus ex praescripto factis, colligitur in prima by respectable authorities, is incorrect; as may be shewn by substituting the definition. What is the meaning of " the change of an imperfect to a perfect mood to the impossible?" The error has been caused by the Aristotelian expression, airayoiyri els to advvarov ; in which, however, diraycdy^ does not mean reduction. The deductio ad impossihile, as it is usually rendered, {ahductio would perhaps be better,) is one species of the (Tv\Xoyi(Tfi6s e$ vTTodeo-eas, (see Appendix, note I,) the object of which is, to prove the truth of a given problem, by inferring a falsehood from the assumption of its conti'adictory. This may be emplo^^ed in the reduction of syllogisms, but it is also used for other purposes, as by Geometers. (Euclid, i. 7.) The correct expression is therefore Reductio per deductionem ad impossibile, or elliptically, Redtictio per imp>ossihile. The aTraywyiy of An. Pr. ii. 25. will be explained hereafter. Any mood may be reduced by the deductio ad impossibile, though in practice it is usually confined to Baroko and Bokardo. *■ Whence the lines, S vult simpliciter verti ; P vero per acci : M vult transponi ; C [Kj per impossibile duci. 88 ARTIS LOGICiE conclusio vel expositas eadem, vel earn inferens, vel prasmissse contradictoria^ ut in exemplo. cEs Nullum A est B Ar Omne C est B: Ergo E Nullum C est ad A. cE Nullum B est A Ik Omne C est B: Ergo rEnt Nullum C est A. dls Aliquod B est A Am Omne B est C: Ergo Is Aliquod C est ad A. dk Omne B est C rl Aliquod A est B: Ergo I Aliquod A est C. hkr Omne A est B Ok Aliquod C non est B: Ergo Aliquod C non est ad A. bkr Omne A est B hk Omne C est A: Ergo rk Omne C est B/ g Archbishop Whately gives an ostensive reduction of Baroko and Bokardo to Ferio and Darii, by converting the major premise by contraposition. Logic, b. ii. c. 3r~^§. 5. RUDIMENTA. 89 §. 7. Reductionis ostensivse validitas sic osten- ditur. Ex praemissis reducendi, per conversionem imperatam^ necessario colliguntur praemissse re- ducti : atque ex iis^ per figuram primam, conclusio reducti : quae vel ipsa conclusio reducendi erit^ vel per illativam conversionem fiet. Reductionis per Impossibile validitas sic osten- ditur. Quoniam praemissae ex hypothesi sunt I semper verae, ergo contradictoria praemissse nun- j quam vera : ergo contradictoria conclusionis nun- I quam vera : (nam has simul veras esse demon- stratur in Barbara) ergo contradictoria conclusionis * semper falsa : ergo conclusio ipsa semper vera, [Reducitur etiam quilibet modus innominis, facto quod praecipitur, ad prsemissas sui subalter- nantis. Tum vero conclusio, quae colligitur in prima, erit vel expositae subalternans, vel in expo- sitam per accidens convertetur. Reductiones' (cum primae ad reliquas, tumAn.Pr. i. 45.1. This had been done before ; partly by Jung, in the Logica Hamburg ensis, B. III. ch. 12. §. 15. and partly by Wolf, Philo- sophia Rationalis, §.384. ^ Since a false conclusion cannot be drawn without at least one false premise, see An. Pr. ii. 2. 1. But in the present syllogism, one premise is given true, being one of those of the original syllogism ; the other, therefore, is false, which is the contradictory of the original conclusion. The syllogism ad impossibile will not always be in Barbara ; though it is so in the reduction of Baroko and Bokardo. ^ Of these reductions, it need only be observed, that they are only possible where the same problem can be proved in both figures ; hence only negative syllogisms can be reduced 90 ARTIS LOGICS earum ad se invicem) bene multas, quod et obviae sint^ et institute nieo minus necessarise, praeter- An. Pr. 1. mitto. Illud tamen notatu dignum est, quod cum Darii ad Camestres, et Ferio ad Cesare redu- catur per impossibile, uterque igitur ad Celarent ; omnisque adeo modus reducitur ad duos universales primae.] §. 8. Perspicuum est ex antedictis 1. Syllogismos simplices, certo atque necessario concludentes, fieri 24 modis : 6 in qualibet figura. An. Pr. i! 11. Et in aliquo istorum modorum probari posse conclusionem quamlibet de inesse ; nempe A uno modo, E quatuor, I septem, O duodecim\ Et An. Pr. I. rursus ; in prima, conclusionem quamcunque : In An. Pr. I. secunda, omnes et solas ne2:ativas : In tertia, omnes 5. ]6. o " An. Pr. I. et solas particulares : In quarta, quamlibet praeter A. De praemissis denique, quod in prima et secunda, major semper universalis est ; in prima et to the second figure, and only particular syllogisms to the third. Barbara, Baroko, and Bokardo, cannot be ostensively reduced to any other figure, except by the use of conversion by contraposition. ^ Kejecting the fourth figure and the subaltern moods, it will be better to say with Aristotle ; A is proved only in one figure and one mood, E in two figures and three moods, I in two figures and four moods, O in three figures and six moods. For this reason, A is declared by Aristotle to be the most difficult proposition to establish, and the easiest to overthrow; O, the reverse. And, generally, universals ai'e most easily overthrown, particulars more easily established. ^ RUDIMENTA. 91 tertia, minor affirmativa: In secunda, praemissarum altera negativa : aliaque ejusmodi ; quae ipsa modorum nomina satis indicant ^ At que hinc facile colligitur, inspecto schemate An, Pr. i. modorum^ quali medio probanda sit quaestio omnis i. 32. 10. de inesse. e. g. Quaestio A probatur in Barbara ; medio, de quo praedicatum quaestionis universaliter affirmatur, quodque de subjecto quaestionis affir- matur itidem universaliter : et sic de caeteris. Adverte tamen quod imperite disputantis est afFerre modum innominem ; ponet enim in prae- missis plusquam opus est ad conclusionem. Quare et innomines hactenus sunt incensi ; quamvis negari nequeant, sicubi per inscitiam adhibentur"". ,. Adverte etiam, quod figura quarta tribus caeteris deterior est ; cum aliis de causis, tum ex hoc praesertim, quod medium dicat de majori, huric de minori, minorem de medio, h. e. medium nugatorie de seipso". ^ See p. 77, note y. "• The invention of the five anonymous moods is attributed by Apuleius to Aristo of Alexandria. " This objection is brought against Galen by Averroes, on Anal. Post. I. 8. It might be better stated, majorem nugatorie de seipso. Reckoning backwards from the conclusion, we find that the major contains the minor, the minor the middle, the middle the major; so that, in fact, the major contains itself. The fourth figure has been defended by Lambert, who declares it to be useful for the discovery or exclusion of the species of a genus. He frames a principle for it, called dictum de reciproco. I. If no M is B, no B is this or that M (Ca- menes). II. If C is or is not this or that B, there are B's 92 ARTIS LOGICS III. Syllogismis etiam adnumerantur aliae argu- mentorum species ; quae nee stricte loquendo Syllogismi sunt, nee ita tamen peccant, ut prop- terea mereantur excludi : in quibus scilicet reticetur argumenti pars aliqua, sed quam proclive est cogi- tatione substituere. Anal. Pr. 1. Enthymema ; cuius antecedens constat pro- II 27 2 Riet.i.*2. positione et judicio ; nam judicium est propositio in mente ° ; e. g. Homo est animal ; ergo est vivens. which are or are not C. (Bramantip, Dimaris, Fesapo, Fresison.) The principle is sufficiently clumsy ; the utility questionable. For the syllogism is not an instrument of discovery ; and how- can we prove the species of a genus by a particular conclusion? •* Some B is C," only proves a separable accident. It may be observed also, that the objection which Lambert urges, and with reason, against the conversion of the second and third figures, viz. that by conversion we often substitute an un- natural and indirect for a natural and direct predication, does not hold as regards the fourth. For, in the first three moods no conversion of premises is needed. By regarding the first stated as the minor, the second as the major, we obtain a much more natural conclusion in the first figure. Fesapo and Fresison establish exceptions, and therefore, on Lambert's theory, should more naturally fall into the third figure. The whole distinction, however, between natural and unnatural predication relates to the matter, not to the form of the thought. o Propositio in ynente. Aldrich had in his mind the absm'd etymology from iv dvtxc?, or as Versorius gives it, " ab en quod est in, thymos, quod est mens, et monos, quod est unum, quasi in mente retinens unam propositionem." The erroneousness of this etymology (besides its intrinsic absurdity) appears from the word hOvfirjixa being found in the Greek language before it assumed a technical meaning; e. g. Soph. CE. C. 292, 1199. Some Logicians attempt to distinguish between the RUDIMENTA. 93 Dicitur etiam Aristoteli Si/llogismus Oratorius ; et, si Integra ejus vis contineatur in unica propositione, senientia Enthifmematica ; utrumque Quintiliano Rhet. ii. , ,, ,. . . 21.6. sententia cum ratione ; ut, Mortalis cum sis, immor- tale ne geras odium. Deest illi ad Syllogismum altera praemissarum ; utrum vero major an minor, ex quaestione dignoscitur. 2. Inductio ; in qua ponitur quantum opus est Anai. Pr. de singulis, et deinde assumitur de universis ; ut, Hic et ille et iste magnes trahit ferrum ; ergo omnis. Est igitur Enthymema quoddam ; nempe Syllo- gismus in Barbara p, cujus minor reticetur. 3. Ejcem^lum ; (Aristoteli Inductio Oratoria'^) knsi.vr. Rhet. I. 2 19 Logical and the Rhetorical Enthymeme, (see Sanderson, b. iii. eh. 8.) The distinction is not authorized by Aristotle, and is liable to the objection which must always lie against a wanton alteration of the meaning of technical terms. For the Enthy- meme of Aristotle, see Appendix, note F. p The supposed minor is, of course, " All magnets are this, that, and the other." In this perversion, Aldrich has been preceded by Zarabella, De Meth. lib. iii. cap. 3. Archbishop Whately departs still further from Aristotle, and makes Induction a Syllogism in Barbara with the major premise suppressed. Thus : " That which belongs to this, that, and the other magnets, belongs to all ; Attracting iron belongs to this, that, and the other ; Therefore it belongs to all." ^ For the real nature of Logical Induction, see Appendix, note G. *> Aldrich considers the Example as an Induction ; i. e. according to his view, as a Syllogism in Barbara with the minor premise suppressed. The supposed minor, according 94 ARTIS LOGICiE iibi quod ponitur de singular! noto, assumitur de simili ignoto : ut, Sylla et Marius Inceravere rem- publicam ; ergo Ccesar et Pompeius lacerahunt. Hujus etiam minor reticetur ; quapropter (ut in caeteris) quaestionem assumi dico ; neque enim colligitur nisi ex posito et subintellecto. 4. Sorites^ ; in cujus Antecedente^ ex ordinata to this view, will be, " Csesar and Pompey are Sylla and Marius." But the example proper is not a logical reasoning at all; being a compound of an imperfect, and therefore illogical, Induction and a Syllogism. See further, Appendix, note H. ' The Sorites is a series of propositions, in which the pre- dicate of each is the subject of the next; the conclusion being formed of the first subject and the last predicate. It may be expanded into a series of syllogisms in the first figure, the conclusion of each being the minor premise of the next. There will be as many syllogisms as there are intermediate propositions between the first premise and the conclusion; the first being the only minor premise stated. Hence there can only be one particular premise in a Sorites, the first ; the others being major premises in the first figure. And the last is the only premise which may be negative : for any previous negative premise would produce a negative conclusion, which could not be used as a minor premise in the next syllogism. The Sorites is not recognised as a distinct kind of reason- ing by Aristotle. Nor is there any reason why it should have been ; as it is merely a combination of ordinary syllogisms, succinctly expressed. Its distinct exposition is attributed to the Stoics. But the principle, as Melanchthon observes, is implied in Categ. 3, 1. and the Sorites itself is alluded to in Anal. Pr. i. 25. 2, 11. There is another form of the Sorites, called the regressive or Goclenian, first given by Goclenius in his Isagoge in Organum Aristotelis. In this, the subject of each proposition is the predicate of the next ; the conclusion being RUDIMENTA. 95 serie terminorum, prsecedens quisque subjicitur sequent!, donee a subjecto qusestionis pervenitur ad prsedicatum, v. g. Homo est anhnal : animal est vivens : vivens est substantia ; ergo Homo est sub- stantia. In Sorite igitur subaudiuntur Syllogism! quot sunt intermediae propositiones ; (vel si mavis, quot in antecedente termini intermedii ;) unde et a curaulo nomen habet. 5. Soriti affinis est Syllogismus, cujus prsemis- sarum altera est sententia Enthymematica^; ut, Nullus injustus est amandus : Omnis Tyrannus {crudelis cum sit) est injustus; ergo Nullus Ty- rannus est amandus. Qui quidem Syllogismus pe- culiare nomen non habet*; praemissae autem En- formed of the last subject and the first predicate. E. g. All D is E, all C is D, all B is C, all A is B ; therefore all A is E. In this, when expanded, the conclusion of each syllogism is the major premise of the next. In this Sorites, only the first premise can be negative and the last particular. This, as Krug has remarked, should really be called the progressive; the ordinary Sorites the regressive. A much more complicated theory of Sorites is given by Herbart, Lehrbuch zur Philosophies §. 70. and by Drobisch, Logik, §• 81 ; but it is of little logical value. The Sorites must not be confounded with the well-known fallacy of the same name, attributed to Eubulides of Miletus, and mentioned by Cicero, De Divinatione, ii. 11, In fact, the name has been loosely applied to various kinds of reasoning. ' On the Enthymematic sentence, see Arist. Khet. ii. 21. 6. ' It is sometimes called an epicheirema. The word originally was synonymous with Dialectic Syllogism. See Top. viii. 11, 12. Of this epicheirema or argumentatio, the Khetoricians enumerated various kinds, tripartita, quadripartita, quinque- partita, dc. See ad Heren. ii. 2. ii. 19. Cic. de Inv. i. 37 sqq. 1.39. 96 ARTIS LOGICtE Anal. Pr. thymematicse antecedens, Aristoteli Prosyllogismus I. kjj. 11. ^^ 1.28.5. est\ 6. Hue denique revocandum est compendium illud disputandi opponentibus usitatissimum, reti- cendi scilicet conclusionem ; cum sit ipsa quaestio, quam respondens non supponitur ignorare. [Admittuntur denique in Scholis etiam Syllo- gismorum formulae, quia contra regulas voce tantum, non sensu, peccant, et mutata phrasi ad canonicas facile revocantur. Suntque nihil aliud quam licentise qusedam Syllogisticse, et in accurata disputatione non videntur admittendse. Anai.Pr. 1. Quaudo pro termino repetendo substituitur vox illi aequipollens. Ut in hoc. Ens naturale constans corpore organico et anima raiionali est homo: Socrates est ejiismodi : ergo est homo, et similibus. Potest enim Sophista abuti ista libertate vel ad nugandum vel ad fallendum. 2. Quando fiunt Syllogismi ex obliquis, qualis est, Omnis hominis equus currit : Socrates est homo ;. ergo Socratis equus currit. Pro minori rectius dixeris Socratis equus est hominis equus, alias con- Quint. Inst. V. 13. Finally, the name Epicheirema was limited to the quadripartite. Cf. Trendelenburg, Elem. §. 33. Schweighfeuser on Epictetus I. 8. For some other variations in the use of the name, see Krug, Logik, §. 113. " Not exactly. The prosyllogism, or antecedent syllogism, of Aristotle, is a syllogism employed to prove one of the premises of another syllogism. It need not be expressed in a curtailed form. See Pacius on Anal. Prior, i. 35 3. Biese, vol. i. p. 157. I RUDIMENTA. 97 sequentia, licet bona, non erit immediata. Atque |illo insuper laborat disputatio omnis ex obliquis, I quod praster necessitatem aperit locum fallaciae, 3. Quando propositio aliqua intelligitur contra quam sonat, e. g. Quod non liahet partes non \intent per dissolutionem partkim : Aniyna liumana non liahet 'partes: ergo anima humana non interit per dissolutionem partium. Nam major sonat nega- tive, intelligitur vero affirmate : puta^ Quod interit &c. habet partes. Vel etiam singula propositiones intelliguntur affirmate, ac si esset Syllogism us, Omne expers est incorruptibile : Anima humana est expers ; ergo anima humana est incorruptihilis. Eodem accenseri possunt Syllogismi quales I Author Artis cogitandi^ vocat Complexos, in quibus etiam dijudicandis jactat se satis imperite. v. g. p. 164. laudat hunc Syllogismum, Lex divina jubet Reges honor ari: Ludovicus XIV est Rex; ergo Lex divina jubet Ludovicum XIV honor ari. Ubi valet certe Argumentum ; Syllogismus tamen est " Author Artis Cogitandi. The work alluded to is "I'Art de penser," commonly called the Port-Royal Logic. This work has been ascribed to various authors, but Avas most probably written by Arnauld, assisted by Nicole ; the first j edition was published at Paris in 1662. Aldrich has on more jthan one occasion spoken too slightingly of this very valuable iwork, the Logic par excellence of the Cartesian Philosophy. I For a better estimate of its merits, the reader is referred to I Stewart's Preliminary Dissertation to the Encyclopaedia Bri- tannica, p. 80. and to the Introduction to the recent able Translation of the Port-Eoyal Logic, by Mr. Baynes. H 98 ARTIS LOGICtE falsissimus, cum habeat quinque terminos. Nam ex conclusione patet quod major terminus est juhet Ludovicmn XlVhonorari, et minor Lex divina: ergo minor Propositio Lex divina jubet Reges honor ari: ergo Medius terminus ^'2/6^^ Reges hono- rari : ergo Major Propositio debuit esse, Quoa jubet Reges honor ari, jubet Ludomcum XIV hono- rari ; et turn valeret Syllogismus ; nee redun- darent duo termini, qui in secunda propositione jam redundant. P. 166. Syllogismum hunc improbat^ Debemus credere Scripturce: Traditio non est Scriptura; ergo non debemus credere Traditioni ; quia eum scil. imperite reducit ad primam, cum tamen Syllo- gismus apertissime hoc dicat in secunda, Objectum jidei divince est Scriptura: Traditio non est Scrip- tura ; ergo Traditio non est Objectum Jidei divi?ice. Ibidem imperite autumat Syllogismum sequen- tem, in quo omnes propositiones videntur affir- mativae, esse in secunda ; salvari vero, quia minor sensu exclusiva, negativam in se contineat. Quod si ipsos Syllogismi terminos rite dignoscere potu- isset, vidisset sane Syllogismum esse in Barbara transpositis praemissis, v. g. Bonus Pastor estparatus animam ponere pro ovibus ; Pauci hoc smculo sunt "^ Syllogismum hunc improbat. In this instance, it is scarcely necessary to observe that the Port-Royal Logicians are right, and Aldrich is wrong. The premise does not state that nothing but Scripture is to be believed ; and therefore the con- clusion drawn is illogical. RUDIMENTA. 99 parati &c. ergo Pauci hoc sceculo sunt Bo?ii Pas- tores. Hujus conclusio perspicue dicit (non de paucis, quod sunt Boni Pastores, sed) de Bonis Pastoribus, quod sunt hoc saeculo pauci. Quare Major terminus est hoc sceculo pauci, et Minor Boni Pastores. Ergo Minor Propositio, Boni Pastores sunt parati &c. et Medius terminus, parati animam ponere pro ovihis, Syllogismus vero hie est. Qui parati sunt animam ponere pro ovihus sunt hoc sceculo pauci : Qui sunt Boni Pastores sunt parati animam ponere pro ovibus : ergo qui sunt Boni Pastores sunt hoc sceculo pauci^. Haec dixisse erat operae pretium, nequis temere repudiaret eos qui, si non videntur, sunt tamen revera Syllogism!.] y Hoc sceculo pauci. Aldrich's solution is untenable. "Few" is not predicated distributively, but collectively. From " wise men are few," we cannot infer, •' Socrates is few." The syllogism, therefore, as stated by Aldrich, becomes a fallacy of division ; though, when tested by common sense, it is un- questionably valid. The Port-Royal Logicians substitute for the minor premise, Multi Pastores hoc scecuIo non sunt parati, dc. which is perhaps the most satisfactory way of treating the proposition, regarded as a single statement. But in fact it contains two distinct assertions; 1st, that some men are prepared ; 2dly, that most men are not. The reasoning should thus be resolved into two distinct syllogisms. See Kant, Logik, §.31. H 2 100 ARTIS LOGICS CAP. IV. De Syllogismls Hypotheiicis^, §. 1. Syllogismus Hypotheticus, est in quo una, duae, vel tres propositiones hypotbeticae. v. g. Si sapit, est beatus : Sapit ; ergo est heatus. Vel, Qui sapit est heatus : Si est Philosophus, sapit ; ergo Si est Philosophus^ est beatus. Vel, Si sapit, est beatus: Si est Philosophus, sapit ; ergo Si est Philosophus, est beatus. Nos de eo tantum loqui instituimus qui est caeteris usitatior, in quo nempe Major Hypothetical * Hypothetical syllogisms, in the present sense of the term, are not treated of by Aristotle. An exposition of them was first sketched out by Theophrastus, which was afterwards further developed by Eudemus and the Stoics. None of these works, however, have come down to us. A few notices may be gathered from the Greek commentators ; but our principal extant authority on the subject is Boethius. Of the crvWo- yiaixol e| vTrodeaecos of Aristotle, which Pacius has confounded, and M. St. Hilaire attempts to identify, with the hypotheticals of Theophrastus, some account will be given in the Appendix, note I. In the Prolegomena Logica, p. 211, I have given a theory of hypotheticals different from that commonly adopted by Logicians. Bnt that theory, though I believe it to be more accurate than that of Aldrich, differs too widely from his text to be admissible here. I have therefore transferred it to the Appendix, note I. ^ This is the only kind of hypothetical syllogism in which the conclusion is categorical. If the minor premise, or both premises, are hypothetical, the conclusion is so too. A syllogism with all three propo?idons hypothetical was called by Theophrastus, di okov vnoB'^iKosy (Scholia, p. 179. a. 16.) RUDIMENTA. 101 Propositio Hypothetica late sumta definitur^ Plures Categoricae per conjunctionem aliquam unitse, et conjunctio vocatur Copula; estque Conditionalis, Disjunctiva, Causalis" &c. ut apud Grammaticos ; unde totideni Hypotheticarum species, suis copulis cognomines. Sed ad Syllogismum non faciunt, Praeter Conditionalem, et Disjunctivam^ ; quarum exempla. Si sapit est beatus, Vel dies est Del nox. Conditionalis habit vim illativam. Unde Con- ditio ipsa, sive pars prior, quae est instar inferentis, Antecedens dici solet ; Assertio, sive pars posterior, quae ration em habet illatae, Consequens ; partiumque inter se connexio. Consequential, •= Causalis, e. g " Because A is B, C is D." This is, of course, only a hypothetical in the loose sense of the above definition. In the same sense were admitted temporal hypo- theticals, "When A is B, C is D ;" locals, "Where A is B, C is D," &c. &c. The causal hypothetical proposition is really a curtailed hypothetical syllogism. " Because A is B, C is D," is equivalent to "If A is B, C is D, and A is B." Cf. Hoff- bauer, Logik, §. '^86. ^ Nothing can be more clumsy than the employment of the word conditional in a specific sense, while its Greek equivalent, hypothetical, is used generically. In Boethius, both terms are properly used as synonymous and generic ; the two species being called conjiinctivi, conjuncti, or connexi, and disjunctivi, or disjunctL Cf. Edinhuryh Review, No. 115, p. '219. Boethii Opera, p. 610. The nomenclature of Boethius is followed by Ramus. With reference to modern usage, however, it will be better to contract the Greek w^ord than to extend the Latin I one. Hypothetical, in the following notes, will be used as I synonymous with conditional. \ ^ It has been questioned whether Hypothetical Syllogisms I can be reduced to Categorical. This question must not be 102 ARTIS LOGICiE Conditionalis cujusque sententia est, quod, data Conditione, datur Assertio ; quod bifariam explicari confounded with the inquiry, whether the hypothetical pro- position is formally the same with the categorical. The latter is answered by Kant in the negative, but that decision does not affect the present question. The reduction of hypothetical syllogisms must be governed by the same rules as that of categoricals ; and in the latter case, it is allowable to substitute for a given proposition another which, though not identical, is implied by it. For instance, a particular converse is employed instead of its universal exposita. So in hypotheticals, if the new propositions contain the same terms, and are immediately deducible from the original ones, the reduction is legitimate. This will generally be the case when the hypothetical pro- position has but three terms ; both clauses having the same subject or the same predicate. The following instances may thus be reduced : — r All B is C, to I All A is B; I .-. All A is C. All A is B, All C is A ; .-. AUG is B. to . I. If All A is B, All A is C) But All A is B ; .-. All A is C. II. If All A is B, All C is B, But All A is B; .-. All C is B. These syllogisms, indeed, were admitted by the Ramists, the great advocates of hypotheticals, to be categorical. But where the hypothetical has four terms, as, " If A is B, C is D," this mode of reduction is not practicable; yet even in this case a categorical syllogism may be constructed, whose propositions, though expressed in different terms, are implied in those of the original syllogism. Thus : Constructive. Destructive. Every case of A being B, is a Every case of A being B, is a case of C being D. case of C being D. This is a case of A being B. This is not a case of C being D. .-. This is a case of C being D. .-.Thisisnotacaseof A beingB. The above directions are all that can be given on the ordinaiy I RUDIMENTA. 103 potest. 1. Si detur Conditio, danda est Assertio ; unde Regula prima: Posita Antecedente, recte ponitur Consequens. 2. Si daretur Conditio, danda esset K^?>eri\o\ unde Regula secunda : Sublata Consequente, recte tollitur Antecedens. Porro hoc unum statuit, Antecedente vera, veram esse Consequentem ; non autem ambas esse simul veras, aut simul falsas, aut una vera, falsam alteram : per illam igitur, sublata Antecedente, poni vel tolli potest Consequens ; aut posita Consequente, poni vel tolli Antecedens. Unde Regula tertia: Sublata Antecedente, vel Posita Consequente, nihil certo colligitur^ Conditionalis igitur Syllogismi duae sunt, nee plures, formulae. I. Quae vocatur Constructiva, Si C. D. tum K. A. Sed C. D. ergo K. A. theory of hypotheticals. The first method of reduction is only approximately true ; and various ingenious examples have been framed by Logicians, to which it is inapplicable. See Krug, §. 82. Fries, §. 62. The truth is, that the so-called hypothetical proposition is really the statement of a conse- quence, which is sometimes formal, sometimes material ; and in the latter case, the consequence is extralogical, and cannot be reduced to any logical form, without additional assump- tions, derived from the matter treated of See Prolegomena Logica, p. 21 J. Appendix, note I. I ' By adopting the adove modes of reduction it may easily be seen, that the violation of this third rule is equivalent, in ! the case of denying the antecedent, to an illicit process of I the major term ; in that of affirming the consequent, to an ! undistributed middle. 104 ARTIS LOGICiE II. Quae dicitur Destructiva^, Si CD. turn K.A. Sed non K. A. ergo non C. D. §.2. QuiE de Conditionali dicta sunt. Disjunctives satis cavent. Ejus enim in Syllogismo positae sententia conditionaliter efferri semper potest \ s The destructive syllogism is naturally reduced to the second figure in the categorical form, and cannot in most cases be brought to the first without considerable awkward- ness. This may be avoided by converting the hypothetical before reduction. A hypothetical proposition is converted by Contraposition ; thus, " If A is B, C is D," to, " If C is not D, A is not B." The syllogism may then be treated as a con- structive. Cf. Hamilton on Eeid, p. 697. Whately's Logic, b. ii. eh. 4. §. 3. Hypothetical as well as Categorical reasonings may be combined in a Sorites. The Hypothetical Sorites consists of a series of propositions, in which the consequent of each is the antecedent of the next ; the conclusion being composed of the first antecedent and the last consequent. Thus : Constructive Sorites. Destructive Sorites. If A is B, C is D. If A is B, C is D. If C is D, E is F. If C is D, E is F. If E is F, G is H. If E is F, G is H. .-.If A is B, G is H. .-. If GisnotH,AisnotB. See Wolf, Phil. Rat. §. 470. ^ With regard to the import of the disjunctive proposition, Logicians are at issue. The majority (Kant among the number) regard it as stating all possible cases ; so that one only of its members can be true. And Aquinas maintains that any disjunctive proposition in which this condition is not observed, is false. On this supposition all the four inferences given by Aldrich are valid. But it may be questioned whether the incompatibility of the members appears in the form of i RUDIMENTA. 105 V, g. Si posita vel C vel D Subsumatur Sed C ergo non D D non C non C ergo D non D C Pro exposita Disjunctiva die conditionaliter every disjunctive proposition. We may happen to know that two alternatives cannot be true together, so that the affirmation of the second necessitates the denial of the first, and the affirmation of the first the denial of the second ; but this, as Boethius observes, is a material, not a formal consequence, whether it be stated in the hypothetical or disjunctive form. It must be allowed that the examples sometimes adduced on this side of the question have not been very happily chosen. It sounds oddly enough to state a known truth as a possible falsehood, as in the instance, " Bellum Trojanum cecinit vel Homerus vel Virgilius.'" But other and more natural specimens have been given ; e. g. " Aut olim Troja fuit, aut historia de hello Trojano est merafabiila." The case is still clearer when both members of the disjunctive are negative, as in the example given by Boethius, " Si enim quis dicat, aut non est album aut non est nigrum, sive album non esse as- sumpserit, non necesse erit esse vel non esse nigrum ; sive nigrum non esse assumpserit, ut sit vel non sit album, nullam faciet necessitatem." On this supposition only two of the above syllogisms are valid, which may be reduced to hypothe- ticals as follows : Constructive. Destructive. If A is not B, C is D. If A is not B, C is D. But A is not B. But C is not T>. .-.CisD. .-. AisB. For a further account, see Wallis, Log. Thes. 2. 106 ARTIS LOGICiE Si C turn non D D non C non C turn D non D C §. 3. SuPEREST Syllogismus quidam Hypothe- ticus redundans^ alio nomine Dilemma' y quia ple- ' Of the word Dilemma, various etymologies have been proposed; 1. a choice of alternatives offered to an adversary; 2. a double premise assumed (X^/x/xa) ; 3. a not veiy probable one given by Keckermann, " a Sis Xafi^dveaOai, quia utrinque capit et constringit adversarium contra quem adducitur." The first seems to be adopted by Aldrich, and is perhaps supported by Cassidorus, Expos, in Ps. 138, 9. "Dilemma, quod fit ex duabus propositionibus pluribusve, ex quibus quicquid electum fuerit, contrarium esse non dubium est." Cf. Victorinus in 1 Rhet. Cic. 86. But whatever be the origin of the word, it was certainly employed as synonymous with the complexio of Cicero, (de Inv. 1. 29.) This is expressly stated by Servius, (on ^n. ii. 675.) who is, I believe, the oldest extant writer in whom the word is found. In this sense it may be defined, (omitting the adversary, as belonging rather to Rhetoric or Dialectic than Logic,) " A syllogism, having a conditional major premise with more than one antecedent, and a dis- junctive minor." Its different forms may be thus exhibited : I. Simple Constructive. If A is B, C is D ; and if E is F, C is D ; But either A is B, or E is F ; .-. C is D. II. Complex Constructive. If A is B, C is D ; 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. \ RUDIMENTA. 107 rumqiie duo (etsi interdum plura) proponit adver- sario capienda ; quorum utrumvis acceperit, causa cadet. Tale est illud Biantis, Si uxorem ducas formosam, hahebis KOLvr]v, communem; si deformem, TTOLPTji/, poenam : ergo Nulla est ducenda^, ^Hoc non valet, nisi ita comparetur, ut partem alteram accipi sit necesse ; utraque autem feriat ; nee possit retorqueri. Quae si vidisset Bias, suo sibi Dilemmate minus placuisset ; neque enim vel formosa uxor vel deformis necessario futura est ; sed est media qusedam pulchritudo, quam Ennius III. Destructive, (always Complex.) If A is B, C is D ; and if E is F, G is H ; But either C is not D, or G is not H ; .*. Either A is not B, or E is not F. There cannot be a simple destructive Dilemma of this kind, as is shewn by Abp. Whately, Logic, b. ii. ch. 4. §. 5. There is another form of reasoning, sometimes called Dilemma, which is also a hypothetico-disjunctive reasoning, but which, instead of having the major premise hypothetical and the minor disjunctive, has both combined in the major; the whole of the disjunctive consequents being denied in the minor, E. g. " If A is B, either C is D, or E is F ; but neither C is D, nor E is F; therefore A is not B." This foi-m is given by Wallis, lib. iii. cap. 19.; as well as by Wolf and Kant. But it is a perversion of the Dilemma proper, and introduces no distinction whatever ; being merely a common disjunctive syllogism, as is shewn by Wallis himself. It is, in fact, the enumeratio, not the complexio, of Cicero. ^ See Gellius, Noct. Att. v. 11. ^ These remarks entirely relate to the matter, and have nothing to do with the Logical character, of the Dilemma. See Whately, ii. 4. 5. 108 ARTIS LOGlCiE statam appellavit ; Favorinus eleganter iixoriam. Porro, nee formosa omnis est communis, nee Arist.Rhet. deformis, poena. Denique Dilemma faeile retor- II 23 15 queri potest. Puta, Si formosam duxero, non hahebo pcenam ; si deformem, non hahebo communem. Dilemma nihil aliud est, quam Inductio Nega- tiva"^ ; in qua Syllogism! Major Conditionalis est "^ This remark is taken from Wallis, and is only applicable to the Dilemma in his sense of the term. The negative induction appears categorically in this form : There are no instances of C being D, nor of E being F. But these are all the possible instances of A being B. .'. There is no instance of A being B. The Dilemma of Aldrich cannot, as it stands, be reduced to this form. The categorical conclusion, e. g. Nulla uxor est ducenda, does not follow from the premises of the Dilemma of Bias ; but requires the additional assumption, that neither matrimonial nuisance is, under any circumstance, to be endured. This brings it to Wallis's form, thus : Si duceyida est uxor, aut formosa ducenda est, aut deformis: Atqui non est ducenda formosa, neque deformis: Ergo, Uxor non est ducenda. (Burgersdyck, Inst. Log. ii. 13.) The Complex Dilemma, as given above, may be reduced, if required, to a series of hypothetical syllogisms, and so to categoricals : thus : Constructive. Destructive.. If E is F, G is H ; If E is F, G is H ; If A is not B, E is F ; If C is D, G is not H ; .-. If A is not B, G is H. .-. If C is D, E is not F. If C is not D, A is not B ; If A is B, C is D ; .-. If C is not D, G is H. .-. If A is B, E is not F. The reduction of the simple Dilemma is obvious enough. RUDIMENT A. 109 cum consequente distributiva : puta. Si omnino, turn sic, vel sic, vel sic; quam afferre Categorice adeo est proclive ut non indigeat prsecepto. But all such reductions, except as serving to vindicate the universality of the syllogistic model, are rather curious than useful. 110 ARTIS LOGICiE CAP. V. De Syllogismo quoad Materiam, §. 1. HtEC de Syllogismo quoad Formam spec- tato. Jam de eodem quoad Materiam, h. e. Certi- tudinem et Evidentiam proposition um ex quibus componitur. Certa autem propositio est, cui nihil occurrit in contrarium, vel quod occurrit instar nihili est; ut, Omnis homo est risibilis^ : Evidens, quae simul a This definition is vague enough : the example, however, shews more clearly what is intended. For risihile was regarded as a property, flowing from, and demonstrable by, the dif- ferentia rationale. We may therefore define a certain pro- position as " a proposition capable of demonstration." It will thus be distinguished from an evident proposition, which is axiomatic and indemonstrable. Both are, of course, necessary, which is essential to demonstrative reasoning : but the former is the conclusion of a demonstration ; the latter, a premise. Waiving the physical question of the necessary connection of risibility and rationality, we may give as examples, of a certain proposition, " The angles of every triangle are equal to two right angles ;" of an evident, " Things which are equal to the same are equal to each other." Such seems clearly to be Aldrich's meaning in the present passage ; in which certa and evidens correspond to what are commonly called immediata immedietate subjecti, and immediata immedietate causa. (Cf. Sanderson, lib. 3. cap. 12. from whom this part is chiefly taken.) Aldrich's subsequent language, however, is by no means consistent. RUDIMENTA. Ill ac percipitur assensum imperat ; ut, Totum est ji majus sua parte: Dubia, in qua haeremus, cum j illius pars utraque valde se probet intellectui ; ut, I Astra regu7it homines ; nam et regere et non regere i videntur. j Dubitanti siquid aliud occurrat, quo pendens animus in alterutram partem propendeat, quod erat Dubium fit Probabile^, Et potest, quod pro- Top.i.i.3. batur, Verum esse, sed probanti tantum Verisimile est. Multis nihilominus assentimur isto modo, et assensui nomen est Opinio^ Est igitur Opinio propositionis tantum probabilis; An. Post. eique nulla competit certitudo ; sed in ipsa sui ratione includit formidinem oppositi. Sunt Opi- nioni tarn en Gradus quidam ad certitudinem, pro diverso pondere rationum quae assensum movent, diversi. Est quod omnibus, quod plerisque, quod Top.i. 1.3. sapientibus videtur ; et quod horum singulis, quod plerisque, quod celeberrimis ; quorum omnium dispar est probabilitas ; quorumdam vero tanta, ut ad certitudinem quam proxime accedat. §. 2. Qui Opinionem (h. e. assensum quemlibet scientia minorem) parit, Syllogismus appellatur ^ "'EvSo^a de ra doKOvvra Traaiv rj toIs TrXeiVrois fj rols aocfyoi^y Kol TovTOLs 1) TTaaiv ^ Tols TrXelarois ^ toIs /xaXtora yvoapi^OLs Koi ivbo^ois. Arist. Top. i. 1.3. Such propositions form the premises of dialectical syllogisms. '^ Aeinerai So^av eivai nepl to dXrjBes fxev 77 ylrev8os, ivbc\op.€Vov oe KoX aK\a>s ex^iv- Tovto d' earit/ vnoKrf^is rrjs dfxev t etvai Koi TrparoiV Koi dfxeo-cov Koi yvaypiixcorepcov Koi npoTepcov koi alricov tov (TvprnepdapLaTos. Anal. Post. i. 2. 2. See further, Appendix, note K. 122 ARTIS LOGlCiE CAP. VL De Methodo'', §. 1. Methodus est talis dispositio partium ali- cujus disciplinae, ut Integra facilius discatur^ * MiOobos in Aristotle is employed with various shades of meaning; 1. for any instrument of acquiring or communicating knowledge; as in de An. i. 1.4. norepov aTrodei^is rls ea-nv ^ diai- p€(Tis Tj Kai Tts oKXtj fieOoBos. Cf. Philoponus, Scholia, p. '^35, a. 10. 2. for knowledge reduced to system ; and thus as equivalent to ima-Tfjfir} : Phys. Ausc. i. 1. 1. Eth. Nic. i. 1. 1. Top. i. 2. 2. 3. for a systematic treatise on any branch of knowledge, synonymous with irpayfiaTeia: Polit. iv. 2. 1. vi. 2. 6. Eth. Nic. i. 2. 9. But method, in the present sense of arrangement^ is not treated of in the logical writings of Aristotle, with the exception of a few rules for the arrangement (rd^is) of a dialec- tical disputation in the eighth book of the Topics. A lost treatise, called Methodica, is mentioned in the Rhetoric, I. 2. Method, as a distinct part of Logic, was first introduced by Ramus, and from him passed to the logical writings of the Cartesians and of Gassendi, by whom it was treated as a fourth part of Logic. Like most of the additions to the Aristotelian system, it was originally the property of the Rhetoricians. ^ Method has been treated of by Logicians in two principal senses. 1. As a process of inference from the known to the unknown ; which is the earlier sense of the term, and sanc- tioned by Aristotle and his Greek interpreters. 2. As an arrangement of truths already known, with a view of com- municating them to others. The last corresponds to the Greek rd^is, and should rather be called Ordo. It is distin- guished from the first by Zabarella and others. Aldrich's definition corresponds only to the second sense of Methodus ; but in his subsequent division he confounds it with the first. RUDIMENTA. 123 Estque duplex. 1. Inventionis, quae disciplinae Eth. Nic. praecepta invenit ; 2. Doctrines, quae tradit. Prior p'hys.Ausc. ! procedit a sensibilibus, et singularibus, quae sunt I nobis notiora, ad intelligibilia, et universalia quae sunt notiora natures ; posterior^ contra ^ Method in either sense is not properly a part of Pure or Formal Logic. It is an application of Logic to the discovery or communication of truths in material science : its rules cannot be determined a priori from the laws of thought ; but must be gathered empirically from the examination of parti- cular sciences, and will require modification in many instances from the particular matter with which they have to deal. <^ The Methodus Inventionis can only be a process of inference : for no arrangemeyit of parts is possible before they have been discovered. The discovery of general principles from individual objects of sense, if limited to the inferential process itself, will be Induction. The term, however, is sometimes extended so as to include the preliminary accumulation of individuals. In this wider sense it will embrace the four successive steps given by Aristotle, Anal. Post. ii. 19. aiaOrjcns, iJ-vfifMrj, einrcipia, inayoiyrj. But the Methodus Inventionis must not be absolutely limited to Induction and its preliminaries, though these are the most important instruments of discovery. In some sciences, as in mathematics, truths are chiefly discovered by demonstration ; and, till so discovered, cannot, of course, be imparted to others by the methodus doctrines. Induction and Syllogism are the only two methods of inference. The Greek commentators, Ammonius and Eu- stratius, enumerate four, adding Division and Definition ; but in these last there is no reasoning process. See Zabarella, de Methodis, lib. iii. cap. 5 sqq. If we extend the method of discovery beyond the process of inference proper, so as to include any accumulation of knowledge, we may distinguish three principal instruments. 1. Pure experience, applicable to 124 ARTIS LOGICS Methodus Doctrinae duplex est. ^Perfecta, aKpoa- IxaTLKT] ; et Imperfecta, e^corepLKr}. Perfecta rur- sus, vel Universalis est, qua Integra disciplina, vel Particularism qua aliqua disciplinae pars docetur. Utraque duplex est. An. Post. 1. Compositoria sive Synthetical, quae inservit L 10. 4. Eth. Nic. I. 2. 5. the acquisition of historical knowledge. 2. Demonstration, applicable to sciences of pure reasoning. 3. Induction, ap- plicable to mixed sciences of reasoning and fact. Cf. Fries, System der Logik, §, 117. ^ The Methodus Doctrines is not in the same sense a process of inference from known to unknown ; for the parts are sup- posed to be known already to the teacher, and are methodically arranged for the benefit of the learner. This then corresponds rather to Order than to Method in the proper sense. It may be an arrangement either of the whole or of a portion of a subject; and is thus either universal or particular. Cf. Zabarella, de Methodis, lib. ii. cap. 20. The distinction between the Perfect and Imperfect Method is not usually recognised by writers on the subject. Aldrich is thinking of the acroaynatic and exoteric teaching of Aristotle and others ; the characteristic feature of the latter being the suppression of certain doctrines as not fitted for a promiscuous audience. Whereas the universal and particular Methods merely relate to the whole and the parts in the same exposition. e On Synthesis and Analysis, and the various employment of both, some remarks will be found in the Appendix, note G. The notion of Synthesis in the present passage corresponds to that of Metaphysical parts and whole, which is there men- tioned as applicable to a syllogistic process from a general principle to its particular application. Not so that of Analysis ; which in the present passage is also a process from the universal to the particular, not from the particular to the universal. By Suhjectum is meant the most general Subject whose pro- perties the Science investigates ; as Magnitude in Geometry^ RUDIMENTA. 125 disciplinis Theoreticis ; et a notione Suhjecti \ incipiens, principia ejus et species investigat, donee a summo genere in ista disciplina per- veniat ad infimam speciem^. 2. Resolutoria siveEth. Nic. Analytical, quae inservit disciplinis Practicis ; etvii. 9!4. ' Metaph. VI. 7. 6. The Principia are the apxaX i^ hv, or axiomatic principles, from which the demonstration commences. Species are the sub- divisions of the general Subject; as the square, the triangle, &C. Cf. Anal. Post. i. 10. 4. liaa-a yap dnodeLKTiKr) eTno-Trjfirj nepl rp'ia iuTLV, ocra re elvai Tiderat [ravra S' earl to yevos, ov to)v koB* avra iraOrjfjLaTcov ia-Ti deojprjTLKrj ) kol to kolvo. Xeyoiieva d^iaiJiaTa, i^ hv Trpoirav a.7rodeiKvv(Ti, koi rpiTov ra TrdOrj, hv tI (rrjfiaLvet eKaarov Xofi^dvei. On the position of these in demonstration, some remarks will be found in Appendix, notes C and K : see also Trendelenburg, Erlauterungen, p. 118. ^ " Exemplum evidens in primis est in scientia physica, I ubi primum tractatur de corpore naturali in genere, deque affectionibus ejus et principiis; post descenditur ad species corporis naturalis, videlicet corpus simplex, coelum, ele- mentum ; post mixtum, idque iterum vel imperfecte mixtum, vel meteora; post perfecte mixtum, idque iterum vel in- animatum, ut metalla, mineralia, vel animatum, idque vel vegetans, ut planta, vel sentiens : idque iterum vel irra- tionale, ubi tractantur omnia animalia bruta: vel rationale, ut homo; atque ita a summo genere ad species infimas devenitur. Eadem methodus observatur in mathematica et physica." Keckermann, Syst. Log. lib. iii. Tract, ii. cap. 1. Cf Zabarella, de Meth. lib. ii. cap. 7. s The Analytic, as well as the Synthetic Method, observes a deductive order from premises to conclusion. Its name then refers, not to the metaphysical relations of Species and Genus as whole and part, but to that common illustration of Aristotle's, by which, in productive or practical operation, the product or end is represented as a whole, and the materials or means as parts. The order of teaching will be the same as that of deliberation ; the reverse of that of operation. The following 126 ARTIS LOGIC.*: a notione Finis incipiens, subjectum, et tandem media mvestigat\ Regulse Method! generales hag sunt. In tra- denda disciplina 1. Nihil desit aut redundet. 2. Singulae partes inter se consentiant. 3. Nihil tractetur quod non sit subjecto aut fini homo- geneum. 4. Singulae partes aptis transitionibus connectantur. passages may illustrate the image. Eth. Nic. iii. 5. 11. oKka Sefxevoi riXos ri, 7ra>s Koi 8ia riva>v ea-rai (TKOirovcn, Kat hia TrXeiovoav jxev (paivofievov yiveadat 8ia tlvos pacrra Koi KoiKXiara €7n(TK07rovcri, 8i evoy d' eTnTeXovfxevov ttcos Blo. tovtov earai KOKelvo 8ta rivos, ecos av eXBacriv em ro Trparov airtov, 6 iv rfj evpeaei ecrxarov ioTiv' 6 yap ^ovXevopcvos eoiKC ^rjTeiv koX dvaXvetv aanep bidypap,p.a . . . koX to ea-)(O-T0v iv rfi dvaXvcrei TrpatTov iv rfj yevicrei. Etll. Nic. vi. 13. 10. ol yap crvWoyiar p.o\ tS)V TrpaKToov dpxrjv exoiTes elaiv, ineidr) roiovSe TO TeXos Kal TO apio-Tov. vii. 9. 4. iv bk Tois irpd^eai to ov eveKa dpxf} coo-Tvep iv roTs fiadrjp.aTiKo'is ai xmoQio-eis. An example of the deliberative and practical processes will be found, Metaph. vi. 7. 7. By subjectum is meant the subjectum operationis, or materia circa quam, more properly called the object; by media, the means by which out of this matter the end is produced. In building, e. g. the house is the end; the materials the subject; the act of building, the means. In Ethics, as treated by Aristotle, happiness is the end; man the subject; virtue the means. ^ Exemplum evidens methodi analyticse ab Aristotele in Ethicis proponitur, ubi libro primo Jinis prsecognoscitur, scilicet felicitas; post subjectum, nimirum hominis appetitus, seu voluntas, et intellectus; sequentibus libris ?7iedia tra- duntur, per quae finis introducitur, videlicet virtutes theo- reticse et practicae." Keckermann, Syst. Log. lib. iii. tr. 2. cap. 1. RUDIMENTA. 127 5. Praecedat in docendo, sine quo alterum intel- ligi non potest, ipsum vero sine altero potest. §. 2. In tradendis disciplinis suis Mathematici hac utuntiir methodo'. 1. Vocum significationem constituunt : h. e. Vocahula artis suo quodque loco sic definiunt, ut legem sibi statuant iis nusquam uti, praeterquam in eo sensu quern explicat defi- nitio. 2. Definitionibus subjungunt Axiomata, quas et kolvols ivvoias vocant-'; h. e. efFata sponte perspicua, quibus in decursu operis utendum vident. 3. Posthaec adjiciunt Postulata, quae ad praxin spectant : suntque per se certa et evidentia ; quae proinde sine probatione concedi suo jure postulant, 4. Hisce positis, propositiones demonstrant; ordine, et, quoad fieri potest, affirmate : una lege con- tenti, ut, quicquid demonstratum eunt, ex ante datis vel probatis manifestum faciant. Caetera, in quibus methodi praeceptores multi sunt et odiosi, non morantur. * Hac utuntur methodo. For a further account of the method of mathematical reasoning, see Appendix, note L, on the Logic of Geometry. J The KOLvai fvvotai of the Mathematicians correspond to the d^ioifxara of Aristotle. The latter term is not used by Euclid ; nor by any of the early Mathematicians in its Ai'istotelian sense. Among the Stoics, axiom was synonymous with pro- position, and in this sense it is mentioned in a passage of Apuleius, quoted p. 43, note a. For a full history of the term and its several uses, see Sir W. Hamilton's note, Reid's Works, p. 764. 128 ARTIS LOGIC.E RUDIMENTA. Mathematicorum methodum in caeteris artibus et scientiis, si ten ere non liceat, aemulari certe licet. Quo ad banc quaeque proprius accedit, eo caeteris perfectior^ et ad docendum aptior videtur. Sed ad ea quae docentur retinenda^ nihil est utilius absoluti operis conspectu ; in quo^ ea quae sunt ante (extra ordinem fortasse) demonstrata, suis quaque in locis, h. e. servata Logicorum methodo, reponantur. I APPENDIX. Solutio Sophismatum *. §. 1. CujuscuNQUE Syllogism! difficultas ad duas Species revocari poterit ; alteram, quas in Argu- menti Materia, alteram, quae in Forma consistit : nam qui has duas expedire noverit, is in tertia, quae ex ambarum complexione oritur, non haerebit. * The examination of Fallacies is extralogical, except when the consequence is formally invalid ; in which case it may be detected by the ordinary rules of syllogism. The following Sophisms are not all susceptible of this solution. They are mostly material fallacies, arising from ambiguity of language or falsity of assertion. But they are not treated of by Aristotle as belonging to the Science of Logic, but to the Art of Dia- lectic, of which, as has been before observed, a considerable portion is material. In fact, Aristotle's Treatise Trepl a-ocfua-TiKav eXey^coj/ is merely an account of the pseudo-refutations prin- cipally in use among the Sophists of his day, whether depend- ing upon equivocal language, false assumption, or illogical reasoning. In relation to Logic, it has little more than a historical value. A strictly logical classification of fallacies should commence by distinguishing, in all the three operations of thought, between the matter which is given to, and the form which is given by the thinking act. Acts of conception, judg- ment, or reasoning which violate the laws of thought, and are therefore defective in form, should be classed as logical fal- lacies ; those which are faulty in the conditions preliminary I to the act of thought should be classed as material. See I further, Prolegomena Logica, p. 237. and below, Appendix, i note M. 130 APPENDIX. Soph. Si incident Materia difficilis, unicum huic malo 9. 1. remedium est, disciplinam unde desumitur argu- mentum, fideliter didicisse ; quod ut facias, Instru- menti operam tibi Logica pr^stabit ; sed ulterius nihil confert. Proprium illi munus est Syllogismi Fornnam explorare ; h. e. Utrum Conclusio ex Praeniissis consequatur propter ipsum Colligendi modum : Sed an ponendje sint Praemiss^ (nisi forte sint pure Logicse) aliunde discendunri est. Sicubi autem Syllogismus qui legitimus non est, videatur tamen ; aut contra ; (quorum utrumque saepissime, et de causis peue infinitis accidit) For- nialem ejus Consequentiam excutere est Artis Logics. Qui hoc opus aggreditur, id sibi negotii datum sciat, ut Difficilem suum Syllogismum, primo in Categoricum purum, vel in plures, si opus sit, con- vertat ; tum ad Canonem accurate exigat ; cujus operis ratio praecedente Libro abunde declarata An. Pr. I. est. Summa rei hue redit. Consideranda est 32. 8. primo Conclusio ; ejusque Termini solerter dis- tinguendi : Prsedicatum enim est Major Terminus Syllogismi ; qui proinde Praemissam quoque Ma- jorem indicabit ; Subject urn pariter Minorem ; et in utraque sese offeret Argumentum sive Terminus Medius : Unde et si desit Prsemissarum alterutra, facile suppleri poterit. Hisce cognitis, nee Figura |: Syllogismi, nee Modus latebit ; qui si legitime, necli tamen vere concludere videatur, quaerendum annonjf aneeps sit aliquis trium Terminorum ? nam si in iis f APPENDIX. 131 nulla lateat ambiguitas, necessario falsa erit altera Praemissarum, Hunc in modum licebit Syllogismum quemvis Categoricum purum explorare ; qualis si non sit qui proponitur, quam facillime fiet, per ea quae priore Libro, extremo Capite tertio^ et toto quarto sunt ostensa. Siquid amplius restet, id Exemplis melius quam Praeceptis docebitur. §. 2. Ordiemur autem a facillimis ; nempe vete- Soph. rum Sophistarum Fallaciis ; quarum 13 species 4.1. enumerat Aristoteles ; sex, qua? multiplicitate die- tionis ; septem, quae aliquo extra dietionem vitio laborarent^ Et erat aliqua fortasse difficultas in '' Of the Aristotelian division of Fallacies into oi napa Tr]v ki^Lv and 01 e^o) T^? Xe^ecos, Arclibishop Whately observes, that it has not hitherto been grounded on any distinct principle : he therefore adopts a conjectural explanation, according to which the former are interpreted as logical Fallacies, in which the conclusion does not follow from the premises ; the latter, as material Fallacies, where the conclusion does follow, the • falsehood being in the assumption. This, however, is not the ancient principle of distinction, which is stated, with more or less clearness, by several Logicians. To go no higher than Sanderson; we find, " Fallacia omnis in dictione ; oritur ex dictionis aliqua multiplicitate. Est autem Multiplex aliud actuale : quando dictio invariata multa significat ; ut in cequivoeatione, et amphiholia. Aliud potentiale : quando dictio quoad prolationem aliquo modo variata, multa significat ; ut in compositione, divisione, et accentu. Aliud phantasticum : quando dictio unum reipsa significans, videtur tarn en multa significare ; ut in jigura dictionis. Fallaciae extra dietionem sunt in quibus contingit deceptio, non tarn ex multiplici aliquo latente in vocibus ipsis, quam ex ignoratione rerum." k2 132 APPENDIX. earum aliquibus, juxta veterem disputandi (h. e. interrogandi) morem propositis; sed profecto nemo tarn obtusus est, qui non easdem Syllogistice pro- positas agnoscat statim, et derideat. V. g. Erit for- tasse qui rogatus Quod non amiserit iitrum habeat necne? non intelligat se captum iri, sive simpliciter habere se, sive non habere respondent: at proposito hujusmodi Syllogismo, Quod non amisisti hahes ; Cornua non amisisti; Ergo hahes: Vel Quod non amisisti non hahes ; Oculos non amisisti ; Ergo non hahes ; quid reponat nemo non videt. This principle is found in Alexander of Aphrodisias, Scholia, p. 298, b. 28.; and still earlier, if the work be genuine, in the Treatise Trepl rav wapa rrjv Xe^iv aofjuo-fj-dTcov, ascribed to Galen. Indeed it may be gathered from Aristotle himself; Soph. Elench 4, 1. 6, 2. 7, 3. Occam states the distinction still more clearly. " Fallaciae in dictione sunt illse penes quas secundum omnes modos peccant sophistica argumenta com- posita ex signis voluntarie institutis. Fallaciae extra dictionem sunt illae penes quas peccant argumenta tam composita ex signis voluntarie institutis quam composita ex signis naturali- ter significantibus." Logica, iii. 4. cap. 1. The former arise from defects in the arbitrary signs of thought, and hence are ' generally confined to a single language, and disappear on ■. being translated into another. The latter are in the thought ^ itself, whether materially, in the false application of notions I to things, or formally, in the violation of the laws by which the operations of the reason should be governed; and thus adhere to the thought, in whatever language it may be ex- pressed. Under this head are thus included both false judgments and illogical reasonings. These Fallacies are connected with language only secondarily and accidentally; the former primarily and essentially. See further, Waitz, vol. ii. p. 582. i i APPENDIX. 133 Fallaciae dictionis, sive m dictione, sex sunt*". §.3. 1. Fallacia cequivocationis, sive iiata ex Soph. . ^ . . , o. • Elench. voce aeqmvoca: ut. Cams est animal; iSirius est 4.. i. id. i. canis ; Ergo, Sirius est animal. In hoc quatuor sunt termini ; quorum duo, vox Canis aequivoce sumpta. 2. Fallacia amphibolice ; sive nata ex sententia Soph. ... ^7 Elencli. ampnibola, h. e. ancipitis structurae ; ut Qiwd tan- 4. 4. i9. i. gitur a Socrate illiid sentit ; Columna tangitur a Socrate ; Ergo Columna sentit. Vox sentit, non sponte, sed in hac structura est ambigua ; cujus vi, in Majori significat Sentit Socrates; in Con- clusione, Sentit Socraiem ; Quare Syllogismus habet quatuor terminos. 3. 4. Fallacia Compositionis **, ubi datum in sensu Soph. ^ Elench. 4.6.20.1. c With the following account of the Fallacies may be com- pared the corresponding chapter in the Rhetoric, ii. 24. In doing so, however, it must be remembered, that the present sophisms occur in a disputation carried on in colloquial form between antagonists, and conforming to established rules ; whereas those are introduced ad lihitum, by an Orator in the course of his speech. Hence, though the principle of deception may be similar, the manner of its application will not always correspond. The same caution is still more necessary in examining modern specimens of Sophistry. ^ This Fallacy, as treated by Aristotle, includes a wrong composition of clauses in a sentence capable of two punc- tuations. In this extension, the examples possible est se- dentem stare, dc. are easily included under Composition ; the sense varying according as sedentem is joined with possihile est, or with stare. The Fallacy of Division, in like manner, will include the separation of clauses which ought to be united. 134 APPENDIX. diviso sumitur in sensu composito ; ut. Duo et Tria sunt Par et Impar ; Quinque sunt Duo et Tria ; Soph. Ergo Quinque sunt Par et Impar ^, Fallacia Divi- 4. 7. 20. 1. sionis, quando datum in sensu composito sumitur in diviso ; ut, Planetce sunt septem : Sol et Luna sunt Planetce; Ergo Sol et Luna sunt septem. Utroque modo quatuor sunt termini si aperte loquaris. V. g. Prioris Syllogismi mens est. Duo et Tria seorsim accepta sunt Par et Impar. Quin- que sunt Duo et Tria in unum composita, &c. Poste- rioris vero, Planetse collective sumpti sunt sep- tem; Sol et Luna sunt Planetse distributive sumpti &c. Unde duplex utrobique Medius. Eien'h " ^\xc referri solent hujusmodi Orationes ; Pos- 4. 6. 20. 4. <( sibile est album esse nigrum ; Possibile est seden- ^* tem stare : dubito an satis recte ; quia tanto " acumine non est opus. Potest quidem album "fieri nigrum ; et Possibile est sedenti stare ; at " si haec velles, incongrue locutus es. Utraque " igitur Oratio est simpliciter neganda ; vel ut " aperte falsa si sit congrua, vel si non sit congrua, " quia non est Propositio." Eiench ^* Fallacia Accentus seu Prosodies^ potius, quando 4. 8. 21* 1. e In these instances, the verbal defect lies in the copula. Two and three are (constitute) five. Two and three are (severally) even and odd. ^ The Fallacia Prosodies, as Aristotle observes, is a Fallacy in writing only, not in speaking. Lepores and lepores have no ambiguity when rightly pronounced. The first example {servus ergo cervus), supposing the pronunciation of both words to be the same, is not properly an instance of this Fallacy. APPENDIX. 135 pro eodem sumuntur quae vel Litera^ vel Spiritu, vel Tempore, vel Accentu sunt diversa : ut. Est servus Ergo est cervus; Est ara Ergo est hara. Est malum (an apple) Ergo malum (an evil). Venatur lepores Ergo et lepores; quibus qui falli potest, debet. 6. Fallacia Figurce dictionis, quando propter Soph. dictiones similes, quod de uno datur de altero 4. 9. 22. i. arripitur : idque vel Grammatice^, ut Musa est 8 Grammatice, i. e. inferring that Poeta is of the feminine gender, because the majority of words with the same termi- nation are so. Logice, inferring that videre belongs to the category oi iroulv, because most infinitive moods of this form are included under it. Thus viewed, it may be classed as in dictione, because the rules of gender and conjugation are dif- ferent in different languages. But the more common form in which this Fallacy would be stated is that of an induction, or rather a number of examples, after the manner of Socrates. Indeed, this very sophism is put into the mouth of Socrates by Aristophanes, Nubes, 681 sqq. Stated in this form, the logical inconsequence is obvious ; as also if it is reduced to syllogism. " Such and such words are feminine; Musa resembles such and such words." Here there is no middle term. This ambiguity is sometimes called multiplex phantasticum. Cf. Petr. Hisp. Summ. Log. Tract, vi. " Est autem multiplex phantasticum, quando aliqaa dictio signihcat unum et videtur significare aliud, propter similitudinem quam habet in parte cum alia dictione : ut videre significat passionem, et videtur significare actionem, propter hoc quod est simile huic verbo, agere.'" In this form, it would seem more naturally to belong to the class extra dictionem. ! In Ehefc. ii. 94. '2. Aristotle gives another form of this ! Fallacy; viz. when a series of detached propositions are so I enunciated as to appear logically connected, not being really I so. See also Soph. Blench. 15. 5. 136 APPENDIX. Foeminini generis. Ergo et Poeta: vel Logice, ut Docere est agere, Ergo et Videre, Haec Materia potius quam Forma peccat : et operose solvi non postulat : ponit aliquid aperte falsum ; quo negato evertitur. ^^^''\ Fallaciae extra dictionem sunt septem^. Elench. ^ 4. 10. Soph. §• "^^ ^' Fallacia Accidentis^ ; quando acciden- f^T^M 1 ^^^^^^^ aliquod confunditur cum eo quod est essen- tittle sen principaliter intentura : ut. Quod emisti Pol^;. J^^^-.M/comedisti, Crudum emisti; Ergo Crudum comedisti: in quo. Quod emisti, et Quale emisti, c,oiifuxi^\xiii\xr\ unde quatuor termini. Soph. 2. Fallacia a Dicto secundum Quid ad Dictum Elench. 6. 2. 25. 1. Simpliciter ; quando proceditur a voce determinate sumpta, ad eandem absolute positam : ut, jEthiops est albus dentes ; Ergo albus: unde quatuor esse Terminos necesse est\ ^ Fallacies extra dictionem embrace all those in which the deception arises from any other cause than ambiguity of language ; whether from a false assumption in the premise, or from the reasoning being unsound. Purely logical fallacies belong, not to the in dictione, but to the extra dictionem. i The example of this Fallacy given by Aristotle is, Coriscus is different from Socrates; Socrates is a man; therefore Coriscus is different from a man. The Fallacy lies in as- suming that whatever is different from a given subject is incompatible with all the predicates {ra o-vfi^aLvovTa) of that subject. The reasoning is thus illogical : Socrates is a man; Coriscus is not Socrates ; therefore Coriscus is not a man. ^ The example as stated by Aristotle will run thus ; .^thiojps APPENDIX. 137 [i 3. Fallacia Isnorationis ElencJiL Elenchus^ Soph. ^ . Elench. proprie Syllogismus est Adversarmm redarguens : 5. 5. 26. i. ! confirmando scil. quod illius sententiae contradicat. 20. i. I Quare in banc incidit Fallaciam qui se putat Ad- E°ench. I versarium redargaere, non servatis Contradicendi Legibiis, (de quibus vide pag. 54.) Qui in bis I peccat, docendus est se nescire Quid sit Con- I tradicere. I 4. Fallacia a non-causa pro causa"^ ; sive sit a Soph. ; ^ Elench. I 5.11.29.1. I non est alhus ; jEtliioys est alhus denies ; Ergo, qui est albus non ^^' ^^' H* est albus. Here there are four terms, and the Conchision, as Aristotle himself observes, is not drawn syllogistically. ^ The Elenchus is defined by Aristotle, a-vWoyiafios dvri- 4)d(T€(os, x\n. Pr. ii. 20. 1. Soph. Elench. 6. 4. The Ignoratio Elenchi consists in neglecting some of the conditions required by the rules of Dialectic for proving the contradictory of any given proposition. This is the case when the conclusion does not logically follow from the premises ; or when the premises themselves are not admitted by the opponent; or when the conclusion, though legitimately deduced from allowed pre- mises, is an apparent, not a real, contradiction of the op- ponent's position, failing in one of the four conditions of contradiction, viz. eodem modo, secundum idem, ad idem, eodem tempore. In this extended sense, every fallacy is an Ignoratio Elenchi, as is observed by Aristotle, Soph. Elench. 6. ] . though the name is especially applied to the last instance. ™ This fallacy, according to Aristotle, most frequently occurs in the deductio ad impossibile, and consists in pretending that the proposition which we wish to refute is the cause of the false conclusion, which in reality follows from other premises; i. e. in maintaining that the conclusion is false because that particular assumption is false. This mode of deception has place in dialectical disputation, from the practice of asking the opponent to grant certain premises. An unnecessary proposition is asked and granted among the rest, and after- 138 APPENDIX. non-vera pro vera; sive a non-tali pro tali'': ut Cometa fulsit ; Ergo Belliim erit ; Nullo modo ; nam si fuerit^ aliis de Causis futurum est. Quod inebriat prohihendum est ; Vinum inehriat ; Nequa- quam vero, sed Abusus vini. Hxc Fallacia bene solvitur negando Causam falsam : melius, addu- cendo germanam. " Hue refertur ab aliquibus (qua de causa non " video) hoc Sophisma ; Qui magis esurit, plus " comedit ; Qui minus comedit, magis esurit ; Ergo '' Qui minus comedit, plus comedit, Sed qui hoc, " vel hujus simile attulerit (ut innumera afFerri " Solent) docendus est congrue loqui : Hoc si " fecerit, dicet in hoc casu. Qui magis esurit plus " comedet ; Qui minus comedit, magis esurit ; Ergo *' Qui minus comedit, plus comedet" Soph. 5. Fallacia Consequentis'', quando infertur quod Elench. 5. 8.28. 1. wards selected as the false assumption. Aldrich's examples refer rather to the rhetorical than to the dialectical form of this fallacy. In this the speaker is guilty merely of a false assertion, attributing a certain effect to a wrong cause. See Ehet. ii. 24. 8. " In the non vera pro vera, there is no connexion between the effect and the supposed cause ; in the non tali pro tali, there is a connexion, but an insufl&cient one ; wine, e. g. does not intoxicate except in certain quantity. This instance, however, more properly belongs to the fallacy a dicta secundum quid ad dictum simpliciter, " Wine (in excess) intoxicates ; therefore. Wine (absolutely) is to be forbidden." ^ The fallacia consequencis is an error in reasoning, as may be clearly seen in the examples given Soph. Elench. 5. 8. and Rhet. ii. 24. 7. e. g. Honey is yellow ; Gall is yellow ; there- APPENDIX. 139 non sequitur : ut. Animal est ; Ergo, Est Homo, Hie memineris, quod si recte ratione uti volumus, Consequentia aut directa, immediata, formalis, aut plane nulla est ; peccat enim contra aliquam Dia- lecticae regulam ; ad quam si provoces, refelletur. 6. Fallacia Petitionis Principii^, cum ut datum Soph. . Elench. assumitur, quod probatum oportuit. V. g. Cum 5. 7. 27. 1. , T • 1 1 • -r Anal. Pr. probatur aliquid vei per seipsum, (quae vocatur 11. 16. 1. Petitio statim,) ut. Homo est, Ergo, est Homo : isl^i. Vel per Synonymum ; ut Ensis est acutus ; Ergo, Gladius : Vel per aeque ignotum ; ut Hie est Pater Melchisedek ; Ergo, Hcec Mater: Vel per ignotius ; ut, Hoc Quadratiim est kujus Trianguli duplum, Quia huic Circulo cequale : Vel per Circulum ; re- sumendo scilicet quod relictum est ; ut si diceres. Ignis est calidus, Ergo urit : et post pauca. Ignis urit, Ergo est calidus, 7. Fallacia "^ plurium interrogationum, quando Soph. plures quaestiones velut una proponuntur ; v. g. 5.13.36.1. Suntne Mel et Pel dulcia f Estne homo animal et fore gall is honey. Here the middle term is undistributed. Another specimen cited by Aristotle is the reasoning of Melissus; "Whatever is generated has a beginning; the universe is not generated ; therefore it has not a beginning." Cf. Phys. Ausc. I. 3. 2. Here there is an illicit process of the major term. p On the 'Petitio Principii, see Appendix, note E. Aristotle enumerates five varieties : which, however, are not the same as those given by Aldrich. See Top. viii. 13. q This is merely a dialectical fallacy; and consists in entrapping an opponent into an answer partly false, by artfully putting two questions as one. 140 APPENDIX. lapis? Evertitui% ad singulas quaestiones distincte respondendo ; sicut fecit Menedemus Eretriensis, qui rogante eum Alexin o, Numquid Pair em ver- her are desiisset ? Nee verheravi, inquit, nee desii\ Atque hae sunt tredecim Sophismatum formulae^ Veteribus usitatiores, quae Tironibus Logicis in exemplum proponi solent. Poterant esse pauci- ores ; nam videntur aliquae coincidere ; et prae- terea tres, Non-causa pro Causa, Petitio Principii, et Plures interrogationes, non sunt Fallaciae proprie dictae, h. e. Syllogismi Forma peccantes* ; sed Vitia male Opponentis. Poterant et plures ""; sed cum hie numerus Aristoteli satisfecisset, idem omnibus post ilium Logicis satisfecit. §. 5. SoPHisMATiBus ex sententia veterum accen- ' Diog. Laert. ii. 135. s These thirteen fallacies are comprised in the mnemonic lines, iEquivocat, Amphi. Componit, Dividit, Ace. Fi. Acci. Quid, Ignorans, Non causa, Con. Petit. Interr. * Aristotle's definition of Fallacy will include logical de- ductions from false premises, as well as illogical deductions from any premises. See Top. i. 1. 3. 'EpiariKos S' eVri avX- Xoyiaixos 6 €k (fjaivoixevcov ivho^cov, firj oirra>v Be, Koi 6 e| iubo^cov fj ^aivofjievav evdo^av (f)aiv6fievos. Aldrich's limitation to Syllogisms faulty in form is quite arbitrary. " Aristotle does not profess to give a complete enumeration of the fallacies ; but only a list of such as may be solved by the Dialectician. There may be innumerable false as- sumptions, on matters not belonging to Dialectic, which must be refuted from the principles of the Science or Art to which they belong. See Soph. Elench. 9. 1 . I APPENDIX. 141 sendae sunt Inexplicabiles (ut vocantur) Rationes, quas Megarici, Stoici, aliique Eristicam professi, propriis nominibus insignivere, Crocodilus, Mentiens, Ohvelatus, &c. quas plerasque collegit Gassendus, et retulit in Libido de Origine et Varietate Logicce : Nos eodem fere ordine explorabimus quo ab illo sunt propositae. 1. Achilles vocatur Argumentum quo usus est Arist.Phys. Ausc. VI. Zeno Lleates, non ut Motum tolleret, quod vulffo o. 3. 1 P 1 T . 1 1 r^ • Top. VIII. sed lalso dicitur ; sed ut ostenderet Continuum 8. 2. non esse infinite divisibile^ quia hoc dato Motus E°ench. 24 5 toUeretur. Argumentum sic se habet. Sit Achilles quantum voles woda^ a^Kv^, puta decuplo velocior Testudine. Quiescente illo, confccerit Testudo partem aliquam (puta decimam) spatii percurrendi. Tum procedat Achilles, idemque spatium per- currat : progredietur interim Testudo per partem ejus decimam, h. e. totius spatii centesimam ; banc conficiat Achilles, et percurret interim Testudo hujus centesimae decimam ; et sic deinceps in infinitum ; quo fiet ut Achilles nunquam asse- quatur Testudinem\ ^ We must not confound the metaphysical difficulties con- nected with the infinite divisibility of space, with the logical difficulty of a false conclusion apparently deduced from true premises. Archbishop Whately evades the latter, by ob- serving, that the sophism cannot be exhibited in a Syllogism. But this confession is in fact a surrender of the syllogistic criterion, as a means of discriminating between sound and unsound reasoning. On the contrary, nothing is easier than to exhibit the reasoning in a Syllogism, and to shew thereby 142 APPENDIX. Ineptum est hoc Sophisma. 1. Quia solvitur ambulando; quod fecit Diogenes ^ 2. Quoniam ex ipsa Hypothesi, Dum Testudo quae praecessit spatio A, conficit ^ A, Achilles conficiet 2 A; that the fallacy does not lie in the form, but in the matter. Thus, representing the whole space to be traversed by a, " Any space equal to ^ + ^^^ + j^^ &c. is infinite, (being the sum of an infinite series.) The space to be passed before Achilles overtakes the tortoise is equal to this sum. There- fore it is infinite." The whole logical mystery of this famous fallacy lies in this, that the major premise is false. The sum of an infinite series may be, and in this case is, finite. This premise is equally false, whether space is or is not divisible ad infinitum. On the metaphysical question connected with the matter of the sophism, see Hegel, Werke, vol. iii. p. 218. Fries, System der Logik, §. 109. Herbart, Einleitung in die Philosophie, §. 139. Trendelenburg, Logische Untersuchwigen, vol. i. p. 179. The solution attempted by Coleridge, {Friend, vol. iii. p. 93.) is refated by Herbart. It may be observed, that Aldrich is mistaken as regards Zeno's object in this Sophism. It was proposed to support the leading tenet of Parmenides, of the unity of all things, by shewing that the identity of rest and motion is a necessary result from the contrary opinion. It does not appear, however, that Zeno advanced this argument seriously. His principal design was to retort the ridicule which had been thrown on the doctrine of Parmenides, by involving his opponents in the same absurdities which they professed to find in his theory. Cf. Plato, Farm. p. 1-28. Arist. Soph. Elench. 10. 2. 38. 4. Cousin. Nouveaux Fragments, Zenon dFlee. y The solution of Diogenes proves nothing. Zeno contends that reason contradicts the evidence of the senses. Diogenes replies that the evidence of the senses contradicts that of reason. Who denied that? APPENDIX. 143 adeoque statim assequetur earn, et antecedet^ Sed hoc (inquies) in casu proposito nunquam fiet; Recte ; Ne enim fiat, in ipso proponendi modo clam inseritur nova conditio. Nam 3. Argumen- tum aliis verbis hoc dicit ; Si Achillem decuplo velociorem praecesserit Testudo ; et uterque meo pergat arhitratu ; Ego perficiam ne Achilles asse- quatur Testudinem: Quare prorsus nunquam asse- quetur. Quae est Fallacia a dicto secundum quid, ad dictum simpliciter. 2. Diodorus Cronus, quod Sophismata Stilponis non solvisset, exinde ovos appellatus est*; id cog- nominis aliunde promeritus, quod ad hunc modum contra Motum disputaret. Mobile movetur vel in quo est loco, vel in quo non est ; At neutrum horum; Ergo No7i omnino, Unde facete ilium lusit Hero- philus, qui ut luxatum illi humerum restitueret rogatus, Tuus (in quit) humerus vel in quo erat loco ^ The futility of this attempt at solution might have been learned from Aristotle, Soph. Elench. 24. 5. It only shews that the contradictory assertion rests also on seemingly valid reasoning ; whereas the duty of the opponent is to shew where the fallacy of Zeno's reasoning lies. * The facetious Iambics in which Diodorus was thus " writ down an ass "' are as follows : Kpoi/e AtoScope, t'is ae dai^ovcov KaKrj "lu avTos avTov iix^akrjs els rdprapov, ^TikTTcovos ov \vcras €7rr] Aluiyixarcibr] ; roiyap cvpedrjs Kpovos "E^a> ye tov poi Kamra re. See Diog. Laert. ii. 1 1 2. 144 APPENDIX. existens excidit, vel in quo non erat. Sed neutrum horum ; Ergo non omnino. Diodori argumento breviter et perspicue respondet Gassendus, Quod movetur moveri a loco in quo erat^ per locum in quo est (sive quern pertransit), ad locum in quo nondum est^ sed futurum est^ 3. Reciprocum vocat Argumentum Gellius, quod Graece dicitur ' AvTicrrpe^ov: cui illustrando con- ficta est Fabula quae Grascorum vanitatem olet. Narrant enim inter Protagorum et Euathlum, vel (ut facetiae locus sit) inter Coracem'' et Tisiam convenisse, ut hunc ille Dialecticam doceret ; idque hac lege, ut diraidium mercedis statim ac- ciperet ; reliquum, cum discipulus causam vicisset. ^ The true solution of the sophism of Diodorus is, that the disjunctive premise is false. " The place where a body is," is contradictory of "the place where a body is not;" as "Englishmen" is contradictory of " not-Englishmen ;" but ** moving in the place where it is," is no more contradictory of" moving in the place where it is not," than " an army com- posed of Englishmen " is contradictory of " an army composed of not-Englishmen." As it would be false to say, " every army must be composed of Englishmen or not-Englishmen," to the exclusion of the third possibility of a mixed force, so it is \ false to say, " Every body must move in the place where it is, or in the place where it is not," to the exclusion of the third possibility of moving partly in the one and partly in the other. This solution is substantially given by Hobbes, I Philosophia Prima, P. 11. c. 8. §. 11. ^ The story is told of Protagoras and Euathlus by Aulus Gellius, V. 10. and by Apuleius, Florid, iv. 18.; of Corax, by (• Sext. Empir. adv. Math. p. 81. Cf. Menag. ad Diog. Laert. ix. 56. APPENDIX. 145 Primam exinde litem cum Discipulo contestatus est Magister, cum mercedis reliquum lege peteret ; apud Judices vero sic agebat : Ego si vicero, Tisia, Tu solves ex sententia, sin minus, ex pacto ; utroque igitur modo solvendum est, Respondit Tisias^ Ego nihil solvo ; Tu si viceris, ex pacto ; sin minus, ex sententia, Tanto utrinque acumine perculsi boni judices, exclamarunt Ka/coi) Kopa/cos" KaKov coov^ causamque in longissimum diem distulerunt. Ineptum erat Coracis Dilemma quia potuit tarn bane retorqueri. Nihilominus callide agebat, si id Judices vidissent. Nam cum mercedem iniqua peteret, causa cadere debebat ; Quamprimum autem cecidisset, ei merces ex pacto debebatur, §. 6. 4. Mentiens quae est Graece ^evdofxepos^, Soph. Chrysippi Syllogismus ne ab ipso quidem solutus, 25. 3. praeter caeteros insolubilis habetur. Eum Cicero^ vii.' 3.^8. sic enuntiat : Si dicis Te mentiri, et verum dicis, men- tiris ; Sed dicis Te mentiri, et verum dicis ; mentiris 'gitur, Congrue loquere, Chrysippe, et intelliges Te vel nihil prorsus, vel nihil dicere difficile. Qui se dicit ^ This Fallacy is attributed to Eubulides of Miletus. See Laert. ii. 138. It is mentioned by Aristotle, Eth. Nic. vii. 3. 8. and consequently must be older than Chrysippus. ' Acad. Quaest. iv. 30. Its solution i& obvious. No one can jlie without lying about something. The something is not stated in the sophism. The questicm as it stands is unmeaning. Is ithis thing very like ? Like what ? i L 146 APPENDIX. mentitumi et verum dicit, mentitiis est ; Qui menti- turum, mentietur, Horum utrumque verum est, et nemini obscurum. Sed qui ut verum simul dicat et mentiatur dicit unum aliquid, cujus partes sibi invicem contradicunt, is nee verum, nee falsum, sed omnino nihil dicit : quando enim sentential pars una evertit alteram, tota nihil prorsus signi- ficat, sed inaniter strepit. Subtilius disputare videbantur qui sic agebant. Cretenses esse mendaces dicit Epimenides Cretensis, Mentitur igitiir ; Ergo Illi sunt veraces ; Ergo et Ille verum dicit ; Ergo Illi rursus sunt mendaces &c, Sed profecto nihil stultius est hoc Argumento, nisi vox Cretenses eos ad unum omnes significet, et Ornnis mendax quicquid dicit mentiatur ^ Videtur hie Mentiens peperisse subtilem illam Scholasticorum de Insoluhilihus doctrinam. " Nam " talia argumenta (inquit Occarn) non possunt fieri " nisi quando actus humanus respicit istum termi- " num Falsum, vel aliquem consimilem affirmative; " vel hunc terminum Verum, vel ahquem consimilem ( "negative^." Esse haec Sophismata ante dixerat; nee vocari Insoluhilia, " quia nuUo modo solvi *' possunt, sed quia cum difficultate solvuntur." Insolubilis exemplum sic proponitur. Incipiatj, Socrates sic loqui, Socrates dicit falsum ; et nihil ■■) f This Fallacy is solved by Fries, §. 109. A man who isit always a liar cannot possibly say or imply " I lie ;" for this would be a truth, and thus he would not be always a liar. « Occam, Logica, iii. 3. cap. 45. I APPENDIX. 147 amplius loquatur : turn interroget aliquis, utrum I vera an falsa sit haec propositi o. Respondeo, nee jveram nee falsam esse, sed nihil significare, nisi aliquid aliud respiciat, quod a Socrate ante dictum j supponitur. Qui enim profert haec verba, Socrates I dicit /ahum, fert judicium de dicto Socratis ; qui- que fert judicium, necessario prsesupponit aliquid de quo judicet : Unde cum sententia praesupponat objectum suum, clarum est eandem numero pro- positionem, et sententiam et ejus objectum esse non posse. Quare et Scholarum subtilitas hie nihil proficit ; nihilque opus est plura dicere de Insolu- bilibus. 5. Fallens /^LoKavOdvcov^, vel ut alii AiaXeXrjOcoy, de Juramento ludit sicut Mentiens de nuda affirma- tione. E. g. Qui jurat se falsum jurare et falsum jurat, vere jurat. Quare eodem fere modo quo Mentiens explicatur. §. 7. 6. 7. Obvelatus, alio nomine Electra, est Soph. Fallacia a dicto secundum Quid ad dictum Simpli- 24. 2. citer. Nam colligere pertendit, quod et Patrem Filius et Soror Fratrem, h. e. Electra Orestem I ^prorsus nesciat, si eundem velo obductum se nescire ! fateatur'. ^ The AiaXaj/^ai/wi; is properly a similar Fallacy to the Electra j and the Obvelatus. The honour of its invention is divided ' between Eubulides and Diodorus Cronus. The example I given by Aldrich is a mere conjecture of Gassendi's. I ^ The Fallacy of the Electra is founded on Sophocles, I l2 148 APPENDIX. 8. 9. AcERVALis et Calvus'', sunt ejusdem Sophis- matis duo tantum Exempla. V. g. Si rogatus a Sophista, neges te Calvum fieri amisso crine uno, duobus, tribus, et sic deinceps ad 99, sed amissis centum concedas; vel eodem modo neges 99 grana Acervum esse, centum autem esse fatearis ; con- cludet ille grano unico adjecto Acervum fieri ; crine unico amisso, Calvitiem. Facile autem re- spondetur, Unum centesimum non esse Unicum ; nam est Unum cum nonaginta novem. Vel si mavis sic ; Fit Acervus, grano uno, sed adjecto ; adeoque non unico, sed cum pluribus aliis. Fit Calvities crine uno, sed post multos alios, amisso. 10. CoRNUTUS et Ceratinus, Ceratine, Ceratis, et Ceras dicitur Sophisma illud ante memoratum. Elect. 1222. It is given as follows by Lucian, Vit. Auct. §. 22. irapearTaTOs yap avrfj tov ^Opecrrov en dypa>Tos, oide fxep *Op€(rTr)Vy OTi ddeXcf)6s aires' ort Se ovtos 'OpecrrT/y, dyvoel. The Obvelatus is of similar character. XPY2. "Uu o-oi, Trapacrnjo-as Tiva €yK€Ka\vp.p€vov, epcopai, tovtov olxrOa ; Ti (fyrjaeis ; AFC. ArjXad^ dyvoeiv, XPY2. 'AXXa /xeV avrbs ovtos rjv 6 Trarrjp 6 cros, ajcrre et tovtov dyvoels, di]Xos el tov Trarepa tov crbv dyvoav. Another variety of the same sophism will be found in Aristotle, Soph. Elench. 24. 2. where it is classed under the Fallacia Accidentis. Diogenes Laertius, ii. §. 108. attributes the Electra and Obvelatus to Eubulides, as well as the Acei'vus, Cornutus, and Calvits. ^ These two Fallacies, which are in fact but one under different names, are alkided to by Horace, Ep. ii. 1. 45. and by Persius, Sat. vi. 80. The Acervus is frequently called Sorites, (cf. Cic. Acad. Qutsst. iv. 49. De Divin. ii. 11.) but must not be confounded with the series of syllogisms of the same name. I APPENDIX. 149 ' Quod non amisisti habes &c. Quae est Petitio \ Principii ; nam supponit Te cornua habuisse. ; Ineptissima haec Fallacia plus acuminis praefert ijuxta veterem Disputandi modum rogando pro- iposita* Erit enim fortasse, qui rogatus. Quod non amiserit, utrum habeat necne? non intelligat se jcaptum iri, si simpliciter respondeat; sive habere jse, sive non habere dicat. Nam eum adiget 'Sophista, ut vel se habere Cornua^ vel non habere j Oculos fateatur. i 11. Acutus sibi videbatur Menedemus (Eretri- ensis scil. quem epLaTiKcoTaTov appellat Laertius) iquum ad hunc modum nugaretur. Diversum, a \Dwerso Diversum est; Prodesse est a Bono Di- \versum; Prodesse igitur non est Bonum\ Quae lest crassa et putida ^quivocatio ; et nihil am- plius. §. 8. 12. Crocodilus"" a Chrysippo inventus, qui ad Fallaciam Consequentis revocari poterit, sic proponitur. Surripuerat infantem Crocodilus ; red- diturum se, hac lege pollicitus, ut divinet mater, utrum apud se reddere an non reddere constituent. Si dicat mater Non reddere ; mentietur si infantem receperit : Si dicat reddere ; non reddet quia hoc est falsum. Quamobrem Chrysippus nihil esse putat difficilius quam responsum matri suggerere. I i Diog. Laert. ii. 134. I ™ This Fallacy is given at length by Lucian, Vit. i^uct. §. 22. 150 APPENDIX. Nec injuria, si lubricum putet divinare ; sed im- merito, si in hoc (ut videtur) hsereat. Quod si puerum Crocodilus non reddere constituent, quamvis id Mater divinaverit non reddet: quasi consilium quod primum intenderat Crocodilus, postquam indicatum est, repudiare non possit, et ex pacto non debeat : nam si Mater recte divina- verit, recepto puero, non mentitur ilia, sed consi- lium mutat Crocodilus. 13. Metens Gepi^cov qui vocatur, ita placuit Zenoni Stoico, ut Sophistae a quo eum didicerat duplum pactae mercedis numerat. Proponente Ammonio"" sic se habet. Si messurus es, nonfortasse metes, foriasse non metes, sed metes omnino ; Pariter, si non messurus es, non fortasse metes, fortasse non metes, sed prorsus non metes. Atqui vel metere te, vel non metere, necessarium est; perit igitur For- tasse, quod in neutra hypotJiesi locum habet, Fortu- natum Sophistam ! qui mercede dupla hunc fumum vendidit ; Vel hoc, vel illud evenire est necesse ; Quare hoc et non illud necessario eventurum est. Nihil amplius dicit qui sic dixerit, Ut vel metas vel non metas est necesse: Ergo Vel necessario metes\ vel necessario non metes, Breviter, haec Fallacia] Divisionis est ; nam in Antecedente, Modus Neces- sario, non tribuitur nisi toti Disjunctivae ; sed inj Consequente dicitur de ejusdem membris seorsimj acceptis. " In de Interp. sect. 2. cap. 10. cf. Menage ad Laert. vii. 25. APPENDIX. 151 14. Ignava Ratio vel *Apyo9 X6yo9 appellatur% qui si valeat nihil est omnino quod agamus in vita. V. g. Si Fatum est cegroto convalescere, sive medicum adhihuerlt sive non adhibuerit, convalescet : Pariter, si illi Fatum est non convalescere, sive medicum adhibuerit, sive non adhibuerit, non convalescet: et alterutrum Fatum est; medicum ergo adhibere nihil attinet, Lepide respondit Chrysippus posse esse Confatalia adhibere medicum et convalescere : Quemadmodum et Zeno^ quando servum furem verberabat, Furari sibi Fatum esse dicenti, et Vapulare respondit. Sed commodius dici vide- tur. Si sit Fatum, hoc valere argumentum ; idque vel solum sufficere ne Fatum esse concedamus. Argumentum hocce et quae praecedunt pp. 143, 144. N°. 2. et 3. ex Dilemmatis legibus facile solvuntur. §. 9. Plura sunt apud Autores Inexplicabilium Rationum nomina ; quorum exempla Gassendus quia nusquam invenisset, ipse reperit. Verum ea relinquimus studiosis ; quibus etiam consulto est relictum, ut quae sunt hactenus explicata, illi explicent in Syllogismos conversa. Exempla Gas- sendi ne desiderent qui libro carent, non pigebit exscribere. Dominans, Kvpcevcou, Themistoclis filius nee Graecis imperat, nee de imperando cogitat : Verum imperat Matri, quae imperat Themistocli, qui » See Cicero, de Facto, c. 12. 152 APPENDIX. Grsecis imperat ; Dominatur itaque Grsecis, et non- dominatur^ , Conficiens, Ylepali/cop, Multum itineris corificit, et non conficit Canis, qui in rota gradiens totum diem, ex eodem tamen loco non recedit. Superpositus vel Superlativus, 'YTrepOerLKo^, Soriti forte affinis ; Ut si roges quota sit palea, quae si mulo super-imponatur ille oneri succumbat ? Soph. Nullus^ OvTL9* HoHio in Communi nee est hie, Elench. 22.12. nec ille, nee alius homo singularis. Ergo Nulhis\ Vel ut tritum Sophisma : Quod Ego sum, Tu non es ; Ego sum homo : Ergo Tu non es. Vel denique ut Chrysippus. Qui est Megaris, non est Athenis ; Homo est Megaris ; Ergo Homo non est Athenis^, P The Fallacy Kupievcoi/ is mentioned by several writers, but not explained by any. Cf. AiTian, Epicteti Dissert, ii. 1^. Lucian, Vit. Auct. c. 22. Plutarch, Sympos. I. i. 5. Gellius, Noct. Att. I. 2. It probably derived its name rather from its supposed dignity as an argument than, as Gassendi con- jectures, from the mention of a ruler. The same may be said of the liepalvoiv or conclusive sophism. ^ This sometimes appears in another form, as one of the various expositions of the celebrated Fallacy of the tertius homo, alluded to by Aristotle, Soph. Elench. 22. 12. Metaph. i. 9. 3. It is given by Alexander, Schol. p. 314. b. 42. In the proposition, dvdpatTros nepiTraTel, the subject is not the Pla- tonic avTodvdpcoTTos, who is immoveable, nor yet any individual man ; therefore there is a third man, distinct from the Idea and from the individuals. Several other forms of this Fallacy are given by Alex, in Metaph. p. 62. ed. Bonitz. Cf. Brandis, de perditis Aristotelis libris, p. 18. Cousin, de la Metaphysiqice d'Aristote, p. 164. Bonitz in Aiist. Met. 990. b. 15. ' Ajnmonius ad Categ. Arist. f. 58. ol OvriBes 7rapdKoyicrp.o\ Kara tqv irap 'Op,r}pa} '08v(r(rea, ep Kaipa Ovtiv iavrov KoKeaavra. APPENDIX. 153 Subjicit Gassendus ex Laertio, has Chrysippi Rogatiunculas. 1. Qui non initiatis indicat mys- 'teria, impie agit. Sed hoc facit Hierophantes ; I Ergo Impie agit. 2. Est quoddam caput ; Id Tu j non habes ; Ergo Caput non habes. 3. Id quod loqueris ex ore tuo egreditur : Currum loqueris ; [Ergo Currus ex ore tuo egreditur. §. 10. Non temperaturos sibi Juvenes satis scio quin dissihant risu, ubi hsec tarn futiHa intellexerint a gravissimis Philosophis serio fuisse proposita ; et Veteribus adeo difficiha haberi, ut Philetas Cous praeceptor Ptolemaei Philadelphi soHus Mentientis explicandi studio confectus interierit. Quamvis autem Aristotehs beneficio^ videantur ista ut sunt llevia, in iis tamen prompte atque artificiose sol- vendis non inutihter sese Juvenes exercebunt : nam in gravissimis Disputationibus, haec eadem recocta Novae prsesertim Philosophise cultores saepissime reponunt. V. g. Gassendus Vacuum quod appellat disse- minatum eodem fere Sophismate demonstrare per- tendit, quo olim Zeno contra motum utebatur : Suamque Hohhius de Necessitate sententiam iisdem propugnat Fallaciis quibus Fatum Stoici : ahaque plurima hujus generis, quae sunt Nobis praetereunda, studiosis inter legendum occurrent. OijTivos TrapaXoyiafxoi) napad^Ly^a. Ei ris iuTLV iv 'Adrjvais, ovtos ovk ea-Tiv iv Meydpois' av6pa>iros 5e ioTiv iv 'Adrjvms' av6pa>iros apa ovk € 164 APPENDIX. Universal, but susceptible of Accidents, from which union are formed various Individuals. Man, for example, is a lowest species ; to this are added certain accidental modifications which form Socrates, and at the same time others which form Plato. These modifications excepted, there is nothing in Socrates which is not at the same time in Plato, nor in Plato, which is not at the same time in Socrates'. Moreover, from these Universal Substances, or rather from the distinctive por- tion of each, certain qualities flow^ or are produced as eflfect from cause. Others, not connected bj causation, are found in the individuals of this or that Species, some universally in all, others partially, in some individuals only. From a series of assumptions of this kind, the expo- sition of the Realist doctrine of Predicables is easy. And this, or some other of the various phases of Scholastic Realism, must of necessity be assumed, if our intention is to explain an old theory, not to construct a new one. On the other hand, we have the modern Logician ;. expounding somewhat in the following style. Genera; and Species have no existence a 'parte Rei, but are t ^ j Ttorj >j ttotI % xsioSai >j ep^£*v yj ttoisIv yj 7roi(r^?iV. "Ectt/ Se oucioc /x-ev wj TVTTM sWslv olov oivQgooTTOs, T-TTTrof TTotrov 8s olov 8i7r>jp^u, t^Ittyj^v TTOiOv 8e oiov Xsuxov. ygufjif/.otTixov' Trgog t» 5e olov hTTkoKTiov, rjfLKTv, jxsi^ov vov Ss olov Iv Auxs/o;, Iv ayogSc' ttots 8e olov 6;)(;fl£j, 'TTsgvTiV xsi(r$on Se olov ocvotxsiToti, xa5»)Tar e%£*v Se olov u7ro8e§cTai, cw7rAio"Tar woislv 8e olov t6jU,v£<, xai'gi* Tracrp^giv §g olov TSfjivsTui, xotisToii. Tojfic. i. 9. Msra to/vuv tuvto. hi hogl(rui^Qsi(ron TSTTagss. "EcTi he tolvtol tov ugi^^ov 8exa, t/ Io-t», Trocrov, ttoiov, 7Fg6$ T«, TToD, -^rore, xsi3jU,a/v£l, TCt 8s TTOiOV, TCt 8s TTOCTo'v, Tfit 8s TTgOf Ti, Ta 8s TTOielv )J Tzmyziv^ TU 8e TTOu, ra 8s ttots, IxacTw toutcov to elvai Tat5T0 (Dj/xa/vsi. From these passages it appears that the Categories were regarded by Aristotle, 1. As an enumeration of i '/ the different significations of simple terms, apart from ^ their connexion in the proposition. 2. As an enurae-i 174 APPENDIX. ration of the several genera under which Aristotle's four heads of predicables fall. 3. As an enumeration of the different modes in which Being may be signified. An examination of the principle of classification is neces- sary, in order that we may determine how far the charges of deficiency and redundancy, so frequently brought against Aristotle's list, can be fairly maintained. The most celebrated of these accusations is that of Kant^ Assuming that Aristotle's design was identical with his own, viz. to enumerate the pure or a priori conceptions of the understanding, he asserts that the classification was made upon no principle ; that it was found by the author to be defective, and the post- predicaments added in consequence ; that the list thus enlarged is still defective ; that it contains forms of the sensibility as well as of the understanding ; {quando, uhi, situs, prius, simul ;) that empirical notions are intruded among the pure (motus), and deduced concepts classed as original {actio, passio) ; and that some original elements are altogether omitted*'. A somewhat similar criticism is given in Mr. Mill's Logic. The Categories he supposes to be " an enume- ration of all things, capable of being named ; an enume- ration by the summa genera, i. e. the most extensive classes into which things could be distributed; which therefore were so many highest Predicates, one or other of which was supposed capable of being affirmed with truth of every nameable thing whatsoever." Thus viewed, he pronounces the list to be both redundant and de- fective. Action, passion, and local situation, ought to be included under relation ; together with position in time {quando), and in space {uhi) ; while the distinction ^ For an account of the earlier criticisms of the Categories by Plotinus, Campanella, and others, see Trendelenburg, Geschichte der Kategorienlehre. ^ Kritik der r. V. p. 80. (ed. Rosenkranz.) Prolegomena, §. 39. APPENDIX. 175 between the latter and situs is merely verbal. On the other hand, all states of mind are omitted entirely ; as they cannot be reckoned either among substances or attributes ^ These objections will stand or fall, according as their authors have rightly or wrongly divined the purpose of Aristotle's classification. Kant is mistaken in supposing that Aristotle added the post-predicaments to complete his list of Categories. The post-predicaments were not so called by Aristotle, and have never been classed by commentators among the Categories. The term is of scholastic origin, and was employed to denote the five subjects treated of by Aristotle after the Categories proper. Kant is equally mistaken in supposing that Aristotle had any intention of classifying the pure forms of the understanding, independent of experience. On the contrary, the Categories belong to the matter of thought, are generalized from experience, and leave altogether untouched the psychological question of the existence of elements a priori^. Any objection, there- fore, based on the inclusion of empirical or the ex- clusion of original elements, is untenable, and rests on a misapprehension of the philosopher's design. Nor yet can we adopt Mr. Mill's opinion, that Aristotle designed a classification of all things capable of being named ; at least not in that point of view in which things are regarded according to their real characteristics as pre- sented to consciousness. The Categories are rather an i enumeration of the different modes of naming things, i classified primarily according to the grammatical dis- I tinctions of speech, and gained, not from the observation j '^ Mill's Logic, vol. i. p. 60. I '^ See Sir W. Hamilton, Edinburgh Review, No. 99. p. 211. Franck, Histoire de la Logique, p. 26. St. Hilaire, Logiqve d'Aristote traduite en Franqais, Preface, p. Ixxx. 176 APPENDIX. of objects, but from the analysis of assertions. This is manifest from the name and from the manner of treat- ment. K.ocTYiyogiu, xtxTYiyogsiv, xaTYjyogYifxot, }caTri'yo^o6[x.svov, xoLTY^yoqiyio^, have all primarily reference to forms of speech ; the term naTYiyopia, being used by Aristotle as well for any predicate term, as for the highest gene- ralizations under which predicates can be classed ^ In the beginning of the treatise on the Categories, terms as combined in a proposition are made to precede terms regarded separately^; and the proposition, as the only assertion capable of truth and falsehood, appears to be regarded as the unit of speech, of which the simple term is but a fractional element^. It is therefore probable, that the Aristotelian distinction of Categories arose from the resolution of the proposition and a classification of the grammatical distinctions indi- cated by its parts. The noun substantive leads us to the category of oua-la, the adjectives of number and of quality to iroa-ov and ttoiov, the adjective of comparison to ^rgos ri, the adverbs of place and time to %oi^ and %ors, the different forms of the verb, intransitive, praeterite, active, and pas- sive, to Ksia-^cn, ep^sjv, TroisTv, and itoLdyzw^. It is true that in his subsequent treatment the philosopher by no means adheres strictly to the grammatical point of view, and that his classification may, even on his own principles, be considerably simplified ; but it must be remembered, that at that time the science of Grammar was in its infancy, that its forms of speech had not been analysed completely, nor its boundaries clearly separated from those of Logic and Metaphysics. f See Trendelenburg, Geschichte der Kategorienlehre, p. 2. The Aristo- telian expression (rx'^iM-ara rrjs Kar-riyoplas will thus primarily mean forms of predication. e See Catei/. ch. 2. h See Categ. ch. 3. Trendelenburg, Kategonenlehre, p. 12. -- ' Trendelenburg, Elementa, §. 3. Kategorienlehre, p. 23. APPENDIX. 177 The omission, therefore, in the Aristotelian list, of separate heads of classification for mental states, cannot be charged as a defect in this point of view, so long as mind and its various states (whatever may be their dif- ference in other respects) are represented by the same verbal forms as substances and attributes. And accord- ingly we find various mental states, faculties, passions, habits, and dispositions, classified together with corre- sponding affections of body, under the head of qualities''. A more valid objection in a grammatical point of view would be, that qualities in their abstract form are ex- pressed by nouns substantive, and should therefore be classed under the category of substance. This objection would be tenable in relation to the distinctions of modern Grammar. But Aristotle appears to have limited the substantive word to terms expressive of the irqchrai oixrlon, or individual substances, and the IsvTsqon oua-lai, or their several genera and species. The latter denote properly the category of substance, or substance considered as one of the possible predicates of a proposition. Words denoting individual substances, being subjects only in the proposition, do not properly indicate a category ^ In reference, therefore, to the treatise of the same name, we might fairly describe the Aristotelian Categories as an enumeration of the different grammatical forms of the possible predicates of a proposition, viewed in relation to the first substance as a subject. And this view is not materially departed fi'om in the other writings of Aristotle. The passage quoted from the Topics, indeed, only con- tinues the same view, stating that those predicates, which in their actual relation to their subjects in a proposition ^ See Categ. ch. 8. ^ Categ. 5. 27. 'Att^ fihvyhp rrjs irpdrris oixrias oi/Se/xia iarl Karrjyopla' kui' ovBevhs yhp xnroKeiixivov \ey€Tai' rwv Se SevTepccu ovcriuv rh fiev elSos Kara rod arj/iow KOTTiyopuTai, rh 5e y4vos Kal Korb. tov etSovs Koi Kara rod arSfiov, N 178 APPENDIX. come under one of the four heads of Genus, Definition, Property, or Accident, come as simple terms under one of the ten Categories. The Metaphysical view of the Categories is not materially different. In that work, Aristotle enumerates the different senses in which the term Being (to ov) is used, in order to determine in what sense it is applied to the object of metaphysical in- quiries"*. Being sometimes signifies the accidental connection of an attribute with a subject, or of two attributes with a common subject. It is also used co- extensively with the Categories in predication ; thus we may say, uv^gooTrog uyia/vst, or avdgMTrog vyiulvcjov so-tIv, avSgco- 7ro$ TS[jt,vsi, or avQgcoTros tsiji.vu)v Idxiv, the verb elvat being admissible as a copula in any proposition, whatever may be the category of its predicate ^ But substance is the vpooTcos ov, the proper object of metaphysics*'. In this account, Aristotle does not appear to have distinguished between the verb substantive, as denoting real existence, and the copula as denoting the coexistence of notions in the mind ; but, as in other places, the Categories are enumerated, not as an exhaustive catalogue of existing things, but as a list of different modes of predicating by the copula. They thus originally belong to Grammar, rather than to Logic or Metaphysics, though the treatment of later philosophers, perhaps in some degree sanctioned by Aristotle himself, has brought them into closer con- nection with the latter sciences, and overlooked their proper relation to the former^. " See Trendelenburg, Kategorienlehre, p. 167. » Metaph. iv. 7. «> Metaph. vi. 1. P Trendelenburg, Kategorienlehre, p. 216'. APPENDIX. 179 Note C. on definition. In the nates to Aldrich's account of Definition, I have endeavoured to explain his language in conformity with the views most commonly found in Logical Treatises* But as these views differ in many respects from those of Aristotle, on which they are supposed to be founded, and as a correct account of the doctrines of that Philosopher will materially assist in the solution of more than one of those vexatce qucestiones which are most perplexing to beginners in Logic, I shall attempt a somewhat fuller exposition here. c ;-Ltj^cutt., In the second Book of the Posterior Analytics, Aristotle mentions three different forms of Definition, in the following words : "Ecttjv a^a 6^os) tj ^povrii icrri }l/6(pos iv v4(p€i. Aristotle's text is not decisive, the one view being rather supported by ch. 8. the other by ch. 10. The question is by no means unimportant; the attempt to reduce these Definitions to a pseudo-Genus and Differentia has fostered a grave error, which will be noticed hereafter. ^ Pacius aud Waitz consider irrucns and Oeais to be sjTionymous. APPENDIX. ] 83 /> expressed ; but it seems probable that he regarded the ^-^^-^^ formal cause only as available for the purposes of De- ^"^^v^ — finition. For a material cause, properly speaking, has no place in attributes, but only in physical substances^; and that which in the former is most nearly analogous to matter, viz. the necessary condition out of which the effect arises, may in such cases be identified with the formal cause. This Aristotle allows in the chapter in question, when he states that the material cause there instanced as a middle term is in fact the same as the formal™. The efficie nt and final causes seem to be ' l'^ excluded, as not being contemporaneous with their I effects, so that from the existence of the one we cannot certainly infer that of the other ''. Whereas the formal ] cause is expressly distinguished as to r/ \y zivoa''^ and the examples given of it in Anal. Post. ii. 12. I. corre- spond exactly to those previously given as Definitions. The other causes only accidentally serve the same pur- : pose, in those instances in which they coincide with the formal p. ' Metaph. vii. 4. 6. Flepi ix\v ohv tols (pvcriKas ov(rias Koi yeuuT^ras h.v6.yKr\ O0TCO fierievai, et ris /ncTeicriv opdws, e^nep &pa atrid re toOto kuI roa-avra, Koi I Set Toi aXTia yuoopi^eiu. 'Eirl 5e tcDj/ (pvaiKwi/ fxkv al5iwu Se oixricov &\\os \6yos. ''laus yap euia ovk exet v\7]u, fj oh Toiavrrjv aK\a [m6uou Kara rSirov Kivr]T-f]y. OvS' '6(ra 5^ (pvcrei fjLcv fiii, ovcla Se, [sc. virdpx^t] ovk ecrri tovtois v\r) aWa rh viroKelfiev ov rj ovaia. OTou ri aXriov eKKei^pews, tIs S\7i ; ov yap etTTiv, a\\' r} aeXi]vyi, '''^ irdcrxov. "" See Anal. Post. ii. 11. 3. n See Anal. Post. ii. 12. 3, 4. and Waitz, Org. vol. ii. p. 411. « Anal. Pr. ii. 11. 1. Metaph. i. 3. 1. !P See Rassow, "Aristotelis de Notionis Definitione Doctrina," p. 16. A very different view has been taken by some Logicians. Crakanthorpe, j for example, maintains that Demonstration can only be, " a causa eflSciente per emanationem, vel a causa efficiente per externum actionem, vel a causa finali;" and he devotes a chapter to shewing that neither the Material nor the Formal cause can be a middle term in Demonstration, though the efficient cause of the Attribute may be the formal cause of the Subject. A similar view is maintained by Sanderson, lib. iii. cap. 15. ^/^ id ^t^^i. * n 184 APPENDIX. We have next to consider the Definitions of Sub- stances. Here too the investigation of cause is the root of the whole inquiry; but the manner in v^^hich it is conducted is not at first sight so obvious as in the former case. To ask the cause of an attribute, is to ask why the subject is so affected. Why, for example, is the moon eclipsed.? But what is meant by the^coMse of .a "^ an, and i n wh at form will the , giiPRtif^Ti bp proposed ? To ask why man exists, is in fact to ask why there are such beings in the world,— a question admitting only of Grangousier's solution "i, — and, when so solved, contri- buting nothing towards the Definition. To ask why a man is a man, is, as Aristotle himself observes, futile ^ The only form in which the question can be put is. Why is this or that individual a man ? What are the essential constituents of the notion Mail, the possession of which entitles Socrates to be reckoned in the class ? Here too the formal cause determines tbe Definition. These Definitions form the first of the three kinds '^> distinguished in Anal. Post. ii. 10. 4. ^^.fl-Tiv 0.00. ooio-fLo^ sic jjt^e v Xoyog To^j^tJ ^Tiv avcarohix Toc. These Definitions are assumed prior to all demonstration', and are real, inas- much as the existence of the objects is assumed with them. The ground of the assumption will vary according to the nature of the object to be defined*. With regard to the third class of Definitions, described as -T^j Tov r/ scTTiv oiTTohl^sMs (TvifMsqcKTi^a, Commcutators But to support this interpretation requires considerable straining of Aristotle's language. q Tristram Shandy, vol. iii. ch. 41. see also Rabelais, liv. 1. ch. 40. •■ Metaph. vi. 17. 2. rb [xhv oZu Sia ri aiirS iariy uvtS, ovdiv ia-ri (riTelv. * Anal. Post. ii. 9. 1. &5r]s, seems rather to mean, " a sentence explanatory of the signifi- cation of a name, or of another sentence ha^dng the force of a name." On the other interpretation, the word eVepos is superfluous, and the example, oTov rh rt crrjfialvei ri icrrip ^ rpiycovov, unintelligible. By x6yos oi/oyuorc^Srjs is therefore meant a sentence whose signification, like that of a single noun, .is one. Such are all real Definitions, of which the example is a specimen. See De Int. 5. 2. Metaph. vi. 4. 16. vi. 12. 2. vii. 6. 2. Alex. Schol. p. 743. a. 81. In the Greek Commentators, on the other hand, \6yos ovofiardSris is clearly used for Nominal Definition. See Philop. Schol. p. 244. b. 31. 186 APPENDIX. There is also no warrant in Aristotle for limiting the means by which Nominal Definition may be effected; as is done by those Logicians who specify synonyms and etymologies. The latter method indeed seems to have trespassed on the domain of Logic from that of Rhetoric. Nor has it the slightest connection with the former, save by an ambiguity of language. The etymology will in nine cases out of ten declare, not the present meaning of the word, but either one that has become obsolete, or some secondary notion, which may account for the imposition of the name, but which at no time formed, strictly speak- ing, any part of its signification. This holds equally of real objects and imaginary. It is only by an equivocation that " bull-piercer" can be assigned as the meaning of " centaur," or the notions of a swine and a quickset fence be combined into that of " hedgehog." Definition by synonym, on the other hand, may be one ^f the means of explaining the signification of a name ; though relatively only, and from the accidental circum- stance of one word being more familiar to the hearer than another ; in which respect all translations from one language into another are equally nominal definitions. It is not, however, specially mentioned by Aristotle^. As a real definition it is obviously inadmissible, as it neither assigns the cause of a phenomenon nor developes the contents of a notion. The above data will also furnish us with an answer to ^ci-^^/i-^^^ question, which, latterly at least, has been a sore puzzle to the tyro in Logic. What are the limits of Definition ? If all real Definition must be by Genus and Differentia, a Synonyms are expressly denied to be real Definitions in the proper sense by Aristotle, Top. I. 5. 1. though admitted to be bpiKd. As Nominal Definitions, they are allowed by Alexander on Metaph. vi. 4. p. 442. ed. Bonitz; but the genuineness of this portion of the Commentary has been questioned. :a ^ APPENDIX. 187 the object defined must in every case be a Species. Summa, Y-c^y^/^''^^^^ Genera and Individuals are in that case alone inde-^^^/u^ ^ finable. And for this limitation, the authority of Aristotle may be cited. On the other hand, Locke ^ assures us that this restriction is erroneous, and that Simple Ideas alone are incapable of Definition ^ The dispute may be reduced to a mere verbal question. For Aristotle does not maintain that all Definitions must be by Gen_us_ajid Differe ntia, but only tho se of S ubstances. In the pas- sages which seem to extend this rule, Definition is used in the narrow sense which has been previously men- tioned*^. For it is obvious, to take the instances adduced above, that " quenching" cannot be called the genus of " thunder," or " interception" of " eclipse," in the same '» Essay, b. iii. 4. 7. But Locke has in this matter been anticipated by Descartes, Princip. i. 10. Sir W. Hamilton (Eeid's Works, p. 220.) main- tains that Aristotle has said the same thing. It is dangerous to dispute any thing which a man of Sir William's learning professes to have dis- covered in so wide a field as Aristotle, especially as he gives no references ; but if the passage alluded to be Metaph. vi. 17. 7. one might be tempted to hazard a different interpretation. T^ aTrAa seem rather to be the elements, (o7r\a adofiaray Met. vii. 1.2.) which have not, like compound substances, received a definite form, and thus are not definable. Cf. Plato, Theaet. p. 205. c. But the words are not sufiiciently decisive to furnish much ground for any theory. A more remarkable passage occurs in Occam's Logic, Pt. i. ch. 23. " Ex praedictis sequitur quod nulla intentio quae est prsecise communis rebus simplieibus carentibus compositione ex materia et forma habet diiferentias essentiales ; quia non habet partes, quamvis possit habere multas differentias accidentales. Ex iUo sequitm- ulterius quod nulla species quae est praecise simplicium est definibilis definitione proprie dicta, sive sit in genere substantiae sive in quocunque alio praedicamento." This," coupled with Occam's Conceptualist theory of Universals, is not very different from Locke's position concerning Simple Ideas. c By Simple Ideas, Locke meant all ideas derived immediately from sensation or reflection. In the formation of these the mind is wholly passive, whereas in the formation from them of Complex Ideas, it is active. Among Simple Ideas derived from sensation, he enumerates solidity, space, figure, rest, and motion ; from reflection, perception and volition ; from both, pleasure and pain. ^ As, for example, Topics, i. 8. 3, Compare Metaph. vi. 4. 12, 16. vi. 5. 5. and Alex, in Metaph. p. 442. 30. ed. Bonitz. 188 APPENDIX. sense as " animal" is of " man." Whereas Locke's simple , ,'Uu.:xf^ ideas are exclusively ideas of attributes. By reference i^'/.r w-'^'T^then to Aristotle's account of the latter, it will plainly v:^ ^'--^ appear that he and Locke mean two very different things - -i^at-'/ww^by Definition. With the former, it is an investigation IJ'Culo*^'^ ' '4. of the objective cause of a phenomenon ; with the latter, ^j^_ , . ^ an analysis of the subjective impression which that / ^phenomenon produces in the mind. The idea of an ' ^j interception of light is not part of the idea eclipse, but the one phenomenon is the physical antecedent and cause of the other. Inquiries of this kind are still classed among the most important problems of Physical Science. What, for example, is light.? Is it a succession of material particles, or the undulations of an elastic medium ? The solution of this question would not be a Definition in Locke's sense of the word ; i. e. it would not be an analysis of the idea of light produced in the mind by sensation. The same may be said of colour. The mental sensation of whiteness or redness is altogether unaffected by the researches of Optics. The external cause of colour, regarded as a quality of bodies, falls directly within the province of the Science ^ The de- termination of such problems will be, in Aristotle's sense^ of the term, Definition. This may be further illustrated by reference to a dis- cussion of Aristotle's which few probably have perused for the first time, without considering it as singularly vague and unsatisfactory. I mean the dissertation on Pleasure, in the tenth Book of the Nicomachean Ethics. We are struck with the absence of any thing like a Definition or Analysis of the emotion ; and a reader who commences the study of the book with some previous knowledge of Locke's theory of Simple Ideas, will probably be disposed to regard it as an attempt to define e Compare on this subject, Reid, Inquiry, ch. vi. sect. 5. APPENDIX, 189 that which is incapable of definition, and which in con- sequence necessarily involves its own failure. The same may be said of the principal opinion which Aristotle controverts. Whether we regard Pleasure with Plato, as consisting in a motion towards a natural state of harmony, or with Aristotle, in the perfect exercise of a power; neither of these can be termed an explanation of the feeling itself, but only of the cause by which it is produced. Pleasure itself remains an indefinite some- thing, consequent on the one or the other. Yet examined according to Aristotle's own view of the definition of ' attributes, we see that pleasure is as fairly defined by the perfection of the exercise of power, as an eclipse by the interception of light ^ There are, however, conditions and limits to thei/u^^ (^^-i^^. definitions of Attributes, though they are not the sameviic^x^^^i-il^ as those of Substances. Every Substance to be definable -ru^^, /T *V^^ must be a Species, Every Attribute must be Si Property , ^-^^.( '^y^ i. e. must be capable of demonstration by its cause. ^.^^^'^-^ a\i^ ^ Accidents then, as merely contingent attributes, are . ,,^ incapable of definition. This limitation, however, is merely relative to the degree of our knowledge of the matter. The advance of Science may transform Acci- dents into Properties, and thus furnish the requisite means of definition. Before concluding the subject, it will be necessary to say a few words on two other points connected with Aristotle's doctrine of Definition. *■ Leibnitz adopts the same view as Aristotle, observing that pleasure admits of a causal, though not of a nominal definition. Nouveaux Essais, ii. 2] . §. 46. In another point of view, simple ideas admit of a definition by logical analysis; viz. when they are considered, not as phenomena presented to the sense, to be resolved into simpler sensible phenomena, but as con- cepts, or general notions, representative of objects of thought, to be resolved into simpler concepts. On this distinction I have remarked elsewhere. See Prolegomena Logica, p. 45. 190 APPENDIX. vT This is perhaps mai-ked by Aristotle's own language. In reference to the one method, he uses KOTO(r/c€uc(^eti' ; to the other, ^77x6?^. J Aristotle does not give any name to the process ; by his Commentators it has been variously denominated the method of Resolution, of Com- position, of Induction. Cf. Edinburgh Review, No. 115. p. 236. ZabareUa, Logic, p. 1212. Pacius on Anal. Post. ii. 13. 21. ^ Scholia, p. 242. b. 35. Trendelenburg.de An.p. 273. Kiihn, de Notionis Definitione, p. 11. 192 APPENDIX. every attempt at such demonstration necessarily involves a petitio principii. The reason is obvious: since a definition can be predicated essentially (Iv tm tI so-ti) of nothing but that of which it is a definition ; and since, to prove a conclusion concerning the essence, the pre- mises must be of the same character ; the middle term assumed must be identical with the minor, and the major premise with the conclusion. Such is Aristotle's theory of Definition. Its funda- mental principle may still, mutatis mutandis, be retained, notwithstanding that the speculations of modern philo- sophy have considerably modified his distinctions of Substances and Attributes. Properly speaking, indeed, all Definition is an inquiry into Attributes. Our com- '; plex notions of Substances can only be resolved into I various Attributes, with the addition of an unknown • substratum: — a something to which we are compelled toi regard these Attributes as belonging^ Man, for example, is analysed into Animality, Rationality, and the some- thing which exhibits these phenomena. Pursue the analysis, and the result is the same. We have a some- thing corporeal, animated, sensible, rational. An un- known constant must always be added to complete the integration; unfortunately we have no means of de- termining its value. Still, this does not affect the basis of the Aristotelian distinction. For some phenomena can be accounted for by other phenomenal causes ; in others, we must acquiesce in the conviction that they are so, merely because they are. It is clearly impossible for the mere hypothesis of an unknown substratum to explain the reason of all the variety of attributes which different objects exhibit. One further question remains. How far Definition properly belongs to the province of Logic, was, as^we ' Cf. Locke, Essay, book ii. ch. 23. APPENDIX. 193 have seen, an early point of dispute among the School- men™. On this question the authority of Aristotle is of little avail for either side. That his treatment of the subject has far more of a material than a formal character is undeniable. And to those who maintain that the Organon of Aristotle is designed as a systematic treatise on a single subject called Logic, such testimony must be decisive as regai'ds both the material character of much of the Science, and its inclusion of Definition. But then it remains, and probably will continue to remain, a problem, to frame a conception of Logic adequate to the province thus assigned to it. This question has been already treated of in the Introduction, and need not be repeated here. It is sufficient to say that, as far as any evidence is furnished, either by the writings of Aristotle himself or by external testimony as to their original connexion, it is no more a departure from the authority of the Stagirite to assign a field to Logic incom- mensurate with that of the Organon, than it is to write a moral treatise on the basis of the Ethics, without including the Politics. Leaving then the question of authority, we may fairly assert that Logic as a formal Science can take no cognisance of the following points. I. It has nothing to do with determining the physical existence of attributes in their subjects ; which is in fact an inquiry into the material truth of the propositions in which such attributes are predicated. It is true that such propositions are by Aristotle considered as the conclusions of Syllogism, and so far their truth is merely formal. But it must be remembered, that no attribute can be syllogis- tically demonstrated of one subject, without being in the premise asserted of another ; and it is upon the material truth of the latter proposition that the certainty of the •" See p. 39, note o. O 194 APPENDIX. former, and the demonstrative character of the whole reasoning, ultimately depends. II. Logic has nothing to do with testing the material correctness of a definition, i. e. ascertaining how far the ^ notions developed in our analysis of a given concept correspond to the principal phenomena exhibited by the objects usually included under that concept; nor even with the inquiry, whether our usage of terms corresponds, with the ordinary language of others. III. Still less does it lie within the province of Logic to perform the functions either of a Dictionary or of an Index to Physical Science ; to convey, that is, information from without, whether concerning the meaning of words or the nature of things, into a mind previously ignorant. Whereas, from the statements of some Logicians, one might almost imagine that they regarded their Science as furnishing, as it were. Logarithmic Tables of things in general ; Catalogues of Genera and Differentiae, to which w^e have only to refer any given object, to obtain full information concerning if". These being excluded, the only office that remains for Logic to perform, is to contribute to the distinctness of a given concept, by an analysis and separate exposition of the different parts contained within it. This operation is n Thus Melanchthoii; Erotemata Dialectica, p. 109. '« Cum quserimus definitionem inspiciuntur tabulae prsedicamentorum. Unde disces an res, de qua dictui^us es, sit substantia an accidens. Et si est accidens, in qua parte sit, in corpore an in anima, &c." And so Keckermann, Syst. Log. Mill. lib. i. cap. 17. " In hunc enim usum istse rerum tabulae et deli- neationes praecipue illic adumbrantur, ut definitum quaeratur, simulque animo lustretur, quid ex parte superiori proxime definite adjaceat; id enim erit ejus Genus : e. g. cupio conficere definitionem Hominis : cogito ergo primum in quo praedicamento sit Homo, et deprehendo ex notis Sub- stantias, esse in praedicamento Substantias: quocirca tabulam hujus prae- dicamenti perlustrans animo, deprehendo hominem proxime collocari sub animalir hinc concludo hoc esse pi'oximum ejus genus. Sic in aliis pro- ceditm- definitis per singiila preedicaraeuta." APPENDIX. 195 analogous to that of drawing formal inferences, virtually contained in their premises, though not explicitly de- veloped". It is a process of self-examination, not dis- similar to the Platonic application of Dialectic, though widely differing as regards the objective truth of its results. For the Logical process furnishes only a sub- jective criterion : it enables us to represent more dis- tinctly to the mind, the notions previously existing there in more or less confusion : its rules direct us to compare concepts one with another, and furnish some security for our own consistency in employing them ; but they do not enable us to ascertain their accordance with externalj' objects, or to add the deficient parts, where they are inadequate representatives of the latter. The mind, like the sky, has its nebulse, which the telescope of Logic may resolve into their component stars. But here the parallel ceases. The Logical instrument discovers no luminary whose rays have not previously entered the eye ; it tells us nothing of their relative distances, of the velocity with which their light travels ; of any thing, in short, which did not form a confused portion of the sensuous representation p. This may seem but beggarly service to be performed by the Art of Arts and Science of Sciences. Inferior certainly it is to the gigantic pur- poses which more than one Logical Titan has essayed to accomplish with the same instrument. But let not its legitimate uses be contemned, because it has abated somewhat of the " vaulting ambition which o'erleaps I itself." It furnishes the mould by which the ever- ' accumulating matter of consciousness is reduced to form i and consistency; it were ungrateful to despise it, because I it does not also dig the metal itself from the mine. « Cf. Anal. Post. i. 24. 11. p Cf. Kant, Logik, Einleitung. V. o 2 19(> appendix. Note D. on material and formal consequence. A Material Consequence is defined by Aldrich to be one in which the conclusion follows from the premises solely by the force of the terms. This in fact means, f rom some un derstood Proposition or Pr opositions, cqn- necting the terms, by the addition of which the mind is enabled to reduce the Consequence to logic al form. This is easily seen, both in Aldrich's example, " Homo est animal. Ergo est vivens," and in the rather more com- plicated instance given by Sanderson, " Socrates est risibilis, ergo, Aliquis homo est rationalis." The latter, when the necessary conditions are supplied, is expanded into two syllogisms. Omne risibile est rationale ; Socrates est risibilis, Ergo, Socrates est rationalis. Socrates est homo. Ergo, Aliquis homo est rationalis. The failure therefore of a Material Consequence takes place when no such connexion exists between the terms as will warrant us in supplying the premises required : i. e. when one or more of the premises so supplied would be false. But to determine this point is obviously beyond the province of the Logician. For this reason, Material Consequence is rightly excluded from Logic. Moreover, even where true premises can be added, and the Consequence legitimately deduced, we cannot, except from knowledge of the matter, determine into what form the reasoning will naturally fall. In^ some cases, as in the example above quoted fi*om Sanderson, APPENDIX. 197 the proof may be given in Categorical Syllogisms. In others, it is far more naturally exhibited in the hypo- thetical form. A hypothetical premise is sometimes the only materially allowable assumption in cases where the given antecedent and consequent have both terms distinct. E. g. A is B, therefore C is D. We may supply, If A is B, C is D ; but to determine the truth of the assumed proposition, whether it be hypothetical or categorical, does not fall within the province of the Logician. It may be questioned, however, whether the mere assumj^tion of a hypothetical premise can make a material consequence formal. See below, Note I. Among these material, and therefore extralogical, Consequences, are to be classed those which Reid adduces as cases for which Logic does not provide ; e. g. ^' Alexander was the son of Philip," therefore " Philip was the father of Alexander ;" '' A is greater than B," therefore " B is less than A." In both these it is our material knowledge of the relations " father and son," " greater and less," that enables us to make the inference. Another of Reid's examples is the following: '* A is equal to B, and B is equal to C, therefore A is equal to C." This reasoning is elliptical, and therefore, as it stands, material; though owing to the suppressed premise being self-evident, its deficiency is apt to be overlooked. Stated in logical form, the syllogism runs thus : Things that are equal to the same are equal to each other ; A and C are equal to the same, Therefore A and C are equal to each others Another example of the same kind is that sometimes called reasoning a fortiori. E. g. " A is greater than B, » Hamilton on Reid, p. 703. ]98 APPENDIX. and B is greater than C, therefore a fortiori A is greater than C." The logical form is, Whatever is greater than a greater than C is greater than C ; A is greater than a greater than C, Therefore A is greater than C. Or if it be required that the a fortiori nature of the reasoning appear in the conclusion, we must state the major, " Whatever is greater than a greater than C is greater than C by a greater difference.'''' Of the same kind is the reasoning " A is equal to B, therefore twice A is equal to twice B." The logical form is, The doubles of equal things are equal ; Twice A and twice B are doubles of equal things, Therefore they are equal. The major premise might be stated more generally, " Equimultiples of equal things are equal." APPENDIX. 199 Note E. is the syllogism a petitio principii ? The eagle of the Libyan fable was killed by an arrow feathered from his own wing. The armoury of the Logician has been fondly imagined to contain the fatal weapon of his own destruction. But the champion destined to wield it, if such there be, is somewhat tardy in his forthcoming. More than one Sir Kay has essayed the adventure of the sword ; the Arthur destined to achieve it remains in all the mysterious dignity of a Coming Man. In other words, many waiters have suc- ceeded in shewing their own ignorance of the nature of the fallacy called Petitio Principii"; they have not been equally successful in proving the invalidity of the Syllogistic process. Let us first endeavour to ascertain what the Petitio Principii really is. The name is a blundering trans- lation of the Aristotelian to Iv oigxV (*^^' "^^ ^^ *§'X^0 aWsla-Qai : i. e. the assumption, not of the principle properly so called^, but, in some form or other, of the question originally proposed for proof. And it is remarkable, that among the five modes of this fallacy enumerated by " Of the numerous absurdities gravely propounded by Logicians in relation to this fallacy, perhaps the happiest is the exquisite etymology of Du Marsais, Logique, p. 81. " Ce mot s'aiDpelle petition de principe, du mot, grec ireTOfiai, qui signijfie volervers quelque chose, et du mot latin principinm, qui veut dire commencement; ainsi faire une petition de pinncipe, c'est recourir en d'autres termes a la meme chose que ce qui a d'abord ete mis en question." ^ "■ Without entering on the vai'ious meanings of the term Principle, which Aristotle defines, in general, that from which any thing exists, is produced, or is known, it is sufficient to say, that it is always used for that on which something else depends ; and thus both for an original luu\ and for an original element." Sir W. Hamilton, Reid's Works, p. 76 L Cf. Arist. Metaph. IV. 1. •}. 200 APPENDIX. Aristotle, one is in form not distinguishable from the legitimate Syllogism *=. Selecting this variety, as that by which most of all the objection is to be sustained, we will proceed to examine its peculiarities. In .the first place, it is manifestly necessary to a Petitio Quissiti^, as the fallacy may more correctly be called, that there should be a question proposed for proof. And hence it was long ago acutely remarked by Petrus Hispanus, that such a fallacy cannot be com- mitted in a Syllogism of inference^. If, that is, the ■ truth of the premises is known beforehand, and the only question is, what may we infer from them ? there is no necessity for begging or assumption of any kind. It is «lear then, that not the Syllogism in general, but at , most only one particular application of it, can beg the ' question. But it nmy be answered, that the truth of such premises never can be ascertained, but by a previous induction embracing all particular cases, and that Syllogistic in- ference is therefore at least futile, since the conclusion drawn must be presumed to be already known. But this answer itself assumes what has never yet been satisfactorily proved, the dependence of all knowledge of Universals on Induction. If axiomatic principles can be acquired in any other way, one class of Syllogisms at least exempt from the charged m / is I ^ Top. "viii. 13.^. Aeurepov Se oTav Kara fxepos Se'ov OTroSeilai «a&oAou tis a'lT'fia'p, oTov iirix^ipcbv on rcov ivavriav fiio. eTTKTTTj/tTj, '6hws rwu ovt iK^Lfxivuv d|twcrete ixlav elvai. d Pacius in Anal. Prior, ii. 16. e " Sciendum quod hasc fallacia non impedit syllogismum inferentem, sed probantem, et ita fallacia pctitionis ])eccat contra syllogismum dialecticum in quantum dialecticus est." Summ. Log. Tract, vi. f Kant's criterion of necessity as the sui-e characteristic of a cognition a priori, has not yet been refuted by those who refer all principles to Induction. APPENDIX. 201 And even with respect to principles allowed to be in- ductive, the actual previous assumption of every possible instance is not necessarily implied. And it is here that an able defender of the Syllogism, Mr. Mill, has taken a low and inadequate ground, a ground too, inconsistent with his own subsequent analysis of the process of Induction. His defence in fact amounts to an abandon- ing of all formal reasoning. All reasoning, he tells us, is really from particulars to particulars. But in that j case, all inference must depend upon the matter, and ^ cannot be reduced to any general type. If, for example, \ I conclude that a man now living is mortal, solely from j the premises, " A, B, and C, who are dead, were mortal, ( and this man resembles them in certain other attributes ) of humanity ;" I may, by an argument of precisely the same form, prove any given man to be six feet high, because A, B, and C, whom he resembles in the common attributes of humanity, were all of that stature. This portion of the question resolves itself into the following. What do we mean when we assert that all . men are mortal ? Is it merely a concise mode of stating \ that Socrates and Plato possess this attribute, in common ^ with a number of other individuals, quos nunc perscribere ) longum est ? If so, to argue, " Socrates is one of the I individuals above mentioned, therefore he is mortal," J is, if not a begging of the question, at least a needless repetition of a previous statement. But, in fact, the Uni versal Proposition m eans no_such things It means that, by virtue of a certain established law, certain attributes, or groups of attributes, are always ^ . so united, that in whatever individuals we find the one, we may look upon them as an infallible mark of the - ■ ' " '^ other. A conviction of this kind however, as it can ^ never be gained by any mere observation of particulars. C L c/vO^c^' tV^^i^<-^^ ^'f 202 APPENDIX. ^t -^ * ^^^ ^* need not presuppose a complete enumeration of c^i /- ;^ - •- Uhem^. For, when one's proofs are aptly chosen, Four are as valid as four dozen." To determine under what conditions such a conviction can be obtained, is a question requiring the analysis of the whole process of Induction. Such an analysis, in many respects most ably performed^, will be found in the third book of Mr. Mill's Logic; but few I think can compare that part of the work with his earlier defence of the Syllogism, without admitting that the two presuppose diflferent and inconsistent theories of the import of % " Hinc jam patet, inductiouem per se nihil producere, ne certitudinem quidem moralem, sine adminiculo propositionum non ab inductione, sed ratione universali pendentium; nam si assent et adminicula ab inductione, indigerent novis adminiculis nee haberetur certitude moralis in infinitum. Sed certitude perfecta ab inductione sperari plane non potest, additis quibuscunque adminiculis, et propositionem banc : totum majus esse sua parte, sola inductione nunquam perfecte sciemus. Mox enim prodibit, qui negabit ob peculiarem quandam rationem in aliis nondum tentatis veram esse." Leibnitz, de Stylo NizoUi. Mr. Mill's adminicula to Induction are certain canons stating the prin- ciples of the Method of Agreement, of DiflFerence, &c. which, together with the whole law of universal causation, he makes dependent upon a weaker evidence than philosophical induction; the inductio per enumerationem simplicem. At the same time he enters his protest against " adducing, as evidence of the truth of a fact in external nature, any necessity which the human mind may be conceived to be imder of believing it." His words, strictly taken, would on his own shewing destroy the evidence of our senses ; for, according to the theory of perception adopted by himself and his favourite authority, Brown, sensations can only be regarded as states of mind, and the only reason we have for referring our internal conscious- ness to an external cause is, that by the constitution of our minds we are necessitated to do so. The admonition of Hooker is not quite obsolete even amid the lights of modern philosophy. " The main principles of Keason are in themselves apparent. For to make nothing evident of itself to man's understanding were to take away all possibility of knowing any thing. And herein that of Theophrastus is true, ' They that seek a reason of all things do utterly overthrow Reason.' " Eccl. Pol. i. 8. o. *» His theory of Causation must however be excepted. ^^ APPENDIX. 203 Universal Propositions. It will be sufficient, however, for my present purpose to observe that, unless the establish- ment of an Universal Proposition requires an explicit^ and conscious examination of every existing and also of/ every possible particular instance, no charge of Petitio ) Principii, or even of vain repetition, can be maintained; against the Syllogism. Those who maintain the ante- I cedent, abandon themselves to an absolute scepticism*; I and against such, no defence of any source of humanJ knowledge can or need be attempted. ^ With regard to the syllogism of proof , we may examine the question a little more closely. The Petitio Principii is a material, not a formal fallacy, and consists in assuming, in demonstration, a non-axiomatic principle as axiomatic, or in dialectic disputation, a non-probable principle as probable ''. It does not affect the form of the reasoning; but depends on the selection of premises, when the syllogism is employed for the particular purpose of proof, demonstrative or dialectic. Those are guilty of it who do not adopt such premises as the laws of the two processes require ; in the one case, propositions axiomatic or deducible from axioms; in the other, probable statements, sanctioned by the general opinion of mankind or the authority of eminent persons. In reading Aristotle's account of this fallacy, it is evident that the whole point of the matter lies in the word aheia-Qoii, or Kaiju^uvsiv ; and that the question to be asked is, not whether the premises virtually contain the con- * Sed ea ratione prorsus evertuntur scientise, et Sceptic! vicere. Nam nunquam constitui possunt ea ratione propositiones perfecte universales ; quia inductione nunquam certus es, omnia individua a te tentata esse ; sed semper intra banc propositionem subsistes, omnia ilia, quae expertus sum, sunt talia; quum vera non possit esse ulla ratio universalis, semper manebit possibile, innumera, quae tu non sis expertus, esse diversa." Leibnitz, de Stylo Nizolii. t See Anal. Pr. ii. 16. Top. viii. 13. 204 APPENDIX. elusion^, but whether such premises can properly be said to be heggedy or assumed"^. It is clear then that Petitio Principii is not the fault with which the Syllogism is chargeable, unless it can be shewn that every statement of an Universal Proposition must be, in this sense of the term, begging or assuming. If there are any cases in which the assertion of such propositions depends on a warranted conviction, not on a gratuitous assumption, from whatever source that conviction may arise, such cases must be exempt from the charge of Petitio Princijoii. And if there be any such cases, the opponents of the Syllogism have themselves unwittingly stumbled upon a fallacy cognate to that with which they taunt its ^ One class of reasonings are perhaps fairly chargeable with the fallacy. I allude to what are commonly called the ■proper syllogisms of the Eamists, which have two Singular Premises. In the first figure, it is evident that the conclusion is not one out of many inferences contained in the major premise, but the very same proposition stated in difierent language. The third figure is open to the same objection, but it may be allowed as an €K0e(ris or expository instance — a process not reckoned by Aristotle as syllogistic. Proper syllogisms in the second figm-e are valid, and frequently serviceable ; but when reduced to the first, (which Aristotle regards as a necessary test of vahdity,) the negative premise must be converted from singular to universal. Nevertheless, as the Petitio Principii is a material, not a logical, fallacy, this does not furnish grounds for objecting to the convenient arrangement by which singular propositions are considered as in syllogism equivalent to universals. They may be regarded, in common v\dth other cases of the same fallacy, as reasonings valid in form^ but unsound from material circumstances. The Proper Syllogisms, however, though a post-AristoteUan innovation, did not originate with Eamus. Aquinas expressly denies that both premises in a syllogism may be singular, and admits the eKOeais as a non-syllogistic process, being an appeal to the senses, not to the reason. See Opusc. xixil. init. Occam, on the other hand, virtually surrenders the whole principle, when he allows that the major premise in the first figure may be singular. Logic, p. iii. cap. 8. •n That axiomatic principles are not of this character, may be seen from Anal. Post. i. JO. 6. Ou/c ecrTi 5' virSOeais ou8' atrTj/xa, t aydyKr] elvai S^^Mmh Koi doKeiv at/dyKT}. APPENDIX. 205 defenders. For the Petitio Principii being in that case a particular misapplication of the syllogistic method, and postulating the latter as a condition of its practicability, they have inverted the relation of prior and posterior, and assumed Petitio Principii to be necessary to the existence of Syllogism. But if, on the other hand, there are no such cases, and the Syllogism is in consequence henceforth to be banished from Philosophy, what do we gain in ex- change ? We reduce the Laws of Thought from neces- sary to contingent. We degrade certainty into proba- bility, and can claim for that only a subjective validity. But until this latter hypothesis is proved, the Syllogism, whatever may be its errors or deficiencies, cannot be comprehended under any one of the fallacies admitted to he such hy the Logician. And this is sufficient as a defence of his own consistency. His method may be an incorrect analysis of the laws of the reasoning process; it may be that there are no such laws at all. But of either of these positions the onus prohandi lies with the assail- ants, not with the defenders of the Syllogism". It is quite enough for the Logician, if he exhibit all that is generally considered valid reasoning in a syllogistic form. If any maintain that a simpler or better type is attainable, he waits with patience till they produce it. If all reasoning is fallacious, he may be contented to behold his theories fall in the general overthrow of all human knowledge. But, pending the decision of this question, he may leave " To the charge of Petitio Principii which Campbell makes against the Syllogism, Archbishop Whately rephes, that it lies a(jainst all arguments whatever; the Syllogism not being a distinct kind of argument, but any argument whatever, stated regularly and at fuU length. And this reply is substantially vahd, even if we reject the Archbishop's mode of exhibiting Induction as a Syllogism in Bai'bara. For the objection of Campbell, if vaUd at all, lies against all formal reasoning ; and logical Induction, in its true analysis, is equally formal with the Syllogism. 206 APPENDIX. his adversaries their choice of one or the other horn of a dilemma. If there are universal principles of truth not entirely dependent on sensation, the existence of such principles will warrant syllogistic inference. If there are not, whatever be the value of our individual sensations, all inference from them, by induction, example, analogy, or any method whatever, is, in respect of objective certainty, worthless. APPENDIX. 207 Note F. on the enthymeme. The Enthynieme is defined by Aristotle, (7vX\oyi(T[Ms \oitsKyi{\ ^f slxoTODv vj )ju.£j/^eIov is defined by Aristotle, Tr^oracrjj uTrohiKTixr}. StmyKulu Yi evdo^o$ ; in which the words necessary and probable do not relate to the modal character of the Proposition in itself, but to the nature of its connexion with the Conclusion which it is adduced to prove j i. e. to its logical validity when the other premise is added "^ ; without which addition, expressed or understood, there is no Enthymeme at all^. But it may be thought that the above examples- do not furnish a sufficient criterion for distinguishing between the two kinds of Enthymeme. If both premises must he mentally, and may be orally, supplied, before there is any Enthymeme at all, how are we to determine whether any given specimen is an instance of reasoning from a sign, or from a likelihood ? Why, for example, in the ^ Rhet. i. 2. 17. ^Pi.vayKa7a fieu oZv Xcyo} 4^ wv yiperai (Tvk\oyi(rix6s. Cf. Anal. Pr. i. 1. 6. SwAAoyto'/xbs Se iari \6yos iu ^ reOevTcau rivwv erepSv Ti ruv Keifieuwu e| au ay Kr}s aufi^aluei. Here sylloyism is used iu its strictest sense. From another passage in the Rhetoric (i. 2. 14.) it has sometimes been imagined that all a-rjixela are necessary, at least as propositions ; and the crrjiJLelov has even been defined, " a proposition in necessary matter ;" as if " necessary matter" were the proper province of Rhetoric. Tlie inter- pretation however is too inconsistent with Aristotle's subsequent language to be tenable. The words in question, if properly belonging to this place, (the res.emblance to Rhet. i. 2. 8. is suspicious,) must be so interpreted as to identify the necessary propositions with one class only of arffiela, the reKfi-fipia. The reference to the Analytics I conceive to allude, not to the account of modal conclusions deduced from modal premises, but to the necessary conclusiveness of premises logically connected, as opposed to the more or less probable conclusiveness of illogical combinations. As a special reference, supply Anal. Pr. i. 27. 12. ^ Anal. Pr. ii. 27. 4. ^Ehv /iey ovv rj /xia Aex^p irpSraais, arifieloy yiverat fiSvov, iau Se ko.) rj cTepa Trpoa\rj5|U,e7ov merely as propositions, and no where says that they may not be combined in the same syllogism. In the instance given, it so happens that the minor premise is a singular proposition, and may fairly be considered a sign of the conclusion. But we might obviously employ a minor premise of another kind, such as, " All malig- nant men are envious ;" in which case there is, properly speaking, no sign employed in the reasoning. But this does not aifect the distinction between the two Pro- positions. A likelihood is such, per se, — a proposition stating a general truth, which w^e are at liberty to apply or not to particular cases. A sign is a sign of something else, — a single fact stated as a proof of something further; which proof may, according to material circumstances, be logically or only morally conclusive. Another question sometimes raised is, " If the En- thymeme has both premises supplied, how is it to be distinguished from the Dialectic Syllogism .?" To which it may be answered, that, taking the word Syllogism in its strictest sense, as a reasoning logically correct, the same argument may in different points of view be con- sidered either as a Syllogism or an Enthymeme. This is, of course, only the case w4th the Tsxfx^giov; the other specimens of the Enthymeme being logically invalid. The argumentation Ix Tsx.[xriglot} is in this sense both an Enthymeme and a Syllogism ; — an Enthymeme on material grounds, inasmuch as its premise is a sign of its conclusion ; — a Syllogism on formal grounds^, inasmuch as it complies with the conditions of logical! APPENDIX. 211 reasoning. It is a Dialectic Syllogism, if employed for the purpose of dialectic disputation ; and, as it usually relates to those subjects to which dialectic disputation is practically applied^, it may in general be regarded as, potentially at least, dialectic*. In fact, it is not as an Enthymeme, but as a Rhetorical Syllogism, that a given specimen of reasoning is dis- tinguished from the Dialectical. The object of the two arts is distinct. That of Dialectic is to convince the Intellect; that of Rhetoric, to persuade the Will. The same instrument may be employed by both, and it is merely the purpose for which it is employed that con- stitutes the distinction between them^. Whether the same means are always available for both purposes ; whether the same informality of reasoning is allowed in Dialectic as in Rhetoric, must depend on the conditions by which the disputants in the former choose to bind them- selves. The Rhetorician has to influence an audience: if he can effect this, he will not always be scrupulous about ^ This, however, is by no means necessary. Matters not usually discussed either by the Dialectician or Orator may equally be proved by means of rcKfi-fipia. For example ; the falling of the thermometer to '32° is a sign of freezing ; the obscuration of the moon in eclipse is a sign that the earth's shadow is interposed between it and the sun. Such subjects are not practically dialectical, at least in Aristotle's view of the art. As far as the mere interrogatory form is concerned, it may be, and was by different Philosophers, applied to all varieties of matter. s This proceeds on the supposition that the Dialectician is bound to logical accuracy in his reasonings ; a restriction which Aristotle at least would regard as salutary. See Anal. Post. i. 6. 10. We need not however suppose that all disputants actually conformed to it. ^ Cf. Crakanthorpe, Logic, lib. v. cap. 1. " Utiique Disciplinge hoc com- mune est, quod doceat probabiliter arguere : finem vero diversum uterque sibi proponit. Quoniam ergo eadem omnino forma probabiliter arguendi uterque utitur, nos hie quod utrisque commune est tractabimus, unicuique liberum rehnquentes, an Dialecticus esse velit, et uti hac forma proba- biliter arguendi ad verum inveniendum ; an Rhetor, et uti eadem forma probabiliter arguendi ad suadendnm aut dissuade ndum." p 2 212 APPENDIX. the logical accuracy of his reasoning. In Dialectic, two champions are opposed to each other: they may, before engaging, dictate the conditions of the combat. As regards the account of the Enthymeme in the Prior Analytics, I am not aware that any further expla- nation is needed^ But in the corresponding chapters of the Rhetoric one or two difficulties remain, an elucida- tion of which, though not strictly within my present province, may perhaps be serviceable to the readers of the latter Treatise. In Rhet. i. 2, 18. we are told, that when the Enthymeme is in the third figure, the (rrifji,slov is to its conclusion as a particular to an universal. In the second figure, on the other hand, as an universal to a particular. The relation in the first figure is not mentioned, but the context seems rather to connect it with the former than with the latter. This passage may be interpreted in two ways. Either we may compare the conclusion of the Enthymeme with the G'rjfteTov itself, or with the major premise of that Syllogism whose minor is the (TYifxmv. In the former interpretation the word (tyi^sIov is used properly for the proposition; in the latter widely, for the reasoning of which such proposition forms a portion. If the first interpretation be adopted, (which seems preferable,) we must compare the two propositions relatively to that term in which they are unlike ; i. e. if they have the same subject, we must compare their > Except perhaps that Aristotle, in Anal. Pr. ii. 27., admits a (rrjfieiou in the second figure, Avhich in the former chapter he condemned. The con- demnation seems to be made on logical groimds. The logical value of two afl&rmative premises in the second figure is absolute zero; whereas the ff-nuelov in the third figure, though faulty as employed to prove an universal conclusion, is valid for particulars. For rhetorical purposes, however, the second figure is also admissible ; an accumulation of Enthymemes, all logically worthless, may amount to a moral certainty. APPENDIX. 213 predicates; if they have the same predicate, we must compare their subjects. According to this method, it will be seen, that in the first figure, the predicate of the sign is to that of its conclusion as part to whole, or as species to genus. Hence its logical validity : whatever subject is included under a species is necessarily included under its genus. But in the second figure the relation is that of whole to part, or of genus to species ; and this is illogical, the whole genus not being included under one of its species. But if we adopt the second interpretation, and compare the major premise with the conclusion, we shall be com- pelled in the first figure to compare together the two subjects, since both propositions have the same predicate. In this case the relation will be inverted ; the premise being to the conclusion as an universal rule to a single instance. In the second figure, we are at liberty to compare either the quantity of the two propositions as determined by their subjects, or the extent of their respective predicates. In either case, however, the result is the same ; the relation remaining that of universal to particular. The Enthymeme in the third figure presents no diffi- culty. Whichever interpretation be adopted, the same proposition, "Pittacus is good," is compared with the conclusion, " All wise men are good." In both cases, the comparison lies between the two subjects, and the relation is that of particular to universal. But perhaps the most difficult passage in this portion of the Rhetoric is that in which Aristotle describes an important, and previously, as he tells us, unnoticed distinction between various classes of Enthymemes. Some of these, he says, belong to Rhetoric, some to other arts and faculties. The same may be said of the connexion of the Syllogism with Dialectic. Dialectical 214 APPENDIX. or Rhetorical reasonings are founded on toVoi ; the others on the peculiar principles of that Science or Art to which they belong^. This passage is generally found puzzling to a beginner on two accounts. Firstly, he is apt to fancy Dialectic synonymous with Logic, and to confound it with the formal Science of that name ; an error which the Com- mentary most likely to fall in his way is not unlikely to confirm. Secondly, having previously seen the Enthy- meme defined as the Rhetorical Syllogism ; there seems some inconsistency in the subsequent observation, that some Enthymemes are Rhetorical, others not so. In explanation it may be observed. Firstly, that Dialectic and Rhetoric are not formal Sciences, but material Arts. Their Logic is not a Logica docens, treating of the general form of Reasoning, but a Logica uteris, treating of Reasoning as applied to a particular matter. That matter is furnished by the T6'7:Q^. Rhetoric and Dialectic do not merely lay down the form in which their reasonings ought to proceed, but likewise provide certain general principles of probability, from which the matter of their major premises is to be drawn. These TOTTOi or common-places hold the same position in the Dialectic Syllogism, as the most universal kind of axioms in the Demonstrative. They are not gained by exclusive observation of any one particular class of objects belonging to this or that art or faculty, but are indifferently applicable to all. Such is the example quoted by Aristotle as 6 rot) jOtaAAov jca) ^ttov tottoj. Of this in the Topics he gives four cases, of which the following may be taken as a specimen. "If the more likely assertion on any subject be untrue, the less likely is probably untrue likewise." A general maxim of this k Rhet. i. 2. 20, 21. APPENDIX. 215 kind is obviously available '^rsg) dixottoov xa) (^v(nxa>v Koti Trsgl Secondly, it may be observed that the Enthymeme is not necessarily confined to the Rhetorical kind of matter. A syllogism from likelihoods or signs, whatever be the object, is an Enthymeme. In like manner, any syl- logism in probable matter may become an instrument of Dialectic reasoning ; whether it be based on the general probabilities which Dialectic materially furnishes, or on more limited assumptions drawn from special observ- ations. The Physician, for example, within the field of his own experience, may know that in nine cases out of ten where a patient exhibits certain symptoms, the disease terminates fatally. The student of history may learn that in the majority of cases revolution leads to anarchy, and anarchy is suppressed by despotism. Either of these may become the basis of a reasoning process in probable matter ; but the Syllogism or Enthymeme is not, properly speaking. Dialectical or Rhetorical, but Medical or Political. And although there is nothing in the Dialectical or Rhetorical Method that prevents its being applied to these or any other special subjects, yet in proportion as any one so applies it, Aristotle regards him as departing from the legitimate matter of Dialectic or Rhetoric, and adopting that of some definite Art or Science ^ For the same reason, when he speaks of the special application of Rhetoric to Political deliberation, he warns us that its object matter must not be consi- dered as that of Rhetoric p'er se, but as primarily and properly belonging to Politics, secondarily only to Rhetoric in one of its practical applications'". ^ Rhet. i. 2. 21. Tavra Se, '6o-C() tis ttu fi4\Tiov iKKeyrjTai ras irpoTcicreis, Kifcrei TTOiijaas &\\7}v iiriarrjfMTjv ttjs 5toAe/cTi/c7]s koI pT)T0piK7Js' hu yap iuTvxri apxcus, ovk4ti SiaKeKTiK^ ovBe pT}T0piK7f a\\' iKeivrj iffrai ^s exet Toy apx^s, « Rhet. i. 4. 4, 5. 216 APPENDIX. A few words in conclusion on the origin of the name Enthymeme. That its etymology is to be found in Iv and Qu[ji.05, is undeniable; but only in the same degree as is also true of svSujxsTcrSa*, sv$v[jnog, and other cognate terms. But that it has no special reference to a premise in the mind, is evident; firstly, because $u[juo; in the Aristotelian phraseology is not " the mind," and has nothing to do with the expression or suppression of premises: secondly, because the word evQuixru^ot occurs in writers earlier than Aristotle, and before it could have assumed its technical meaning. To ascertain the true derivation, however, is not so easy as to refute a palpably absurd one. If, however, we were compelled to make a suggestion, the following, though not confidently put forward, has at least the merit of not being positively ridiculous. Ac- cording to the analogy of words of the same termination, such as

5-) Therefore, Some A is not C. And then, i7i consequence of the previous agreement, hut not of the Syllogism, it is allowed that some A is not B. ^ We must except M. St. Hilaire, wlio professes to discover the ordinary Hypotheticals in Anal. Prior, i. 44. 1. But the text of Aristotle wiU^ardly Avarrant the assertion. Cf. Sir W. Hamilton's Discussions, p. 152. (2d Ed.) b See Anal.Pr. i. 23. 2. APPENDIX. 229 The Syllogism in form is an ordinary Categorical in tlieT third figure ; the Conclusion, however, not being the ^ original question, but the antecedent of a Hypothetical ; Proposition, of which the question is the consequent^ The uTiuyoiyYi sis to d^uvurov is also Categorical, so far as it is Syllogistic. In this, the Conclusion syllogistically proved is a falsehood ; the original question being- inferred only by Hypothesis, because a falsehood results from the assumption of its contradictory''. The Hypothesis in this case is, that the contradictory is true®. Thus, if it be required to prove that some A is not B, we reason from the assumption of the contradictory, All AisBn All C is A; U(^^xXo7io-/x6s e| vwodea-ecos.) Therefore, All Cis B.j *= *Ev a-nacTi yap 6 [xkv avkKoyiafxhs ylverai npbs rh ix&TaKajxQav6ixivov, rh S' ^^CLpxrjS TT^paipeTai Si^ o/moAoyias ¥i rivos &\\7]S virodecrecos. Anal. Pf. i. 23. 11. Th ixeTaAajix^ai/6/jL€vov is explained by Alexander as applying to the conclusion of the syllogism, because it is taken in a different manner from that in which it was originally enunciated; being at first part of a conditional agreement, and afterwards a categorical conclusion. For this reason, the syllogism is said to be /caret fieTaXri^l/iv. Anal. Pr. i. 29. 5. Were it not for this authority, it would seem simpler to interpret /AeraAr/il/ts merely " change of question ;" the disputant turning from the original question to the proof of another on which it is supposed to depend. Concerning the other kind of hypothetical syllogisms mentioned in the same passage, those KaTo. iroi6Tr]Ta, we have no data for even a plausible conjecture. M. St. Hilaire's explanation is forced. Philoponus, (Scholia, p. 178, b. 9.) says it is a syllogism, ck rov fxaAXov, ^ e/c rod ^rrov, ^ ck rov ujxoiov, which probably originated the explanation of Burgersdyck, Inst. Log. ii. 14. *' Quo scilicet probatur quod minus probabile est, ea couditione, ut probatum sit quod magis probabile est." ^ Anal. Pr. i. 23. 8. lidvT^s yap ol Sia toD oBwdrov irepaivovTes rh fxev ^evdos crvXKoyi^ovrai, rh S' e| ctpx^s i^ viroOeaews S^LKVVovariv '6rav a8vuar6v rt (rvfi^aiiyrj ttjs avri^dcrecDs TeOdarjs. I have substituted a mere symbolical syllogism for the instance given by Aristotle, on account of its intricacy, and the length requisite to expand it. The reader will find it explained by Waitz, vol. i. p. 430. "^ Anal. Pr. i. 29. 3. UaAiu d Set/crt/cws a-vWeXSyicTTai tI) A rcf E fj-rjo^ul virdpx^iu, vTro9efx4i/ois virdpx^tv tiv\ dia rov aSwdrov deix^VO'crai ovSevl vndpxou. 230 APPENDIX. The Conclusion being supposed to be a known false- hood. This mode of reasoning, as exhibited by Aristotle, does not directly appear in the same form as the former. For in this the hypothesis is a premise ; the conclusion being the impossibility which has not been previously enunciated. In the former, the premises are both new assumptions ; the conclusion being the antecedent of the conditional proposition which was agreed upon as a hypothesis. Both, however, agree thus far, that the syllogistic portion of each does not differ in form from an ordinary Syllogism; and that in neither is the original question syllogistically proved. The notices of these Syllogisms in Aristotle are, it must be confessed, sufficiently scanty. Thus much, however, may fairly be gathered. Firstly, that, as regards form, they are merely the common Categorical Syllogisms applied to a particular purpose. Secondly, that their conclusiveness, as regards the original question, is by way of material, not of formal conse- quence. The syllogism by agreement obviously refers to dialectic disputation, and furnishes the grounds for a mere argumentum ad hominem, in consequence of a previous admission. Apart from this special appli- cation, which does not appear in the syllogism, the proof amounts to this : No X is C ; All X is A ; Therefore, Some A is not C. Therefore, (by material consequence,) Some A is not B. In the uTroiycoyri slg to ddvvccTov, the proof is of the same character. It has indeed no special reference to Dialectic, and is frequently employed in demonstration^; Aristotle's f For tlie principle of contradiction may be assumed as self-evident, without any convention between disputants. And in this lies the principal APPENDIX. 231 own example being taken from Geometry. But still its connexion with the original question is not formal, but material ; for we assume, All A is B ; All C is A ; Therefore, All C is B. And this conclusion, from material grounds, we know to be false. We also know (materially again) that the minor premise is true ; and all that is logical in the process is the consequent decision that the major must be false, and hence, by the principle of contradiction, that the original question is true. But one step only is wanting, to convert these material consequences into formal ones. We have in the o-vXXo- y*o-jw,oj If ofjioXoyiotg clearly the germ of the Conditional Syllogisms of Theophrastus. It needs but to commence with the original hypothesis, not as a mere dialectic convention, but as a proposition having its own inde- pendent value, and we have at once a distinct form of argumentation, to which the Aristotelian specimen is related merely as a prosyllogism supporting one of the premises. This done, no great sagacity is required to see that the prosyllogism may in this, as in any other case, be omitted or not, according to the material character of the premise which it supports. To the dTTotycayY) slg to d^uvarov may in like manner be traced the origin of the Disjunctive Syllogism. The most natural proceeding in this case is to state the two contradictory propositions as alternatives, one of them being disproved by a prosyllogism. Either Some A is not B, or All A is B ; in which case All Cis A; Therefore, All C is B. difference between the deductio ad impossibile and the syllogism of agree- ment, See Anal. Pr. i. 44. 3. 232 APPENDIX. This conclusion being manifestly false, we have no choice but to admit the other alternative. The pro- syllogism in this case, as in the former, may be omitted, if the falsehood of the alternative is evident without it. We have thus the Disjunctive Syllogism. We may agree therefore with M. St. Hilaire thus far, that, though the form of the Hypothetical Syllogism is not explicitly exhibited in the extant writings of Aristotle, we have nevertheless the data from which it needs but one step to develope it. Whether that step was taken by Aristotle himself in a lost work, or supplied by his disciples, is a point of little consequence; though external testimony is decidedly in favour of the latter supposition. Far more important, in a logical point of view, is the inquiry whether the hypothetical syllogism, by whom- soever analysed, is a legitimate addition to the forms of reasoning acknowledged in Aristotle's Organon ; and consequently, whether its omission can fairly be cen- sured as a deficiency in that work. On this question, I find myself compelled to hold an opinion different from that of the Logicians whose views have been mainly followed in the present work. By Kant and his followers, the Hypothetical Pro- position is described as representing a form of judgment essentially distinct from the Categorical; the latter being thoroughly assertorial, the former problematical in its constituent parts, assertorial only as regards the relation between them. Two judgments, each in itself false, may thus be hypothetically combined into a single truth ; and this combination cannot be reduced into : categorical form^. The Hypothetical Syllogism, in like manner, is a form of reasoning distinct from the cate- g See Kant, Logik, §. 25. Ki'ug, Loylk, §. 57. Fries, System der Logik, §, 02. APPENDIX. 233 gorical and not reducible to it, being based on a different law of thought, namely, the Logical Principle of Sufficient Reason, a ratione ad rationatum, a negatione rationati ad negationem rationis valet consequential. Of this principle, as applied to judgments, I have elsewhere remarked, that it is not a law of thought, but only a statement of the necessity of some law or other ^ As applied to syllogisms, it has the same character. It states the fact, that whenever a condition, whether material cause of a fact or formal reason of a conclusion, exists, the conditioned fact or conclusion exists also. Thus viewed, it is not the law of any distinct reasoning process, but a statement of the conditions in which laws of nature or of thought are operative. When a material cause exists, its material effect follows, and the pheno- menon indicates a law of nature: when a logical premise is given, its logical conclusion follows, and the result indicates a law of thought. What law^ must in each case be determined by the particular features of the phenomenon or reasoning in question; but a statement of this kind is distinguished from laws of thought, properly so called, by the fact, that it cannot be ex- pressed in a symbolical form : we require the introduction of a definite notion. Cause, Reason, Condition, or some- thing of the kind, which is a special object of thought, not the general representative of all objects whatever. The principle in question is thus only a statement of the peculiar character of certain matters about which we may think, and not a law of the form of thought in general. It is obvious that the relation of premises and con- clusion in a syllogism may, like any other relation of condition and conditioned, be expressed in the form of a hypothetical proposition : " If all A is B, and all C is ^ Kant, §. 76. Krug, §. 82. Fries, §. 58. " See Prolegomena Logica, p. 197. 234 APPENDIX. A, then all C is B :" and the actual assertion of the truth of these premises will furnish at once a so-called hypothetical syllogism : " But all A is B, and all C is A, therefore all C is B." This was observed by Fries, who hence rightly maintains that analytical hypothetical judgments are formal syllogisms^. It is strange that, after this, he should not have gone a step further, and discovered that synthetical hypothetical judgments are assertions of material consequences. The judgment, "If A is B, C is D," asserts the existence of a conse- quence necessitated by laws other than those of thought, and consequently out of the province of Logic. The addition of a minor premise and conclusion in the so- called hypothetical syllogism, is merely the assertion that this general material consequence is verified in a particular case. The distinction so much insisted on by the Kantians, of the problematical character of the two members of a hypothetical judgment, is, like the whole Kantian doc- trine of modality, of no consequence in formal Logic. All formal thinking is, as regards the material character of its objects, problematical only. Formal Conception pronounces that certain objects of thought may possibly exist, leaving their actual existence to be determined by experience. Formal Judgment decides on the possible coexistence of certain concepts; and Formal Reasoning, on the truth of a conclusion, subject to the hypothesis of the truth of its premises. To state that this hypothesis is in a certain instance true, adds nothing to the logical part of the reasoning, but only verifies the empirical preliminaries which the Logician in every case assumes as given. To exhibit a formal consequence hypothetically, is only a needless reassertion of the existence of data which the act ^ System der Loyik, §. 44. APPENDIX. 235 of thought presupposes. To exhibit a material eon- sequence hjpothetically, is not to make it formal, but only to state that, in a certain given instance, a con- sequence not cognisable by Logic takes place. The sequence of " C is D," from " A is B," is not one whit more logical than it was before ; it is only stated to take place materially in the present case. The omission of hypothetical syllogisms has fre- quently been blamed as a defect in Aristotle's Organon ; and his French translator takes some fruitless pains to strain his text, in order to make out that he does in fact treat of them^ If there is any truth in the preceding observations, it will follow, that Aristotle understood the limits of Logic better than his critics ; and that his translator had better have allowed the omission as a merit than have attempted to deny it as a fault. When the hypothetical proposition states a formal consequence, the reasoning grounded upon it may always be reduced to categorical. When it states a material consequence, it states what the Logician, as such, cannot take into account. Aristotle is therefore quite right in saying, that in this case the conclusion : is not proved, but conceded"^. Syllogism may be em- ployed as a logical proof of the antecedent: the con- sequent is admitted to follow on grounds which the Logician, as such, does not investigate, but which may be warranted by the principles of this or that material science. The true character of hypothetical reasoning is lost sight of in the examples commonly selected by Logicians, which have for their subject o. proper name, and indicate, not a general relation of reason and consequent between ' St. Hilaire, Loyique (TAristote Traduite en Fran<^ais, Preface, p. Ix. •° Anal. Prior. \. 23. 11. 236 APPENDIX. two notions, but certain accidental circumstances in the history of an individual. The adoption of this type has led to the logical anomaly, that the propositions of a hypothetical syllogism are generally stated without any designate quantity; whereas it is obvious that, wherever concepts are compared together in any form of reasoning, two distinct conclusions may follow, according to the quantity assigned. For example, to the premise, ^' If men are wise, they will consult their permanent interests," we may supply two minors and conclusions, in the con- structive form, according as we affirm the antecedent of all men or of some. It thus becomes necessary to dis- tinguish between two different kinds of apparent hypo- thetical syllogisms, those in which the inference is from a general hypothesis to all or some of its special instances, and those in which a relation between two individual facts is assumed as a hypothesis leading to a singular conclusion. The former contain a general relation of determining and determined notion, which may always be expressed in three terms ; the occasional employment of four being only an accidental variety of language. Thus the general assertion, " If any country is justly governed, the people are happy," is equivalent to, " If any country is justly governed, it has happy people." This we may apply to special instances ; all countries, some countries^ or this country, being asserted to be justly governed: and this is properly hypothetical reasoning. The latter denote only a material connection between two single facts, either of which may, to certain minds possessed of certain additional knowledge, be an indication of the other ; but the true ground of the inference is contained in this additional knowledge, and not in the mere hypothetical coupling of the facts by a conjunction. This is not hypothetical reasoning^; APPENDIX. 237 i. e. it is not reasoning from the hypothesis^ but from other circumstances not mentioned in the hypothesis at all°. It thus appears, that the only hypothetical judgment which can be employed as the real major premise of a syllogism, may be expressed in the form, " If any A is B, it is C," where A, B, and C represent concepts or general notions. The complete categorical equivalent to this is, " Every A which is B is C, because it is B," which admits of two interpretations, according as B stands for the physical cause of the fact, or for the logical reason of our knowing it. In the latter case, the judgment is analytical, and represents a disguised formal consequence with B as a middle term ; e. g. " Every man who is learned has studied, because he is learned." Here the notion of study is implied in that of learning, and the major premise is, " All learned beings have studied." The hypothetical proposition thus becomes a complete syllogism, to which the sub- n This may be made clearer by an example. The following is cited by Fries, as an instance of a hypothetical proposition, not reducible to cate- gorical form. " If Caius is free from business, he is writing poetry." This may be interpreted to mean either, generally, " whenever Caius is dis- engaged, he writes poetry ;" or, specially, " if he is now disengaged, he is now writiiig poetry." Under the former interpretation, it is a general hypothesis, which may be applied as a major premise to particular instances : but in this case the true form of the reasoning is, " All times when Caius is disengaged, are times when lie writes poetry; and the present is such a time," Under the latter intei-pretation, it is one of the cases of a material connection of two facts mentioned in the text. Now in this last case, it is obvious that the inference is really made, not from the hypothesis, but from some circumstance kno-\vn to the reasoner, but not appearing in the proposition. Any man being asked, " Why do you infer that Caius, being now disengaged, is writing poetry?" would reply, " Because he told me he should do so ;" or something of the kind. Assuredly he would never dream of replying, " Because if he is now disengaged he is writing." In this case then he does not reason from the hypothesis, and the expressed propositions do not compose a syl- logism. 238 APPENDIX. sequent consequence is related as an episyllogisni ». In the former case, where B stands for a physical cause, the judgment is synthetical, and indicates a material consequence, which it requires some additional know- ledge of facts to reduce to formal: e. g. "All wax exposed to the fire melts, because it is exposed." Here, on material grounds, we know that we cannot supply the premise, "All bodies exposed to the fire melt;" but only, "All bodies soluble by heat and exposed to the fire melt." In this case the consequence is extralogical, and requires additional data not given in the thought. But here also, when the judgment in question is em- ployed as the premise of a reasoning, the conclusion follows categorically ; though the premise itself cannot, as it stands, be proved by a prosyllogism^. The Disjunctive Judgment is usually described as representing a whole divided into two or more parts mutually exclusive of each other; and th« Disjunctive Syllogism is supposed to proceed either from the affirm- ation of one member to the denial of the rest, or from the denial of all but one to the affirmation of that one, by the Principle of Excluded Middle "i. Categorical Analysis. All learned beings have studied : All learned men are learned « Thus : Hypothetical Syllogism. If any man is learned, he has studied : Some men are learned ; '. Some men have studied. .'.All learned men have studied : Some men are learned men ; . Some men have studied. P The analysis in this case may be exhibited thus : Hypothetical Syllogism. If any wax is exposed to the fire it melts : This wax is exposed to the fire ; .• . This wax melts. The parenthesis indicates the material ground of the major premise, q Kant, §. 27 sqq. 77, 78. Krug, §. 57, 84, 85. Fries, §. 33, 59. Categorical Equivalent. AU wax exposed to the fire melts (because exposed) : This wax is exposed to the fire ; .*. This wax melts. ^~ APPENDIX. 239 This can scarcely be regarded as a correct analj^sis of the process, unless the two members are formally stated as contradictory. The Principle of Excluded Middle asserts that every thing is either A or not A, that of two contradictories, one must exist in every object; as the Principle of Contradiction asserts that they cannot both exist. But if the two members are not stated as contra- dictories, if my disjunctive premise is, "All C is either A or B," I make the material assertion that All C which is not A is B. If then I reason, " This C is not A'^, there- fore it is B," I employ the Principle of Identity in addi- tion to that of Excluded Middle. Again, if I maintain that No C can be both A and B, I make the material assertion that No C which is A is B ; and from hence to reason, "This C is A, therefore it is not B," requires not the Principle of Excluded Middle, but that of Contra- diction. In the first case, the Excluded Middle does not lead directly to the conclusion, but only to the con- traposition of the minor premise. When we deny this C to be A, this principle enables us to assert that it is not-A, and hence to bring the reasoning under the Prin- ciple of Identity. But in the second case, in which one of the opposed members is affirmed^ the ground on which we deny the other, is not because both cannot be false, but because both cannot be true. It may be questioned whether this second inference is warranted by the form of the disjunctive premise. Boe- thius calls it a material consequence^ ; and, in spite of the many eminent authorities on the other side, I am still disposed to think he is right. But let us grant for a moment the opposite view, and allow that the proposition, " All C is either A or B," implies, as a condition of its •■ The indefinite minor, "but it is not A," is as objectionable in this syllogism as in the conditional. * Be Syll. Hyp. lib. i. Opera, p. 616. Cf. Galen. Isagoge Dial. p. 11. 240 APPENDIX. truth, " No C can be both*." Thus viewed, it is in reality a complex proposition, containing two distinct asser- tions, each of which may be the ground of two distinct processes of reasoning, governed by two opposite laws. Surely it is essential to all clear thinking, that the two should be separated from each other, and not confounded under one form by assuming the Law of Excluded Middle to be, what it is not, a complex of those of Identity and Contradiction. Thus distinguished, the moods of the disjunctive syllogism are mere verbal variations from the categorical form, and may easily be brought under its laws ^ * Aquinas, Opusc. xlviii. De Enunciatlone, c. xiv. Ki'ug, Logik 1 Thus: Modus tollendo ponens. Every C which is not A is B. Every ^ Some |-C is a C which is not A. This i •.ItisB. Modus ponendo tollens. No C which is A is B. Every \ Some r C is a C which is A. This ) .'. It is not B. The first is governed hy the Principle of Identity, and the second by the Principle of Contradiction. APPENDIX. 241 Note K. on the demonstrative syllogism. Scientific knowledge {ro sTrhrad^oLi)^ except when of axiomatic principles ''', requires a conviction of the neces- sity of the proposition known, and a knowledge of its cause''. This is produced by the Demonstrative or Scientific Syllogism, which, according to Aristotle's definition, is e^ uKri^cLv koc) TrgcuTcov xu) df^ecroov koc) yvcogi[jt,a}' Tegctiv KOi) TrgoTsgcjQV xal ahtcov rov av^'KegaoriioLTO^^. As the conclusions of this Syllogism are necessary, so must also be the premises ; this necessity consists in their being 'per se, in either the first or the second sense of that expression*^. If any of these conditions are not complied with ; e. g. if the premise, though containing a In the strict sense of the terras, iiria-raadai is said of necessary truths which we receive by deduction from higher truths ; vo€7v, of those which we receive as evident of themselves. Hence the principal meaning of the corresponding terms, iirKTriiixT] and vovs. The latter, however, or rather its result, is sometimes called eTrto-r^/xTj avairSSeiKros. Cf. Anal. Post. i. 3. 2, 3. i. 33. 1. ii. 19. 7. Eth. Nic. vi. 9. 9. The word '6poi, in the first and last of these places, does not mean, as Pacius explains, simple terms, hut, as M. St. Hilaire renders, '• les propositions immediates," i. e. axioms — the limits from which Demonstration commences. b Anal. Post. i. 3. 1 . <^ Anal. Post. i. 2. 2. By Jirst and immediate are here meant the same thing ; i. e. not demonstrable by a middle term from any higher truth ; yvcapifMcaTepa sc. (pvcrei, not rjfuv, i. e. more universal. ^ Of necessity, three degrees are enumerated. Anal. Post. i. 4. Kar^ iravrSs, /ca0' avrd, and ^ avrS; usually rendered, de omni, per se, and quatenus ipsum. Of per se, as applied to a proposition, four senses are given. 1. When the predicate is part of the definition of the subject. 2. When the subject is part of the definition of the predicate. 3. When existence is predicated of a substance. 4. When the subject is the external efl&cient cause of the predicate. Propositions in Demonstration proper must be per se either in the first or second meaning. See Anal. Post. i. R 242 APPENDIX. the cause of the conclusion, is not the first cause, (in which case the syllogism is not 1^ ajxeVwvej or if the premise be an effect and not a cause of the conclusion, or if the premise, though immediate, be a remote and not a proximate cause of the conclusion, — under these circumstances, there is no Demonstration, in the proper sense of the term, as we only know the fact, but not the caused From the above data, the scholastic successors of Aristotle have constructed the following specimen of demonstratio jootissima, Omne animal rationale est risihile ; Omnia homo est animal rationale : ergo Omnis homo est risibilis. In this syllogism all three propositions are per se ; the major premise and the conclusion in the second manner; for the subject ^owo, and consequently awm«/ rationale, forms part of the definition of the attribute risihile : the minor premise is per se in the first manner ; for animal rationale, its predicate, is the definition of homo. In all the propositions of this Demonstration, the predicate and subject are coextensive, and the pro- e From this it may fairly be inferred that the demonstratio propter quid sit per causam non primam, would not alone be regarded by Aristotle as a Demonstration, though it may form a subordinate portion of a complex Demonstration. The ambiguity of the word ^/ietros, which has partly led to the discrepancies on this point, has been explained before. See p. 119. f See Anal. Post, i, 13. The distinction between demonstratio propter quid potissima and non potissima cannot fairly be attributed to Aristotle. The whole of the chapters of the first book of the Posterior Analytics, from the first to the thirteenth inclusive, treat of one kind of Demonstration only. The passages in the second book, (ch. 17 and 18.) which seem to favoui' the distinction, are treating only of the inferior sense of Demon- stration, in which it is applicable to to irecpvKOTa ws iirl rh iroXv. Cf. Anal. Pr. i. 13. 5, 6. An. Post. i. 8. 3. i. 30. APPENDIX. 243 position simply convertible. This is requisite, in order to comply with the condition of quatenus ipsum. This Demonstration is exceedingly satisfactory, if we are only allowed to assume all the conditions on which its validity depends; viz. 1. that risibility does flow as an effect from rationality as a cause; 2. that the major premise, in which this causation is asserted, is an axiomatic principle, cognoscible a priori, and, as such, carrjdng with its cognition, the conviction of necessity ; 3. that the conclusion is not a mere repetition, in dif- ferent words, of the major premise ; homo and animal rationale being identical ; 4. that any Demonstration acknowledged to be valid can be resolved into the above form. But w^aiving the consideration of these questions, which are more easily asked than answered^, we may find a simpler way of testing the demonstratio potissima, by going back to the original authority. For Aristotle's examples are principally taken, as is natural, from the Mathematics; and it is to a Geometrical theorem that the tests of xa6' auTo and ^ olvto are expressly applied"*. Can it be believed, then, that Aristotle regarded the following as a correct analysis of Geometrical Demonstration } Every rectilinear figure of three sides has its angles equal to two right angles ; Every triangle is a rectilinear figure of three sides ; therefore Every triangle has its angles equal to two right angles. & " Si scrupulosius inquiratur in rem banc ; Num qua sit essentialis connexio inter ration alitatem et risibilitatem, quo sit ea propria causa hujus, seu causa per se ; ut Kationalitas, propter ipsam sui Essentiam, non possit esse absque Eisibilitate ; neque hsec absque ilia : et quidem immediata, absque interventu alius considerationis qua connectatur ; atque adcBquata, ut ad omnes rationales extendatur atque ad bos solos : subtilior forsan esset inquisitio quam ut ei facile satisfiat." Wallis, Log. lib. 3. cap. 22. ^ Anal. Post. i. 4. 6. Kat t^ rpiydoucf ^ rplywvov 8vo opQai Koi yap Ka6' avrh rh rplyuvou 5vo opQais tcrov. R 2 244 APPENDIX. It is not denied that there are passages in Aristotle which may seem to countenance this interpretation ; but there are others so palpably inconsistent with it that we are compelled to seek for a new explanation of the former. In the first place, Aristotle distinctly condemns the assumption of Definitions as a Petitio Princijni^ a charge to which the above example is obviously liable ; the real question to be proved being, that the three-sided figure has its angles equal to two right angles, whether it is called a triangle or not. In the second place, he says that Demonstration proceeds from axioms, and cites as a specimen of the latter, " If equals be taken from equals, the remainders are equal ''." These axioms, he says, are common to many classes of objects ; but, in any single Science, need only be assumed to an extent commensurate with the object-matter of that Science. The above axiom, for example, is true of other things besides Geometrical Magnitudes, but it is suflicient for the Geometer to assume it as true of these only. Now if an axiom of this kind be the major premise in a Demonstration, it is manifest that its predicate will also be the predicate of the Conclusion ; and that the logical form of that Conclusion will be, not "All triangles are figures having their angles equal to two right angles," but, " Triangles and figures having their angles equal to two right angles are equal to each other." The immediate Syllogism from which this proposition is proved by Euclid, may be logically stated as follows : » Top. viii. 13. 2. k Anal. Post. i. 7. l.i. 10.2. APPENDIX. 245 " Magnitudes equal to the adjacent exterior and interior angles of a triangle are equal to each other ; The three interior angles and two right angles are equal to the adjacent exterior and interior angles ; Therefore, they are equal to each other." The major premise of this Syllogism is an immediate deduction from the first axiom ; thus : "Magnitudes which are equal to the same are equal to each other ; Magnitudes equal to the adjacent exterior and interior angles are equal to the same ; Therefore, they are equal to each other i." That the true syllogistic analysis of Geometrical Demon- strations will always be in this form, the axioms standing as major premises, and the constructions in each case furnishing the proper minor, is evident. It only remains to see whether the text of Aristotle can be accommodated to this interpretation as well as to the other. With some passages it evidently tallies much better. The places in which the axioms are mentioned in connexion w4th demonstration have never been satis- factorily explained on the scholastic interpretation"". There are others which prima facie appear to favour 1 See Wolf, Philosophia Bationalis, §. 492. 551. 552. 798. Mill, Logic, vol. i. p. 285. Sir W. Hamilton, Eeid's Works, p. 702. "> The diflficulty is evaded rather than surmounted by distinguishing immediate propositions from axioms, and saying that the latter are employed in demonstration virtually but not actually. Aquinas, Opusc. 48. de Syll. Dem. cap. 6. Cf. Zabarella, in I. An. Post. Cont. 57, 58. Crakanthorpe, Log. lib. iv. cap. 1. For, in the first place, Aristotle expressly calls the axioms immediate principles of syllogism, and principles from which we demonstrate. In the second place, any principle which virtually enters and confirms the premises of a demonstration must, if the syllogistic theory be worth any thing, be capable of syllogistic connexion with the premises which '> it confirms : and until this connexion is formally exhibited, no demon- ' stration can be logically complete. 246 APPENDIX. the latter ; but, when both interpretations require some straining- of Aristotle's language, it is due to the memory of the Father of Logic to give him the benefit of that which does not convict him of flagrant error in the application of his own principles. Referring back to the Syllogism above given, the major premise may fairly be regarded as per se ; the subject forming part of the definition of the predicate. For Equality, in the limited sense in which it is employed in Geometry, is a property of Magnitudes; and the latter, as the first and proper subject, will appear in the definition of Geometrical Equality. This definition has been found by some Geometers in the eighth axiom of Euclid; "Magnitudes which coincide are equal;" which, stated in the Aristotelian form, would be, " Equality is the Coincidence of Magnitudes^" The mingr premise may also be considered 0^% per se. For our definition of a right angle is, that it is half the sum of the two adjacent angles formed by one straight line with another ; and our notion of two right angles is that of the sum of the same two adjacent angles. As regards the Conclusion, we need not trouble ourselves with reducing it to the requisite conditions, inasmuch as it is expressly said by Aristotle to comply with them. This compliance does not directly appear in the only form in which the proposition can be syllogistically proved ; but in the equipollent statement, that the triangle is a figure of which the interior angles are equal to two right angles. The predicate in this case states a property of the triangle, in the definition of which property, if any be attempted, the proper subject must be included. A demonstration of this kind certainly falls short, in some respects, of the scholastic model. The predicate " Cf. Stewart, Elements, Part II. ch. iii. Sect. ii. 2. APPENDIX. 247 and subject in each proposition, as stated, are not con- vertible ; and the middle term is not a definition of the minor. But of these requisitions, the first seems to be founded on an erroneous interpretation of Aristotle, according to which that Philosopher is supposed to speak of the Propositions as they appear when strictly enunciated in logical form; not (as seems more probable) of the same Propositions as ordinarily stated by the Geometer*'. With regard to the second condition, the text of Aristotle does not warrant its imposition. He says indeed, that the middle term in demonstration must be a definition of the major^; and the precept is intel- ligible enough, if we rightly understand his theory of the Definition of Attributes. As regards the minor term, it would be difficult to produce a single passage where this condition is clearly laid down as a law of Demonstration; and there is more than one with which it w^ould be no easy task to reconcile it. If it be thought somewhat over-bold to repudiate positions which so many eminent Logicians have regarded as legitimate deductions from the text of Aristotle ; it must be remembered that w^e have other data for interpretation besides the mere weight of autho- rity. Aristotle's theory of demonstration is principally framed wdth reference to Geometry : the Scholastic examples, on the other hand, are Physical. The medi- aeval state of Physical science was perhaps such as to justify, or at least to account for, the Logical and Meta- physical fictions connected with it, and to give a seeming validity to the most potent demonstration of Risibility as an emanation from Rationality; though that emanation o In this way we may interpret such passages as Anal. Post. i. 4. 6. i. 5. 6.ii. 17.3. P Anal. Post. ii. 17. 3. The meaning of this has already been explained. See note C. 248 APPENDIX. was never dreamed of by Aristotle, and will scarcely claim implicit belief in the present day. But it is not merely because the revolution effected in this branch of Science has invalidated the individual example, that the inter- pretation is objected to ; but because the words of Aris- totle himself expressly direct us to another criterion. The Demonstrations of Geometry are still extant in the same form in which they existed in the days of the Stagirite. Though Euclid himself, the oldest remaining Geometer, is a few years younger than Aristotle •*, yet, except on the very improbable hypothesis that he was the original inventor of the whole contents of his Elements, that work must be regarded as furnishing a fair specimen of the demonstrations treated of in the Posterior Analytics. By this touchstone, Aristotle and his interpreters may be tested. When any modern Herlinus or Dasypodius' shall exhibit a single demon- stration of Euclid in the form of a scholastic demonstratio potissima^ we may then recognise this foundling of the Schoolmen as the legitimate offspring of their master^ Till that is done, we must continue to believe that Aristotle was sufficiently acquainted with the use of his own instrument, to be able to give a correct Logical Analysis of the Demonstrations of Geometry. q Euclid floiurislied in the reign of Ptolemy Lagus, B.C. 823—283. This period, however, probably corresponds to the close, not to the commence- ment, of his life. This would make him partly contemporary mth, though about thirty years junior to, Aristotle. r Of the remarkable work of these two "zealous but thick-headed Logicians," as Sir W. Hamilton calls them, a specimen will be found in the next note. 8 See on this point the criticisms of Ramus, Scholce Mathematicce, 1. ui. and of Wolf, Phil. Bat. §. 498. Both, however, treat the scholastic form as Aristotehan. APPENDIX. 249 Note L. on the logic of geometry. The Propositions which have been regarded by- different writers as constituting the foundation of geo- metrical demonstration, may be classified as follows. I. Definitions, analysing the complex notions of the [ several magnitudes or figures. II. Postulates, assuming the existence of the objects ' defined. ' III. Axioms proper to Geometry, or synthetical judg- f ments, stating self-evident properties of certain magni- ^ tudes. . IV. General axioms % or analytical judgments, logically j /involving the notions of equality or inequality. Some one or more of these, under various names, (for the language of the several writers has been by no means uniform,) have been selected at different times as the fundamental assumptions or premises fi'om which the conclusions of Geometry may be demonstrated. A brief examination of each may perhaps help to clear the question. I. According to Stewart, the properties of geometrical figures follow from the Definitions of those figures ; the general axioms being mere barren truisms, and the axioms proper, (such as the 10th, 1 1th, and 12th of Euclid,) being theorems requiring demonstration. In this theory, * I have retained the language of the modern editions of Euclid, as that most familiar to the majority of readers. At the same time it may be observed, that this language departs widely from the original text of Euclid himself. In that text the general axioms are called common notions (/cotvai iuvoiai), while the axioms proper are included among the postulates (atTrj^aTo). •250 APPENDIX. mathematical necessity becomes identified with logical, being only the result of the harmony of a process of thought with its original assumption. This consequence is accepted by Stewart himself, as well as by Archbishop Whately, who speaks of the denial of geometrical pro- positions as self-contradictory^ . This view may be refuted either directly or by a reductio ad ahsurdum ; for, firstly, it rests on an un- tenable assertion ; secondly, it leads to an inadmissible consequence. Firstly. If the properties of a figure follow from the definition of that figure, it must either be because they are implied in some one attribute of that definition, or because they are implied in the whole. A triangle e. g. will have its angles equal to two right angles, either because it is a rectilinear figure, or because it is of three sides, or because it is both. The two first suppositions are manifestly false : the third begs the question ; for why the notion of a triangle, regarded as a complex whole, has this property, is the very point at issue. Hence it appears that the Definitions of Geometry, so far as they are employed in demonstration, are merely nominal. From the analysis of the complex notion no conclusion is derived. The Definition only serves to connect the notion as a whole wath the name triangle. The question, w^hy a rectilinear figure of three sides, be it called triangle or not, has its angles equal to two right angles, remains unanswered. Secondly. If geometrical reasoning is merely "the logical filiation of consequences which follow from an assumed hypothesis," there is no reason why its con- clusions should be more important than those of any b This view is also adopted by M. Cousin in Ms Lectures on Kant, apparently as an exposition of the opinion of Kant himself, to \^ch however it is diametrically opposed. APPENDIX. 251 other analysis of imaginary notions, such as (to use ? Mr. Mill's illustration) a deduction of the physiological properties of an imaginary animal, or the political history of an imaginary commonwealth. The whole character and history of mathematical science militates ^ against the admission of this consequence. II. Mr. Mill, while agreeing with Stewart that mathe- matical necessity is merely hypothetical and conse- quential, saw clearly that Stewart's doctrine concerning Definitions was untenable. This led him to adopt the second theory, according to which geometrical inferences ' depend on Postulates assuming the existence of the objects defined. Thus a triangle has its angles equal to two right angles, because there may really exist a rectilinear figure having three sides ; and this existence is implied, though not verbally expressed, in the defi- nition. This theory derives some apparent support from the use of the principle of superposition. When, for instance, the demonstration of the fourth proposition of Euclid supposes the triangle A B C to be applied to the triangle D E F, it clearly assumes the existence of both triangles, not merely as general notions, which are identical in thought, but as distinct individual magnitudes, occupy- ing space, and capable of being transferred from one position in space to another. One non-entity cannot be applied to another. Thus far Mr. Mill's position is unquestionably true ; but 1 think it may be shewn to be not itself the fundamental assumption of Geometry, but a consequence derivable from a higher assumption. The existence is clearly only that which is implied in the possible construction of the figure. The actual or possible existence in nature of a body so figured is not once appealed to in the demonstration, and might be denied without affecting its validity. The Postulate, 252 APPENDIX. therefore, implies the possible construction of a figure, such as is contemplated in the proposition. But this construction is mental, not manual. The figure as drawn upon paper is only a representative of the figure as imagined by the mind, and might be dis- pensed with altogether if the latter could be kept before us with sufficient steadiness. This brings us to Kant's principle of the possibility of mathematical science, viz. the power of constructing the objects of its concepts ; i. e. of presenting them a priori in a pure intuition. But how is this construction itself possible, and what conditions is it required to fulfil } Mr. Mill regards it as only possible a posteriori, and as subject to the same conditions as an object of sense. He says, " the points, lines, circles, and squares, which any one has in his mind, are simply copies of the points, lines, circles, and squares which he has known in his experience. We can reason about a line as if it had no breadth ; but we cannot conceive a line without breadths" This is true ; but the author is mistaken in supposing such a con- ception to be necessary to establish the a priori character of Mathematics. The true Postulate is not that of the possible existence of an object corresponding to the definition, but of one fulfilling the conditions of the proper axiom. We are not required to conceive a straight line as length without breadth : we are required to conceive it as such that two straight lines cannot enclose a space. The definition itself is but an im- perfect attempt to describe in general terms w^hat is known much more clearly by the image. It may serve to lead the thoughts of the learner to the proper image ; but it was itself founded on a previous image in the mind of the teacher; and if the definition and the image differ, the former is in fault, not the latter. -~ e Logic, b. ii. ch. v. APPENDIX. 253 III. This brings us to our third theory, which is that maintained bj Kant. According to this theory, the fundamental assumptions of Geometry oxe Prober Axioms, or synthetical judgments a priori; and the possibility of forming such judgments depends on the power of con- structing the objects to which they refer in a pure intuition, i. e. in an intuition containing no adventitious element external to the mind itself. The images of geometrical figures differ from all others in being, not represented modifications of body, but presented modi- fications of space ; and the universal validity of the synthetical judgments is a consequence of the universal presence of space as the form of every possible per- ception of body. Three of these synthetical judgments are given in the 10th, 11th, and 12th axioms of Euclid; and either these or other axioms analogous to these must be assumed as evident by intuition, before any of the properties of more complex figures can be made known by demon- stration. I do not say that Euclid has given the best and simplest forms of these axioms, but that in some form or other they are indispensable. To regard all such axioms as possibly demonstrable theorems is to be ignorant of the logical conditions under which demon- stration is possible; for a synthetical judgment is de- monstrable only on the condition that another synthetical judgment may be assumed. 0» yoiq uTravToov tl,YiTovvTss \oyov ccvaigov(ri Xoyov. It may be true that the image which gives rise to the intuitive perception of the axiom, is not consciously contemplated as more perfect than the corresponding figure as seen in a body; but this does not prove that the axiom is really generalized from the latter. The inadequacy of sensible magnitudes for mathematical certainty does not arise from that of which we are 254 APPENDIX. immediately conscious, but from that of which we are not. The straight line as perceived is a quality of body; the straight line as imagined is a modification of space. The portions of the two actually presented at any time may not apparently diifer from each other; but our empirical knowledge or ignorance of body may suggest actual or possible variations not perceived in the in- tuition; for the qualities of body have an objective existence independently of our perception, and therefore may or may not be adequately perceived at any one time. We see, for example, that a line running along the earth's surface is apparently straight; but we know that it is in reality an arc of the earth's curvature, and might be seen to be so in another position or with more acute organs. But the straight line in space exists only as imagined, and is imagined only as mathematically exact. The intuition, therefore, is adequate and valid for any extent of space, and in any portion. The apparent straightness of the visible line is the result of an imperfection in our bodily organs ; and with more acute senses we might perceive its deviation. The presented straightness of the imaginary line results from the exactness of our constructive power ; and a superior excellence in this would only enable us to extend the same image to a greater length, or to retain it more steadily before the mind. IV. The Synthetical Axioms are thus the ground of all that is properly geometrical in our fundamental assump- tions ; but the Analytical Axioms are employed also, as expressing general conceptions of equality and inequality under which geometrical magnitudes may be brought. Stewart was led into his erroneous view of definitions by his contempt for the syllogism, which he would not allow to be under any circumstances the type of demon- strative reasoning. In this contempt Mr. Mill does not APPENDIX. 255 participate, and he has accordingly exhibited the fifth proposition of Euclid demonstrated in syllogistic form. In this demonstration we see both analytical and syn- thetical axioms employed as major premises ; the former as general formulae, founded on the conception of equality; the latter as the means of applying this general conception to geometrical magnitudes, in which the test of equality is coincide7ice. One or the other will be employed in different syllogisms, according as the major term to be proved is equality or coincidence. The minor premises are furnished by the conditions, given or constructed, of the particular figure. Against the form of the geometrical syllogism as exhibited by Mr. Mill the logician will have no ob- jections to allege ; though the metaphysician will not be disposed to acquiesce in his statement that the axioms of both kinds are gained by induction. And it is not strictly accurate to represent the first three axioms of Euclid as capable of proof by an imaginary super- position. To the axioms in their general form this prin- ciple is inapplicable ; for coincidence is not the test of equality in general, but only of equality in superficial magnitudes. To the axioms as employed in Geometry the principle of superposition may be applied : but even here it adds nothing to their evidence. Magnitudes given as the sums of equal magnitudes are ipso facto thought as equal ; and to have recourse to super- position tends to confound the evidence of logical necessity resting on the laws of thought with that of geometrical necessity resting on the conditions of in- tuition. Much error and confusion on this subject might have been avoided, had modern philosophers observed Aristotle's distinction between a^%at 10 coy, or assumptions from which we reason, and «g%ai Treqi o, or assumptions 25G APPENDIX. about the objects of our reasoning. In the former class he rightly places the axioms; in the latter, the definitions. But the true distinction between the axioms proper and the definitions, as synthetical and analytical judg- ments, has not, I think, been as yet accurately carried out in reference to Geometry. The above remarks were written as an appendix to a pamphlet of mine on the Limits of Demonstrative Science, published in 1853. In the remainder of this note, I propose to resume a question which was then only partially considered, and to point out what appears to be the chief deficiency in the logical arrangement of geometrical principles. Plato asserted that mathematical demonstration was founded on hypotheses^. Aristotle in like manner enu- merates hypotheses, along with definitions, among the proper principles of science ^ By this term both philo- sophers appear to have meant the same thing ; namely, that the real existence of the objects of demonstration is not proved, but supposed. If there exist any where two perfect straight lines, those lines cannot enclose a space ; and if there exists any where a figure formed by three such lines, it has its angles equal to two right angles. But this supposed existence of the objects cannot be verified by any process of mathematical reasoning. To bridge over the chasm which separates thoughts from things ; to determine how far a subjective necessity of thinking indicates a corresponding objective necessity of existence, is the office, not of Mathematics, but of a Science of Being, of Metaphysics, or, as Plato would say, of Dialectic. But though objective existence is beyond the province d Rep. vi. p. 510. C. « Anal. Post. i. 2. 7, APPENDIX. 257 of the mathematician, there is a further condition of subjective existence, which he is bound to verify for himself, by an appeal to pure intuition; i. e. by con- structing in his mind an image corresponding to each assumed conception. As far as mere nomenclature is concerned, we might employ the term Mangle to denote a rectilinear figure of two sides, or the term hieentrical circle to denote a figure in which all straight lines drawn from two interior points to the circumference are equal to each other. There is no logical contradiction in such definitions; and those who maintain that all mathematical certainty depends on experience, are bound in consistency to admit that these conceptions are no more absurd than those of a centaur or a hippo- gryph; representing objects no otherwise inconceivable than that experience has shewn them to have no real existence. Hence it follows, that no expression in Geometry which combines together a plurality of attributes can be regarded as a pure definition. For the assumption that such attributes can coexist in an image or figure is either demonstrable or indemonstrable. In the former case the definition is coupled with a theorem, in the latter with an axiom. Thus, for example, to define a triangle as a rectilinear figure of three sides involves the as- sumption, that three straight lines can enclose a space, which is quite as much an axiom as the assumption that two cannot. Again, to define an acute angled triangle as one that has three acute angles involves the assumption, that three straight lines inclined at acute angles to each other will enclose a space. Accordingly we find in the ordinary editions of Euclid many of the definitions accompanied by figures, which furnish an evidence of the possibility of the conception by a direct appeal to the intuition. 258 APPENDIX. From this we may conclude that the numerous attempts of Geometers to diminish or get rid of their axioms have been steps in a wrong direction. The number of axioms, instead of being diminished, should be very considerably increased; and the errors that have hitherto prevailed on the nature and foundation of Geometrical reasoning have been mainly owing to the manner in which many indispensable assumptions have been either omitted altogether, or concealed among the definitions. Some valuable hints on this point may be gathered from a very able and interesting paper by Professor De Morgan, printed in the Companion to the Almanac for 1849. The following extracts indicate a principle which might be pursued to further results. " Book I. Definitions. Of these, iii, vi, xiii, are obvious statements, but not definitions of words ; viii, xxvi, xxxi to xxxiv, are never subsequently used; xviii, if semicircle have its etymological meaning, as seems the intention, is a theorem, which ought to be iii. 1. The remaining definitions are of two kinds: first, those which do not explain their terms, but demand a notion already existing in the student's mind; they are i, ii, iv, v, vii, ix: secondly, purely verbal definitions ; they are x, xi, xii, xiv to xvii, xix to XXX, and xxxv. Insist on angle as a magnitude ; on the comparison of angles as to greater, equal, or less, by superposition ; on the rights of angles equal to and greater than two right angles. The angle made by a straight line with its own continuation is a definite angular magnitude ; and its half is the best definition of a right angle. It is to be regretted that there is no single phrase for " two right angles." " Postulates and axioms : In Euclid, postulates and common notions. All Geometrical demands are postulates in Euclid; his axioms or common notions are in every instance notions common to all kinds of magnitude as APPENDIX. 259 well as space magnitudes. Restore this; that is, let the postulates be, Simson's postulates, and axioms, x, xi, xii ; but instead of xi, substitute " if two right lines coincide in two points, they coincide when produced," as more self-evident. From this it is seen that the doubles of all right angles are equal, and thence that all right angles are equal ; and this should come between I. 12. and I. 13. as a proof of the theorem, "all right angles are equal." For xii substitute " two lines which cut one another are not both parallel to any third line," from which, after I. 28. prove Simson's axiom xii as a theorem. Remark that the distinction of postulate and axiom, as 'problem and theorem^ could not have been Euclid's notion, for he does not recognise the last distinction ; both are with him simply propositions. The expressed six postulates of Euclid are not the only ones which occur ; others are tacitly adopted, as will presently appear. Nothing should be tacitly assumed by those who will not assume without express statement, that " two straight lines cannot inclose a space." "I. 1. The following postulates are demanded: "if two figures which have one or more points in common have each a point which is not in the other, the bound- aries of those figures must cut," and " every point is without or within a circle, according as its distance from the centre is more or less than the radius." With less, the intersection of the circles cannot be proved. I. 4. This postulate is assumed, " any figure may be removed from place to place without alteration of form, and a plane figure may be turned round on the plane." But for this right to turn, I. 4. would not prove I. 6." In the general principles of Professor De Morgan's criticism I fully concur, though slightly differing from one or two of his details. Definitions iii. and vi. are syn- thetical judgments, not developing the conceptions of s 2 200 APPENDIX. the point and straight line, but affirming a property of each. These then should be classed among the axioms, or", as Mr. De Morgan more properly terms them, the postulates. Definitions i, ii, iv, v, vii, viii, ix, are not really employed as conceptions, but only serve to refer us to the corresponding intuition ; which in every case is the basis of one or more axioms, implied, if not expressly stated. Among such axioms must be classed the follow- ing assumptions. '' Two lines can meet each other, and the place where they meet is always a single point." " Two lines can intersect each other, and the place where they intersect is always a single point." (These are properties of the point, and assumptions of the possibility of angles.) "A straight line may lie in and form part of a superficies." Definitions xiii, xiv, xvi, are the only purely verbal ones ; for Definitions x, xi, xii, and xvii, assume that straight lines can be drawn to comply with certain specified conditions; and the others, being definitions of figures, assume that lines under specified conditions can enclose a space. The above remarks will sufficiently shew in what respects the attempts of Geometers to dispense with axioms have failed. They have not been aware that every synthetical judgment assumed without demon- stration is a axiom. They have attempted to deal, not very successfully, with the expressed axioms of Euclid; but they have neglected, and in their own attempts have assumed, principles equally axiomatic, though only understood; and they have not been aware that an assumption resting on an appeal to the senses or to the imagination is as much an unproved assumption as one which appeals to the thought; for of the one we can only say that we are so constituted that we cannot but perceive it, and of the other, that we are so con- stituted that we cannot but think it. APPENDIX. 261 An ingenious and instructive but unsuccessful attempt of this kind is made in Colonel Thompson's " Geometry without Axioms." The author every where identifies intelligible magnitudes with sensible; and this identifi- cation gives rise to a multitude of subordinate assump- tions, inadmissible in strict demonstration, but which, if admissible, would be as much axioms as any thing in Euclid. By identifying intelligible magnitudes with sensible, it is implied that all the perfections which are conceived to exist in magnitudes regarded as modi- fications of space may also be pei^ceived to exist in similar magnitudes regarded as portions of bodies. The perfect straight line and the perfect triangle and the perfect circle are not merely imaginable forms, but tangible substances. But it is further assumed by the author, that the sensible properties of bodies, whose very existence can only be proved by the testimony of expe- rience, may exist, along with the Geometrical qualities, in a manner in which experience has never presented them. Thus " figures of all kinds, lines and points," are "always considered as exhibited on a hard body of some kind, which causes the position of the several parts or points to be fixed with relation to one another; and will, on occasion, be supposed to be turned about an assigned point or points, in any manner that can be shown to be practicable with the hard body on which they are under- stood to be represented. Nevertheless, the application of one object to another will, when required, be imagined to take place without bar of corporeal substance ; — that is to say, without impediment from the existence of other parts than those it is desired to compare." In other words, the surface of a solid and the linear boundary of a surface may be considered ad libitum as in or out of connection with the bodies of which they form part, retaining in both cases the attributes of body, such as 262 APPENDIX. hardness. Surely such assumptions as these, be they legitimate or illegitimate, are to be treated as postulates or axioms. At any rate they are not definitions. But further: a Body is defined to be "any thing that can be made the object of touch ;" and a hard body is " a body which resists all change of form." But bodies which resist all change of form are assumed at the same time not to resist all change of size ; for the genesis of the straight line and the proof of the axiom of parallels are made to depend on a supposed inflation of the sphere. Here is another implied postulate or axiom. " A hard body may be increased or diminished in size without losing its hardness." Empirically, this is untrue. A body which resists all change of form can never in practice be expanded or contracted ad libitum. To assume it as imaginably true is to assume an axiom, not a definition. Again : the author attempts to prove the majority of the axioms of Euclid by superposition ; laying down beforehand these two definitions; " Things which occupy the same place, are said to coincide;" and, "Magnitudes which, if their boundaries were applied to one another, would coincide, or might be made capable of doing so by a different arrangement of parts, are called equal.'* In the latter definition again there is an assumed postu- late : " The parts of a body may be arranged in any way, without affecting the magnitude of the body." Otherwise the two meanings of the term equal are a mere equi- vocation; and the demonstration of the equality of any two given bodies is a mere play upon words. A is equal to B because it actually coincides with it. C is equal to B because it may be made to coincide with it. But how do 1 know that it is the same C before and after the change in the arrangement of its parts ? If I may^ssert that the two bodies are notv equal, because a different APPENDIX. 263 arrangement of parts may make them so, why may I not assert that they are now equal, because by taking away a part of one of them they may become so ? But even after this assumption is made, it may be questioned whether the principle of superposition can be legitimately applied to magnitudes considered as exhibited on a hard body. Magnitudes in space can be constructed a priori in a pure intuition, and in any one part of space, as readily as in any other. Hence they may be transported by the same intuition from one position in space to another, and all their constituent attributes with them ; for they contain no attribute which is not presented in the image. But the empirical qualities of a hard body cannot be constructed a priori in a pure intuition; and tangibility, which the author adopts as the test of corporeity, cannot be conveyed into the mental image by the construction, nor conceived to exist, so long as it is transferred from one place to another solely by the imagination. If I draw two triangles upon paper, I can only shew their coincidence as bodies by cutting one out and placing it on the other. Thus the statements of Geometry are reduced to empirical truths dependent on actual measurement; a method quite as applicable to theorems as to axioms, and which, con- sistently carried out, would dispense with demonstration altogether. For if I may prove by measurement that magnitudes which are equal to the same are equal to each other, I may apply the same test with equal direct- ness to shew that the angles of a triangle are equal to two right angles. On the whole then, notwithstanding the ingenuity and ability of many of the details of Colonel Thompson's work, I cannot help thinking that he has failed in his attempt to demonstrate a system of Geometry without axioms. Such a demonstration, if successful, would be •2(i4 APPENDIX. a solvitur ambulando to the entire argument of the present note. But no such attempt has as yet succeeded ; and on logical grounds I think it may be made abundantly manifest that none ever can succeed. As an appropriate conclusion to this note, 1 subjoin a specimen of Euclid reduced to syllogisms, extracted from the very curious and rare Analyses Geometries of Herlinus and Dasypodius. I have selected the fifth proposition of the first book, as that which has also been analysed by Mr. MilP. To the curious in such subjects it may be interesting to compare the two demonstrations. PjlOPOSITIO V. Theorema. Tmv l(TO(rx.s\cov rgiyoovoov u\ Trgos tj5 /Sacrg/ yooviui 'l(roti otWriKuis glo"/* KOLi Trqoorsyi^Kfi^BKTm rcov 'icrwv euSsiwv, at mo t^v ^olg'iv yu^vioLi 'i(Ta.i otWYjXone; 'k(TOVTcn. Triangulorum qui duo sequalia habent latera, anguli ad basin sunt aequales. Et productis aequalibus illis rectis, etiam qui sub basi sunt anguli, inter se erunt aequales. Sit triangulus aequicrurus a/3y, habens latus a/3 aequale lateri ay, et ducantur lineis a/3, ay, Itt^ £uQslix$ linesB /35, ys. 6 . Sio^to-jxoV. Dico quod angulus a/3y est aequalis angulo ay/3. Et quod angulus y/35 est gequaiis angulo /3ys. ^ xaro- G-KeuYj. Sumatur in linea /35 punctum quodvis ^. Tolla- tur a majore linea ae, minori a^ aequalis linea uyj, per pro- positionem tertiam. Ducan- tur rectse ^y, >?/3. ^ Logic, b. ii. chap. iv. APPENDIX. 265 Syllogismi quatuor. Primus. Quicunque duo trianguli habent duo latera duobus lateribus aequalia, alterum alteri, et angulum angulo aequalem, qui gequalibus lineis continetur, etiam basin basihabebunt sequalem, et reliquos angulos reliquis angulis sequales, alterum alteri, quos aequalia latera sub- tendunt. Trianguli /3a»j, ya? habent duo latera /3a, aij, aequalia duobus lateribus ya, a?, alterum alteri, latus /3a lateri ya, et latus a>j lateri a?. Et habent angulum /3a)j communera. Ergo. Trianguli j3a>j, yoii!^, habent basin /3>j aequalem basi y^, et angulum a/3>j aequalem angulo uy}^, et angulum a>j/3 aequalem angulo u^y. Explicatio. Major est propositio quarta. Minoris pars prima est uttoSso-is. Secunda est nota Ix tv)? xaracxeu^f. Tertia est nota per se. Secundus. Si ab aequalibus tollantur aequalia, quae relinquuntur sunt aequalia. A lineis aequalibus a?, «>j, tolle lineas aequales a/3, uy. Ergo. Manet recta /3?, aequalis rectae y)j. Explicatio. Major est xoiv^ hvoiu. Minoris pars prior est nota ?x t>5? xarao-xsy^j. Posterior est i>7r6$s(ng. Tertius. Quicunque duo trianguli habent &c. ut syllog. pri. Trianguli /3>3y, y?/3, habent duo latera ^>j, r^y, aequalia duobus lateribus y?, ^/3, alterum alteri, latus /3>) lateri y?, et latus r\y lateri ?i3, et habent angulum /S>3y aequalem angulo y?/3. Ergo. Trianguli /Srjy, y?6, habent angulum /3y)j aequalem angulo y/3^, et angulum y/3)j aequalem angulo /3y?. Explicatio. Major est propositio quarta. Minoris pars prima et tertia est conclusio syllog. primi. Secunda est conclusio syll. secundi. Quartus. Si ab aequalibus tollantur aequalia, quae relinquuntur sunt aequalia. Ab aequalibus angulis aj8»), uy}^, tolle aequales angulos y/3>j, /3y^. Ergo. Manet angulus a/3y, aequalis angulo ay/3. Explicatio. Major est xo»v^ twoiu. Minoris pars prior est conclusio syll. primi. Posterior est conclusio syll. 266 APPENDIX. tertii. to o-uf^Trg^ao-jtAa. Ex conclusione syll. quarti liquet trianguli a/3y, angulos a/3y, ay/3, qui sunt ad basin esse aequales. Et ex conclusione syll. tertii liquet angulos /3yr}, y^5, qui sunt sub basi esse aequales. Triangulorum igitur qui duo habent sequalia latera, &c. oirsg shi hl^ai. appendix. 267 Note M. on the classification of fallacies. It has been before observed % that Aristotle's Treatise TTsg) ao^KTTiKwv iKkyyjfiv has properly only a historical value ; that it is important as an account of modes of reasoning in use at the period to which it refers; but that it is not, and does not profess to be, a classification based on any logical principle. Its divisions, however, have been followed without question by the majority of subsequent logicians, centuries after the circumstances which gave it its chief value had ceased to exist; and its language has become in a manner classical, though not always restricted to the sense originally intended by its author. Petitlo Principii and Ignoratio Elenchi still hold their place as recognised forms of fallacy; and the continued use of the Aristotelian nomenclature, at different times and under different circumstances, has given in some respects a permanent value to that which originally was designed only for a temporary purpose. It is not therefore intended in the present note to pro- pose an entirely different classification and nomenclature, but only to point out certain principles, according to which, if Logic is regarded as the Science of the Laws of Thought, an arrangement of Fallacies may be at- tempted on properly logical grounds, and some of the deficiencies of the received enumeration supplied. The Aristotelian list is confined to Fallacies connected with Reasoning. But if Logic is the Science, not of the Laws of Reasoning only, but of those of Thought in gene- ral, it will follow that the spurious forms of Conception and Judgment are equally entitled to a place among Logical Fallacies. And if all the processes of Thought, so far » See above, p. 129, note a. 268 APPENDIX. as they come within the province of Logic, are governed by the same laws, we may naturally expect to find some resemblance between the illegitimate forms of each. The resemblance, as will be seen hereafter, is by no means perfect; but the same general principles of classi- fication will be found applicable to the various processes of Thought, whether we are examining their legitimate or their illegitimate results. The first and most obvious principle of division is into Formal and Material Fallacies, according as the source of the deception lies in the act of thought itself, or in the object upon which, or the circumstances under which, it is exercised. Strictly speaking, Formal Fallacies alone come under the cognisance of the Logica docens, or Logic properly so called; as being apparent but not real thoughts, or at least not the kind of thoughts which they profess to be. Material Fallacies, where the thought is legitimate, but the relation to things inaccurate, belong properly to the province of the Logica utens, and can only be adequately guarded against by that branch of knowledge which takes cognisance of the things. A minute division of Material Fallacies may thus be carried on to an indefinite extent ; for any object about which we think may be represented in thought inaccurately or untruly. The Logician must content himself with indicating the most general prin- ciples of such a division; and that not strictly as a portion of the theory of his science, but as a hint for its application to practice. To these two classes of Fallacies, which are those which suggest themselves a priori, as implied in the idea of any possible exercise of thought, it becomes necessary in practice to add a third class, comprising those which arise from the ambiguities of language. Words, whether written, or^ spoken, or exhibited in some other system of signs, are APPENDIX. 209 proved by experience to be universally necessary in practice, both to the formation and to the communication of thought; and any defect in this indispensable instru- ment is communicated to the operations which it per- forms. This was clearly seen by Aristotle and his followers, who have assigned a prominent, indeed too prominent, a place to language in their classification, by dividing Fallacies, in the first instance, into those in dictione and those extra dictionem; according as the de- ception does or does not depend upon the particular words in which the reasoning is conveyed^. Looking to the actual position of language in relation to thought, it will be better to adopt a threefold division of Fallacies; those in the Thought, those in the Matter, and those in the Language ; the last corresponding to the fallacice in dic- tione of Aristotle; the two former representing a still more important though often neglected distinction, which is lost sight of in the vague negation of extra dictionem. In the application of this principle of division to the several operations of Thought, as exhibited in the follow- ing Table, some slight differences will present themselves, which in some instances will explain themselves, while in others a few preliminary words of explanation may be desirable. Fallacies of Language, it is obvious, will become more numerous as the process of thought be- comes more complicated. While a concept can be misapprehended only in the term (whether expressed by one word or more) in which it is conveyed, a Judgment may be ambiguous, either in the meaning of one of its terms, or in its entire construction ; and a Reasoning admits of still further ambiguity, from the repetition of a term or sentence in different senses. Hence a different enumeration of Fallacies in dictione will be required in different parts of the Table. *» For some further remarks on this division, see p. 131, note b. 270 APPENDIX. As regards Formal or Logical Fallacies, a fuller ex- planation may be needed. The ultimate test of the logical validity of any thought is conceivahility. This test may be applied to judgments and reasonings, as well as to concepts. A concept is logically real if it is conceivable; that is to say, if its constituent parts can be combined with each other in an unity of representation. If it complies with this criterion, it is real as a thought : whether its supposed object be real as a thing, is a question with which Logic has no concern. A judgment, again, is logically true or necessary, (for Logic recognises no truth short of necessity,) if its contradictory is incon- ceivable : it is logically false or impossible, if it is itself inconceivable; but if two contradictory assertions are both equally conceivable, it does not lie within the pro- vince of Logic to determine their truth or falsehood. A reasoning, in like manner, is logically necessary, if the contradictory of the conclusion cannot be conceived as true, consistently with the assumed truth of the premises : it is logically impossible, if the conclusion itself cannot be so conceived. If, however, the conclusion and its contradictory are equally conceivable along with the assumed truth of the premises, the conclusion may or may not have a material value, but it is one which cannot be recognised by Logic. But though the test of conceivahility is thus applicable to judgments and reasonings, as well as to concepts, it is applicable in a different manner. A given combination of attributes may be inconceivable, either because it contains too little, or because it contains too much. That is to say, it may either be defective in the con- ditions under which alone attributes can be united in representation, or it may contain such attributes as mutually exclude one another. Thus, inasmuch as unity of representation is only possible under the condition APPENDIX. 271 of limitation by difference, because the thing repre- sented must be known as an actual object, and not as the universe of all possible objects, it follows that the indefinite ideas corresponding to the terms Thing, Ex- istence, Being in general, are not conceivable, as having no distinctive characteristic. They may be elements of the conceivable; that is to say, they may become conceivable when combined with and determined by other attributes; but so long as they are given as isolated, and therefore as unconditioned, they are inconceivable. The logical rule here violated is the Law of Identity, which requires that every object should be conceived as itself, and as distinguished from every thing else. Here the supposed Concept contains too little. On the other hand, if the given attributes are incompatible with each other, the rule violated is the Law of Contradiction, which requires that two contradictory attributes should not be united in the same object. Here the supposed Concept contains too much. The third law of thought, that of Excluded Middle, may also be violated in relation to the same process, if we attempt to conceive an object of which neither of two contradictory attributes is predicable. Here again, the supposed Concept contains too little. But it is obvious that these three laws cannot all be equally violated in a pretended act of Judgment or of Reasoning. In Judgment, the concepts are already given ; and nothing remains to be done, but to connect them together by an affirmative or negative copula. Here there is no room for a deficiency of attributes; which would affect the conceivability of the terms themselves, not the possibility of their union in a judgment. The only logical fallacy possible must consist in uniting notions which are essentially distinct, or in separating such as are essentially the same. In Reasoning, again, the truth of the premises and the conceivability of the 272 APPENDIX. terms, are not examined, but assumed; and the only pos- sible logical fault must consist in drawing a conclusion incompatible with the premises themselves, or with some- thing which they imply. In these two cases, the only possible instances of inconceivability must arise from a direct or indirect Contradiction. A Fallacy, according to Aristotle, is a reasoning which, either in matter or form or both, appears to be that which it is not^. Extending this definition from the process of reasoning to that of thought in general, we may regard any thought as fallacious, which, in form or matter, has an apparent but not a real validity ; and a Logical or Formal Fallacy is one which exhibits an ap- parent but not a real conformity to the Laws of Thought. An apparent thought may thus be formally fallacious in two ways ; either generally, because it is not a thought at all ; or specially, because it is not the kind of thought which it professes to be. For the elements of a judg- ment may be perfectly legitimate as objects of con- ception, but self-destructive when united together as parts of a judgment; and the premises and conclusion of a syllogism may be valid, even all together, as in- dependent judgments, yet involve a concealed contra- diction when placed in the relation of antecedents and consequent in an act of reasoning. Thus, if it be argued "All A is B, C is not A, therefore C is not B," it is obvious that the three statements, viewed merely as judg- ments, may be all true together. But when we view them as parts of a syllogism, we assert that C is not B, because it is not A; in other words, that nothing can be B which is not A, or that every B must be A. Whereas the premise, in stating that all A is B, leaves it open as at least a pos- c Topics i. 1. 3. 'EpiffTiKhs S' iarl (rvWoyi(riJ.hs 6 e/c (paivofidvwv ivSo^p, fjL^ &vTOi)v 54, Koi 6 e| iuSS^ciJU f) (paLvofxivwv 4v56^wv cpaivSfxepos. See also So}>h. Elench. c. 2. APPENDIX. 273 sible truth that some B is not A. Hence the same belief is regarded as possible and impossible at the same time ; and thus the conclusion, though not directly at variance with what the premise asserts, cannot be drawn consistently with what it permits. Hence these and cognate forms of reasoning are classed in the Table as violating the Law of Contradiction indirectly; and the conclusion is noted as formally invalid, though mate- rially it may be either true or false. Thus the whole process may be valid as a series of judgments, but not as a reasoning ; and the thought, therefore, is not the kind of thought which it professes to be. On the other hand, if a conclusion is drawn opposed to that which the laws of thought require, the conclusion is neither materially nor formally possible ; and the supposed reasoning is in reality no thought at all. Thus we may, verbally at least, argue, " All A is B, C is A, therefore C is not B ;" which requires- us to conceive C as being at the same time B and not B. Here the Law of Contradiction is violated directly. The relation of logical fallacies to this law will be seen much more clearly, if, in accordance with the system of Sir William Hamilton, we assign to the predicate as well as to the subject of every proposition an expressed mark of quantity. To attempt a complete enumeration of Material Fallacies would be an endless as well as a profitless task. Under the head of Reasoning, it has been thought sufficient to arrange in their proper places the members of the usually received list. The arrangement has been made according to the instances given by Aldrich and other modern Logicians, as being most familiar to the majority of readers. These, however, occasionally differ in points of detail from those which are found in the original text of Aristotle. The discrepancy is of little consequence ; as the notes to the corresponding portion T 274 APPENDIX. of Aldrich's text will in most instances enable the reader to compare and classify Aristotle's examples for himself. Indeed, Aristotle himself confesses that the arrangement is in some degree arbitrary, and that the same Fallacy will admit of being classed under different heads. As regards Material Fallacies of Conception and Judg- ment, I have contented myself with indicating, in the most general way, the sources of Obscurity and Indistinctness in Concepts, and of Falsity in Judgments. A concept is obscure, when it cannot be distinguished as a whole from certain others : it is indistinct, when its several com- ponent parts cannot be distinguished from each other^. The obscurity or indistinctness of a concept may ob- viously arise, either from accidental circumstances, such as the want of a sufficient observation of the object on the part of this or that individual thinker, or from circumstances essential to the concept itself, such as the want of those conditions which experience shews us to be indispensable to all clear or distinct thinking. Under this head may be classed the notions, so familiar to all students of Logic, of summum genus and injlma species. Both of these terms represent limits to which we may indefinitely approximate in thought, but which we never actually attain. Neither of them can be regarded as logically inconceivable ; for, under different conditions of the matter of our thought, both might be practically apprehended. But, in actual thinking, it becomes manifest that our several concepts present in all cases such an affinity or continuity one with another, that it is im- possible, on the one hand, to fix on two cognate genera which possess no common element to form a higher genus, (until we arrive at abstractions too empty to be d This distinction is due to Leibnitz. See his Meditationes de CognitionCf Veritate et Ideis. Opera, ed. Erdmann, p. 79. APPENDIX. 275 conceived at all,) or, on the other hand, to arrest the process of subdivision at any limited number of at- tributes, as the greatest number that can possibly be united in one concept^. Thus the notion of a logical highest genus, that is, of a concept so simple as to be incapable of further analysis, is essentially obscure ; for, in actual thought, we find that, so long as there is limitation and difference, there is also community, and, therefore, a possibility of further analysis f. Again, the notion of a logical lowest e The Highest Genus and Lowest Species of Logic must not be con- founded Avith the same terms as applicable to this or that branch of natural science. The Highest Genus in any special science is the general class, comprehending all the objects whose properties that science in- vestigates : the different Lowest Species are the classes at which that special investigation terminates. In Geometry, for example, under the sKmmum genus of magnitudes in space, we find these coordinate injimce species of triangles, the equilateral, the isosceles, and the scalene. The Geo- metrical properties of the figures are not affected by further subdivision. But the Logician, as such, knows nothing of Geometrical Imiitations. To him the highest genus and lowest species are limits of the possibility of thought ; the former denoting a notion so simple as to admit of no further subtraction, the latter^ a notion so complex as to admit of no further addition. In thought, the notion of an equilateral triangle whose sides are three feet long is a subordinate species to that of an equilateral triangle in general. f It is not easy to draw the line between the materially and the formally inconceivable. Being in general (^ns), and such like abstractions, may be regarded as formally inconceivable, as having no contents. But these abstractions are not necessarily identical with the notion of a highest genus ; — indeed, the majority of Logicians have placed the summa genera in the Categories, of which Ens and the other transcendents were regarded as predicable equivocally, or analogously, but not univocally. But the Categories, again, are practically inconceivable perse; for a substance is only known by its attribiTtes, and an attribute as existing in a substance. But it is at least supposable that, under other conditions of experience, we might arrive at notions suflSciently definite to be conceivable, yet so diverse as not to admit of classification under a higher genus ; and this is virtually admitted by Kant, who, notwithstanding, regards the laws of homogeneity, specification, and continuity as logical principles of the reason. I prefer to consider them as empirical, though perhaps indicating psychological conditions of experience. Thus viewed, they are not, properly 276 APPENDIX. species, or a combination of all conceivable compatible attributes, is essentially indistinct; for the number of such attributes is indefinite, and, to go through them in thought, enumerating and distinguishing one from another, would require an infinite grasp of mind, and ah infinite length of time, for its accomplishment. Another class of notions may be specified as materially inconceivable ; those, namely, which, though presenting no logical contradiction, contain attributes materially heterogeneous, and thus incompatible with each other. Such combinations of attributes as circular virtue, or coloured thought, are of this character. "Black spirits and white, red spirits and grey," are only con- ceivable by investing the spirits with a body for the occasion, and not by connecting the idea of colour with that of spirituality. To the same class belong all com- binations of attributes inconsistent with the a priori conditions of intuition; such as a bilinear figure; which, though not logically contradictory, are mathematically inconceivable. These must be carefully distinguished from those notions which, though empirically known to be unreal, are yet perfectly consistent as thoughts; such as the conception of a centaur, or of a golden mountain. In respect of these last. Logic recognises no distinction between the real and the unreal. An opposite class of notions materially inconceivable, are those which are defective, as separating attributes whose union is testified by experience to be indispensable to conception. Thus, inasmuch as we know by experience, that no surface can be conceived, without being of some colour, and that no colour can be conceived, except on some surface, the conceptions of an uncoloured surface or an unextended colour, though they present no logical contradiction, speaking, laws of thought ; and thus, as far as Logic is concerned, they belong to the matter of thought, not to the form. APPENDIX. 277 must be classed as essentially, though materially, incon- ceivable^. As regards the truth or falsehood of Judgments, Logic properly takes cognisance of Formal Truth or Falsehood only, which depends on the agreement or disagreement of a thought with its own laws. Material Truth, which is sometimes defined as consisting in the agreement of the thought with its object, might be more correctly explained as consisting in the agreement of the object as represented in thought with the object as presented in intuition ; for the object exists, relatively to us, only as given in some form of intuition. But, however it may be defined, it is manifest that no general law or criterion of material truth and falsehood can be given ; for the essence of such truth consists in its adapting itself in every case to the diversities of this or that special presentation''. To enumerate in detail all the various sources of material falsehood would be impossible ; I have contented myself with referring to the three general heads of Mathematical, Metaphysical, and Physical Judgments; which appear to possess essen- tially different degrees of certain t}^ or impossibility. These propositions will admit of a different classification, according to the theories held by different writers as to their origin. By some, mathematical judgments will be classed with physical, as due solely to experience : by others, they will be merged in logical truth or falsehood, as owing their evidence to laws of thought. Metaphysical judgments, again, will be considered by some as purely empirical : while by others they will be referred to s The error of those philosophers who maintain that colour can be conceived without extension is exposed by Sir W. Hamilton, Reid's Works, p. 143. h That a general criterion of material truth is not only impossible but self-contradictory, is shewn by Kant, Logik, Einleitmig, VII. 278 APPENDIX. certain fundamental laws of human belief, originating in the constitution of the mind itself. Into the various controversies connected with these questions it would be irrelevant now to enter. The reasons for the classification which I have adopted will be found given at length in a separate work, to which for the present I must content myself with referring i. i See Prolegomena Logica, chap. iv. and v. ;s. Of Reasoning. In the Matter. Conception given as unconditioned. (Law of Identity,) e. g. Being in general. Cc S( (1 Bctly. tion logi- htssible, as Directly.iing what (by Statem^e permits. e.g. a surface '^^^^^^^^ white and not aaterially ut is not Conceptioif^^y-^ impq Attributes heterogeneous. e. g. circular virtue, or bilinear figure. Undistributed Middle. In the Language. (Fallaciee in Dictione.) Of a Term. I In itself. In its relation. (iEquivocatio, (Compositio, Accentus, Divisio.) Figura Dictionis.) Of a Propo- sition. (Amphibolia.) j false , jding sa pro Premise doubtful. (including Fetitio Principii.) Conclusion irrelevant. (Ignoratio Elenchi.) tionum.) Judgi Directly. Contradiction as: e. g. black is not W'*^ In the Language. Judgments ambiguous. In a single Term. (iEquivocatio.) In the whole Proposition. (Amphibolia.) 278 APPENDIX. certain fundamental laws of human belief, originating in the constitution of the mind itself. Into the various controversies connected with these questions it would be irrelevant now to enter. The reasons for the classification which I have adopted will be found given at length in a separate work, to which for the present I must content myself with referring i. * See Prolegomena Logica, chap. iv. and v. H TABLE OF FORMAL AND MATERIAL FALLACIES. FALLACIES Of Conceptit Of Judgment. In the Matter. Conception given as Conception given a; unconditioned. (Law self- contradictory. of Identity,) e. g. Being in general. (Law of Contradii Conception given as formally defective. (Law of Excluded Middle) e. g. a sur- face neither white nor not white. Directly. Indirectly. (by Statement) (by Inference) e.g. a surface both e.g. a surface both white and not white. white and black. Conceptions materially impossible. In the Language, where a single term admits of more than Attributes heterogeneous, e, g, circular virtue, or bilinear figure. Matter defective. As a whole. e. g. an uncoloured surface. (Obscure.) Conceptions materially incomplete. In the pai-ts. (Indistmct.) 1 Essentially. Accidentally. Essentially. Accidentally, (summum genus.) (from imperfect (infima species.) (from want of observation.) analysis.) Of Reasoning. In the Form. (Fallacia Consequentls) conclusion implies a contradiction of a premise. In the Matter. Directly. Conclusion logically impossible, as contra- dicting what the premise asserts. (This consequence can be neither for- mally nor materially valid.) Indirectly. Contradiction logi- cally inadmissible, as contradicting what the premise permits. (This consequence may be materially valid, but is not formally.) Illicit Process of Major. Of a Term. In itself. In its relation, (.ffiquivocatio, (Compositio, In the Language. (Fallaciffi in Dictione.) Of a Propo- sition. (Amphibolia.) Accentus, Figura Dictionis.) Divisio.) Term imperfectly conceived. (Accidens, A dicto secundum quid.) Premise false . (including Non causa pro causa, Plurium Interrogationum.) Premise doubtfiil. Conclusion irrelevant, (including (Ignoratio Elenchi.) Petitio Principii.) In the Form. Judgments logically false. Directly. Contradiction asserted, In the Matter. Judgments materially false. In the Language. Judgments ambiguous, Indirectly. Contradiction implied, g. black is not black. e. g. black is white. At variance with At variance with a priori intuition. empirical intuition. (Mathematically false.) (Physically false.) At variance with the conditions of personal consciousness. (Metaphysically false.) In a single Term. (,^quivocatio.) In the whole Proposition. (Amphibolia.) Works by the same Author, PUBLISHED BY W. GRAHAM, OXFOKD. PEOLEGOMENA LOGICA. An INQUIRY into the PSYCHOLOGICAL Character of LOGICAL PROCESSES. Price 9s. " L'auteur se moiitre tout a fait au courant des travaux de I'ecole fran9aise, et semble beaucoup s'eii rapprocber pour les doctrines. Par I'objet de ses discussions, 11 se rattacbe egalement a I'ecole ecossaise, telle qu'elle s'est transformee entre les mains de M. Hamilton. Ce livre est surtout interessant comme symptome de I'interet que les universites anglaises semblent vouloir prendre a un ordre de recherches auxquelles elles etaient jusqu'ici rest^es etrang^res, et comme temoignage de I'influence de I'ecole fran^aise chez nos voisins d'outre-mer." Journal des Savants, Mars, 1852. "The author has discussed the vaiious points which he has selected, with an acuteness and analytical power which must at once rank him with the ablest writers on the subject. ... We wish our limits would allow of om- giving a complete view of the whole dissertation respecting these two fundamental principles, [those of causahty and substance.] No part of the book exhibits more to advantage the analytical power of the \\Titer's mind, and his original talent for this kind of inquiry; Avhich must be acknowledged by all who can follow him through the maze of conflicting theories, whatever opinion may be entertained of the questions them- selves. . . . We can only add, that we deem the work, as a whole, to be one of the most important contributions to psychological science that has yet appeared. The style is, for the most part, eminently clear, the examples for illustration, generally well chosen ; and the book is well adapted accurately to inform all who can and will patiently digest it, on the true bearing of most of the great questions of speculative philosophy, and especially on the connexion between Psychology and Logic." Journal of Psychological Medicine, January, 1854. "In this connexion we must recommend the study of an important Avork in the higher literature of philosophy', the " Prolegomena Logica" of Mr. Mansel. In any critical discussion of recent English philosophical books, this acute and learned work should occupy a large space. Along with his other writings, it entitles Mr. Mansel to a foremost place among living British psychologists and logicians." Professor Fraser, Essays in Philosophy, p. 170. ** The Prolegomena Logica of Mansel, a work of which Oxford may be proud." J. G. Phillimore, Principles and Maxims of Jurisprudence, p. 394. 2 THE LIMITS OF DEMONSTRATIVE SCIENCE, considered in a Letter to the Rev. William Whewell, D.D. Price Is. iid. " Mr. Mansel has also subsequently, in answer to an able Letter of Dr. Whewell, more fully discussed the question, and placed the matter on its proper footing, in a most satisfactory pamphlet, " The Limits of Demonstrative Science considered." Sir W. 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