  The Second Book of the Analytica Priora seems conceived with a view mainly to Dialectic and Sophistic, as the First Book bore more upon Demonstration.1 Aristotle begins the Second Book by shortly recapitulating what he had stated in the First; and then proceeds to touch upon some other properties of the Syllogism. Universal syllogisms (those in which the conclusion is universal) he says, have always more conclusions than one; particular syllogisms sometimes, but not always, have more conclusions than one. If the conclusion be universal, it may always be converted — simply, when it is negative, or per accidens, when it is affirmative; and its converse thus obtained will be proved by the same premisses. If the conclusion be particular, it will be convertible simply when affirmative, and its converse thus obtained will be proved by the same premisses; but it will not be convertible at all when negative, so that the conclusion proved will be only itself singly.2 Moreover, in the universal syllogisms of the First figure (Barbara, Celarent), any of the particulars comprehended under the minor term may be substituted in place of the minor term as subject of the conclusion, and the proof will hold good in regard to them. So, again, all or any of the particulars comprehended in the middle term may be introduced as subject of the conclusion in place of the minor term; and the conclusion will still remain true. In the Second figure, the change is admissible only in regard to those particulars comprehended under the subject of the conclusion or minor term, and not (at least upon the strength of the syllogism) in regard to those comprehended under the middle term. Finally, wherever the conclusion is particular, the change is admissible, though not by reason of the syllogism in regard to particulars comprehended under the middle term; On the chapter in general he remarks (note, p. 204):— “Cette thÉorie des conclusions diverses, soit patentes soit cachÉes, d’un mÊme syllogisme, est surtout utile en dialectique, dans la discussion; oÙ il faut faire la plus grande attention À ce qu’on accorde À l’adversaire, soit explicitement, soit implicitement.” This illustrates the observation cited in the preceding note from the Scholiasts. Aristotle has hitherto regarded the Syllogism with a view to its formal characteristics: he now makes an important observation which bears upon its matter. Formally speaking, the two premisses are always assumed to be true; but in any real case of syllogism (form and matter combined) it is possible that either one or both may be false. Now, Aristotle remarks that if both the premisses are true (the syllogism being correct in form), the conclusion must of necessity be true; but that if either or both the premisses are false, the conclusion need not necessarily be false likewise. The premisses being false, the conclusion may nevertheless be true; but it will not be true because of or by reason of the premisses.4 The true conclusion is not true by reason of these false premisses, but by reason of certain other premisses which are true, and which may be produced to demonstrate it. Compare Analyt. Poster. I. ii. p. 71, b. 19. First, he would prove that if the premisses be true, the conclusion must be true also; but the proof that he gives does not seem more evident than the probandum itself. Assume that if A exists, B must exist also: it follows from hence (he argues) that if B does not exist, neither can A exist; which he announces as a reductio ad absurdum, seeing that it contradicts the fundamental supposition of the existence of A.5 Here the probans is indeed equally evident with the probandum, but not at all more evident; one who disputes the latter, will dispute the former also. Nothing is gained in the way of proof by making either of them dependent on the other. Both of them are alike self-evident; that is, if a man hesitates to admit either of them, you have no means of removing his scruples except by inviting him to try the general maxim upon as many particular cases as he chooses, and to see whether it does not hold good without a single exception. In regard to the case here put forward as illustration, Aristotle has an observation which shows his anxiety to maintain Having laid down the principle, that the conclusion may be true, though one or both the premisses are false, Aristotle proceeds, at great length, to illustrate it in its application to each of the three syllogistic figures.8 No portion of the Analytica is traced out more perspicuously than the exposition of this most important logical doctrine. It is possible (he then continues, again at considerable length) to invert the syllogism and to demonstrate in a circle. That is, you may take the conclusion as premiss for a new syllogism, together with one of the old premisses, transposing its terms; and thus you may demonstrate the other premiss. You may do this successively, first with the major, to demonstrate the minor; next, with the minor, to demonstrate the major. Each of the premisses will thus in turn be made a demonstrated conclusion; and the circle will be complete. But this can be done perfectly only in Barbara, and when, besides, all the three terms of the syllogism reciprocate with each other, or are co-extensive in import; so that each of the two premisses admits of being simply converted. In all other cases, the process of circular demonstration, where possible at all, is more or less imperfect.9 Having thus shown under what conditions the conclusion Of this reversing process, one variety is what is called the Reductio ad Absurdum; in which the conclusion is reversed by taking its contradictory (never its contrary), and then joining this last with one of the premisses, in order to prove the contradictory By the Reductio ad Absurdum you can in all the three figures demonstrate all the four varieties of conclusion, universal and particular, affirmative and negative; with the single exception, that you cannot by this method demonstrate in the First figure the Universal Affirmative.15 With this exception, every true conclusion admits of being demonstrated by either of the two ways, either directly and ostensively, or by reduction to the impossible.16 In the Second and Third figures, though not in the First, it is possible to obtain conclusions even from two premisses which are contradictory or contrary to each other; but the conclusion will, as a matter of course, be a self-contradictory one. Thus if in the Second figure you have the two premisses — All Science is good; No Science is good — you get the conclusion (in Camestres), No Science is Science. In opposed propositions, Aristotle now passes to certain general heads of Fallacy, or general liabilities to Error, with which the syllogizing process is beset. What the reasoner undertakes is, to demonstrate the conclusion before him, and to demonstrate it in the natural and appropriate way; that is, from premisses both more evident in themselves and logically prior to the conclusion. Whenever he fails thus to demonstrate, there is error of some kind; but he may err in several ways: (1) He may produce a defective or informal syllogism; (2) His premisses may be more unknowable than his conclusion, or equally unknowable; (3) His premisses, instead of being logically prior to the conclusion, may be logically posterior to it.19 Distinct from all these three, however, Aristotle singles out and dwells upon another mode of error, which he calls Petitio Principii. Some truths, the principia, are by nature knowable through or in themselves, others are knowable only through other things. If you confound this distinction, and ask or assume something of the latter class as if it belonged to the former, you commit a Petitio Principii. You may commit it either by assuming at once that which ought to be demonstrated, or by assuming, as if it were a principium, something else among those matters which in natural propriety would be demonstrated When the problem is such, that it is uncertain whether A can be predicated either of C or of B, if you then assume that A is predicable of B, you may perhaps not commit Petitio Principii, but you certainly fail in demonstrating the problem; for no demonstration will hold where the premiss is equally uncertain with the conclusion. But if, besides, the case be such, that B is identical with C, that is, either co-extensive and reciprocally convertible with C, or related to C as genus or species, — in either of these cases you commit Petitio Principii by assuming that A may be predicated of B.21 For seeing that B reciprocates with C, you might just as well demonstrate that A is predicable of B, because it is predicable of C; that is, you might demonstrate the major premiss by means of the minor and the conclusion, as well as you can demonstrate the conclusion by means of the major and the minor premiss. If you cannot so demonstrate the major premiss, this is not because the structure of the syllogism forbids it, but because the predicate of the major premiss is more extensive than the subject thereof. If it be co-extensive and convertible with the subject, we shall have a circular proof of three propositions in which each may be alternately premiss and conclusion. The like will be the case, if the Petitio Principii is in the minor premiss and not in the major. In the First syllogistic figure it may be in either of the premisses; in the Second figure it can only be in the minor premiss, and that only in one mode (Camestres) of the figure.22 This chapter, in which Aristotle declares the nature of Petitio Principii, is obscure and difficult to follow. It has been explained at some length, first by Philoponus in the Scholia (p. 192, a. 35, b. 24), afterwards by Julius Pacius (p. 376, whose explanation is followed by M. B. St. Hilaire, p. 288), and by Waitz, (I. p. 514). But the translation and comment given by Mr. Poste appear to me the best: “Assuming the conclusion to be affirmative, let us examine a syllogism in Barbara:—
And let us first suppose that the major premiss is a Petitio Principii; i.e. that the proposition All B is A is identical with the proposition All C is A. This can only be because the terms B and C are identical. Next, let us suppose that the minor premiss is a Petitio Principii: i.e. that the proposition All C is B is identical with the proposition All C is A. This can only be because B and A are identical. The identity of the terms is, their convertibility or their sequence (?p???e?, ?peta?). This however requires some limitation; for as the major is always predicated (?p???e?, ?peta?) of the middle, and the middle of the minor, if this were enough to constitute Petitio Principii, every syllogism with a problematical premiss would be a Petitio Principii.” (See the Appendix A, pp. 178-183, attached to Mr. Poste’s edition of Aristotle’s Sophistici Elenchi.) Compare, about Petitio Principii, Aristot. Topic. VIII. xiii. p. 162, b. 34, in which passage Aristotle gives to the fallacy called Petitio Principii a still larger sweep than what he assigns to it in the Analytica Priora. Mr. Poste’s remark is perfectly just, that according to the above passage in the Analytica, every syllogism with a problematical (i.e. real as opposed to verbal) premiss would be a Petitio Principii; that is, all real deductive reasoning, in the syllogistic form, would be a Petitio Principii. To this we may add, that, from the passage above referred to in the Topica, all inductive reasoning also (reasoning from parts to whole) would involve Petitio Principii. Mr. Poste’s explanation of this difficult passage brings into view the original and valuable exposition made by Mr. John Stuart Mill of the Functions and Logical Value of the Syllogism. — System of Logic, Book II. ch. iii. sect 2:— ”It must be granted, that in every syllogism, considered as an argument to prove the conclusion, there is a Petitio Principii,” &c. Petitio Principii, if ranked among the Fallacies, can hardly be extended beyond the first of the five distinct varieties enumerated in the Topica, VIII. xiii. The meaning of some lines in this chapter (p. 65, a. 17-18) is to me very obscure, after all the explanations of commentators. We must be careful to note, that when Aristotle speaks of a principium as knowable in itself, or true in itself, he does not mean that it is innate, or that it starts up in the mind ready made without any gradual building up or preparation. What he means is, that it is not demonstrable deductively from anything else prior or more knowable by nature than itself. He declares (as we shall see) that principia are acquired, and mainly by Induction. Next to Petitio Principii, Aristotle indicates another fallacious or erroneous procedure in dialectic debate; misconception or Instead of the preposition pa??, Aristotle on two occasions employs d?? — ??t? ??? ?sta? d?? t?? ?p??es?? — p. 65, b. 33, p. 66, a. 3. The preposition pa??, with acc. case, means on account of, owing to, &c. See MatthiÆ and KÜhner’s Grammars, and the passage of Thucydides i. 141; ?a? ??ast?? ?? pa?? t?? ?a?t?? ???e?a? ??eta? ???e??, ??e?? d? t??? ?a? ???? ?p?? ?a?t?? t? p???de??, &c., which I transcribe partly on account of Dr. Arnold’s note, who says about pa?? here:— “This is exactly expressed in vulgar English, all along of his own neglect, i. e. owing to his own neglect.” Aristotle tells us that this was a precaution which the defender of a thesis was obliged often to employ in dialectic debate, in order to guard against abuse or misapplication of Reductio ad Absurdum on the part of opponents, who (it appears) sometimes In impugning the thesis and in extracting from your opponent the proper concessions to enable you to do so, you will take care to put the interrogations in such form and order as will best disguise the final conclusion which you aim at establishing. If you intend to arrive at it through preliminary syllogisms (prosyllogisms), you will ask assent to the necessary premisses in a confused or inverted order, and will refrain from enunciating at once the conclusion from any of them. Suppose that you wish to end by showing that A may be predicated of F, and suppose that there must be intervening steps through B, C, D, E. You will not put the questions in this regular order, but will first ask him to grant that A may be predicated It will be his business to see that he is not thus tripped up in the syllogistic process.33 If you ask the questions in the order above indicated, without enunciating your preliminary conclusions, he must take care not to concede the same term twice, either as predicate, or as subject, or as both; for you can arrive at no conclusion unless he grants you a middle term; and no term can be employed as middle, unless it be repeated twice. Knowing the conditions of a conclusion in each of the three figures, he will avoid making such concessions as will empower you to conclude in any one of them.34 If the thesis which he defends is affirmative, the elenchus by which you impugn it must be a negative; so that he will be careful not to concede the premisses for a negative conclusion. If his thesis be negative, your purpose will require you to meet him by an affirmative; accordingly he must avoid granting you any sufficient premisses for an affirmative conclusion. He may thus make it impossible for you to prove syllogistically the contrary or contradictory of his thesis; and it is in proving this that the elenchus or refutation consists. If he will not grant you any affirmative proposition, nor any universal proposition, you know, by the rules previously laid down, that no valid syllogism can be constructed; since nothing can be inferred either from two premisses both negative, or from two premisses both particular.35 Waitz (p. 520) explains ?atas???????es?a?, “disputationum et interrogationum laqueis aliquem irretire.” This is, I think, more correct than the distinction which M. BarthÉlemy St. Hilaire seeks to draw, “entre le Catasyllogisme et la RÉfutation,” in the valuable notes to his translation of the Analytica Priora, p. 303. The vague and general way in which Aristotle uses the term ?p??????, seems to be best rendered by our word belief. See Trendelenburg ad Aristot. De AnimÂ, p. 469; Biese, Philos. des Aristot. i. p. 211. We thus, by help of the universal, acquire a theoretical knowledge of particulars, but we do not know them by the special observation properly belonging to each particular case: so that we may err in respect to them without any positive contrariety between our cognition and our error; since what we know is the universal, while what we err in is the particular. We may even know that A is predicable of all B, and that B is predicable of all C; and yet we may believe that A is not predicable of C. We may know that every mule is barren, and that the animal before us is a mule, yet still we may believe her to be in foal; for perhaps we may never have combined in our minds the particular case along with the universal proposition.41 A fortiori, therefore, we may make the like mistake, if we know the universal only, and do not know the particular. And this is perfectly possible. For take any one of the visible particular instances, even one which we have already inspected, so soon as it is out of sight we do not know it by actual and present Complete cognition (t? ??e??e??, according to the view here set forth) consists of one mental act corresponding to the major premiss; another corresponding to the minor; and a third including both the two in conscious juxta-position. The third implies both the first and the second; but the first and the second do not necessarily imply the third, nor does either of them imply the other; though a person cognizant of the first is in a certain way, and to a certain extent, cognizant of all the particulars to which the second applies. Thus the person who knows Ontology (the most universal of all sciences, t?? ??t?? ? ??), knows in a certain way all scibilia. Metaphys. A., p. 982, a. 21: t??t?? d? t? ?? p??ta ?p?stas?a? t? ???sta ????t? t?? ?a????? ?p?st??? ??a??a??? ?p???e??· ??t?? ??? ??d? p?? p??ta t? ?p??e?e?a. Ib. a. 8: ?p??a???e? d? p??t?? ?? ?p?stas?a? p??ta t?? s?f?? ?? ??d??eta?, ? ?a?’ ??ast?? ????ta ?p?st??? a?t??. See the Scholia of Alexander on these passages, pp. 525, 526, Brandis; also Aristot. Analyt. Post. I. xxiv. p. 86, a. 25; Physica, VII. p. 247, a. 5. Bonitz observes justly (Comm. ad Metaphys. p. 41) as to the doctrine of Aristotle: “Scientia et ars versatur in notionibus universalibus, solutis ac liberis À conceptu singularum rerum; ideoque, etsi orta est À principio et experientiÂ, tradi tamen etiam iis potest qui careant experientiÂ.” It is impossible, however, for a man to believe that one contrary is predicable of its contrary, or that one contrary is identical with its contrary, essentially and as an universal proposition; though he may believe that it is so by accident (i.e. in some particular case, by reason of the peculiarities of that Whenever (Aristotle next goes on to say) the extremes of a syllogism reciprocate or are co-extensive with each other (i.e. when the conclusion being affirmative is convertible simply), the middle term must reciprocate or be co-extensive with both.46 If there be four terms (A, B, C, D), such that A reciprocates with B, and C with D, and if either A or C must necessarily be predicable of every subject; then it follows that either B or D must necessarily also be predicable of every subject. Again, if either A or B must necessarily be predicable of every subject, but never both predicable of the same at once; and if, either C or D must be predicable of every subject, but never both predicable of the same at once; then, if A and C reciprocate, B and D will also reciprocate.47 When A is predicable of all B and all C, but of no other subject besides, and when B is predicable of all C, then A and B must reciprocate with each other, or be co-extensive with each other; that is, B may be predicated of every subject of which A can be predicated, though B cannot be predicated of A itself.48 Again, when A and B are predicable of all C, and when C reciprocates with B, then A must also be predicable of all B.49 We may remark that this recognition by Aristotle of a class of universal affirmative propositions in which predicate and subject reciprocate, contrived in order to force Induction into the syllogistic framework, is at variance with his general view both of reciprocating propositions and of Induction. He tells us (Analyt. Post. I. iii. p. 73, a. 18) that such reciprocating propositions are very rare, which would not be true if they are taken to represent every Induction; and he forbids us emphatically to annex the mark of universality to the predicate; which he has no right to do, if he calls upon us to reason on the predicate as distributed (Analyt. Prior. I. xxvii., p. 43, b. 17; De Interpret. p. 17, b. 14). It is probable that Aristotle here understood the object of ???? (as it is conceived through most part of the Symposion of Plato) to be a beautiful youth: (see Plato, Sympos. pp. 218-222; also Xenophon, Sympos. c. viii., Hiero, c. xi. 11, Memorab. I. ii. 29, 30). Yet this we must say — what the two women said when they informed SimÆtha of the faithlessness of Delphis (Theokrit. Id. ii. 149) —
Such is the relation of the terms of a syllogism in regard to reciprocation and antithesis. Let it next be understood that the canons hitherto laid down belong not merely to demonstrative and dialectic syllogisms, but to rhetorical and other syllogisms also; all of which must be constructed in one or other of the three figures. In fact, every case of belief on evidence, whatever be the method followed, must be tested by these same canons. We believe everything either through Syllogism or upon Induction.51 Waitz in his note (p. 532) says: “Fit Inductio, cum per minorem terminum demonstratur medium prÆdicari de majore.” This is an erroneous explanation. It should have been: “demonstratur majorem prÆdicari de medio.” Analyt. Prior. II. xxiii. 68, b. 32: ?a? t??p?? t??? ??t??e?ta? ? ?pa???? t? s??????s?· ? ?? ??? d?? t?? ?s?? t? ????? t? t??t? de????s??, ? d? d?? t?? t??t?? t? ????? t? ?s?. I have transcribed this Greek text as it stands in the editions of Buhle, Bekker, Waitz, and F. Didot. Yet, notwithstanding these high authorities, I venture to contend that it is not wholly correct; that the word a??????, which I have emphasized, is neither consistent with the context, nor suitable for the point which Aristotle is illustrating. Instead of a??????, we ought in that place to read ??????; and I have given the sense of the passage in my English text as if it did stand ?????? in that place. I proceed to justify this change. If we turn back to the edition by Julius Pacius (1584, p. 377), we find the text given as follows after the word ?????? (down to that word the text is the same): t? d? G ??? ?p???e? t? ?· p?? ??? t? G a??????· ???? ?a? t? ?, t? ? ???? ?????, pa?t? ?p???e? t? G. e? ??? ??t?st??fe? t? G t? ?, ?a? ? ?pe?te??e? t? ?s??, ?????? t? ? t? ? ?p???e??. Earlier than Pacius, the edition of Erasmus (Basil. 1550) has the same text in this chapter. Here it will be seen that in place of the words given in Waitz’s text, p?? ??? t? ?????? a??????, Pacius gives p?? ??? t? G a??????: annexing however to the letter G an asterisk referring to the margin, where we find the word ?????? inserted in small letters, seemingly as a various reading not approved by Pacius. And M. BarthÉlemy St. Hilaire has accommodated his French translation (p. 328) to the text of Pacius: “Donc A est À C tout entier, car tout C est longÈve.” Boethius in his Latin translation (p. 519) recognizes as his original p?? ??? t? ?????? a??????, but he alters the text in the words immediately preceding:— “Ergo toti B (instead of toti C) inest A, omne enim quod sine cholera est, longÆvum,” &c. (p. 519). The edition of Aldus (Venet. 1495) has the text conformable to the Latin of Boethius: t? d? ? ??? ?p???e? t? ?· p?? ??? t? ?????? a??????. Three distinct Latin translations of the 16th century are adapted to the same text, viz., that of Vives and Valentinus (Basil. 1542); that published by the Junta (Venet. 1552); and that of Cyriacus (Basil. 1563). Lastly, the two Greek editions of Sylburg (1587) and Casaubon (Lugduni 1590), have the same text also: t? d? ? ??? ?p???e? t? ?· p?? ??? [t? G] t? ?????? a??????. Casaubon prints in brackets the words [t? G] before t? ??????. Now it appears to me that the text of Bekker and Waitz (though Waitz gives it without any comment or explanation) is erroneous; neither consisting with itself, nor conforming to the general view enunciated by Aristotle of the Syllogism from Induction. I have cited two distinct versions, each different from this text, as given by the earliest editors; in both the confusion appears to have been felt, and an attempt made to avoid it, though not successfully. Aristotle’s view of the Syllogism from Induction is very clearly explained by M. BarthÉlemy St. Hilaire in the instructive notes of his translation, pp. 326-328; also in his Preface, p. lvii.:— “L'induction n’est au fond qu’un syllogisme dont le mineur et le moyen sont d’extension Égale. Du reste, il n’est qu’une seule maniÈre dont le moyen et le mineur puissent Être d’Égale extension; c’est que le mineur se compose de toutes les parties dont le moyen reprÉsente la totalitÉ. D’une part, tous les individus: de l’autre, l’espÈce totale qu’ils forment. L’intelligence fait aussitÔt Équation entre les deux termes Égaux.” According to the Aristotelian text, as given both by Pacius and the others, A, the major term, represents longÆvum (long-lived, the class-term or total); B, the middle term, represents vacans bile (bile-less, the class-term or total); C, the minor term, represents the aggregate individuals of the class longÆvum, man, horse, mule, &c. Julius Pacius draws out the Inductive Syllogism, thus:—
Convertible into a Syllogism in Barbara:—
Here the force of the proof (or the possibility, in this exceptional case, of converting a syllogism in the Third figure into another in Barbara of the First figure) depends upon the equation or co-extensiveness (not enunciated in the premisses, but assumed in addition to the premisses) of the minor term C with the middle term B. But I contend that this is not the condition peremptorily required, or sufficient for proof, if we suppose C the minor term to represent omne longÆvum. We must understand C the minor term to represent omne vacans bile, or quicquid vacat bile: and unless we understand this, the proof fails. In other words, homo, equus, asinus, &c. (the aggregate of individuals), must be co-extensive with the class-term bile-less or vacans bile: but they need not be co-extensive with the class-term long-lived or longÆvum. In the final conclusion, the subject vacans bile is distributed; but the predicate longÆvum is not distributed; this latter may include, besides all bile-less animals, any number of other animals, without impeachment of the syllogistic proof. Such being the case, I think that there is a mistake in the text as given by all the editors, from Pacius down to Bekker and Waitz. What they give, in setting out the terms of the Aristotelian Syllogism from Induction, is: ?st? t? ? a??????, t? d’ ?f’ ? ?, t? ????? ? ????, ?f’ ? d? G, t? ?a?’ ??ast?? a??????, ???? ?????p?? ?a? ?pp?? ?a? ??????. Instead of which the text ought to run, ?f’ ? d? G, t? ?a?’ ??ast?? ??????, ???? ????. ?. ?p. ?. ??. That these last words were the original text, is seen by the words immediately following: t? d? G ??? ?p???e? t? ?. p?? ??? t? ?????? a??????. For the reason thus assigned (in the particle ???) is irrelevant and unmeaning if G designates t? ?a?’ ??ast?? a??????, while it is pertinent and even indispensable if G designates t? ?a?’ ??ast?? ??????. Pacius (or those whose guidance he followed in his text) appears to have perceived the incongruity of the reason conveyed in the words p?? ??? t? ?????? a??????; for he gives, instead of these words, p?? ??? t? G a??????. In this version the reason is indeed no longer incongruous, but simply useless and unnecessary; for when we are told that A designates the class longÆvum, and that G designates the individual longÆva, we surely require no reason from without to satisfy us that A is predicable of all G. The text, as translated by Boethius and others, escapes that particular incongruity, though in another way, but it introduces a version inadmissible on other grounds. Instead of t? d? G ??? ?p???e? t? ?, p?? ??? t? ?????? a??????, Boethius has t? d? ? ??? ?p???e? t? ?, p?? ??? t? ?????? a??????. This cannot be accepted, because it enunciates the conclusion of the syllogism as if it were one of the premisses. We must remember that the conclusion of the Aristotelian Syllogism from Induction is, that A is predicable of B, one of the premisses to prove it being that A is predicable of the minor term C. But obviously we cannot admit as one of the premisses the proposition that A may be predicated of B, since this proposition would then be used as premiss to prove itself as conclusion. If we examine the Aristotelian Inductive Syllogism which is intended to conduct us to the final probandum, we shall see that the terms of it are incorrectly set out by Bekker and Waitz, when they give the minor term G as designating t? ?a?’ ??ast?? a??????. This last is not one of the three terms, nor has it any place in the syllogism. The three terms are:
There is no term in the syllogism corresponding to the individual longÆva or long-lived animals; this last (I repeat) has no place in the reasoning. We are noway concerned with the totality of long-lived animals; all that the syllogism undertakes to prove is, that in and among that totality all bile-less animals are included; whether there are or are not other long-lived animals besides the bile-less, the syllogism does not pretend to determine. The equation or co-extensiveness required (as described by M. BarthÉlemy St. Hilaire in his note) is not between the individual long-lived animals and the class, bile-less animals (middle term), but between the aggregate of individual animals known to be bile-less and the class, bile-less animals. The real minor term, therefore, is (not the individual long-lived animals, but) the individual bile-less animals. The two premisses of the Inductive Syllogism will stand thus:—
And, inasmuch as the subject of the minor proposition is co-extensive with the predicate (which, if quantified according to Hamilton’s phraseology, would be, All bile-less animals), so that the proposition admits of being converted simply, — the middle term will become the subject of the conclusion, All bileless animals are long-lived. Julius Pacius translates this: “Si igitur convertatur t? G cum B, nec medium excedat, necesse est t? ? t? ? inesse.” These Latin words include the same grammatical ambiguity as is found in the Greek original: medium, like t? ?s??, may be either an accusative case governed by excedat, or a nominative case preceding excedat. The same may be said of the other Latin translations, from Boethius downwards. But M. BarthÉlemy St. Hilaire in his French translation, and Sir W. Hamilton in his English translation (Lectures on Logic, Vol. II. iv. p. 358, Appendix), steer clear of this ambiguity. The former says: “Si donc C est rÉciproque À B, et qu’il ne dÉpasse pas le moyen, il est nÉcessaire alors que A soit À B:” to the same purpose, Hamilton, l. c. These words are quite plain and unequivocal. Yet I do not think that they convey the meaning of Aristotle. In my judgment, Aristotle meant to say: “If then C reciprocates with B, and if the middle term (B) does not stretch beyond (the minor C), it is necessary that A should be predicable of B.” To show that this must be the meaning, we have only to reflect on what C and B respectively designate. It is assumed that C designates the sum of individual bile-less animals; and that B designates the class or class-term bile-less, that is, the totality thereof. Now the sum of individuals included in the minor (C) cannot upon any supposition overpass the totality: but it may very possibly fall short of totality; or (to state the same thing in other words) the totality may possibly surpass the sum of individuals under survey, but it cannot possibly fall short thereof. B is here the limit, and may possibly stretch beyond C; but cannot stretch beyond B. Hence I contend that the translations, both by M. BarthÉlemy St. Hilaire and Sir W. Hamilton, take the wrong side in the grammatical alternative admissible under the words ?a? ? ?pe?te??e? t? ?s??. The only doubt that could possibly arise in the case was, whether the aggregate of individuals designated by the minor did, or did not, reach up to the totality designated by the middle term; or (changing the phrase) whether the totality designated by the middle term did, or did not, stretch beyond the aggregate of individuals designated by the minor. Aristotle terminates this doubt by the words: “And if the middle term does not stretch beyond (the minor).” Of course the middle term does not stretch beyond, when the terms reciprocate; but when they do not reciprocate, the middle term must be the more extensive of the two; it can never be the less extensive of the two, since the aggregate of individuals cannot possibly exceed totality, though it may fall short thereof. I have given in the text what I think the true meaning of Aristotle, departing from the translations of M. BarthÉlemy St. Hilaire and Sir W. Hamilton. From Induction he proceeds to Example. You here take in (besides the three terms, major, middle, and minor, of the Syllogism) a fourth term; that is, a new particular case analogous to the minor. Your purpose here is to show — not, as in the ordinary Syllogism, that the major term is predicable of the minor, but, as in the Inductive Syllogism — that the major term is predicable of the middle term; and you prove this conclusion, not (as in the Inductive Syllogism) through the minor term, but through the new case or fourth term analogous to the minor.57 Let A represent evil or mischievous; B, war against neighbours, generally; C, war of Athens against Thebes, an event to come and under deliberation; D, war of Thebes against Phokis, a past event of which the issue is known to have been signally mischievous. You assume as known, first, that A is predicable of D, i.e. that the war of Thebes against Phokis has been disastrous; next, that B is predicable both of C and of D, i.e. that each of the two wars, of Athens against Thebes, and of Thebes against Phokis, is a war of neighbours against neighbours, or a conterminous war. Now from the premiss that A is predicable of D, along with the premiss that B is predicable of D, you infer that A is predicable of the class B, or of conterminous wars generally; and hence you draw the farther inference, that A is also predicable of C, another particular case under the same class B. The inference here is, in the first instance, from part to whole; and finally, through that whole, from the one part to another part of the same whole. Induction includes in its major premiss all the particulars, declaring all of them to be severally subjects of the major as predicate; hence it infers as conclusion, that the major is also predicable of the middle or class-term comprising all these particulars, but comprising no others. Example includes not all, but only one or a few particulars; inferring from it or them, first, to the entire If we turn to ch. xxvii. p. 70, a. 30-34, we shall find Aristotle on a different occasion disallowing altogether this so-called Syllogism from Example. These chapters respecting Induction and Example are among the most obscure and perplexing in the Aristotelian Analytica. The attempt to throw both Induction and Example into the syllogistic form is alike complicated and unfortunate; moreover, the unsatisfactory reading and diversities in the text, among commentators and translators, show that the reasoning of Aristotle has hitherto been imperfectly apprehended.59 From some of his phrases, we see that he was aware of the essential antithesis between Induction and Syllogism; yet the syllogistic forms appear to have exercised such fascination over his mind, that he could not be satisfied without trying to find some abnormal form of Syllogism to represent and give validity to Induction. In explaining generally what the Syllogism is, and The Inductive Syllogism, as constructed by Aristotle, requires a reciprocating minor premiss. It may, indeed, be cited (as I have already remarked) in support of Hamilton’s favourite precept of quantifying the predicate. The predicate of this minor must be assumed as quantified in thought, the subject being taken as co-extensive therewith. Therefore Hamilton’s demand that it shall be quantified in speech has really in this case that foundation which he erroneously claims for it in all cases. He complains that Lambert and some other logicians dispense with the necessity of quantifying the predicate of the minor by making it disjunctive; and adds the remarkable statement that “the recent German logicians, Herbart, Twesten, Drobisch, &c., following Lambert, make the Inductive Syllogism a byeword” (p. 366). I agree with them in thinking the attempted transformation of Induction into Syllogism very unfortunate, though my reasons are probably not the same as theirs. Trendelenburg agrees with those who said that Aristotle’s doctrine about the Inductive Syllogism required that the minor should be disjunctively enunciated (Logische Untersuchungen, xiv. p. 175, xvi. pp. 262, 263; also ErlÄuterungen zu den Elementen der Aristotelischen Logik, ss. 34-36, p. 71). Ueberweg takes a similar view (System der Logik, sect. 128, p. 367, 3rd ed.). If the Inductive Inference is to be twisted into Syllogism, it seems more naturally to fall into an hypothetical syllogism, e. g.:—
The central idea of the Syllogism, as defined by Aristotle, is that of a conclusion following from given premisses by necessary sequence;60 meaning by the term necessary thus much and no more — that you cannot grant the premisses, and deny the conclusion, without being inconsistent with yourself, or falling into contradiction. In all the various combinations of propositions, set forth by Aristotle as the different figures and modes of Syllogism, this property of necessary sequence is found. But it is a property which no Induction can ever possess.61 When Aristotle professes to point out a particular mode of Syllogism to which Induction conforms, he can only do so by falsifying the process of Induction, and by not accurately distinguishing between what is observed and what is inferred. In the case which he takes to illustrate the Inductive Syllogism — the inference from all particular bile-less animals to the whole class bile-less — he assumes that we have ascertained the attribute to belong to all the particulars, and that the inductive inference consists in passing from all of them to the class-term; the passage from premisses to conclusion being here necessary, and thus falling under the definition of Syllogism; since, to grant the premisses, and yet to deny the conclusion, involves a contradiction. But this doctrine misconceives what the inductive inference really is. We never can observe all the particulars of a class, which is indefinite as to number of particulars, and definite only in respect of the attributes connoted by the class-term. We can only observe some Aristotle states very clearly:— “We believe everything either through Syllogism, or from Induction.”63 Here, as well as in several other passages, he notes the two processes as essentially distinct. The Syllogism requires in its premisses at least one general proposition; nor does Aristotle conceive the “generalities as the original data:”64 he derives them from antecedent Induction. The two processes are (as he says) opposite in a certain way; that is, they are complementary halves of the same whole; Induction being the establishment of those universals which are essential for the deductive march of the Syllogism; while the two together make up the entire process of scientific reasoning. But he forgets or relinquishes this antithesis, when he presents to us the Inductive process as a given variety of Syllogism. And the objection to such a doctrine becomes the more manifest, I will here add that, though Aldrich himself (as I stated at the beginning of this note) treats the argument from Induction as a defective or informal Syllogism, his anonymous Oxonian editor and commentator takes a sounder view. He says (pp. 176, 177, 184, ed. 1823. Oxon.):— “The principles acquired by human powers may be considered as twofold. Some are intuitive, and are commonly called Axioms; the other class of general principles are those acquired by Induction. But it may be doubted whether this distinction is correct. It is highly probable, if not certain, that those primary Axioms generally esteemed intuitive, are in fact acquired by an inductive process; although that process is less discernible, because it takes place long before we think of tracing the actings of our own minds. It is often found necessary to facilitate the understanding of those Axioms, when they are first proposed to the judgment, by illustrations drawn from individual cases. But whether it is, as is generally supposed, the mere enunciation of the principle, or the principle itself, which requires the illustration, may admit of a doubt. It seems probable, however that, such illustrations are nothing more than a recurrence to the original method by which the knowledge of those principles was acquired. Thus, the repeated trial or observation of the necessary connection between mathematical coincidence and equality, first authorizes the general position or Axiom relative to that subject. If this conjecture is founded in fact, it follows that both primary and ultimate principles have the same nature and are alike acquired by the exercise of the inductive faculty.” “Those who acquiesce in the preceding observations will feel a regret to find Induction classed among defective or informal Syllogisms. It is in fact prior in its order to Syllogism; nor can syllogistic reasoning he carried on to any extent without previous Induction” (p. 184). To us the particulars of sense stand first, and are the earliest objects of knowledge. To us, means to the large variety of individual minds, which grow up imperceptibly from the simple capacities of infancy to the mature accomplishments of adult years; each acquiring its own stock of sensible impressions, remembered, compared, associated; and each learning a language, which both embodies in general terms and propositions the received classification of objects, and communicates the current emotional beliefs. We all begin by being learners; and we ascend by different paths to those universal notions and beliefs which constitute the common fund of the advanced intellect; developed in some minds into principia of philosophy with their consequences. By nature, or absolutely, these principia are considered as prior, and as forming the point of departure: the advanced position is regarded as gained, and the march taken is not that of the novice, but that of the trained adult, who having already learnt much, is doubly equipped either for learning more or for teaching others; who thus stands on a summit Such is the antithesis between notiora natur (or simpliciter) and notiora nobis (or quoad nos), which Aristotle recognizes as a capital point in his philosophy, and insists upon in many of his writings. The antithesis is represented by Example and Induction, in the point of view — quoad nos — last mentioned; by Syllogism or Deduction, in the other point of view — naturÂ. Induction (he says),68 or the rising from particulars to universals, is plainer, more persuasive, more within the cognizance of sensible perception, more within the apprehension of mankind generally, than Syllogism; but Syllogism is more cogent and of greater efficacy against controversial opponents. What he affirms here about Induction is equally true about the inference from Example, that is, the inference from one or some particulars, to other analogous particulars; the rudimentary intellectual process, common to all human and to many animal minds, of which Induction is an improvement and an exaltation. While Induction will be more impressive, and will carry assent more easily with an ordinary uncultivated mind, an acute disputant may always deny the ultimate inference, for the denial The inductive interrogations of Sokrates relating to matters of common life, and the way in which they convinced ordinary hearers, are strikingly illustrated in the Memorabilia of Xenophon, especially IV. vi.: p??? ???sta ?? ??? ??da, ?te ?????, t??? ??????ta? ????????ta? pa?e??e? (15). The same can hardly be said of the Platonic dialogues. Both the two main points of Aristotle’s doctrine — the antithesis between Induction and Deduction, and the dependence of the latter process upon premisses furnished by the former, so that the two together form the two halves of complete ratiocination and authoritative proof — both these two are confused and darkened by his attempt to present the Inductive inference and the Analogical or Paradeigmatic inference as two special forms of Syllogistic deduction.70 But when we put aside this attempt, and adhere to Aristotle’s main doctrine — of Induction as a process antithetical to and separate from Deduction, yet as an essential preliminary thereto, — we see that it forms the basis of that complete and comprehensive System of Logic, recently elaborated in the work of Mr. John Stuart Mill. The inference from Example (i.e. from some particulars to other similar particulars) is distinguished by Aristotle from Induction, and is recognized by him as the primitive intellectual energy, common to all men, through which Induction is reached; its results he calls Experience (?pe???a), and he describes it as the real guide, more essential than philosophical generalities, to exactness of But though this restricted conception of Logic or the theory of Reasoning has arisen naturally from Aristotle’s treatment, I maintain that it does not adequately represent his view of that theory. In his numerous treatises on other subjects, scarcely any allusion is made to the Syllogism; nor is appeal made to the rules for it laid down in the Analytica. His conviction that the formalities of Deduction were only one part of the process of general reasoning, and that the value of the final conclusion depended not merely upon their being correctly performed, but also upon the correctness of that initial part whereby they are supplied with matter for premisses — is manifested as well by his industry (unrivalled among his contemporaries) in collecting multifarious facts, as by his specific declarations respecting Induction. Indeed, a recent most erudite logician, Sir William Hamilton, who insists upon the construction of Logic in its strictest sense as purely formal, blames Aristotle72 for having transgressed this boundary, and for introducing other considerations bearing on diversities of matter and of material evidence. The charge so made, to whatever extent it is well-founded, does rather partake of the nature of praise; inasmuch as it evinces Aristotle’s larger views of the theory of Inference, and confirms his own statement that the Deductive process was only the last half of it, presupposing a prior Induction. It is only this last half that Aristotle has here analysed, setting forth its formal conditions with precepts founded thereupon; while he claims to have accomplished the work by long and patient investigation, having found not the smallest foundation laid by others, and In objecting to A universally, you take a term comprehending the original subject; in objecting particularly, a term comprehended by it. Of the new term in each case you deny the original predicate, and have thus, as a major premiss, E. For a minor premiss, you affirm, in the first case, the new term as predicate of the original subject (less comprehensive); in the second case, the original subject (more comprehensive) as predicate of the new term. This gives you, in the first case, a conclusion in Celarent (Fig. I.), and, in the second, a conclusion in Felapton (Fig. III.); opposed, the one universally or contrarily, the other particularly or contradictorily, to the original proposition. The Enthymeme is a syllogism from Probabilities or Signs;77 the two being not exactly the same. Probabilities are propositions commonly accepted, and true in the greater number of cases; such as, Envious men hate those whom they envy, Persons who are beloved look with affection on those who love Aristotle throws in the remark (a. 24), that, when one premiss only of the Enthymeme is enunciated, it is a Sign; when the other is added, it becomes a Syllogism. In the examples given to illustrate the description of the Enthymeme, that which belongs to the First figure has its three terms and two propositions specified like a complete and regular Syllogism; but when we come to the Third and Second figures, Aristotle gives two alternate ways of stating each: one way in full, with both premisses enunciated, constituting a normal, though invalid, Syllogism; the other way, with only one of the premisses enunciated, the other being suppressed as well-known and familiar. Among logicians posterior to Aristotle, the definition given of the Enthymeme, and supposed to be derived from Aristotle was, that it was a Syllogism with one of the premisses suppressed — ?????at??. Sir W. Hamilton has impugned this doctrine, and has declared the definition to be both absurd in itself, and not countenanced by Aristotle. (Lectures on Logic, Vol. I. Lect. xx. p. 386, seq.) I think Hamilton is mistaken on this point. (See Mr. Cope’s Introd. to Arist. Rhetoric, p. 103, seq.) Even in the present chapter Aristotle distinctly alludes to the monolemmatic enunciation of the Enthymeme as one mode of distinguishing it from a full Syllogism; and in the Rhetorica he brings out this characteristic still more forcibly. The distinction is one which belongs to Rhetoric more than to Logic; the rhetor, in enunciating his premisses, must be careful not to weary his auditors; he must glance at or omit reasons that are familiar to them; logical fulness and accuracy would be inconsistent with his purpose. The writers subsequent to Aristotle, who think much of the rhetorical and little of the logical point of view, bring out the distinction yet more forcibly. But the rhetorical mode of stating premisses is often not so much an omission either of major or minor, as a confused blending or packing up of both into one. Aristotle concludes his Analytica Priora by applying this doctrine of Signs to determine the limits within which Physiognomy Here the treatise ends; but the reader will remember that, in describing the canons laid down by Aristotle for the Syllogism with its three Figures and the Modes contained therein, I confined myself to the simple Assertory syllogism, postponing for the moment the long expositions added by him about Modal syllogisms, involving the Possible and the Necessary. What is proper to be said about this complicated and useless portion of the Analytica Priora, may well come in here; for, in truth, The Possible or Problematical, however, in this latter complete sense — What may or may not be — exhibits various modifications or gradations. 1. The chances on either side may be conceived as perfectly equal, so that there is no probability, and we have no more reason for expecting one side of the alternative than the other; the sequence or conjunction is indeterminate. Aristotle construes this indeterminateness in many cases (not as subjective, or as depending upon our want of complete knowledge and calculating power, but) as objective, insuperable, and inherent in many phenomenal agencies; characterizing it, under the names of Spontaneity and Chance, as the essentially unpredictable. 2. The chances on both sides may be conceived as unequal and the ratio between them as varying infinitely: the usual and ordinary tendency of phenomena — what Aristotle calls Now, within the range of these limits lie what Aristotle describes as Signs and Probabilities; in fact, all the marks which we shall presently come to as distinguishing the dialectical syllogism from the demonstrative. But here is involved rather the matter of the Syllogism than its form. The form indeed is so far implicated, that (as Aristotle justly remarks at the end of the Analytica Priora84), the First figure is the only one that will prove both conjunctions and disjunctions, as well constant as occasional; the Third figure proves only occasional conjunctions and occasional disjunctions, not constant; the Second figure will prove no conjunctions at all, but only disjunctions, constant as well as occasional. Here a difference of form is properly pointed out as coupled with and founded on a difference of matter. But the special rules given by Aristotle, early in the present treatise, for the conversion of Modal Propositions, and the distinctions that he draws as to the modal character of the conclusion according as one or other of the premisses belongs to one or other of the different modes, — are both prolix and of little practical value.85 What he calls the Necessary might indeed, from the point of view now reached, cease to be recognized as a separate mode at all. The Certain and the Problematical are real modes of the Proposition; objective correlates to the subjective phases called Belief and Doubt. But no proposition can be more than certain: the word necessary, in strictness, implies only a peculiarity of the evidence on which our belief is grounded. Granting certain given premisses to be true, a given conclusion must be true also, if we would avoid inconsistency and contradiction. |
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