VI. ANALYTICA PRIORA II

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; it is not admissible as regards the minor term, which is itself particular.[3]

[Footnote 1: This is the remark of the ancient Scholiasts. See Schol. p. 188, a. 44, b. 11.]

[Footnote 2: Analyt. Prior. II. i. p. 53, a. 3-14.]

[Footnote 3: Analyt. Prior. II. i. p. 53, a. 14-35. M. Barthélemy St. Hilaire, following Pacius, justly remarks (note, p. 203 of his translation) that the rule as to particulars breaks down in the cases of Baroco, Disamis, and Bocardo.

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]

[Footnote 4: Analyt. Prior. II. ii. p. 53, b. 5-10: [Greek: e)x a)lêthô=n me\n ou)=n ou)k e)/sti pseu=dos sullogi/sasthai, e)k pseudô=n d' e)/stin a)lêthe/s, plê\n ou) dio/ti a)ll' o(/ti; tou= ga\r dio/ti ou)k e)/stin e)k pseudô=n sullogismo/s; di' ê(\n d' ai)ti/an, e)n toi=s e(pome/nois lechthê/setai.]

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.

[Footnote 5: Ibid. II. ii. p. 53, b. 11-16.]

In regard to the case here put forward as illustration, Aristotle has an observation which shows his anxiety to maintain the characteristic principles of the Syllogism; one of which principles he had declared to be--That nothing less than three terms and two propositions, could warrant the inferential step from premisses to conclusion. In the present case he assumed, If A exists, then B must exist; giving only one premiss as ground for the inference. This (he adds) does not contravene what has been laid down before; for A in the case before us represents two propositions conceived in conjunction.[6] Here he has given the type of hypothetical reasoning; not recognizing it as a variety per se, nor following it out into its different forms (as his successors did after him), but resolving it into the categorical syllogism.[7] He however conveys very clearly the cardinal principle of all hypothetical inference--That if the antecedent be true, the consequent must be true also, but not vice versâ; if the consequent be false, the antecedent must be false also, but not vice versâ.

[Footnote 6: Analyt. Prior. II. ii. p. 53, b. 16-25. [Greek: to\ ou)=n A ô(/sper e(\n kei=tai, du/o prota/seis sullêphthei=sai.]]

[Footnote 7: Aristotle, it should be remarked, uses the word [Greek: katêgoriko/s], not in the sense which it subsequently acquired, as the antithesis of [Greek: u(pothetiko/s] in application to the proposition and syllogism, but in the sense of affirmative as opposed to [Greek: sterêtiko/s].]

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.

[Footnote 8: Analyt. Prior. II. ii.-iv. p. 53, b. 26-p. 57, b. 17. At the close (p. 57, a. 36-b. 17), the general doctrine is summed up.]

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]

[Footnote 9: Ibid. II. v.-viii. p. 57, b. 18-p. 59, a. 35.]

Having thus shown under what conditions the conclusion can be employed for the demonstration of the premisses, Aristotle proceeds to state by what transformation it can be employed for the refutation of them. This he calls converting the syllogism; a most inconvenient use of the term convert ([Greek: a)ntistre/phein]), since he had already assigned to that same term more than one other meaning, distinct and different, in logical procedure.[10] What it here means is reversing the conclusion, so as to exchange it either for its contrary, or for its contradictory; then employing this reversed proposition as a new premiss, along with one of the previous premisses, so as to disprove the other of the previous premisses--i.e. to prove its contrary or contradictory. The result will here be different, according to the manner in which the conclusion is reversed; according as you exchange it for its contrary or its contradictory. Suppose that the syllogism demonstrated is: A belongs to all B, B belongs to all C; Ergo, A belongs to all C (Barbara). Now, if we reverse this conclusion by taking its contrary, A belongs to no C, and if we combine this as a new premiss with the major of the former syllogism, A belongs to all B, we shall obtain as a conclusion B belongs to no C; which is the contrary of the minor, in the form Camestres. If, on the other hand, we reverse the conclusion by taking its contradictory, A does not belong to all C, and combine this with the same major, we shall have as conclusion, B does not belong to all C; which is the contradictory of the minor, and in the form Baroco: though in the one case as in the other the minor is disproved. The major is contradictorily disproved, whether it be the contrary or the contradictory of the conclusion that is taken along with the minor to form the new syllogism; but still the form varies from Felapton to Bocardo. Aristotle shows farther how the same process applies to the other modes of the First, and to the modes of the Second and Third figures.[11] The new syllogism, obtained by this process of reversal, is always in a different figure from the syllogism reversed. Thus syllogisms in the First figure are reversed by the Second and Third; those in the second, by the First and Third; those in the Third, by the First and Second.[12]

[Footnote 10: Schol. (ad Analyt. Prior. p. 59, b. 1), p. 190, b. 20, Brandis. Compare the notes of M. Barthélemy St. Hilaire, pp. 55, 242.]

[Footnote 11: Analyt. Prior. II. viii.-x. p. 59, b. 1-p. 61, a. 4.]

[Footnote 12: Ibid. x. p. 61, a. 7-15.]

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 or contrary of the other premiss.[13] The Reductio ad Absurdum is distinguished from the other modes of reversal by these characteristics: (1) That it takes the contradictory, and not the contrary, of the conclusion; (2) That it is destined to meet the case where an opponent declines to admit the conclusion; whereas the other cases of reversion are only intended as confirmatory evidence towards a person who already admits the conclusion; (3) That it does not appeal to or require any concession on the part of the opponent; for if he declines to admit the conclusion, you presume, as a matter of course, that he must adhere to the contradictory of the conclusion; and you therefore take this contradictory for granted (without asking his concurrence) as one of the bases of a new syllogism; (4) That it presumes as follows:--When, by the contradictory of the conclusion joined with one of the premisses, you have demonstrated the opposite of the other premiss, the original conclusion itself is shown to be beyond all impeachment on the score of form, i.e. beyond impeachment by any one who admits the premisses. You assume to be true, for the occasion, the very proposition which you mean finally to prove false; your purpose in the new syllogism is, not to demonstrate the original conclusion, but to prove it to be true by demonstrating its contradictory to be false.[14]**

[Footnote 13: Analyt. Prior. II. xi. p. 61, a. 18, seq.]

[Footnote 14: Ibid. p. 62, a. 11: [Greek: phanero\n ou)=n o(/ti ou) to\ e)nanti/on, a)lla\ to\ a)ntikei/menon, u(pothete/on e)n a(/pasi toi=s sullogismoi=s. ou(/tô ga\r to\ a)nagkai=on e)/stai kai\ to\ a)xi/ôma e)/ndoxon. ei) ga\r kata\ panto\s ê)\ kata/phasis ê)\ a)po/phasis, deichthe/ntos o(/ti ou)ch ê( a)po/phasis, a)na/gkê tê\n kata/phasin a)lêtheu/esthai.] See Scholia, p. 190, b. 40, seq., Brand.]

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]

[Footnote 15: Ibid. p. 61, a. 35-p. 62, b. 10; xii. p. 62, a. 21. Alexander, ap. Schol. p. 191, a. 17-36, Brand.]

[Footnote 16: Ibid. xiv. p. 63, b. 12-21.]

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, the same predicate must be affirmed and denied of the same subject in one of the three different forms--All and None, All and Not All, Some and None. This shows why such conclusions cannot be obtained in the First figure; for it is the characteristic of that figure that the middle term must be predicate in one premiss, and subject in the other.[17] In dialectic discussion it will hardly be possible to get contrary or contradictory premisses conceded by the adversary immediately after each other, because he will be sure to perceive the contradiction: you must mask your purpose by asking the two questions not in immediate succession, but by introducing other questions between the two, or by other indirect means as suggested in the Topica.[18]

[Footnote 17: Analyt. Prior. II. xv. p. 63, b. 22-p. 64, a. 32. Aristotle here declares Subcontraries (as they were later called),--Some men are wise, Some men are not wise,--to be opposed only in expression or verbally ([Greek: kata\ tê\n le/xin mo/non]).]

[Footnote 18: Ibid. II. xv. p. 64, a. 33-37. See Topica, VIII. i. p. 155, a. 26; Julius Pacius, p. 372, note. In the Topica, Aristotle suggests modes of concealing the purpose of the questioner and driving the adversary to contradict himself: [Greek: e)n de\ tô=s Topikoi=s paradi/dôsi metho/dous tô=n kru/pseôn di' a(\s tou=to dothê/setai] (Schol. p. 192, a. 18, Br.). Compare also Analyt. Prior. II. xix. p. 66, a. 33.]

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]

[Footnote 19: Ibid. II. xvi. p. 64, b. 30-35: [Greek: kai\ ga\r ei) o(/lôs mê\ sullogi/zetai, kai\ ei) di' a)gnôstote/rôn ê)\ o(moi/ôs a)gnô/stôn, kai\ ei) dia\ tô=n u(ste/rôn to\ pro/teron; ê( ga\r a)po/deixis e)k pistote/rôn te kai\ prote/rôn e)stin.... ta\ me\n di' au(tô=n pe/phuke gnôri/zesthai, ta\ de\ di' a)/llôn.]]

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 by means of a principium. Thus, there is (let us suppose) a natural propriety that C shall be demonstrated through A; but you, overlooking this, demonstrate B through C, and A through B. By thus inverting the legitimate order, you do what is tantamount to demonstrating A through itself; for your demonstration will not hold unless you assume A at the beginning, in order to arrive at C. This is a mistake made not unfrequently, and especially by some who define parallel lines; for they give a definition which cannot be understood unless parallel lines be presupposed.[20]

[Footnote 20: Analyt. Prior. II. xvi. p. 64, b. 33-p. 65, a. 9. Petere principium is, in the phrase of Aristotle, not [Greek: tê\n a)rchê\n ai)tei=sthai], but [Greek: to\ e)n a)rchê=| ai)tei=sthai] or [Greek: to\ e)x a)rchê=s ai)tei=sthai] (xvi. p. 64, b. 28, 34).]

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] The essence of Petitio Principii consists in this, that you exhibit as true per se that which is not really true per se.[23] You may commit this fault either in Demonstration, when you assume for true what is not really true, or in Dialectic, when you assume as probable and conformable to authoritative opinion what is not really so.[24]**

[Footnote 21: Ibid. p. 65, a. 1-10.]

[Footnote 22: Ibid. p. 65, a. 10: [Greek: ei) ou)=n tis, a)dê/lou o)/ntos o(/ti to\ A u(pa/rchei tô=| G, o(moi/ôs de\ kai\ o(/ti tô=| B, ai)toi=to tô=| B u(pa/rchein to\ A, ou(/pô dê=lon ei) to\ e)n a)rchê=| ai)tei=tai, a)ll' o(/ti ou)k a)podei/knusi, dê=lon; ou) ga\r a)rchê\ a)podei/xeôs to\ o(moi/ôs a)/dêlon. ei) me/ntoi to\ B pro\s to\ G ou(/tôs e)/chei ô(/ste tau)to\n ei)=nai, ê)\ dê=lon o(/ti a)ntistre/phousin, ê)\ u(pa/rchei tha/teron thate/rô|, to\ e)n a)rchê=| ai)tei=tai. kai\ ga\r a)/n, o(/ti tô=| B to\ A u(pa/rchei, di' e)kei/nôn deiknu/oi, ei) a)ntistre/phoi. nu=n de\ tou=to kôlu/ei, a)ll' ou)ch o( tro/pos. ei) de\ tou=to poioi=, to\ ei)rême/non a)\n poioi= kai\ a)ntistre/phoi ô(s dia\ triô=n.]

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:--

All B is A. . All C is B. . . All C is A.

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 ([Greek: u(pa/rchei, e(/petai]). This however requires some limitation; for as the major is always predicated ([Greek: u(pa/rchei, e(/petai]) 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.]

[Footnote 23: Analyt. Prior. II. xvi. p. 65, a. 23-27: [Greek: to\ ga\r e)x a)rchê=s ti/ du/natai, ei)/rêtai ê(mi=n, o(/ti to\ di' au(tou= deiknu/nai to\ mê\ di' au(tou= dê=lon.--tou=to d' e)/sti, to\ mê\ deiknu/nai.]

The meaning of some lines in this chapter (p. 65, a. 17-18) is to me very obscure, after all the explanations of commentators.]

[Footnote 24: Ibid. p. 65, a. 35; Topic. VIII. xiii. p. 162, b. 31.]

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 misstatement of the real grounds on which a conclusion rests--Non per Hoc. You may impugn the thesis (set up by the respondent) directly, by proving syllogistically its contrary or contradictory; or you may also impugn it indirectly by Reductio ad Absurdum; i.e. you prove by syllogism some absurd conclusion, which you contend to be necessarily true, if the thesis is admitted. Suppose you impugn it in the first method, or directly, by a syllogism containing only two premisses and a conclusion: Non per Hoc is inapplicable here, for if either premiss is disallowed, the conclusion is unproved; the respondent cannot meet you except by questioning one or both of the premisses of your impugning syllogism.[25] But if you proceed by the second method or indirectly, Non per Hoc may become applicable; for there may then be more than two premisses, and he may, while granting that the absurd conclusion is correctly made out, contend that the truth or falsehood of his thesis is noway implicated in it. He declares (in Aristotle's phrase) that the absurdity or falsehood just made out does not follow as a consequence from his thesis, but from other premisses independent thereof; that it would stand equally proved, even though his thesis were withdrawn.[26] In establishing the falsehood or absurdity you must take care that it shall be one implicated with or dependent upon his thesis. It is this last condition that he (the respondent) affirms to be wanting.[27]

[Footnote 25: Analyt. Prior. II. xvii. p. 65, b. 4: [Greek: o(/tan a)naire/thê| ti deiktikôs dia\ tô=n A, B, G], &c.; xviii. 66, a. 17: [Greek: ê)\ ga\r e)k tô=n du/o prota/seôn ê)\ e)k pleio/nôn pa=s e)sti\ sullogismo/s; ei) me\n ou)=n e)k tô=n du/o, tou/tôn a)na/gkê tê\n me\n e(te/ran ê)\ kai\ a)mphote/ras ei)=nai pseudei=s;] &c. Whoever would understand this difficult chapter xvii., will do well to study it with the notes of Julius Pacius (p. 360), and also the valuable exposition of Mr. Poste, who has extracted and illustrated it in Appendix B. (p. 190) of the notes to his edition of the Sophistici Elenchi. The six illustrative diagrams given by Julius Pacius afford great help, though the two first of them appear to me incorrectly printed, as to the brackets connecting the different propositions.]

[Footnote 26: Ibid. II. xvii. p. 65, b. 38, b. 14, p. 66, a. 2, 7: [Greek: to\ mê\ para\ tou=to sumbai/nein to\ pseu=dos--tou= mê\ para\ tê\n the/sin ei)=nai to\ pseu=dos--ou) para\ tê\n the/sin sumbai/nei to\ pseu=dos--ou)k a)\n ei)/ê para\ tê\n the/sin.]

Instead of the preposition [Greek: para/], Aristotle on two occasions employs [Greek: dia/--ou(/tô ga\r e)/stai dia\ tê\n u(po/thesin]--p. 65, b. 33, p. 66, a. 3.

The preposition [Greek: para/], with acc. case, means on account of, owing to, &c. See Matthiæ and Kühner's Grammars, and the passage of Thucydides i. 141; [Greek: kai\ e(/kastos ou) para\ tê\n e(autou= a)me/leian oi)etai bla/psein, me/lein de/ tini kai\ a)/llô| u(pe\r e(autou= ti proi+dei=n], &c., which I transcribe partly on account of Dr. Arnold's note, who says about [Greek: para\] here:--"This is exactly expressed in vulgar English, all along of his own neglect, i. e. owing to his own neglect."]

[Footnote 27: Ibid. II. xvii. p. 65, b. 33: [Greek: dei= pro\s tou\s e)x a)rchê=s o(/rous suna/ptein to\ a)du/naton; ou(/tô ga\r e)/stai dia\ tê\n u(po/thesin.]]

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 took credit for success, when they had introduced and demonstrated some absurd conclusion that had little or no connection with the thesis.[28] But even when the absurd conclusion is connected with the thesis continuously, by a series of propositions each having a common term with the preceding, in either the ascending or the descending scale, we have here more than three propositions, and the absurd conclusion may perhaps be proved by the other premisses, without involving the thesis. In this case the respondent will meet you with Non per Hoc:[29] he will point out that his thesis is not one of the premisses requisite for demonstrating your conclusion, and is therefore not overthrown by the absurdity thereof. Perhaps the thesis may be false, but you have not shown it to be so, since it is not among the premisses necessary for proving your absurdum. An absurdum may sometimes admit of being demonstrated by several lines of premisses,[30] each involving distinct falsehood. Every false conclusion implies falsity in one or more syllogistic or prosyllogistic premisses that have preceded it, and is owing to or occasioned by this first falsehood.[31]

[Footnote 28: Analyt. Prior. II. xvii. p. 65, a. 38: [Greek: o(\ polla/kis e)n toi=s lo/gois ei)ô/thamen le/gein], &c. That the Reductio ad Absurdum was sometimes made to turn upon matters wholly irrelevant, we may see from the illustration cited by Aristotle, p. 65, b. 17.]

[Footnote 29: In this chapter of the Analytica, Aristotle designates the present fallacy by the title, Non per Hoc, [Greek: ou) para\ tou=to--ou) para\ tê\n the/sin sumbai/nei to\ pseu=dos]. He makes express reference to the Topica (i.e. to the fifth chapter of Sophist. Elenchi, which he regards as part of the Topica), where the same fallacy is designated by a different title, Non Causa pro Causâ, [Greek: to\ a)nai/tion ô(s ai)/tion tithe/nai]. We see plainly that this chapter of the Anal. Priora was composed later than the fifth chapter of Soph. El.; whether this is true of the two treatises as wholes is not so certain. I think it probable that the change of designation for the same fallacy was deliberately adopted. It is an improvement to dismiss the vague term Cause.]

[Footnote 30: Ibid. II. xvii. p. 66, a. 11: [Greek: e)pei\ tau)to/ ge pseu=dos sumbai/nein dia\ pleio/nôn u(pothe/seôn ou)de\n i)/sôs a)/topon, oi(=on ta\s parallê/lous sumpi/ptein], &c.]

[Footnote 31: Ibid. II. xviii. p. 66, a. 16-24: [Greek: o( de\ pseudê\s lo/gos gi/netai para\ to\ prô=ton pseu=dos], &c.]

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 of B; next, that D may be predicated of E; afterwards, that B may be predicated of C, &c. You will thus try to obtain all the concessions requisite for your final conclusion, before he perceives your drift. If you can carry your point by only one syllogism, and have only one middle term to get conceded, you will do well to put the middle term first in your questions. This is the best way to conceal your purpose from the respondent.[32]

[Footnote 32: Analyt. Prior. II. xix. p. 66, a. 33-b. 3: [Greek: chrê\ d' o(/per phila/ttesthai paragge/llomen a)pokrinome/nous, au)tou\s e)picheirou=ntas peira=sthai lantha/nein.--ka)\n di' e(no\s me/sou gi/nêtai o( sullogismo/s, a)po\ tou= me/sou a)/rchesthai; ma/lista ga\r a)\n ou(/tô la/nthanoi to\n a)pokrino/menon.] See the explanation of Pacius, p. 385. Since the middle term does not appear in the conclusion, the respondent is less likely to be prepared for the conclusion that you want to establish. To put the middle term first, in enunciating the Syllogism, is regarded by Aristotle as a perverted and embarrassing order, yet it is the received practice among modern logicians.]

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]

[Footnote 33: Analyt Prior. II. xix. p. 66, a. 25-32: [Greek: pro\s de\ to\ mê\ katasullogi/zesthai paratêrête/on, o(/tan a)/neu tô=n sumperasma/tôn e)rôta=| to\n lo/gon], &c.

Waitz (p. 520) explains [Greek: katasullogi/zesthai], "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.]

[Footnote 34: Ibid. II. xix. p. 66, a. 25-32.]

[Footnote 35: Ibid. xx. p. 66, b. 4-17. The reader will observe how completely this advice given by Aristotle is shaped for the purpose of obtaining victory in the argument and how he leaves out of consideration both the truth of what the opponent asks to be conceded, and the belief entertained by the defendant. This is exactly the procedure which he himself makes a ground of contemptuous reproach against the Sophists.]

We have already seen that error may arise by wrong enunciation or arrangement of the terms of a syllogism, that is, defects in its form; but sometimes also, even when the form is correct, error may arise from wrong belief as to the matters affirmed or denied.[36] Thus the same predicate may belong, immediately and essentially, alike to several distinct subjects; but you may believe (what is the truth) that it belongs to one of them, and you may at the same time believe (erroneously) that it does not belong to another. Suppose that A is predicable essentially both of B and C, and that A, B, and C, are all predicable essentially of D. You may know that A is predicable of all B, and that B is predicable of all D; but you may at the same time believe (erroneously) that A is not predicable of any C, and that C is predicable of all D. Under this state of knowledge and belief, you may construct two valid syllogisms; the first (in Barbara, with B for its middle term) proving that A belongs to all D; the second (in Celarent, with C for its middle term) proving that A belongs to no D. The case will be the same, even if all the terms taken belong to the same ascending or descending logical series. Here, then, you know one proposition; yet you believe the proposition contrary to it.[37] How can such a mental condition be explained? It would, indeed, be an impossibility, if the middle term of the two syllogisms were the same, and if the premisses of the one syllogism thus contradicted directly and in terms, the premisses of the other: should that happen, you cannot know one side of the alternative and believe the other. But if the middle term be different, so that the contradiction between the premisses of the one syllogism and those of the other, is not direct, there is no impossibility. Thus, you know that A is predicable of all B, and B of all D; while you believe at the same time that A is predicable of no C, and C of all D; the middle term being in one syllogism B, in the other, C.[38] This last form of error is analogous to what often occurs in respect to our knowledge of particulars. You know that A belongs to all B, and B to all C; you know, therefore, that A belongs to all C. Yet you may perhaps be ignorant of the existence of C. Suppose A to denote equal to two right angles; B, to be the triangle generally; C, a particular visible triangle. You know A B the universal proposition; yet you may at the same time believe that C does not exist; and thus it may happen that you know, and do not know, the same thing at the same time. For, in truth, the knowledge, that every triangle has its three angles equal to two right angles, is not (as a mental fact) simple and absolute, but has two distinct aspects; one as concerns the universal, the other as concerns the several particulars. Now, assuming the case above imagined, you possess the knowledge in the first of these two aspects, but not in the second; so that the apparent contrariety between knowledge and no knowledge is not real.[39] And in this sense the doctrine of Plato in the Menon is partially true--that learning is reminiscence. We can never know beforehand particular cases per se; but in proportion as we extend our induction to each case **successively, we, as it were, recognize that, which we knew beforehand as a general truth, to be realized in each. Thus when we ascertain the given figure before us to be a triangle, we know immediately that its three angles are equal to two right angles.[40]

[Footnote 36: Analyt. Prior. II. xxi. p. 66, b. 18: [Greek: sumbai/nei d' e)ni/ote, katha/per e)n tê=| the/sei tô=n o(/rôn a)patô/metha, kai\ kata\ tê\n u(po/lêpsin gi/nesthai tê\n a)pa/tên.]

The vague and general way in which Aristotle uses the term [Greek: u(po/lêpsis], seems to be best rendered by our word belief. See Trendelenburg ad Aristot. De Animâ, p. 469; Biese, Philos. des Aristot. i. p. 211.]

[Footnote 37: Ibid. II. xxi. p. 66, b. 33: [Greek: ô(/ste o(/ pôs e)pi/statai, tou=to o(/lôs a)xioi= mê\ u(polamba/nein; o(/per a)du/naton.]]

[Footnote 38: Ibid. II. xxi. p. 67, a. 5-8.]

[Footnote 39: Analyt. Prior. II. xxi. p. 67, a. 19: [Greek: ou(/tô me\n ou)=n ô(s tê=| katho/lou ou)=de to G o(/ti du/o o)rthai/, ô(s de\ tê=| kath' e(/kaston ou)k oi)=den, ô(/st' ou)ch e(/xei ta\s e)nanti/as] (sc. [Greek: e)pistê/mos]).]

[Footnote 40: Ibid. a. 22: [Greek: ou)damou= ga\r sumbai/nei proepi/stasthai to\ kath' e(/kaston, a)ll' a(/ma tê=| e)pagôgê=| lamba/nein tê\n tô=n kata\ me/ros e)pistê/mên ô(/sper a)nagnôri/zontas], &c. Cf. Anal. Post. I. ii. p. 71, b. 9, seq.; Plato, Menon, pp. 81-82.]

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 cognition; we only know it, partly from the remembrance of past special inspection, partly from the universal under which it falls.[42] We may know in one, or other, or all, of these three distinct ways: either by the universal; or specially (as remembered): or by combination of both--actual and present cognition, that is, by the application of a foreknown generality to a case submitted to our senses. And as we may know in each of these three ways, so we may also err or be deceived in each of the same three ways.[43] It is therefore quite possible that we may know, and that we may err or be deceived about the same thing, and that, too, without any contrariety. This is what happens when we know both the two premisses of the syllogism, but have never reflected on them before, nor brought them into conjunction in our minds. When we believe that the mule before us is in foal, we are destitute of the actual knowledge; yet our erroneous belief is not for that reason contrary to knowledge; for an erroneous belief, contrary to the universal proposition, must be represented by a counter-syllogism.[44]

[Footnote 41: Ibid. II. xxi. p. 67, a. 36: [Greek: ou) ga\r e)pi/statai o(/ti to\ A tô=| G, mê\ suntheôrô=n to\ kath' e(ka/teron.]]

[Footnote 42: Analyt. Prior. II. xxi. p. 67, a. 39: [Greek: ou)de\n ga\r tô=n ai)sthêtô=n e)/xô tê=s ai)sthê/seôs geno/menon i)/smen, ou)/d' a)\n ê)|sthême/noi tugcha/nômen, ei) mê\ ô(s tô=| katho/lou kai\ tô=| e)/chein tê\n oi)kei/an e)pistê/mên, a)ll' ou)ch ô(s tô=| e)nergei=n.]

Complete cognition ([Greek: to\ e)nergei=n], 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, [Greek: tou= o)/ntos ê(=| o)/n]), knows in a certain way all scibilia. Metaphys. A., p. 982, a. 21: [Greek: tou/tôn de\ to\ me\n pa/nta e)pi/stasthai tô=| ma/lista e)/chonti tê\n katho/lou e)pistê/mên a)nagkai=on u(pa/rchein; ou(/tos ga\r oi)=de/ pôs pa/nta ta\ u(pokei/mena.] Ib. a. 8: [Greek: u(polamba/nomen dê\ prô=ton me\n e)pi/stasthai pa/nta to\n sopho\n ô(s e)nde/chetai, mê\ kath' e(/kaston e)/chonta e)pistê/mên au)tô=n.] 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."]

[Footnote 43: Analyt. Prior. II. xxi. p. 67, b. 3: [Greek: to\ ga\r e)pi/stasthai le/getai trichô=s, ê)\ ô(s tê=| katho/lou, ê)\ ô(s tê=| oi)kei/a|, ê)\ ô(s tô=| e)nergei=n; ô(/ste kai\ to\ ê)patê=sthai tosautachô=s.]]

[Footnote 44: Ibid. b. 5: [Greek: ou)de\n ou)=n kôlu/ei kai\ ei)de/nai kai\ ê)patê=sthai peri\ au)to/, plê\n ou)k e)nanti/ôs. o(/per sumbai/nei kai\ tô=| kath' e(kate/ran ei)do/ti tê\n pro/tasin kai\ mê\ e)peskemme/nô| pro/teron. u(polamba/nôn ga\r ku/ein tê\n ê(mi/onon ou)k e)/chei tê\n kata\ to\ e)nergei=n e)pistê/mên, ou)d' au)= dia\ tê\n u(po/lêpsin e)nanti/an a)pa/tên tê=| e)pistê/mê|; sullogismo\s ga\r ê( e)nanti/a a)pa/tê tê=| katho/lou.] About erroneous belief, where a man believes the contrary of a true conclusion, adopting a counter-syllogism, compare Analyt. Post. I. xvi. p. 79, b. 23: [Greek: a)/gnoia kata\ dia/thesin].]

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 case). In various ways this last is possible; but this we reserve for fuller examination.[45]

[Footnote 45: Analyt. Prior. II. xxi. p. 67, b. 23: [Greek: a)ll' i)/sôs e)kei=no pseu=dos, to\ u(polabei=n tina\ kakô=| ei)=nai to\ a)gathô=| ei)=nai, ei) mê\ kata\ sumbebêko/s; pollachô=s ga\r e)gchôrei= tou=th' u(polamba/nein. e)piskepte/on de\ tou=to be/ltion.] This distinction is illustrated by what we read in Plato, Republic, v. pp. 478-479. The impossibility of believing that one contrary is identical with its contrary, is maintained by Sokrates in Plato, Theætetus, p. 190, B-D, as a part of the long discussion respecting [Greek: pseudê\s do/xa]: either there is no such thing as [Greek: pseudê\s do/xa], or a man may know, and not know, the same thing, ibid. p. 196 C. Aristotle has here tried to show in what sense this last-mentioned case is possible.]

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]

[Footnote 46: Ibid. II. xxii. p. 67, b. 27, seq. In this chapter Aristotle introduces us to affirmative universal propositions convertible simpliciter; that is, in which the predicate must be understood to be distributed as well as the subject. Here, then, the quantity of the predicate is determined in thought. This is (as Julius Pacius remarks, p. 371) in order to lay down principles for the resolution of Induction into Syllogism, which is to be explained in the next chapter. In these peculiar propositions, the reason urged by Sir W. Hamilton for his favourite precept of verbally indicating the quantity of the predicate, is well founded as a fact: though he says that in all propositions the quantity of the predicate is understood in thought, which I hold to be incorrect.

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).]

[Footnote 47: Ibid. II. xxii. p. 68, a. 2-15.]

[Footnote 48: Ibid. a. 16-21. [Greek: plê\n au)tou= tou= A]. Waitz explains these words in his note (p. 531): yet I do not clearly make them out; and Alexander of Aphrodisias declared them to assert what was erroneous ([Greek: e)spha/lthai le/gei], Schol. p. 194, a. 40, Brandis).]

[Footnote 49: Ibid. II. xxii. p. 68, a. 21-25.]

Lastly, suppose two pairs of opposites, A and B, C and D; let A be more eligible than B, and D more eligible than C. Then, if A C is more eligible than B D, A will also be more eligible than D. For A is as much worthy of pursuit as B is worthy of avoidance, they being two opposites; the like also respecting C and D. If then A and D are equally worthy of pursuit, B and C are equally worthy of avoidance; for each is equal to each. Accordingly the two together, A C, will be equal to the two together, B D. But this would be contrary to the supposition; since we assumed A to be more eligible than B, and D to be more eligible than C. It will be seen that on this supposition A is more worthy of pursuit than D, and that C is less worthy of avoidance than B; the greater good and the lesser evil being more eligible than the lesser good and the greater evil. Now apply this to a particular case of a lover, so far forth as lover. Let A represent his possession of those qualities which inspire reciprocity of love towards him in the person beloved; B, the absence of those qualities; D, the attainment of actual sexual enjoyment; C, the non-attainment thereof. In this state of circumstances, it is evident that A is more eligible or worthy of preference than D. The being loved is a greater object of desire to the lover qua lover than sexual gratification; it is the real end or purpose to which love aspires; and sexual gratification is either not at all the purpose, or at best only subordinate and accessory. The like is the case with our other appetites and pursuits.[50]

[Footnote 50: Analyt. Prior. II. xxii. p. 68, a. 25-b. 17. Aristotle may be right in the conclusion which he here emphatically asserts; but I am surprised that he should consider it to be proved by the reasoning that precedes.

It is probable that Aristotle here understood the object of [Greek: e)/rôs] (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)--[Greek: Kê)=|pe/ moi a)/lla te polla/, kai\ ô(s a)/ra De/lphis e)/ratai; Kê)/|te min au)=te gunaiko\s e)/chei po/thos, ei)/te kai\ a)ndro/s, Ou)k e)/phat' a)treke\s i)/dmen.]]

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]

[Footnote 51: Ibid. II. xxiii. p. 68, b. 13: [Greek: a(/panta ga\r pisteu/omen ê)\ dia\ sullogismou= ê)\ e)x e)pagôgê=s.]]

Though Aristotle might seem, even here, to have emphatically contrasted Syllogism with Induction as a ground of belief, he proceeds forthwith to indicate a peculiar form of Syllogism which may be constructed out of Induction. Induction, and the Syllogism from or out of Induction (he says) is a process in which we invert the order of the terms. Instead of concluding from the major through the middle to the minor (i.e. concluding that the major is predicable of the minor), we now begin from the minor and conclude from thence through the middle to the major (i.e. we conclude that the major is predicable of the middle).[52] In Syllogism as hitherto described, we concluded that A the major was predicable of C the minor, through the middle B; in the Syllogism from Induction we begin by affirming that A the major is predicable of C the minor; next, we affirm that B the middle is also predicable of C the minor. The two premisses, standing thus, correspond to the Third figure of the Syllogism (as explained in the preceding pages) and would not therefore by themselves justify anything more than a particular affirmative conclusion. But we reinforce them by introducing an extraneous assumption:--That the minor C is co-extensive with the middle B, and comprises the entire aggregate of individuals of which B is the universal or class-term. By reason of this assumption the minor proposition becomes convertible simply, and we are enabled to infer (according to the last preceding chapter) an universal affirmative conclusion, that the major term A is predicable of the middle term B. Thus, let A (the major term) mean the class-term, long-lived; let B (the middle term) mean the class-term, bile-less, or the having no bile; let C (the minor term) mean the individual animals--man, horse, mule, &c., coming under the class-term B, bile-less.[53] We are supposed to know, or to have ascertained, that A may be predicated of all C; (i.e. that all men, horses, mules, &c., are long-lived); we farther know that B is predicable of all C (i.e. that men, horses, mules, &c., belong to the class bile-less). Here, then, we have two premisses in the Third syllogistic figure, which in themselves would warrant us in drawing the particular affirmative conclusion, that A is predicable of some B, but no more. Accordingly, Aristotle directs us to supplement these premisses[54] by the extraneous assumption or postulate, that C the minor comprises all the individual animals that are bile-less, or all those that correspond to the class-term B; in other words, the assumption, that B the middle does not denote any more individuals than those which are covered by C the minor--that B the middle does not stretch beyond or overpass C the minor.[55] Having the two premisses, and this postulate besides, we acquire the right to conclude that A is predicable of all B. But we could not draw that conclusion from the premisses alone, or without the postulate which declares B and C to be co-extensive. The conclusion, then, becomes a particular exemplification of the general doctrine laid down in the last chapter, respecting the reciprocation of extremes and the consequences thereof. We thus see that this very peculiar Syllogism from Induction is (as indeed Aristotle himself remarks) the opposite or antithesis of a genuine Syllogism. It has no proper middle term; the conclusion in which it results is the first or major proposition, the characteristic feature of which it is to be immediate, or not to be demonstrated through a middle term. Aristotle adds that the genuine Syllogism, which demonstrates through a middle term, is by nature prior and more effective as to cognition; but that the Syllogism from Induction is to us plainer and clearer.[56]

[Footnote 52: Analyt. Prior. II. xxiii. p. 68, b. 15: [Greek: e)pagôgê\ me\n ou)=n e)sti\ kai\ o( e)x e)pagôgê=s sullogismo\s to\ dia\ tou= e(te/rou tha/teron a)/kron tô=| me/sô| sullogi/sasthai; oi(=on ei) tô=n AG me/son to\ B, dia\ tou= G dei=xai to\ A tô=| B u(pa/rchon; ou(/tô ga\r poiou/metha ta\s e)pagôga/s.]

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: [Greek: kai\ tro/pon tina\ a)ntikei=tai ê( e)pagôgê\ tô=| sullogismô=|; o( me\n ga\r dia\ tou= me/sou to\ a)/kron tô=| tri/tô| dei/knusin, ê( de\ dia\ tou= tri/tou to\ a)/kron tô=| me/sô|.]]

[Footnote 53: Ibid. II. xxiii. p. 68, b. 18: [Greek: oi(=on e)/stô to\ A makro/bion, to\ d' e)ph' ô(=| B, to\ cholê\n mê\ e)/chon, e)ph' ô(=| de\ G, to\ kath' e(/kaston makro/bion, oi(=on a)/nthrôpos kai\ i(/ppos kai\ ê(mi/onos. tô=| dê\ G o(/lô| u(pa/rchei to\ A; pa=n ga\r to\ a)/cholon makro/bion; a)lla\ kai\ to\ B, to\ mê\ e)/chein cholê/n, panti\ u(pa/rchei tô=| G. ei) ou)=n a)ntistre/phei to\ G tô=| B kai\ mê\ u(pertei/nei to\ me/son, a)na/gkê to\ A tô=| B u(pa/rchein.]

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 [Greek: makro/bion], which I have emphasized, is neither consistent with the context, nor suitable for the point which Aristotle is illustrating. Instead of [Greek: makro/bion], we ought in that place to read [Greek: a)/cholon]; and I have given the sense of the passage in my English text as if it did stand [Greek: a)/cholon] 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 [Greek: ê(mi/onos] (down to that word the text is the same): [Greek: tô=| dê\ G o(/lô| u(pa/rchei to\ A; pa=n ga\r to\ G makro/bion; a)lla\ kai\ to\ B, to\ mê\ e)/chon cholê/n, panti\ u(pa/rchei tô=| G. ei) ou)=n a)ntistre/phei to\ G tô=| B, kai\ mê\ u(pertei/nei to\ me/son, a)na/gkê to\ A tô=| B u(pa/rchein.] 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, [Greek: pa=n ga\r to\ a)/cholon makro/bion], Pacius gives [Greek: pa=n ga\r to\ G makro/bion]: annexing however to the letter [Greek: G] an asterisk referring to the margin, where we find the word [Greek: a)/cholon] 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 [Greek: pa=n ga\r to\ a)/cholon makro/bion], 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: [Greek: tô=| dê\ B o(/lô| u(pa/rchei to\ A; pa=n ga\r to\ a)/cholon makro/bion]. 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: [Greek: tô=| dê\ B o(/lô| u(pa/rchei to\ A; pa=n ga\r [to\ G] to\ a)/cholon makro/bion]. Casaubon prints in brackets the words [Greek: [to\ G]] before [Greek: to\ a)/cholon].

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:--

1. Omnis homo, equus, asinus, &c., est longævus. 2. Omnis homo, equus, asinus, &c., vacat bile. Ergo: 3. Quicquid vacat bile, est longævum.

Convertible into a Syllogism in Barbara:--

1. Omnis homo, equus, asinus, &c., est longævus. 2. Quicquid vacat bile, est homo, equus, asinus, &c. Ergo: 3. Quicquid vacat bile, est longævum.

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: [Greek: e)/stô to\ A makro/bion, to\ d' e)ph' ô(=| B, to\ cholên mê\ e)/chon, e)ph' ô(=| de\ G, to\ kath' e(/kaston makro/bion, oi(=on a)/nthrôpos kai\ i(/ppos kai\ ê(mi/onos.] Instead of which the text ought to run, [Greek: e)ph' ô(=| de\ G, to\ kath' e(/kaston a)/cholon, oi(=on a)/nthr. k. i(/p. k. ê(mi/]. That these last words were the original text, is seen by the words immediately following: [Greek: tô=| dê\ G o(/lô| u(pa/rchei to\ A. pa=n ga\r to\ a)/cholon makro/bion]. For the reason thus assigned (in the particle [Greek: ga/r]) is irrelevant and unmeaning if [Greek: G] designates [Greek: to\ kath' e(/kaston makro/bion ], while it is pertinent and even indispensable if [Greek: G] designates [Greek: to\ kath' e(/kaston a)/cholon]. Pacius (or those whose guidance he followed in his text) appears to have perceived the incongruity of the reason conveyed in the words [Greek: pa=n ga\r to\ a)/cholon makro/bion]; for he gives, instead of these words, [Greek: pa=n ga\r to\ G makro/bion]. 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 [Greek: G] designates the individual longæva, we surely require no reason from without to satisfy us that A is predicable of all [Greek: 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 [Greek: tô=| dê\ G o(/lô| u(pa/rchei to\ A, pa=n ga\r to\ a)/cholon makro/bion], Boethius has [Greek: tô=| dê\ B o(/lô| u(pa/rchei to\ A, pa=n ga\r to\ a)/cholon makro/bion]. 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 [Greek: G] as designating [Greek: to\ kath' e(/kaston makro/bion]. This last is not one of the three terms, nor has it any place in the syllogism. The three terms are:

1. A--major--the class-term or class [Greek: makro/bion]--longævum. 2. B--middle--the class term or class [Greek: a)/cholon]--bile-less. 3. C--minor--the individual bile-less animals, man, horse, &c.

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:--

Men, Horses, Mules, &c., are long-lived (major). Men, Horses, Mules, &c., are bile-less (minor).

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.]

[Footnote 54: Analyt. Prior. II. xxiii. p. 68, b. 27: [Greek: dei= de\ noei=n to\ G to\ e)x a(pa/ntôn tô=n kath' e(/kaston sugkei/menon; ê( ga\r e)pagôgê\ dia\ pa/ntôn.]]

[Footnote 55: Analyt. Prior. II. **xxiii. p. 68, p. 23: [Greek: ei) ou)=n a)ntistre/phei to\ G tô=| B, kai\ mê\ u(pertei/nei to\ me/son, a)na/gkê to\ A tô=| B u(pa/rchein.]

Julius Pacius translates this: "Si igitur convertatur [Greek: to\ G] cum B, nec medium excedat, necesse est [Greek: to\ A tô=| B] inesse." These Latin words include the same grammatical ambiguity as is found in the Greek original: medium, like [Greek: to\ me/son], 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 [Greek: kai\ mê\ u(pertei/nei to\ me/son]. 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.]

[Footnote 56: Analyt. Prior. II. xxiii. p. 68, b. 30-38: [Greek: e)/sti d' o( toiou=tos sullogismo\s tê=s prô/tês kai\ a)me/sou prota/seôs; ô(=n me\n ga/r e)sti me/son, dia\ tou= me/sou o( sullogismo/s, ô(=n de\ mê/ e)sti, di' e)pagôgê=s.--phu/sei me\n ou)=n pro/teros kai\ gnôrimô/teros o( dia\ tou= me/sou sullogismo/s, ê(mi=n d' e)narge/steros o( dia\ tê=s e)pagôgê=s.]]

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 class, next, to some new analogous particular belonging to the class.[58]

[Footnote 58: Analyt. Prior. II. xxiv. p. 69, a. 1-19**. Julius Pacius (p. 400) notes the unauthorized character of this so-called Paradeigmatic Syllogism, contradicting the rules of the figures laid down by Aristotle, and also the confused manner in which the scope of it is described: first, to infer from a single example to the universal; next, to infer from a single example through the universal to another parallel case. To which we may add the confused description in p. 69, a. 17, 18, where [Greek: to\ a)/kron] in the first of the two lines signifies the major extreme--in the second of the two the minor extreme. See Waitz's note, p. 533.

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 what Induction is, he informs us that the Syllogism presupposes and rests upon the process of Induction as its postulate. For there can be no valid Syllogism without an universal proposition in one (at least) of the premisses; and he declares, unequivocally, that universal propositions are obtained only through Induction. How Induction operates through the particular facts of sense, remembered, compared, and coalescing into clusters held together by associating similarity, he has also told us; it is thus that Experience, with its universal notions and conjunctions, is obtained. But this important process is radically distinct from that of syllogizing, though it furnishes the basis upon which all syllogizing is built.

[Footnote 59: Sir W. Hamilton (Lectures on Logic, vol. i. p. 319) says justly, that Aristotle has been very brief and unexplicit in his treatment of Induction. Yet the objections that Hamilton makes to Aristotle are very different from those which I should make. In the learned and valuable Appendix to his Lectures (vol. iv. pp. 358-369), he collects various interesting criticisms of logicians respecting Induction as handled by Aristotle. Ramus (in his Scholæ Dialecticæ, VIII. xi.) says very truly:--"Quid vero sit Inductio, perobscure ab Aristotele declaratur; nec ab interpretibus intelligitur, quo modo syllogismus per medium concludat majus extremum de minore; inductio, majus de medio per minus."

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.:--

If this, that, and the other magnet attract iron, all magnets attract iron; But this, that, and the other magnet do attract iron: Ergo, &c.]

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 of the particulars, a greater or smaller proportion. Now it is in the transition from these to the totality of particulars, that the real inductive inference consists; not in the transition from the totality to the class-term which denotes that totality and connotes its determining common attribute. In fact, the distinction between the totality of particulars and the meaning of the class-term, is one not commonly attended to; though it is worthy of note in an analysis of the intellectual process, and is therefore brought to view by Aristotle. But he employs it incorrectly as an intermediate step to slur over the radical distinction between Induction and Syllogism. He subjoins:[62]--"You must conceive the minor term C (in the Inductive Syllogism) as composed of all the particulars; for Induction is through all of them." You may say that Induction is through all the particulars, if you distinguish this totality from the class-term, and if you treat the class-term as the ultimate terminus ad quem. But the Induction must first travel to all the particulars; being forced to take start from a part only, and then to jump onward far enough to cover the indefinite unobserved remainder. This jump is the real Induction; and this can never be brought under the definition of Syllogism; for in the best and most certain Induction the sequence is never a necessary one: you may grant the premisses and deny the conclusion without contradicting yourself.

[Footnote 60: Alexander intimates that Aristotle enunciated "necessary sequence" as a part of his definition of Syllogism, for the express purpose of distinguishing it from Induction, which is a sequence not necessary (Schol. ad Top. p. 253, a. 19, Br.): [Greek: to\ d' e)x a)na/gkês proskei/menon e)n tô=| o(/rô|, tê=s **e)pagôgê=s chôri/zei to\n sullogismo/n; **e)/sti me\n ga\r kai\ e)pagôgê\ lo/gos e)n ô(=| tethe/ntôn tinô=n e(/tero/n ti tô=n keime/nôn sumbai/nei, a)ll' ou)k e)x a)na/gkês.]]

[Footnote 61: Alexander (in his Scholia on the Metaphysica, E. i. p. 406**, ed. Bonitz) observes truly: [Greek: a)ll' ei) e)k tê=s ai)sthê/seôs kai\ tê=s e)pagôgê=s pi/stis, ou)k e)/stin a)po/deixis, pro\s pa=san ga\r e)pagôgê\n du/natai/ tis e)ni/stasthai kai\ mê\ e)a=|n to\ katho/lou sumperai/nein.]]

[Footnote 62: Analyt. Prior. II. xxiii. p. 68, b. 27: [Greek: dei= de\ noei=n to\ G to\ e)x a(pa/ntôn tô=n kath' e(/kaston sugkei/menon; ê( ga\r e)pagôgê\ dia\ pa/ntôn.] See Professor Bain's 'Inductive Logic,' chap. i. s. 2, where this process is properly criticised.]

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, since in constructing his Inductive Syllogism, he is compelled to admit either that there is no middle term, or that the middle term is subject of the conclusion, in violation of the syllogistic canons.[65]

[Footnote 63: Ibid. II. xxiii. p. 68, b. 13: [Greek: a(/panta ga\r pisteu/omen ê)\ dia\ sullogismou= ê)\ e)x e)pagôgê=s]. Here Induction includes Example, though in the next stage he puts the two apart. Compare Anal. Poster. I. i. p. 71, a. 9.]

[Footnote 64: See Mr. John Stuart Mill's System of Logic, Bk. II. ch. iii. a. 4, p. 219, 5th ed.]

[Footnote 65: Aldrich (Artis Log. Rudim. ch. iii. 9, 2, p. 175) and Archbishop Whately (Elem. of Logic, ch. i. p. 209) agree in treating the argument of Induction as a defective or informal Syllogism: see also to the same purpose Sir.** W. Hamilton, Lectures on Logic, vol. i. p. 322. Aldrich treats it as a Syllogism in Barbara, with the minor suppressed; but Whately rejects this, because the minor necessary to be supplied is false. He maintains that the premiss suppressed is the major, not the minor. I dissent from both. It appears to me that the opinion which Whately pronounces to be a fallacy is the real truth: "Induction is a distinct kind of argument from the Syllogism" (p. 208). It is the essential property of the Syllogism, as defined by Aristotle and by every one after him, that the truth of the conclusion follows necessarily from the truth of its premisses: that you cannot admit the premisses and reject the conclusion without contradicting yourself. Now this is what the best Induction never attains; and I contend that the presence or absence of this important characteristic is quite enough to constitute "two distinct kinds of argument." Whately objects to Aldrich (whom Hamilton defends) for supplying a suppressed minor, because it is "manifestly false" (p. 209). I object to Whately's supplied major, because it is uncertified, and therefore cannot be used to prove any conclusion. By clothing arguments from Induction in syllogistic form, we invest them with a character of necessity which does not really belong to them. The establishment of general propositions, and the interpretation of them when established (to use the phraseology of Mr. Mill), must always be distinct mental processes; and the forms appropriate to the latter, involving necessary sequence, ought not to be employed to disguise the want of necessity--the varying and graduated probability, inherent in the former. Mr. Mill says (Syst. Log. Bk. III. ch. iii. s. 1, p. 343, 5th ed.:)--"As Whately remarks, every induction is a syllogism with the major premiss suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism, by supplying a major premiss." Even in this modified phraseology, I cannot admit the propriety of throwing Induction into syllogistic forms of argument. By doing this we efface the special character of Induction, as the jump from particular cases, more or fewer, to an universal proposition comprising them and an indefinite number of others besides. To state this in forms which imply that it is a necessary step, involving nothing more than the interpretation of a higher universal proposition, appears to me unphilosophical. Mr. Mill says with truth (in his admirable chapter explaining the real function of the major premiss in a Syllogism, p. 211), that the individual cases are all the evidence which we possess; the step from them to universal propositions ought not to be expressed in forms which suppose universal propositions to be already attained.

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).]

We must presume Syllogisms without a middle term, when we read:--"The Syllogism through a middle term is by nature prior, and of greater cognitive efficacy; but to us the Syllogism through Induction is plainer and clearer."[66] Nor, indeed, is the saying, when literally taken, at all well-founded; for the pretended Syllogisms from Induction and Example, far from being clear and plain, are more involved and difficult to follow than Barbara and Celarent. Yet the substance of Aristotle's thought is true and important, when considered as declaring the antithesis (not between varieties of Syllogisms, but) between Induction and Example on the one part, and Syllogism (Deduction) on the other. It is thus that he sets out the same antithesis elsewhere, both in the Analytica Posteriora and the Topica.[67] Prior and more cognizable by nature or absolutely, prior and more cognizable to us or in relation to us--these two are not merely distinct, but the one is the correlate and antithesis of the other.

[Footnote 66: Analyt. Prior. II. xxiii. p. 68, b. 35: [Greek: phu/sei me\n ou)=n pro/teros kai\ gnôrimô/teros o( dia\ tou= me/sou sullogismo/s, ê(mi=n d' e)narge/steros o( dia\ tê=s e)pagôgê=s.]]

[Footnote 67: Analyt. Post. I. ii. p. 72, a. 2, b. 29; Ethic. Nik. VI. iii**. p. 1139, b. 28: [Greek: ê( me\n dê\ e)pagôgê\ a)rchê/ e)sti kai\ tou= katho/lou=, o( de\ sullogismo\s e)k tô=n katho/lou. ei)si\n a)/ra a)rchai\ e)x ô(=n o( sullogismo/s, ô(=n ou)k e)/sti sullogismo/s; e)pagôgê\ a)/ra.] Compare Topica, I. xii. p. 105, a. 11; VI. iv. pp. 141, 142**; Physica, I. i. p. 184, a. 16; Metaphysic. E. iv. p. 1029, b**. 4-12. Compare also Trendelenburg's explanation of this doctrine, Erläuterungen zu den Elementen der Aristotelischen Logik, sects. 18, 19, 20, p. 33, seq.]

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 from whence he surveys nature as a classified and coherent whole, manifesting herself in details which he can interpret and sometimes predict. The path of knowledge, seen relatively to us, is one through particulars, by way of example to fresh particulars, or by way of induction to universals. The path of knowledge, by nature or absolutely, is from universals by way of deduction either to new universals or to new particulars. By the cognitive nature of man, Aristotle means the full equipment, of and for cognition, which our mature age exhibits; notiora naturâ are the acquisitions, points of view, and processes, familiar in greater or less perfection to such mature individuals and societies. Notiora nobis are the facts and processes with which all of us begin, and which belong to the intellect in its highest as well as its lowest stage; though, in the higher stages, they are employed, directed, and modified, by an acquired intellectual capital, and by the permanent machinery of universal significant terms in which that capital is invested.

Such is the antithesis between notiora naturâ (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 involves no contradiction. But the rightly constructed Syllogism constrains assent;[69] the disputant cannot grant the premisses and deny the conclusion without contradicting himself. The constraining force, however, does not come into accurate and regulated working until the principles and conditions of deductive reasoning have been set forth--until the Syllogism has been analysed, and the characteristics of its validity, as distinguished from its invalidity, have been marked out. This is what Aristotle teaches in the Analytica and Topica. It admits of being set out in regular figure and mode--forms of premisses with the conclusion appropriate to each; and the lesson must be learnt before we can know how far the force of deductive reasoning, which begins with the notiora naturâ, is legitimately binding and trustworthy.

[Footnote 68: Aristot. Topica, I. xii. p. 105, a. 13-19: [Greek: e)pagôgê\ de\ ê( a)po\ tô=n kath' e(/kaston e)pi\ ta\ katho/lou e)/phodos; oi(=on ei) e)/sti kubernê/tês o( e)pista/menos kra/tistos kai\ ê(ni/ochos, kai\ o(/lôs e)sti\n o( e)pista/menos peri\ e(/kaston a)/ristos. e)/sti d' ê( me\n e)pagôgê\ pithanô/teron kai\ saphe/steron kai\ kata\ tê\n ai)/sthêsin gnôrimô/teron, kai\ toi=s polloi=s koino/n; o( de\ sullogismo\s biastikô/teron kai\ pro\s tou\s a)ntilogikou\s e)nerge/steron.] Also the same treatise. VI. iv. p. 141, b. 17.

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.: [Greek: polu\ ma/lista ô(=n e)gô\ oi)=da, o(/te le/goi, tou\s a)kou/ontas o(mologou=ntas parei=chen] (15). The same can hardly be said of the Platonic dialogues.]

[Footnote 69: Bacon, Novum Organ. I. Aphor. 13:--"Syllogismus assensum constringit, non res."]

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 ([Greek: e)mpeiri/a]), and he describes it as the real guide, more essential than philosophical generalities, to exactness of performance in detail.[71] Mr. John Mill has been the first to assign to Experience, thus understood, its full value and true position in the theory of Ratiocination; and to show that the Paradeigmatic process exhibits the prime and ultimate reality of all Inference, the real premisses and the real conclusion which Inference connects together. Between these two is interposed the double process of which Induction forms the first half and Deduction the second; neither the one nor the other being indispensable to Inference, but both of them being required as securities for Scientific inference, if we desire to have its correctness tested and its sufficiency certified; the real evidence, whereby the conclusion of a Syllogism is proved, being the minor premiss, together with (not the major premiss itself, but) the assemblage of particular facts from which by Induction the major premiss is drawn. Now Aristotle had present to his mind the conception of Inference as an entire process, enabling us from some particular truths to discover and prove other particular truths: he considers it as an unscientific process, of which to a limited extent other animals besides man are capable, and which, as operative under the title of Experience in mature practical men, is a safer guide than Science amidst the doubts and difficulties of action. Upon this foundation he erects the superstructure of Science; the universal propositions acquired through Induction, and applied again to particulars or to lower generalities, through the rules of the deductive Syllogism. He signalizes, with just emphasis, the universalizing point of view called Science or Theory; but he regards it as emerging from particular facts, and as travelling again downwards towards particular facts. The misfortune is, that he contents himself with barely recognizing, though he distinctly proclaims the necessity of, the inductive part of this complex operation; while he bestows elaborate care upon the analysis of the deductive part, and of the rules for conducting it. From this disproportionate treatment, one half of Logic is made to look like the whole; Science is disjoined from Experience, and is presented as consisting in Deduction alone; every thing which is not Deduction, is degraded into unscientific Experience; the major premiss of the Syllogism being considered as part of the proof of the conclusion, and the conclusion being necessarily connected therewith, we appear to have acquired a locus standi and a binding cogency such as Experience could never supply; lastly, when Aristotle resolves Induction into a peculiar variety of the Syllogism, he appears finally to abolish all its separate dignity and jurisdiction. This one-sided view of Logic has been embraced and perpetuated by the Aristotelian expositors, who have carefully illustrated, and to a certain extent even amplified, the part which was already in comparative excess, while they have added nothing to the part that was in defect, and have scarcely even preserved Aristotle's recognition of it as being not merely legitimate but essential. The vast body of Inductive Science, accumulated during the last three centuries, has thus, until recently, been allowed to grow up, as if its proofs and processes had nothing to do with Logic.

[Footnote 70: Heyder (in his learned treatise, Darstellung der Aristotelischen und Hegelschen Dialektik, p. 226), after having considered the unsatisfactory process whereby Aristotle attempts to resolve Induction into a variety of Syllogism, concludes by a remark which I think just:--"Aus alle dem erhellt zur Genüge, dass sich Aristoteles bei dem Versuch die Induction auf eine Schlussform zurückzuführen, selbst sich nicht recht befriedigt fühlte, und derselbe wohl nur aus seinem durchgängigen Bestreben zu erklären ist, alles wissenschaftliche Verfahren in die Form des Schlusses zu bringen; dass dagegen, seiner eigentlichen Meinung und der strengen Consequenz seiner Lehre zu Folge, die Induction zum syllogistischen und beweisenden Verfahren einen in dem Begriff der beiden Verfahrungsweisen liegenden Gegensatz bildete, was sich ihm dann auch auf das Verhältniss der Induction zur Begriffsbestimmung ausdehnen musste."]

[Footnote 71: Aristot. Analyt. Prior. II. xxiii. p. 68, b. 12; xxvi. p. 69, a. 17. Analyt. Post. II. xix. p. 99, b. 30, seq**.; xiii. p. 97, b. 7. Topica, VIII. i. p. 155, b. 35; p. 156, b. 10; p. 157, a. 14-23; p. 160, a. 36. Metaphys. A. i. p. 980, b. 25-p. 981, a. 30. This first chapter of the Metaphysica is one of the most remarkable passages of Aristotle, respecting the analytical philosophy of mind.]

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 Aristotle[72] 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 bespeaks indulgence[73] as for a first attempt requiring to be brought to completion by others. He made this first step for himself; and if any one would make a second step, so as to apply the same analysis to the other half, and to bring out in like manner the formal conditions and principles of Induction, we may fairly believe that Aristotle would have welcomed the act, as filling up what he himself recognized to be a gap in the entire compass of Reasoning. As to his own achievement, it is certain that he could not have composed the Analytica and Topica, if he had not had before him many specimens of the deductive process to study and compare. Neither could the inductive process have been analysed, until after the examples of successful advance in inductive science which recent years have furnished. Upon these examples, mainly, has been based the profound System of Mr. John Stuart Mill, analysing and discriminating the formalities of Induction in the same way as those of Deduction had before been handled by Aristotle; also fusing the two together as co-operative towards one comprehensive scheme of Logic--the Logic of Evidence generally, or of Truth as discoverable and proveable. In this scheme the Syllogistic Theory, or Logic of Consistency between one proposition and others, is recognized as an essential part, but is no longer tolerated as an independent whole.[74]

[Footnote 72: See his Discussions on Philosophy, p. 139, seq.; Lectures on Logic, vol. i. p. 27.]

[Footnote 73: See the remarkable paragraph at the close of the Sophistici Elenchi, already quoted (supra, p. 140, note).]

[Footnote 74: Mr. John Stuart Mill says (Bk. II. ch. i. sect. 3): **"Induction is inferring a proposition from premisses less general than itself, and Ratiocination is inferring a proposition from premisses equally or more general." Again in another passage: "We have found that all Inference, consequently all Proof, and all discovery of truths not self-evident, consists of inductions, and the interpretation of inductions; that all our knowledge, not intuitive, comes to us exclusively from that source. What Induction is, therefore, and what conditions render it legitimate, cannot but be deemed the main question of logic--the question which includes all others. It is however one which professed writers on logic have almost entirely passed over. The generalities of the subject, indeed, have not been altogether neglected by metaphysicians; but, for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths, their analysis of the inductive operation, even when unexceptionable as to correctness, has not been specific enough to be made the foundation of practical rules, which might be for Induction itself what the rules of the Syllogism are for interpretation of Induction" (Bk. III. ch. i. s. 1. p. 313.)--"The business of Inductive Logic is to provide rules and models (such as the Syllogism and its rules are for ratiocination) to which if inductive arguments conform, those arguments are conclusive, and not otherwise. This is what the Four Methods profess to be, and what I believe they are universally considered to be by experimental philosophers, who had practised all of them long before any one sought to reduce the practice to theory" (Bk. III. ch. ix. s. 5, p. 471, 5th ed.)--See also the same point of view more copiously set forth, in Mr. Mill's later work, 'Examination of Sir W. Hamilton's Philosophy' (ch. xx. pp. 454-462, 3rd ed.): "It is only as a means to material truth that the formal (or to speak more clearly, the conditional) validity of an operation of thought is of any value; and even that value is only negative: we have not made the smallest positive advance towards right thinking, by merely keeping ourselves consistent in what is perhaps systematic error. This by no means implies that Formal Logic, even in its narrowest sense, is not of very great, though purely negative value."--"Not only however is it indispensable that the larger Logic, which embraces all the general conditions of the ascertainment of truth, should be studied in addition to the smaller Logic, which only concerns itself with the conditions of consistency; but the smaller Logic ought to be (at least, finally) studied as part of the greater--as a portion of the means to the same end; and its relation to the other parts--to the other means--should be distinctly displayed."]

After adverting to another variety of ratiocinative procedure, which he calls Apagoge or Abduction (where the minor is hardly more evident than the conclusion, and might sometimes conveniently become a conclusion first to be proved),[75] Aristotle goes on to treat of Objection generally--the function of the dialectical respondent. The Enstasis or Objection is a proposition opposed not to a conclusion, but to the proposition set up by the defendant. When the proposition set up by him is universal, as it must be if he seeks to establish an universal conclusion, your objection may be either universal or particular: you may deny either the whole of his proposition, or only one portion of the particulars contained under it; the denial of one single particular, when substantiated, being enough to overthrow his universal. Accordingly, your objection, being thus variously opposed to the proposition, will lie in the syllogistic figures which admit opposite conclusions; that is, either in the First or Third; for the Second figure admits only negative conclusions not opposed to each other. If the defendant has set up an Universal Affirmative, you may deny the whole and establish a contrary negative, in the First figure; or you may deny a part only, and establish a contradictory negative, in the Third figure. The like, if he has set up an Universal Negative: you may impugn it either by an universal contrary affirmative, in the First figure; or by a particular contradictory affirmative, in the Third figure.[76]

[Footnote 75: Analyt. Prior. II. xxv. p. 69, a. 20-36.]

[Footnote 76: Ibid. II. xxvi. p. 69, a. 37-b. 37.

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 them. We call it a Sign, when one fact is the antecedent or consequent of another, and therefore serves as mark or evidence thereof. The conjunction may be either constant, or frequent, or merely occasional: if constant, we obtain for the major premiss of our syllogism a proposition approaching that which is universally or necessarily true; if not constant but only frequent or occasional, the major premiss of our syllogism will at best only be probable. The constant conjunction will furnish us with a Syllogism or Enthymeme in the First figure; the significant mark being here a genuine middle term--subject in the major premiss, and predicate in the minor. We can then get a conclusion both affirmative and universally true. In other cases, we cannot obtain premisses for a syllogism in the First figure, but only for a syllogism in the Second or Third. In the Third figure, since we get by right no universal conclusions at all, but only particular conclusions, the conclusion of the Enthymeme, though it may happen to be true, is open to refutation. Where by the laws of Syllogism no affirmative conclusion whatever is possible, as in the Second figure, the conclusion obtained by Enthymeme is altogether suspicious. In contrast with the Sign in these figures, that which enters as an effective middle term into the First figure, should be distinguished under the name of Proof ([Greek: tekmê/rion].)[78]

[Footnote 77: Ibid. II. xxvii. p. 70, a. 10: [Greek: e)nthu/mêma me\n ou)=n e)sti\ sullogismo\s e)x ei)ko/tôn ê)\ sêmei/ôn; lamba/netai de\ to\ sêmei=on trichô=s, o(sachô=s kai\ to\ me/son e)n toi=s schê/masi.]]

[Footnote 78: Analyt. Prior. II. xxvii. p. 70, a. 31-b. 6.

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--[Greek: monolê/mmatos]. 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 as a science is practicable. The basis upon which it rests is this general fact or postulate: That in all natural affections of the animal, bodily changes and mental changes accompany each other. The former, therefore, may become signs or proofs of the latter,[79] if, in each class of animals, we can discriminate the one specific bodily phenomenon which attaches to each mental phenomenon. Thus, the lion is a courageous animal. What is the bodily sign accompanying a courageous disposition? It is (we assume here) the having extremities of great size. This belongs to all lions, as a proprium; in the sense that, though it may or does belong also to some individuals of other races (as men), it does not belong to any other entire race. Physiognomy as a science will, then, be possible, if we can find races of animals which have only one characteristic mental attribute, and if we can discover what is the physical attribute correlating with it.[80] But the difficulties are greater when the same race has two characteristic mental attributes (e.g. lions are both courageous and generous), each with its correlative physical attribute; for how can we tell which belongs to which? We have then to study individuals of other races possessing one of these attributes without the other; thus, if we find that courageous men, who are not generous, agree in having large extremities, we may infer that this last circumstance is, in the lion, the correlative mark of his courage and not of his generosity. The physiognomonic inference will be expressed by a syllogism in the First figure, in which the major term (A) reciprocates and is convertible with the middle term (B), while B stretches beyond (or is more extensive than) the minor (C); this relation of the terms being necessary, if there is to be a single mark for a particular attribute.[81]

[Footnote 79: Analyt. Prior. II. xxvii. p. 70, b. 7-16: [Greek: ei)/ tis di/dôsin a(/ma metaba/llein to\ sô=ma kai\ tê\n psuchê/n, o(/sa phusika/ e)sti pathê/mata;--sumpa/schein ga\r a)llê/lois u(pokei=tai.] See the Aristotelian treatise entitled [Greek: Phusiognômonika/], pp. 808-809, Bekk.]

[Footnote 80: Ibid. II. xxvii. p. 70, b. 22. About the characteristics of the lion see Aristot. Physiognom. p. 809, b. 14-36: [Greek: ta\ peri\ tê\n psuchê\n dotiko\n kai\ e)leu/theron, megalo/psuchon kai\ philo/nikon, kai\ prau+\ kai\ di/kaion kai\ philo/storgon pro\s a(\ a)\n o(milê/sê|.]]

[Footnote 81: Ibid. II. xxvii. p. 70, b. 31-36.]

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 doctrines just laid down about Probabilities, Signs, and Proofs, bring us back to the Modals under a different set of phrases. The Possible or Problematical is that, of the occurrence or reality of which we doubt, neither believing nor disbelieving it, not being prepared to assert either that it is, or that it is not; that which may be or may not be. It is our manner of speaking, when we have only signs or probabilities to guide us, and not certain proofs. The feeling of doubt is, as a psychological phenomenon, essentially distinct from the feeling of belief which, in its objective aspect, correlates with certainty or matter of fact; as well as from the feeling of disbelief, the correlate of which can only be described negatively. Every man knows these feelings by his own mental experience. But in describing the feeling of doubt, as to its matter or in its objective aspect, we must take care to use phrases which declare plainly both sides of its disjunctive or alternative character. The Possible is, That which either may be or may not be. As That which may be, it stands opposed to the Impossible; as That which may not be, it stands opposed to the Necessary. It thus carries with it negation both of impossibility and of necessity; but, in common parlance, the first half of this meaning stands out prominently, and is mistaken for the whole. Aristotle, as we saw previously, speaks equivocally on this point, recognizing a double signification of the term: he sometimes uses it in the sense opposed only to impossible, maintaining that what is necessary must also be possible; sometimes in the truer sense, opposed both to necessity and to impossibility.[82]

[Footnote 82: Aristot. De Interpret. xiii. p. 22. Analyt. Prior. I. xiii. p. 32, a. 21, 29, 36, xiv. p. 33, b. 22; xix. p. 38, a. 35.]

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 Nature--prevails in the majority of cases, but not in all; being liable to occasional counteraction from Chance and other forces. Thus, between Necessity and perfect constancy at one extreme (such as the rotation of the sidereal sphere), and Chance at the other, there may be every shade of gradation; from natural agency next below the constant, down to the lowest degree of probability.[83]

[Footnote 83: Analyt. Prior. I. xiii. p. 32, b. 5-19. [Greek: to\ d' a)o/riston tô=| mêde\n ma=llon ou(/tôs ê)\ e)kei/nôs]. Compare Metaphys. K. p. 1064, b. 32.]

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 Priora[84]), 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]

[Footnote 84: Analyt. Prior. II. xxvii. p. 70, a. 2-38. Compare what is said here about [Greek: ei)ko/s, sêmei=on, tekmê/rion], with the first chapter of the Topica, and the dialectic syllogism as there described: [Greek: o( e)x e)ndo/xôn sullogizo/menos].]

[Footnote 85: Ibid. I. viii.-xxii. p. 29, b. 29-p. 40, b. 16.]

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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VII. ANALYTICA POSTERIORA I

In the two books of Analytica Priora, Aristotle has carried us through the full doctrine of the functions and varieties of the Syllogism; with an intimation that it might be applied to two purposes--Demonstration and Dialectic. We are now introduced to these two distinct applications of the Syllogism: first, in the Analytica Posteriora, to Demonstration; next, in the Topica, to Dialectic. We are indeed distinctly told that, as far as the forms and rules of Syllogism go, these are alike applicable to both;[1] but the difference of matter and purpose in the two cases is so considerable as to require a distinct theory and precepts for the one and for the other.

[Footnote 1: Analyt. Prior. I. xxx. p. 46, a. 4-10; Analyt. Post. I. ii. p. 71, a. 23.]

The contrast between Dialectic (along with Rhetoric) on the one hand and Science on the other is one deeply present to the mind of Aristotle. He seems to have proceeded upon the same fundamental antithesis as that which appears in the Platonic dialogues; but to have modified it both in meaning and in terminology, dismissing at the same time various hypotheses with which Plato had connected it.

The antithesis that both thinkers have in view is Opinion or Common Sense versus Science or Special Teaching and Learning; those aptitudes, acquirements, sentiments, antipathies, &c., which a man imbibes and appropriates insensibly, partly by his own doing and suffering, partly by living amidst the drill and example of a given society--as distinguished from those accomplishments which he derives from a teacher already known to possess them, and in which both the time of his apprenticeship and the steps of his progress are alike assignable.

Common Sense is the region of Opinion, in which there is diversity of authorities and contradiction of arguments without any settled truth; all affirmations being particular and relative, true at one time and place, false at another. Science, on the contrary, deals with imperishable Forms and universal truths, which Plato regards, in their subjective aspect, as the innate, though buried, furniture of the soul, inherited from an external pre-existence, and revived in it out of the misleading data of sense by a process first of the cross-examining Elenchus, next of scientific Demonstration. Plato depreciates altogether the untaught, unexamined, stock of acquirements which passes under the name of Common Sense, as a mere worthless semblance of knowledge without reality; as requiring to be broken up by the scrutinizing Elenchus, in order to impress a painful but healthy consciousness of ignorance, and to prepare the mind for that process of teaching whereby alone Science or Cognition can be imparted.[2] He admits that Opinion may be right as well as wrong. Yet even when right, it is essentially different from Science, and is essentially transitory; a safe guide to action while it lasts, but not to be trusted for stability or permanence.[3] By Plato, Rhetoric is treated as belonging to the province of Opinion, Dialectic to that of Science. The rhetor addresses multitudes in continuous speech, appeals to received common places, and persuades: the dialectician, conversing only with one or a few, receives and imparts the stimulus of short question and answer; thus awakening the dormant capacities of the soul to the reminiscence of those universal Forms or Ideas which are the only true Knowable.

[Footnote 2: Plato, Sophistes, pp. 228-229; Symposion, pp. 203-204; Theætetus, pp. 148, 149, 150. Compare also 'Plato and the Other Companions of Sokrates,' Vol. I. chs. vi.-vii. pp. 245-288; II. ch. xxvi. p. 376, seq.]

[Footnote 3: Plato, Republic, v. pp. 477-478; Menon, pp. 97-98.]

Like Plato, Aristotle distinguishes the region of Common Sense or Opinion from that of Science, and regards Universals as the objects of Science. But his Universals are very different from those of Plato: they are not self-existent realities, known by the mind from a long period of pre-existence, and called up by reminiscence out of the chaos of sensible impressions. To operate such revival is the great function that Plato assigns to Dialectic. But in the philosophy of Aristotle Dialectic is something very different. It is placed alongside of Rhetoric in the region of Opinion. Both the rhetor and the dialectician deal with all subjects, recognizing no limit; they attack or defend any or all conclusions, employing the process of ratiocination which Aristotle has treated under the name of Syllogism; they take up as premisses any one of the various opinions in circulation, for which some plausible authority may be cited; they follow out the consequences of one opinion in its bearing upon others, favourable or unfavourable, and thus become well furnished with arguments for and against all. The ultimate foundation here supposed is some sort of recognized presumption or authoritative sanction[4]--law, custom, or creed, established among this or that portion of mankind, some maxim enunciated by an eminent poet, some doctrine of the Pythagoreans or other philosophers, current proverb, answer from the Delphian oracle, &c. Any one of these may serve as a dialectical authority. But these authorities, far from being harmonious with each other, are recognized as independent, discordant, and often contradictory. Though not all of equal value,[5] each is sufficient to warrant the setting up of a thesis for debate. In Dialectic, one of the disputants undertakes to do this, and to answer all questions that may be put to him respecting the thesis, without implicating himself in inconsistencies or contradiction. The questioner or assailant, on the other hand, shapes his questions with a view to refute the thesis, by eliciting answers which may furnish him with premisses for some syllogism in contradiction thereof. But he is tied down by the laws of debate to syllogize only from such premisses as the respondent has expressly granted; and to put questions in such manner that the respondent is required only to give or withhold assent, according as he thinks right.

[Footnote 4: Aristot. Topica, I. x. p. 104, a. 8, xi. p. 104, b. 19. Compare Metaphysica, A. p. 995, a. 1-10.]

[Footnote 5: Analyt. Post. I. xix. p. 81, b. 18: [Greek: kata\ me\n ou)=n do/xan sullogizome/nois kai\ mo/non dialektikô=s dê=lon o(/ti tou=to mo/non skepte/on, ei) e)x ô(=n e)nde/chetai e)ndoxota/tôn gi/netai o( sullogismo/s, ô(/st' ei) kai\ e)/sti ti tê=| a)lêthei/a| tô=n AB me/son, dokei= de\ mê/, o( dia\ tou/tou sullogizo/menos sullelo/gistai dialektikô=s, pro\s d' a)lê/theian e)k tô=n u(parcho/ntôn dei= skopei=n.] Compare Topica, VIII. xii. p. 162, b. 27.]

We shall see more fully how Aristotle deals with Dialectic, when we come to the Topica: here I put it forward briefly, in order that the reader may better understand, by contrast, its extreme antithesis, viz., Demonstrative Science and Necessary Truth as conceived by Aristotle. First, instead of two debaters, one of whom sets up a thesis which he professes to understand and undertakes to maintain, while the other puts questions upon it,--Demonstrative Science assumes a teacher who knows, and a learner conscious of ignorance but wishing to know. The teacher lays down premisses which the learner is bound to receive; or if they are put in the form of questions, the learner must answer them as the teacher expects, not according to his own knowledge. Secondly, instead of the unbounded miscellany of subjects treated in Dialectic, Demonstrative Science is confined to a few special subjects, in which alone appropriate premisses can be obtained, and definitions framed. Thirdly, instead of the several heterogeneous authorities recognized in Dialectic, Demonstrative Science has principia of its own, serving as points of departure; some principia common to all its varieties, others special or confined to one alone. Fourthly, there is no conflict of authorities in Demonstrative Science; its propositions are essential, universal, and true per se, from the commencement to the conclusion; while Dialectic takes in accidental premisses as well as essential. Fifthly, the principia of Demonstrative Science are obtained from Induction only; originating in particulars which are all that the ordinary growing mind can at first apprehend (notiora nobis), but culminating in universals which correspond to the perfection of our cognitive comprehension (notiora naturâ.)[6]

[Footnote 6: Aristot. Topica, VI. iv. p. 141, b. 3-14. [Greek: oi( polloi\ ga\r ta\ toiau=ta prognôri/zousin; ta\ me\n ga\r tê=s tuchou/sês, ta\ d' a)kribou=s kai\ perittê=s dianoi/as katamathei=n e)sti/n.] Compare in Analyt. Post. I. xii. pp. 77-78, the contrast between [Greek: ta\ mathê/mata] and [Greek: oi( dia/logoi].]

Amidst all these diversities, Dialectic and Demonstrative Science have in common the process of Syllogism, including such assumptions as the rules of syllogizing postulate. In both, the conclusions are hypothetically true (i.e. granting the premisses to be so). But, in demonstrative syllogism, the conclusions are true universally, absolutely, and necessarily; deriving this character from their premisses, which Aristotle holds up as the cause, reason, or condition of the conclusion. What he means by Demonstrative Science, we may best conceive, by taking it as a small [Greek: te/menos] or specially cultivated enclosure, subdivided into still smaller separate compartments--the extreme antithesis to the vast common land of Dialectic. Between the two lies a large region, neither essentially determinate like the one, nor essentially indeterminate like the other; an intermediate region in which are comprehended the subjects of the treatises forming the very miscellaneous Encyclopædia of Aristotle. These subjects do not admit of being handled with equal exactness; accordingly, he admonishes us that it is important to know how much exactness is attainable in each, and not to aspire to more.[7]

[Footnote 7: Aristot. Ethic. Nikom. I. p. 1094, b. 12-25; p. 1098, a. 26-b. 8; Metaphys. A. p. 995, a. 15; Ethic. Eudem. I. p. 1216, b. 30-p. 1217, a. 17; Politic. VII. p. 1328, a. 19; Meteorolog. I. p. 338, a. 35. Compare Analyt. Post. I. xiii. p. 78, b. 32 (with Waitz's note, II. p. 335); and I. xxvii. p. 87, a. 31.

The passages above named in the Nikomachean Ethica are remarkable: [Greek: le/goito d' a)\n i(kanô=s, ei) kata\ tê\n u(pokeime/nên u(/lên diasaphêthei/ê; to\ ga\r a)kribe\s ou)ch o(moi/ôs e)n a(/pasi toi=s lo/gois e)pizêtête/on, ô(/sper ou)d' e)n toi=s dêmiourgoume/nois. tê\n a)kri/beian mê\ o(moi/ôs e)n a(/pasin e)pizêtei=n (chrê/), a)ll' e)n e(ka/stois kata\ tê\n u(pokeime/nên u(/lên, kai\ e)pi\ tosou=ton e)ph' o(/son oi)kei=on tê=| methodô=|.] Compare Metaphys. E. p. 1025, b. 13: [Greek: a)podeiknu/ousin ê)\ a)nagkai/oteron ê)\ malakô/teron.]

The different degrees of exactness attainable in different departments of science, and the reasons upon which such difference depends are well explained in the sixth book of Mr. John Stuart Mill's System of Logic, vol. II. chap. iii. pp. 422-425, 5th ed. Aristotle says that there can be no scientific theory or cognition about [Greek: to\ sumbebêko/s] which he defines to be that which belongs to a subject neither necessarily, nor constantly, nor usually, but only on occasion (Metaphys. E. p. 1026, b. 3, 26, 33; K. p. 1065, a. 1, meaning [Greek: to\ sumbebêko\s mê\ kath' au(to/],--Analyt. Post. I. 6, 75, a. 18; for he uses the term in two different senses--Metaph. [Greek: D]. p. 1025, a. 31). In his view, there can be no science except about constant conjunctions; and we find the same doctrine in the following passage of Mr. Mill:--"Any facts are fitted, in themselves, to be a subject of science, which follow one another according to constant laws; although those laws may not have been discovered, nor even be discoverable by our existing resources. Take, for instance, the most familiar class of meteorological phenomena, those of rain and sunshine. Scientific inquiry has not yet succeeded in ascertaining the order of antecedence and consequence among these phenomena, so as to be able, at least in our regions of the earth, to predict them with certainty, or even with any high degree of probability. Yet no one doubts that the phenomena depend on laws. . . . . Meteorology not only has in itself every requisite for being, but actually is, a science; though from the difficulty of observing the facts upon which the phenomena depend (a difficulty inherent in the peculiar nature of those phenomena), the science is extremely imperfect; and were it perfect, might probably be of little avail in practice, since the data requisite for applying its principles to particular instances would rarely be procurable.

"A case may be conceived of an intermediate character between the perfection of science, and this its extreme imperfection. It may happen that the greater causes, those on which the principal part of the phenomena depends, are within the reach of observation and measurement; so that, if no other causes intervened, a complete explanation could be given, not only of the phenomenon in general, but of all the variations and modifications which it admits of. But inasmuch as other, perhaps many other, causes, separately insignificant in their effects, co-operate or conflict in many or in all cases with those greater causes, the effect, accordingly, presents more or less of aberration from what would be produced by the greater causes alone. Now if these minor causes are not so constantly accessible, or not accessible at all, to accurate observation, the principal mass of the effect may still, as before, be accounted for, and even predicted; but there will be variations and modifications which we shall not be competent to explain thoroughly, and our predictions will not be fulfilled accurately, but only approximately.

"It is thus, for example, with the theory of the Tides. . . . . And this is what is or ought to be meant by those who speak of sciences which are not exact sciences. Astronomy was once a science, without being an exact science. It could not become exact until not only the general course of the planetary motions, but the perturbations also, were accounted for and referred to their causes. It has become an exact science because its phenomena have been brought under laws comprehending the whole of the causes by which the phenomena are influenced, whether in a great or only in a trifling degree, whether in all or only in some cases, and assigning to each of those causes the share of effect that really belongs to it. . . . . The science of human nature falls far short of the standard of exactness now realized in Astronomy; but there is no reason that it should not be as much a science as Tidology is, or as Astronomy was when its calculations had only mastered the main phenomena, but not the perturbations."]

In setting out the process of Demonstration, Aristotle begins from the idea of teaching and learning. In every variety thereof some præcognita must be assumed, which the learner must know before he comes to be taught, and upon which the teacher must found his instruction.[8] This is equally true, whether we proceed (as in Syllogism) from the more general to the less general, or (as in Induction) from the particular to the general. He who comes to learn Geometry must know beforehand the figures called circle and triangle, and must have a triangular figure drawn to contemplate; he must know what is a unit or monad, and must have, besides, exposed before him what is chosen as the unit for the reasoning on which he is about to enter. These are the præcognita required for Geometry and Arithmetic. Some præcognita are also required preparatory to any and all reasoning: e.g., the maxim of Identity (fixed meaning of terms and propositions), and the maxims of Contradiction and of Excluded Middle (impossibility that a proposition and its contradictory can either be both true or both false.)[9] The learner must thus know beforehand certain Definitions and Axioms, as conditions without which the teacher cannot instruct him in any demonstrative science.

[Footnote 8: Analyt. Post. I. i. pp. 71-72; Metaphys. A. IX. p. 992, b. 30.]

[Footnote 9: Aristot. Analyt. Post. I, i. p. 71, a. 11-17. [Greek: a(/pan ê)\ phê=sai ê)\ a)pophê=sai a)lêthe/s].]

Aristotle, here at the beginning, seeks to clear up a difficulty which had been raised in the time of Plato as between knowledge and learning. How is it possible to learn at all? is a question started in the Menon.[10] You either know a thing already, and, on this supposition, you do not want to learn it; or you do not know it, and in this case you cannot learn it, because, even when you have learnt, you cannot tell whether the matter learnt is what you were in search of. To this difficulty, the reply made in the Menon is, that you never do learn any thing really new. What you are said to learn, is nothing more than reminiscence of what had once been known in an anterior life, and forgotten at birth into the present life; what is supposed to be learnt is only the recall of that which you once knew, but had forgotten. Such is the Platonic doctrine of Reminiscence. Aristotle will not accept that doctrine as a solution; but he acknowledges the difficulty, and intimates that others had already tried to solve it without success. His own solution is that there are two grades of cognition: (1) the full, complete, absolute; (2) the partial, incomplete, qualified. What you already know by the first of these grades, you cannot be said to learn; but you may learn that which you know only by the second grade, and by such learning you bring your incomplete cognition up to completeness.

[Footnote 10: Plato, Menon. p. 80.]

Thus, you have learnt, and you know, the universal truth, that every triangle has its three angles equal to two right angles; but you do not yet know that A B C, D E F, G H I, &c., have their two angles equal to two right angles; for you have not yet seen any of these figures, and you do not know that they are triangles. The moment that you see A B C, or hear what figure it is, you learn at one and the same time two facts: first, that it is a triangle; next, by virtue of your previous cognition, that it possesses the above-mentioned property. You knew this in a certain way or incompletely before, by having followed the demonstration of the universal truth, and by thus knowing that every triangle had its three angles equal to two right angles; but you did not know it absolutely, being ignorant that A B C was a triangle.[11]

[Footnote 11: Aristot. Analyt. Post. I. i. p. 71, a. 17-b. 8: [Greek: e)/sti de\ gnôri/zein ta\ me\n pro/teron gnôri/zonta, tô=n de\ kai\ a)/ma lamba/nonta tê\n gnô=sin, oi(=on o(/sa tugcha/nei o)/nta u(po\ to\ katho/lou, ô(=n e)/chei tê\n gnô=sin. o(/ti me\n ga\r pa=n tri/gônon e)/chei dusi\n o)rthai=s i)/sas, proê/|dei; o(/ti de\ to/de to\ e)n tô=| ê(mikukli/ô| tri/gôno/n e)stin, a(/ma e)pago/menos e)gnô/risen.--pri\n d' e)pachthê=nai ê)\ labei=n sullogismo/n, tro/pon me/n tina i)/sôs phate/on e)pi/stasthai, tro/pon d' a)/llon ou)/. o(\ ga\r mê\ ê)/|dei ei) e)/stin a(plô=s, tou=to pô=s ê)/|dei o(/ti du/o o)rtha\s e)/chei a(plô=s? a)lla\ dê=lon ô(s ô(di\ me\n e)pi/statai, o(/ti katho/lou e)pi/statai, a(plô=s d' ou)k e)pi/statai.--ou)de\n (oi)=mai) kôlu/ei, o(\ mantha/nei, e)/stin ô(s e)pi/stasthai, e)/sti d' ô(s a)gnoei=n; a)/topon ga\r ou)k ei) oi)=de/ pôs o(\ mantha/nei, a)ll' ei) ô(di/, oi(=on ê(=| mantha/nei kai\ ô(/s.] Compare also Anal. Post. I. xxiv. p. 86, a. 23, and Metaph. A. ii. p. 982, a. 8; Anal. Prior. II. xxi. p. 67, a. 5-b. 10.)

Aristotle reports the solution given by others, but from which he himself dissented, of the Platonic puzzle. The respondent was asked, Do you know that every Dyad is even?--Yes. Some Dyad was then produced, which the respondent did not know to be a Dyad; accordingly he did not know it to be even. Now the critics alluded to by Aristotle said that the respondent made a wrong answer; instead of saying I know every Dyad is even, he ought to have said. Every Dyad which I know to be a Dyad is even. Aristotle pronounces that this criticism is incorrect. The respondent knows the conclusion which had previously been demonstrated to him; and that conclusion was, Every triangle has its three angles equal to two right angles; it was not, Every thing which I know to be a triangle has its three angles equal to two right angles. This last proposition had never been demonstrated, nor even stated: [Greek: ou)demi/a ga\r pro/tasis lamba/netai toiau/tê, o(/ti o(\n su\ oi)=das a)rithmo/n, ê)\ o(\ su\ oi)=das eu)thu/grammon, a)lla\ kata\ panto/s] (b. 3-5).

This discussion, in the commencement of the Analytica Posteriora (combined with Analyt. Priora, II. xxi.), is interesting, because it shows that even then the difficulties were felt, about the major proposition of the Syllogism, which Mr. John Stuart Mill has so ably cleared up, for the first time, in his System of Logic. See Book II. ch. iii. of that work, especially as it stands in the sixth edition, with the note there added, pp. 232-233. You affirm, in the major proposition of the Syllogism, that every triangle has its three angles equal to two right angles; does not this include the triangle A, B, C, and is it not therefore a petitio principii? Or, if it be not so, does it not assert more than you know? The Sophists (upon whom both Plato and Aristotle are always severe, but who were valuable contributors to the theory of Logic by fastening upon the weak points) attacked it on this ground, and raised against it the puzzle described by Aristotle (in this chapter), afterwards known as the Sophism entitled [Greek: o( e)gkekalumme/nos] (see Themistius Paraphras. I. i.; also 'Plato and the Other Companions of Sokrates,' Vol. III. ch. xxxviii. p. 489). The critics whom Aristotle here cites and disapproves, virtually admitted the pertinence of this puzzle by modifying their assertion, and by cutting it down to "Everything which we know to be a triangle has its three angles equal to two right angles." Aristotle finds fault with this modification, which, however, is one way of abating the excess of absolute and peremptory pretension contained in the major, and of intimating the want of a minor to be added for interpreting and supplementing the major; while Aristotle himself arrives at the same result by admitting that the knowledge corresponding to the major proposition is not yet absolute, but incomplete and qualified; and that it is only made absolute when supplemented by a minor.

The very same point, substantially, is raised in the discussion between Mr. John Stuart Mill and an opponent, in the note above referred to. "A writer in the 'British Quarterly Review' endeavours to show that there is no petitio principii in the Syllogism, by denying that the proposition All men are mortal, asserts or assumes that Socrates is mortal. In support of this denial, he argues that we may, and in fact do, admit the general proposition without having particularly examined the case of Socrates, and even without knowing whether the individual so named is a man or something else. But this of course was never denied. That we can and do draw inferences concerning cases specifically unknown to us, is the datum from which all who discuss this subject must set out. The question is, in what terms the evidence or ground on which we draw these conclusions may best be designated--whether it is most correct to say that the unknown case is proved by known cases, or that it is proved by a general proposition including both sets of cases, the known and the unknown? I contend for the former mode of expression. I hold it an abuse of language to say, that the proof that Socrates is mortal, is that all men are mortal. Turn it in what way we will, this seems to me asserting that a thing is the proof of itself. Whoever pronounces the words, All men are mortal, has affirmed that Socrates is mortal, though he may never have heard of Socrates; for since Socrates, whether known to be a man or not, really is a man, he is included in the words, All men, and in every assertion of which they are the subject. . . . . The reviewer acknowledges that the maxim (Dictum de Omni et Nullo) as commonly expressed--'Whatever is true of a class is true of everything included in the class,' is a mere identical proposition, since the class is nothing but the things included in it. But he thinks this defect would be cured by wording the maxim thus: 'Whatever is true of a class is true of everything which can be shown to be a member of the class:' as if a thing could be shown to be a member of the class without being one."

The qualified manner in which the maxim is here enunciated by the reviewer (what can be shown to be a member of the class) corresponds with the qualification introduced by those critics whom Aristotle impugns ([Greek: lu/ousi ga\r ou) pha/skontes ei)de/nai pa=san dua/da a)rti/an ou)=san, a)ll' ê(\n i)/sasin o(/ti dua/s]); and the reply of Mr. Mill would have suited for these critics as well as for the reviewer. The puzzle started in the Platonic Menon is, at bottom, founded on the same view as that of Mr. Mill, when he states that the major proposition of the Syllogism includes beforehand the conclusion. "The general principle, (says Mr. Mill, p. 205), instead of being given as evidence of the particular case, cannot itself be taken for true without exception, until every shadow of doubt which could affect any case comprised in it is dispelled by evidence aliunde; and then what remains for the syllogism to prove? From a general principle we cannot infer any particulars but those which the principle itself assumes as known."

To enunciate this in the language of the Platonic Menon, we learn nothing by or through the evidence of the Syllogism, except a part of what we have already professed ourselves to know by asserting the major premiss.]

Aristotle proceeds to tell us what is meant by knowing a thing absolutely or completely ([Greek: a(plô=s]). It is when we believe ourselves to know the cause or reason through which the matter known exists, so that it cannot but be as it is. That is what Demonstration, or Scientific Syllogism, teaches us;[12] a Syllogism derived from premisses true, immediate, prior to, and more knowable than the conclusion--causes of the conclusion, and specially appropriate thereto. These premisses must be known beforehand without being demonstrated (i.e. known not through a middle term); and must be known not merely in the sense of understanding the signification of the terms, but also in that of being able to affirm the truth of the proposition. Prior or more knowable is understood here as prior or more knowable by nature (not relatively to us, according to the antithesis formerly explained); first, most universal, undemonstrable principia are meant. Some of these are Axioms, which the learner must "bring with him from home," or know before the teacher can instruct him in any special science; some are Definitions of the name and its essential meaning; others, again, are Hypotheses or affirmations of the existence of the thing defined, which the learner must accept upon the authority of the teacher.[13] As these are the principia of Demonstration, so it is necessary that the learner should know them, not merely as well as the conclusions demonstrated, but even better; and that among matters contradictory to the principia there should be none that he knows better or trusts more.[14]

[Footnote 12: Aristot. Analyt. Post I. ii. p. 71, b. 9-17. Julius Pacius says in a note, ad c. ii. p. 394: "Propositio demonstrativa est prima, immediata, et indemonstrabilis. His tribus verbis significatur una et eadem conditio; nam propositio prima est, quæ, quod medio caret, demonstrari nequit."

So also Zabarella (In lib. I. Post. Anal. Comm., p. 340, Op. ed. Venet. 1617): "Duæ illæ dictiones (primis et immediatis) unam tantum significant conditionem ordine secundam, non duas; idem namque est, principia esse medio carentia, ac esse prima."]

[Footnote 13: Aristot. Analyt. Post. I. ii. p. 72, a. 1-24; Themistius, Paraphr. I. ii. p. 10, ed. Spengel; Schol. p. 199, b. 44. Themistius quotes the definition of an Axiom as given by Theophrastus: [Greek: A)xi/ôma/ e)sti do/xa tis], &c. This shows the difficulty of adhering precisely to a scientific terminology. Theophrastus explains an axiom to be a sort of [Greek: do/xa], thus lapsing into the common loose use of the word. Yet still both he and Aristotle declare [Greek: do/xa] to be of inferior intellectual worth as compared with [Greek: e)pistê/mê] (Anal. Post. I. xxiii.), while at the same time they declare the Axiom to be the very maximum of scientific truth. Theophrastus gave, as examples of Axioms, the **maxim of Contradiction, universally applicable, and, "If equals be taken from equals the remainders will be equal," applicable to homogeneous quantities. Even Aristotle himself sometimes falls into the same vague employment of [Greek: do/xa], as including the Axioms. See Metaphys. B. ii. p. 996, b. 28; [Greek: G]. iii. p. 1005, b. 33.]

[Footnote 14: Aristot. Anal. Post. I. ii. p. 72, a. 25, b. 4. I translate these words in conformity with Themistius, pp. 12-13, and with Mr. Poste's translation, p. 43. Julius Pacius and M. Barthélemy St. Hilaire render them somewhat differently. They also read [Greek: a)meta/ptôtos], while Waitz and Firmin Didot read [Greek: a)meta/peistos], which last seems preferable.]

In Aristotle's time two doctrines had been advanced, in opposition to the preceding theory: (1) Some denied the necessity of any indemonstrable principia, and affirmed the possibility of, demonstrating backwards ad infinitum; (2) Others agreed in denying the necessity of any indemonstrable principia, but contended that demonstration in a circle is valid and legitimate--e.g. that A may be demonstrated by means of B, and B by means of A. Against both these doctrines Aristotle enters his protest. The first of them--the supposition of an interminable regress--he pronounces to be obviously absurd: the second he declares tantamount to proving a thing by itself; the circular demonstration, besides, having been shown to be impossible, except in the First figure, with propositions in which the predicate reciprocates or is co-extensive with the subject--a very small proportion among propositions generally used in demonstrating.[15]

[Footnote 15: Aristot. Analyt. Post. I. iii. p. 72, b. 5-p. 73, a. 20: [Greek: ô(/st' e)peidê\ o)li/ga toiau=ta e)n tai=s a)podei/xesin], &c.]

Demonstrative Science is attained only by syllogizing from necessary premisses, such as cannot possibly be other than they are. The predicate must be (1) de omni, (2) per se, (3) quatenus ipsum, so that it is a Primum Universale; this third characteristic not being realized without the preceding two. First, the predicate must belong, and belong at all times, to everything called by the name of the subject. Next, it must belong thereunto per se, or essentially; that is, either the predicate must be stated in the definition declaring the essence of the subject, or the subject must be stated in the definition declaring the essence of the predicate. The predicate must not be extra-essential to the subject, nor attached to it as an adjunct from without, simply concomitant or accidental. The like distinction holds in regard to events: some are accidentally concomitant sequences which may or may not be realized (e.g., a flash of lightning occurring when a man is on his journey); in others, the conjunction is necessary or causal (as when an animal dies under the sacrificial knife).[16] Both these two characteristics (de omni and per se) are presupposed in the third (quatenus ipsum); but this last implies farther, that the predicate is attached to the subject in the highest universality consistent with truth; i.e., that it is a First Universal, a primary predicate and not a derivative predicate. Thus, the predicate of having its three angles equal to two right angles, is a characteristic not merely de omni and per se, but also a First Universal, applied to a triangle. It is applied to a triangle, quatenus triangle, as a primary predicate. If applied to a subject of higher universality (e.g., to every geometrical figure), it would not be always true. If applied to a subject of lower universality (e.g., to a right-angled triangle or an isosceles triangle), it would be universally true and would be true per se, but it would be a derivative predicate and not a First Universal; it would not be applied to the isosceles quatenus isosceles, for there is a still higher Universal of which it is predicable, being true respecting any triangle you please. Thus, the properties with which Demonstration, or full and absolute Science, is conversant, are de omni, per se, and quatenus ipsum, or Universalia Prima;[17] all of them necessary, such as cannot but be true.]

[Footnote 16: Aristot. Analyt. Post. I. iv. p. 73, a. 21, b. 16.

[Greek: Ta\ a)/ra lego/mena e)pi\ tô=n a(plô=s e)pistêtô=n kath' au(ta\ ou(/tôs ô(s e)nupa/rchein toi=s katêgoroume/nois ê)\ e)nupa/rchesthai di' au(ta/ te/ e)sti kai\ e)x a)na/gkês] (b. 16, seq.). Line must be included in the definition of the opposites straight or curve. Also it is essential to every line that it is either straight or curve. Number must be included in the definition of the opposites odd or even; and to be either odd or even is essentially predicable of every number. You cannot understand what is meant by straight or curve unless you have the notion of a line.

The example given by Aristotle of causal conjunction (the death of an animal under the sacrificial knife) shows that he had in his mind the perfection of Inductive Observation, including full application of the Method of Difference.]

[Footnote 17: Aristot. Analyt. Post. I. iv. p. 73, b. 25-p. 74, a. 3. [Greek: o(\ toi/nun to\ tucho\n prô=ton dei/knutai du/o o)rtha\s e)/chon ê)\ o(tiou=n a)/llo, tou/tô| prô/tô| u(pa/rchei katho/lou, kai\ ê( a)po/deixis kath' au(to\ tou/tou katho/lou e)sti\, tô=n d' a)/llôn tro/pon tina\ ou) kath' au(to/; ou)de\ tou= i)soske/lous ou)k e)/sti katho/lou a)ll' e)pi\ ple/on.]

About the precise signification of [Greek: katho/lou] in Aristotle, see a valuable note of Bonitz (ad Metaphys. Z. iii.) p. 299; also Waitz (ad Aristot. De Interpr. c. vii.) I. p. 334. Aristotle gives it here, b. 26: [Greek: katho/lou de\ le/gô o(\ a)\n kata\ panto/s te u(pa/rchê| kai\ kath' au(to\ kai\ ê(=| au)to/.] Compare Themistius, Paraphr. p. 19, Spengel. [Greek: To\ kath' au(to/] is described by Aristotle confusedly. [Greek: To\ katho/lou], is that which is predicable of the subject as a whole or summum genus: [Greek: to\ kata\ panto/s], that which is predicable of every individual, either of the summum genus or of any inferior species contained therein. Cf. Analyt. Post. I. xxiv. p. 85, b. 24: [Greek: ô(=| ga\r kath' au(to\ u(pa/rchei ti, tou=to au)to\ au(tô=| ai)/tion]--the subject is itself the cause or fundamentum of the properties per se. See the explanation and references in Kampe, Die Erkenntniss-theorie des Aristoteles, ch. v. pp. 160-165.]

Aristotle remarks that there is great liability to error about these Universalia Prima. We sometimes demonstrate a predicate to be true, universally and per se, of a lower species, without being aware that it might also be demonstrated to be true, universally and per se, of the higher genus to which that species belongs; perhaps, indeed, that higher genus may not yet have obtained a current name. That proportions hold by permutation, was demonstrated severally for numbers, lines, solids, and intervals of time; but this belongs to each of them, not from any separate property of each, but from what is common to all: that, however, which is common to all had received no name, so that it was not known that one demonstration might comprise all the four.[18] In like manner, a man may know that an equilateral and an isosceles triangle have their three angles equal to two right angles, and also that a scalene triangle has its three angles equal to two right angles; yet he may not know (except sophistically and by accident[19]) that a triangle in genere has its three angles equal to two right angles, though there be no other triangles except equilateral, isosceles, and scalene. He does not know that this may be demonstrated of every triangle quatenus triangle. The only way to obtain a certain recognition of Primum Universale, is, to abstract successively from the several conditions of a demonstration respecting the concrete and particular, until the proposition ceases to be true. Thus, you have before you a brazen isosceles triangle, the three angles whereof are equal to two right angles. You may eliminate the condition brazen, and the proposition will still remain true. You may also eliminate the condition isosceles; still the proposition is true. But you cannot eliminate the condition triangle, so as to retain only the higher genus, geometrical figure; for the proposition then ceases to be always true. Triangle is in this case the Primum Universale.[20]

[Footnote 18: Aristot. Analyt. Post I. v. p. 74, a. 4-23. [Greek: a)lla\ dia\ to\ mê\ ei)=nai ô)nomasme/non ti pa/nta tau=ta e(/n, a)rithmoi/, mê/kê, chro/nos, sterea/, kai\ ei)/dei diaphe/rein a)llê/lôn, chôri\s e)lamba/neto.] What these four have in common is that which he himself expresses by [Greek: Poso/n]--Quantum--in the Categoriæ and elsewhere. (Categor. p. 4, b. 20, seq.; Metaph. [Greek: D]. p. 1020, a. 7, seq.)]

[Footnote 19: Aristot. Analyt. Post. I. v. p. 74, a. 27: [Greek: ou)/pô oi)=de to\ tri/gônon o(/ti du/o o)rthai=s, ei) mê\ to\n sophistiko\n tro/pon ou)de\ katho/lou tri/gônon, ou)/d' ei) mêde/n e)sti para\ tau=ta tri/gônon e(/teron.] The phrase [Greek: to\n sophistiko\n tro/pon] is equivalent to [Greek: to\n sophistiko\n **tro/pon to\n kata\ sumbebêko/s], p. 71, b. 10. I see nothing in it connected with Aristotle's characteristic of a Sophist (special professional life purpose--[Greek: tou= bi/ou tê=| proaire/sei], Metaphys. [Greek: G]. p. 1004, b. 24): the phrase means nothing more than unscientific.]

[Footnote 20: Aristot. Analyt Post I. v. p. 74, a. 32-b. 4.]

In every demonstration the principia or premisses must be not only true, but necessarily true; the conclusion also will then be necessarily true, by reason of the premisses, and this constitutes Demonstration. Wherever the premisses are necessarily true, the conclusion will be necessarily true; but you cannot say, vice versâ, that wherever the conclusion is necessarily true, the syllogistic premisses from which it follows must always be necessarily true. They may be true without being necessarily true, or they may even be false: if, then, the conclusion be necessarily true, it is not so by reason of these premisses; and the syllogistic proof is in this case no demonstration. Your syllogism may have true premisses and may lead to a conclusion which is true by reason of them; but still you have not demonstrated, since neither premisses nor conclusion are necessarily true.[21] When an opponent contests your demonstration, he succeeds if he can disprove the necessity of your conclusion; if he can show any single case in which it either is or may be false.[22] It is not enough to proceed upon a premiss which is either probable or simply true: it may be true, yet not appropriate to the case: you must take your departure from the first or highest universal of the genus about which you attempt to demonstrate.[23] Again, unless you can state the why of your conclusion; that is to say, unless the middle term, by reason of which the conclusion is necessarily true, be itself necessarily true,--you have not demonstrated it, nor do you know it absolutely. Your middle term not being necessary may vanish, while the conclusion to which it was supposed to lead abides: in truth no conclusion was known through that middle.[24] In the complete demonstrative or scientific syllogism, the major term must be predicable essentially or per se of the middle, and the middle term must be predicable essentially or per se of the minor; thus alone can you be sure that the conclusion also is per se or necessary. The demonstration cannot take effect through a middle term which is merely a Sign; the sign, even though it be a constant concomitant, yet being not, or at least not known to be, per se, will not bring out the why of the conclusion, nor make the conclusion necessary. Of non-essential concomitants altogether there is no demonstration; wherefore it might seem to be useless to put questions about such; yet, though the questions cannot yield necessary premisses for a demonstrative conclusion, they may yield premisses from which a conclusion will necessarily follow.[25]

[Footnote 21: Ibid. vi. p. 74, b. 5-18. [Greek: e)x a)lêthô=n me\n ga\r e)/sti kai\ mê\ a)podeiknu/nta sullogi/sthai, e)x a)nagkai/ôn d' ou)k e)/stin a)ll' ê)\ a)podeiknu/nta; tou=to ga\r ê)/dê a)podei/xeô/s e)stin.] Compare Analyt. Prior. I. ii. p. 53, b. 7-25.]

[Footnote 22: Aristot. Analyt. Post. I. vi. p. 74, b. 18: [Greek: sêmei=on d' o(/ti ê( a)po/deixis e)x a)nagkai/ôn, o(/ti kai\ ta\s e)nsta/seis ou(/tô phe/romen pro\s tou\s oi)ome/nous a)podeiknu/nai, o(/ti ou)k a)na/gkê], &c.]

[Footnote 23: Ibid. vi. p. 74, b. 21-26: [Greek: dê=lon d' e)k tou/tôn kai\ o(/ti eu)ê/theis oi( lamba/nein oi)o/menoi kalô=s ta\s a)rcha/s, e)a\n e)/ndoxos ê)=| ê( pro/tasis kai\ a)lêthê/s, oi(=on oi( sophistai\ o(/ti to\ e)pi/stasthai to\ e)pistê/mên e)/chein;], &c.]

[Footnote 24: Aristot. Analyt. Post. I. vi. p. 74, b. 26-p. 75, a. 17.]

[Footnote 25: Ibid. vi. p. 75, a. 8-37.

On the point last mentioned, M. Barthélemy St. Hilaire observes in his note, p. 41: "Dans les questions de dialectique, la conclusion est nécessaire en ce sens, qu'elle suit nécessairement des prémisses; elle n'est pas du tout nécessaire en ce sens, que la chose qu'elle exprime soit nécessaire. Ainsi il faut distinguer la nécessité de la forme et la nécessité de la matière: ou comme disent les scholastiques, necessitas illationis et necessitas materiæ. La dialectique se contente de la première, mais la demonstration a essentiellement besoin des deux."]

In every demonstration three things may be distinguished: (1) The demonstrated conclusion, or Attribute essential to a certain genus; (2) The Genus, of which the attributes per se are the matter of demonstration; (3) The Axioms, out of which, or through which, the demonstration is obtained. These Axioms may be and are common to several genera: but the demonstration cannot be transferred from one genus to another; both the extremes as well as the middle term must belong to the same genus. An arithmetical demonstration cannot be transferred to magnitudes and their properties, except in so far as magnitudes are numbers, which is partially true of some among them. The demonstrations in arithmetic may indeed be transferred to harmonics, because harmonics is subordinate to arithmetic; and, for the like reason, demonstrations in geometry may be transferred to mechanics and optics. But we cannot introduce into geometry any property of lines, which does not belong to them quâ lines; such, for example, as that a straight line is the most beautiful of all lines, or is the contrary of a circular line; for these predicates belong to it, not quâ line, but quâ member of a different or more extensive genus.[26] There can be no complete demonstration about perishable things, or about any individual line, except in regard to its attributes as member of the genus line. Where the conclusion is not eternally true, but true at one time and not true at another, this can only be because one of its premisses is not universal or essential. Where both premisses are universal and essential, the conclusion must be eternal or eternally true. As there is no demonstration, so also there can be no definition, of perishable attributes.[27]

[Footnote 26: Ibid. vii. p. 75, a. 38-b. 20. Mr. Poste, in his translation, here cites (p. 50) a good illustrative passage from Dr. Whewell's Philosophy of the Inductive Sciences, Book II. ii.:--"But, in order that we may make any real advance in the discovery of truth, our ideas must not only be clear; they must also be appropriate. Each science has for its basis a different class of ideas; and the steps which constitute the progress of one science can never be made by employing the ideas of another kind of science. No genuine advance could ever be obtained in Mechanics by applying to the subject the ideas of space and time merely; no advance in Chemistry by the use of mere mechanical conceptions; no discovery in Physiology by referring facts to mere chemical and mechanical principles." &c.]

[Footnote 27: Aristot. Analyt. Post. I. viii. p. 75, b. 21-36. Compare Metaphys. Z. p. 1040, a. 1: [Greek: dê=lon o(/ti ou)k a)\n ei)/ê au)tô=n (tô=n phthartô=n) ou)/th' o(rismo\s ou)/t' a)po/deixis]. Also Biese, Die Philosophie des Aristoteles, ch. iv. p. 249.]

For complete demonstration, it is not sufficient that the premisses be true, immediate, and undemonstrable; they must, furthermore, be essential and appropriate to the class in hand. Unless they be such, you cannot be said to know the conclusion absolutely; you know it only by accident. You can only know a conclusion when demonstrated from its own appropriate premisses; and you know it best when it is demonstrated from its highest premisses. It is sometimes difficult to determine whether we really know or not; for we fancy that we know, when we demonstrate from true and universal principia, without being aware whether they are, or are not, the principia appropriate to the case.[28] But these principia must always be assumed without demonstration--the class whose essential constituent properties are in question, the universal Axioms, and the Definition or meaning of the attributes to be demonstrated. If these definitions and axioms are not always formally enunciated, it is because we tacitly presume them to be already known and admitted by the learner.[29] He may indeed always refuse to grant them in express words, but they are such that he cannot help granting them by internal assent in his mind, to which every syllogism must address itself. When you assume a premiss without demonstrating it, though it be really demonstrable, this, if the learner is favourable and willing to grant it, is an assumption or Hypothesis, valid relatively to him alone, but not valid absolutely: if he is reluctant or adverse, it is a Postulate, which you claim whether he is satisfied or not.[30] The Definition by itself is not an hypothesis; for it neither affirms nor denies the existence of anything. The pupil must indeed understand the terms of it; but this alone is not an hypothesis, unless you call the fact that the pupil comes to learn, an hypothesis.[31] The Hypothesis or assumption is contained in the premisses, being that by which the reason of the conclusion comes to be true. Some object that the geometer makes a false hypothesis or assumption, when he declares a given line drawn to be straight, or to be a foot long, though it is neither one nor the other. But this objection has no pertinence, since the geometer does not derive his conclusions from what is true of the visible lines drawn before his eyes, but from what is true of the lines conceived in his own mind, and signified or illustrated by the visible diagrams.[32]

[Footnote 28: Ibid. ix. p. 75, b. 37-p. 76, a. 30.]

[Footnote 29: Ibid. x. p. 76, a. 31-b. 22.]

[Footnote 30: Aristot. Analyt. Post. I. x. p. 76, b. 29-34: [Greek: e)a\n me\n dokou=nta lamba/nê| tô=| mantha/nonti, u(poti/thetai, kai\ e)/stin ou)/ch a(plô=s u(po/thesis, a)lla\ pro\s e)kei=non mo/non, a)\n de\ ê)\ mêdemi/a=s e)nou/sês do/xês ê)\ kai\ e)nanti/as e)nou/sês lamba/nê| to\ au)to/, ai)tei=tai. kai\ tou/tô| diaphe/rei u(po/thesis kai\ ai)/têma], &c. Themistius, Paraphras. p. 37, Spengel.]

[Footnote 31: Ibid. p. 76, b. 36: [Greek: tou=to d' ou)ch u(po/thesis, ei) mê\ kai\ to\ a)kou/ein u(po/thesi/n tis ei)=nai phê/sei]. For the meaning of [Greek: to\ a)kou/ein], compare [Greek: o( a)kou/ôn], infra, Analyt. Post. I. xxiv. p. 85, b. 22.]

[Footnote 32: Ibid. p. 77, a. 1: [Greek: o( de\ geôme/três ou)de\n sumperai/netai tô=| tê/nde ei)=nai tê\n grammê\n ê(\n au)to\s e)/phthegktai, a)lla\ ta\ dia\ tou/tôn dêlou/mena.]

Themistius, Paraphr. p. 37: [Greek: ô(/sper ou)d' oi( geôme/trai ke/chrêntai tai=s grammai=s u(pe\r ô(=n diale/gontai kai\ deiknu/ousin, a)ll' a(\s e)/chousin e)n tê=| psuchê=|, ô(=n ei)si\ su/mbola ai( grapho/menai.]

A similar doctrine is asserted, Analyt. Prior. I. xli. p. 49, b. 35, and still more clearly in De Memoria et Reminiscentia, p. 450, a. 2-12.]

The process of Demonstration neither requires, nor countenances, the Platonic theory of Ideas--universal substances beyond and apart from particulars. But it does require that we should admit universal predications; that is, one and the same predicate truly applicable in the same sense to many different particulars. Unless this be so, there can be no universal major premiss, nor appropriate middle term, nor valid demonstrative syllogism.[33]

[Footnote 33: Aristot. Analyt. Post. I. xi. p. 77, a. 5-9.]

The Maxim or Axiom of Contradiction, in its most general enunciation, is never formally enunciated by any special science; but each of them assumes the Maxim so far as applicable to its own purpose, whenever the Reductio ad Absurdum is introduced.[34] It is in this and the other common principles or Axioms that all the sciences find their point of contact and communion; and that Dialectic also comes into communion with all of them, as also the science (First Philosophy) that scrutinizes the validity or demonstrability of the Axioms.[35] The dialectician is not confined to any one science, or to any definite subject-matter. His liberty of interrogation is unlimited; but his procedure is essentially interrogatory, and he is bound to accept the answer of the respondent--whatever it be, affirmative or negative--as premiss for any syllogism that he may construct. In this way he can never be sure of demonstrating any thing; for the affirmative and the negative will not be equally serviceable for that purpose. There is indeed also, in discussions on the separate sciences, a legitimate practice of scientific interrogation. Here the questions proper to be put are limited in number, and the answers proper to be made are determined beforehand by the truths of the science--say Geometry; still, an answer thus correctly made will serve to the interrogator as premiss for syllogistic demonstration.[36] The respondent must submit to have such answer tested by appeal to geometrical principia and to other geometrical propositions already proved as legitimate conclusions from the principia; if he finds himself involved in contradictions, he is confuted quâ geometer, and must correct or modify his answer. But he is not bound, quâ geometer, to undergo scrutiny as to the geometrical principia themselves; this would carry the dialogue out of the province of Geometry into that of First Philosophy and Dialectic. Care, indeed, must be taken to keep both questions and answers within the limits of the science. Now there can be no security for this restriction, except in the scientific competence of the auditors. Refrain, accordingly, from all geometrical discussions among men ignorant of geometry and confine yourself to geometrical auditors, who alone can distinguish what questions and answers are really appropriate. And what is here said about geometry, is equally true about the other special sciences.[37] Answers may be improper either as foreign to the science under debate, or as appertaining to the science, yet false as to the matter, or as equivocal in middle term; though this last is less likely to occur in Geometry, since the demonstrations are accompanied by diagrams, which help to render conspicuous any such ambiguity.[38] To an inductive proposition, bringing forward a single case as contributory to an ultimate generalization, no general objection should be offered; the objection should be reserved until the generalization itself is tendered.[39] Sometimes the mistake is made of drawing an affirmative conclusion from premisses in the Second figure; this is formally wrong, but the conclusion may in some cases be true, if the major premiss happens to be a reciprocating proposition, having its predicate co-extensive with its subject. This, however, cannot be presumed; nor can a conclusion be made to yield up its principles by necessary reciprocation; for we have already observed that, though the truth of the premisses certifies the truth of the conclusion, we cannot say vice versâ that the truth of the conclusion certifies the truth of the premisses. Yet propositions are more frequently found to reciprocate in scientific discussion than in Dialectic; because, in the former, we take no account of accidental properties, but only of definitions and what follows from them.[40]

[Footnote 34: Ibid. a. 10, seq.]

[Footnote 35: Ibid. a. 26-30: [Greek: kai\ ei)/ tis katho/lou peirô=|to deiknu/nai ta\ koina/, oi(=on o(/ti a(/pan pha/nai ê)\ a)popha/nai, ê)\ o(/ti i)/sa a)po\ i)/sôn, ê)\ tô=n toiou/tôn a)/tta.] Compare Metaph. K. p. 1061**, b. 18.]

[Footnote 36: Aristot. Analyt. Post. I. xii, p. 77, a. 36-40; Themistius, p. 40.

The text is here very obscure. He proceeds to distinguish Geometry especially (also other sciences, though less emphatically) from [Greek: ta\ e)n toi=s dialo/gois] (I. xii. p. 78, a. 12).

Julius Pacius, ad Analyt. Post. I. viii. (he divides the chapters differently), p. 417, says:--"Differentia interrogationis dialecticæ et demonstrativæ hæc est. Dialecticus ita interrogat, ut optionem det adversario, utrum malit affirmare an negare. Demonstrator vero interrogat ut rem evidentiorem faciat; id est, ut doceat ex principiis auditori notis."]

[Footnote 37: Ibid. I. xii. p. 77, b. 1-15; Themistius, p. 41: [Greek: ou) ga\r ô(/sper tô=n e)ndo/xôn oi( polloi\ kritai/, ou(/tô kai\ tô=n kat' e)pistê/mên oi( a)nepistê/mones].]

[Footnote 38: Analyt. Post. I. xii. p. 77, b. 16-33. Propositions within the limits of the science, but false as to matter, are styled by Aristotle [Greek: pseudographê/mata]. See Aristot. Sophist. Elench. xi. p. 171, b. 14; p. 172, a. 1.

"L'interrogation syllogistique se confondant avec la proposition, il s'ensuit que l'interrogation doit être, comme la proposition, propre à la science dont il s'agit." (Barthélemy St Hilaire, note, p. 70). Interrogation here has a different meaning from that which it bears in Dialectic.]

[Footnote 39: Ibid. I. xii. p. 77**, b. 34 seq. This passage is to me hardly intelligible. It is differently understood by commentators and translators. John Philoponus in the Scholia (p. 217, b. 17-32, Brandis), cites the explanation of it given by Ammonius, but rejects that explanation, and waits for others to supply him with a better. Zabarella (Comm. in Analyt. Post. pp. 426, 456, ed. Venet 1617) admits that as it stands, and where it stands, it is unintelligible, but transposes it to another part of the book (to the end of cap. xvii., immediately before the words [Greek: phanero\n de\ kai\ o(/ti], &c., of c. xviii.), and gives an explanation of it in this altered position. But I do not think he has succeeded in clearing it up.]

[Footnote 40: Ibid. I. xii. p. 77, b. 40-p. 78, a. 13.]

Knowledge of Fact and knowledge of the Cause must be distinguished, and even within the same Science.[41] In some syllogisms the conclusion only brings out [Greek: to\ o(/ti]--the reality of certain facts; in others, it ends in [Greek: to\ dio/ti]--the affirmation of a cause, or of the Why. The syllogism of the Why is, where the middle term is not merely the cause, but the proximate cause, of the conclusion. Often, however, the effect is more notorious, so that we employ it as middle term, and conclude from it to its reciprocating cause; in which case our syllogism is only of the [Greek: o(/ti]; and so it is also when we employ as middle term a cause not proximate but remote, concluding from that to the effect.[42] Sometimes the syllogisms of the [Greek: o(/ti] may fall under one science, those of the [Greek: dio/ti] under another, namely, in the case where one science is subordinate to another, as optics to geometry, and harmonics to arithmetic; the facts of optics and harmonics belonging to sense and observation, the causes thereof to mathematical reasoning. It may happen, then, that a man knows [Greek: to\ dio/ti] well, but is comparatively ignorant [Greek: tou= o(/ti]: the geometer may have paid little attention to optical facts.[43] Cognition of the [Greek: dio/ti] is the maximum, the perfection, of all cognition; and this, comprising arithmetical and geometrical theorems, is almost always attained by syllogisms in the First figure. This figure is the most truly scientific of the three; the other two figures depend upon it for expansion and condensation. It is, besides, the only one in which universal affirmative conclusions can be obtained; for in the Second figure we get only negative conclusions; in the Third, only particular. Accordingly, propositions declaring Essence or Definition, obtained only through universal affirmative conclusions, are yielded in none but the First figure.[44]

[Footnote 41: Ibid. I. xiii. p. 77, a. 22 seq.]

[Footnote 42: Themistius, p. 45: [Greek: polla/kis sumbai/nei kai\ a)ntistre/phein a)llê/lois to\ ai)tion kai\ to\ sêmei=on kai\ a)/mphô dei/knusthai di' a)llê/lôn, dia\ tou= sêmei/ou me\n ô(s to\ o(/ti, dia\ thate/rou de\ ô(s to\ dio/ti.]

"Cum enim vera demonstratio, id est [Greek: tou= dio/ti], fiat per causam proximam, consequens est, ut demonstratio vel per effectum proximum, vel per causam remotam, sit demonstratio [Greek: tou= o(/ti]" (Julius Pacius, Comm. p. 422).

M. Barthélemy St. Hilaire observes (Note, p. 82):--"La cause éloignée non immédiate, donne un syllogisme dans la seconde figure.--Il est vrai qu'Aristote n'appelle cause que la cause immédiate; et que la cause éloignée n'est pas pour lui une véritable cause."

See in Schol. p. 188, a. 19, the explanation given by Alexander of the syllogism [Greek: tou= dio/ti].]

[Footnote 43: Analyt. Post. I. xiii. p. 79, a. 2, seq.: [Greek: e)ntau=tha ga\r to\ me\n o(/ti tô=n ai)sthêtikô=n ei)de/nai, to\ de\ dio/ti tô=n mathêmatikô=n], &c. Compare Analyt. Prior. II. xxi. p. 67, a. 11; and Metaphys. A. p. 981, a. 15.]

[Footnote 44: Analyt. Post. I. xiv. p. 79, a. 17-32.]

As there are some affirmative propositions that are indivisible, i.e., having affirmative predicates which belong to a subject at once, directly, immediately, indivisibly,--so there are also some indivisible negative propositions, i.e., with predicates that belong negatively to a subject at once, directly, &c. In all such there is no intermediate step to justify either the affirmation of the predicate, or the negation of the predicate, respecting the given subject. This will be the case where neither the predicate nor the subject is contained in any higher genus.[45]

[Footnote 45: Ibid. I. xv. p. 79, a. 33-b. 22. The point which Aristotle here especially insists upon is, that there may be and are immediate, undemonstrable, negative (as well as affirmative) predicates: [Greek: phanero\n ou)=n o(/ti e)nde/chetai/ te a)/llo a)/llô| mê\ u(pa/rchein a)to/môs]. (Themistius, Paraphr. p. 48, Spengel: [Greek: a)/mesoi de\ prota/seis ou) katapha/seis mo/non ei)si/n, a)lla\ kai\ a)popha/seis o(moi/ôs ai(\ mê\ du/nantai dia\ sullogismou= deichthê=nai, au(=tai d' ei)si\n e)ph' ô(=n ou)dete/rou tô=n o(/rôn a)/llos tis o(/lou katêgorei=tai.]) It had been already shown, in an earlier chapter of this treatise (p. 72, b. 19), that there were affirmative predicates immediate and undemonstrable. This may be compared with that which Plato declares in the Sophistes (pp. 253-254, seq.) about the intercommunion [Greek: tô=n genô=n kai\ tô=n ei)dô=n] with each other. Some of them admit such intercommunion, others repudiate it.]

In regard both to these propositions immediate and indivisible, and to propositions mediate and deducible, there are two varieties of error.[46] You may err simply, from ignorance, not knowing better, and not supposing yourself to know at all; or your error may be a false conclusion, deduced by syllogism through a middle term, and accompanied by a belief on your part that you do know. This may happen in different ways. Suppose the negative proposition, No B is A, to be true immediately or indivisibly. Then, if you conclude the contrary of this[47] (All B is A) to be true, by syllogism through the middle term C, your syllogism must be in the First figure; it must have the minor premiss false (since B is brought under C, when it is not contained in any higher genus), and it may have both premisses false. Again, suppose the affirmative proposition, All B is A, to be true immediately or indivisibly. Then if you conclude the contrary of this (No B is A) to be true, by syllogism through the middle term C, your syllogism may be in the First figure, but it may also be in the Second figure, your false conclusion being negative. If it be in the First figure, both its premisses may be false, or one of them only may be false, either indifferently.[48] If it be in the Second figure, either premiss singly may be wholly false, or both may be partly false.[49]

[Footnote 46: Analyt. Post. I. xvi. p. 79, b. 23: [Greek: a)/gnoia kat' a)po/phasin--a)/gnoia kata\ dia/thesin]. See Themistius, p. 49, Spengel. In regard to simple and uncombined ideas, ignorance is not possible as an erroneous combination, but only as a mental blank. You either have the idea and thus know so much truth, or you have not the idea and are thus ignorant to that extent; this is the only alternative. Cf. Aristot. Metaph. [Greek: Th]. p. 1051, a. 34; De Animâ, III. vi. p. 430, a. 26.]

[Footnote 47: Analyt. Post. I. xvi. p. 79, b. 29. M. Barthélemy St. Hilaire remarks (p. 95, n.):--"Il faut remarquer qu'Aristote ne s'occupe que des modes universels dans la première et dans la seconde figure, parceque, la démonstration étant toujours universelle, les propositions qui expriment l'erreur opposée doivent l'être comme elle. Ainsi ce sont les propositions contraires, et non les contradictoires, dont il sera question ici."

For the like reason the Third figure is not mentioned here, but only the First and Second: because in the Third figure no universal conclusion can be proved (Julius Pacius, p. 431).]

[Footnote 48: Analyt. Post. I. xvi. p. 80, a. 6-26.]

[Footnote 49: Ibid. a. 27-b. 14: [Greek: e)n de\ tô=| me/sô| schê/mati o(/las me\n ei)=nai ta\s prota/seis a)mphote/ras pseudei=s ou)k e)nde/chetai--e)pi/ ti d' e(kate/ran ou)de\n kôlu/ei pseudê= ei)=nai.]]

Let us next assume the affirmative proposition, All B is A, to be true, but mediate and deducible through the middle term C. If you conclude the contrary of this (No B is A) through the same middle term C, in the First figure, your error cannot arise from falsity in the minor premiss, because your minor (by the laws of the figure) must be affirmative; your error must arise from a false major, because a negative major is not inconsistent with the laws of the First figure. On the other hand, if you conclude the contrary in the First figure through a different middle term, D, either both your premisses will be false, or your minor premiss will be false.[50] If you employ the Second figure to conclude your contrary, both your premisses cannot be false, though either one of them singly may be false.[51]

[Footnote 50: Analyt. Post. I. xvi. p. 80, b. 17-p. 81, a. 4.]

[Footnote 51: Ibid. p. 81, a. 5-14.]

Such will be the case when the deducible proposition assumed to be true is affirmative, and when therefore the contrary conclusion which you profess to have proved is negative. But if the deducible proposition assumed to be true is negative, and if consequently the contrary conclusion must be affirmative,--then, if you try to prove this contrary through the same middle term, your premisses cannot both be false, but your major premiss must always be false.[52] If, however, you try to prove the contrary through a different and inappropriate middle term, you cannot convert the minor premiss to its contrary (because the minor premiss must continue affirmative, in order that you may arrive at any conclusion at all), but the major can be so converted. Should the major premiss thus converted be true, the minor will be false; should the major premiss thus converted be false, the minor may be either true or false. Either one of the premisses, or both the premisses, may thus be false.[53]

[Footnote 52: Ibid. xvii. p. 81, a. 15-20.]

[Footnote 53: Ibid. a. 20-34. Mr. Poste's translation (pp. 65-70) is very perspicuous and instructive in regard to these two difficult chapters.]

Errors of simple ignorance (not concluded from false syllogism) may proceed from defect or failure of sensible perception, in one or other of its branches. For without sensation there can be no induction; and it is from induction only that the premisses for demonstration by syllogism are obtained. We cannot arrive at universal propositions, even in what are called abstract sciences, except through induction of particulars; nor can we demonstrate except from universals. Induction and Demonstration are the only two ways of learning; and the particulars composing our inductions can only be known through sense.[54]

[Footnote 54: Analyt. Post. I. xviii. p. 81, a. 38-b. 9. In this important chapter (the doctrines of which are more fully expanded in the last chapter of the Second Book of the Analyt. Post.), the text of Waitz does not fully agree with that of Julius Pacius. In Firmin Didot's edition the text is the same as in Waitz; but his Latin translation remains adapted to that of Julius Pacius. Waitz gives the substance of the chapter as follows (ad Organ. II. p. 347):-- "Universales propositiones omnes inductione comparantur, quum etiam in iis, quæ a sensibus maxime aliena videntur et quæ, ut mathematica ([Greek: ta\ e)x a)phaire/seôs]), cogitatione separantur à materia quacum conjuncta sunt, inductione probentur ea quæ de genero (e. g., de linea vel de corpore mathematico), ad quod demonstratio pertineat, prædicentur [Greek: kath' au(ta/] et cum ejus natura conjuncta sint. Inductio autem iis nititur quæ sensibus percipiuntur; nam res singulares sentiuntur, scientia vero rerum singularium non datur sine inductione, non datur inductio sine sensu."]

Aristotle next proceeds to show (what in previous passages he had assumed)[55] that, if Demonstration or the syllogistic process be possible--if there be any truths supposed demonstrable, this implies that there must be primary or ultimate truths. It has been explained that the constituent elements assumed in the Syllogism are three terms and two propositions or premisses; in the major premiss, A is affirmed (or denied) of all B; in the minor, B is affirmed of all C; in the conclusion, A is affirmed (or denied) of all C.[56] Now it is possible that there may be some one or more predicates higher than A, but it is impossible that there can be an infinite series of such higher predicates. So also there may be one or more subjects lower than C, and of which C will be the predicate; but it is impossible that there can be an infinite series of such lower subjects. In like manner there may perhaps be one or more middle terms between A and B, and between B and C; but it is impossible that there can be an infinite series of such intervening middle terms. There must be a limit to the series ascending, descending, or intervening.[57] These remarks have no application to reciprocating propositions, in which the predicate is co-extensive with the subject.[58] But they apply alike to demonstrations negative and affirmative, and alike to all the three figures of Syllogism.[59]

[Footnote 55: Analyt. Prior. I. xxvii. p. 43, a. 38; Analyt. Post. I. ii. p. 71, b. 21.]

[Footnote 56: Analyt. Post. I. xix. p. 81, b. 10-17.]

[Footnote 57: Ibid. p. 81, b. 30-p. 82, a. 14.]

[Footnote 58: Ibid. p. 82, a. 15-20. M. Barthélemy St. Hilaire, p. 117:--"Ceci ne saurait s'appliquer aux termes réciproques, parce que dans les termes qui peuvent être attribués réciproquement l'un à l'autre, on ne peut pas dire qu'il y ait ni premier ni dernier rélativement à l'attribution."]

[Footnote 59: Analyt. Post. I. xx., xxi. p. 82, a. 21-b. 36.]

In Dialectical Syllogism it is enough if the premisses be admitted or reputed as propositions immediately true, whether they are so in reality or not; but in Scientific or Demonstrative Syllogism they must be so in reality: the demonstration is not complete unless it can be traced up to premisses that are thus immediately or directly true (without any intervening middle term).[60] That there are and must be such primary or immediate premisses, Aristotle now undertakes to prove, by some dialectical reasons, and other analytical or scientific reasons.[61] He himself thus distinguishes them; but the distinction is faintly marked, and amounts, at most, to this, that the analytical reasons advert only to essential predication, and to the conditions of scientific demonstration, while the dialectical reasons dwell upon these, but include something else besides, viz., accidental predication. The proof consists mainly in the declaration that, unless we assume some propositions to be true immediately, indivisibly, undemonstrably,--Definition, Demonstration, and Science would be alike impossible. If the ascending series of predicates is endless, so that we never arrive at a highest generic predicate; if the descending series of subjects is endless, so that we never reach a lowest subject,--no definition can ever be attained. The essential properties included in the definition, must be finite in number; and the accidental predicates must also be finite in number, since they have no existence except as attached to some essential subject, and since they must come under one or other of the nine later Categories.[62] If, then, the two extremes are thus fixed and finite--the highest predicate and the lowest subject--it is impossible that there can be an infinite series of terms between the two. The intervening terms must be finite in number. The Aristotelian theory therefore is, that there are certain propositions directly and immediately true, and others derived from them by demonstration through middle terms.[63] It is alike an error to assert that every thing can be demonstrated, and that nothing can be demonstrated.

[Footnote 60: Ibid. xix. p. 81, b. 18-29.]

[Footnote 61: Ibid. xxi. p. 82, b. 35; xxii. p. 84, a. 7: [Greek: logikô=s me\n ou)=n e)k tou/tôn a)/n tis pisteu/seie peri\ tou= lechthe/ntos, a)nalutikô=s de\ dia\ tô=nde phanero\n suntomô/teron.] In Scholia, p. 227, a. 42, the same distinction is expressed by Philoponus in the terms [Greek: logikô/tera] and [Greek: pragmatôde/stera]. Compare Biese, Die Philosophie des Aristoteles, pp. 134, 261; Bassow, De Notionis Definitione, pp. 19, 20; Heyder, Aristot. u. Hegel. Dialektik, pp. 316, 317.

Aristotle, however, does not always adhere closely to the distinction. Thus, if we compare the logical or dialectical reasons given, p. 82, b. 37, seq., with the analytical, announced as beginning p. 84, a. 8, seq., we find the same main topic dwelt upon in both, namely, that to admit an infinite series excludes the possibility of Definition. Both Alexander and Ammonius agree in announcing this as the capital topic on which the proof turned; but Alexander inferred from hence that the argument was purely dialectical ([Greek: logiko\n e)pichei/rêma]), while Ammonius regarded it as a reason thoroughly convincing and evident: [Greek: o( me/ntoi philo/sophos] (Ammonius) [Greek: e)/lege mê\ dia\ tou=to le/gein logika\ ta\ e)picheirê/mata; e)narge\s ga\r o(/ti ei)si\n o(rismoi/, ei) mê\ a)katalêpsi/an ei)saga/gômen] (Schol. p. 227, a. 40, seq., Brand.).]

[Footnote 62: Analyt. Post. I. xxii. p. 83, a. 20, b. 14. Only eight of the ten Categories are here enumerated.]

[Footnote 63: Ibid. I. xxii. p. 84, a. 30-35. The paraphrase of Themistius (pp. 55-58, Spengel) states the Aristotelian reasoning in clearer language than Aristotle himself. Zabarella (Comm. in Analyt. Post. I. xviii.; context. 148, 150, 154) repeats that Aristotle's proof is founded upon the undeniable fact that there are definitions, and that without them there could be no demonstration and no science. This excludes the supposition of an infinite series of predicates and of middle terms:--"Sumit rationem à definitione; si in predicatis in quid procederetur ad infinitum, sequeretur auferri definitionem et omnino essentiæ cognitionem; sed hoc dicendum non est, quum omnium consensioni adversetur" (p. 466, Ven. 1617).]

It is plain from Aristotle's own words[64] that he intended these four chapters (xix.-xxii.) as a confirmation of what he had already asserted in chapter iii. of the present treatise, and as farther refutation of the two distinct classes of opponents there indicated: (1) those who said that everything was demonstrable, demonstration in a circle being admissible; (2) those who said that nothing was demonstrable, inasmuch as the train of predication upwards, downwards, and intermediate, was infinite. Both these two classes of opponents agreed in saying, that there were no truths immediate and indemonstrable; and it is upon this point that Aristotle here takes issue with them, seeking to prove that there are and must be such truths. But I cannot think the proof satisfactory; nor has it appeared so to able commentators either of ancient or modern times--from Alexander of Aphrodisias down to Mr. Poste.[65] The elaborate amplification added in these last chapters adds no force to the statement already given at the earlier stage; and it is in one respect a change for the worse, inasmuch as it does not advert to the important distinction announced in chapter iii., between universal truths known by Induction (from sense and particulars), and universal truths known by Deduction from these. The truths immediate and indemonstrable (not known through a middle term) are the inductive truths, as Aristotle declares in many places, and most emphatically at the close of the Analytica Posteriora. But in these chapters, he hardly alludes to Induction. Moreover, while trying to prove that there must be immediate universal truths, he neither gives any complete list of them, nor assigns any positive characteristic whereby to identify them. Opponents might ask him whether these immediate universal truths were not ready-made inspirations of the mind; and if so, what better authority they had than the Platonic Ideas, which are contemptuously dismissed.

[Footnote 64: Analyt. Post. I. xxii. p. 84, a. 32: [Greek: o(/per e)/phame/n tinas le/gein kat' a)rcha/s], &c.]

[Footnote 65: See Mr. Poste's note, p. 77, of his translation of this treatise. After saying that the first of Aristotle's dialectical proofs is faulty, and that the second is a petitio principii, Mr. Poste adds, respecting the so-called analytical proof given by Aristotle:--"It is not so much a proof, as a more accurate determination of the principle to be postulated. This postulate, the existence of first principles, as concerning the constitution of the world, appears to belong properly to Metaphysics, and is merely borrowed by Logic. See Metaph. ii. 2, and Introduction." In the passage of the Metaphysica ([Greek: a]. p. 994) here cited the main argument of Aristotle is open to the same objection of petitio principii which Mr. Poste urges against Aristotle's second dialectical argument in this place.

Mr. John Stuart Mill, in his System of Logic, takes for granted that there must be immediate, indemonstrable truths, to serve as a basis for deduction; "that there cannot be a chain of proof suspended from nothing;" that there must be ultimate laws of nature, though we cannot be sure that the laws now known to us are ultimate.

On the other hand, we read in the recent work of an acute contemporary philosopher, Professor Delboeuf (Essai de Logique Scientifique, Liège, 1865, Pref. pp. v, vii, viii, pp. 46, 47:)--"Il est des points sur lesquels je crains de ne m'être pas expliqué assez nettement, entre autres la question du fondement de la certitude. Je suis de ceux qui repoussent de toutes leurs forces l'axiome si spécieux qu'on ne peut tout démontrer; cette proposition aurait, à mes yeux, plus besoin que toute autre d'une démonstration. Cette démonstration ne sera en partie donnée que quand on aura une bonne fois énuméré toutes les propositions indémontrables; et quand on aura bien défini le caractère auquel on les reconnait. Nulle part on ne trouve ni une semblable énumération, ni une semblable définition. On reste à cet égard dans une position vague, et par cela même facile à défendre."

It would seem, by these words, that M. Delboeuf stands in the most direct opposition to Aristotle, who teaches us that the [Greek: a)rchai\] or principia from which demonstration starts cannot be themselves demonstrated. But when we compare other passages of M. Delboeuf's work, we find that, in rejecting all undemonstrable propositions, what he really means is to reject all self-evident universal truths, "C'est donc une véritable illusion d'admettre des vérités évidentes par elles-mêmes. Il n'y a pas de proposition fausse que nous ne soyons disposés d'admettre comme axiome, quand rien ne nous a encore autorisés à la repousser" (p. ix.). This is quite true in my opinion; but the immediate indemonstrable truths for which Aristotle contends as [Greek: a)rchai\] of demonstration, are not announced by him as self-evident, they are declared to be results of sense and induction, to be raised from observation of particulars multiplied, compared, and permanently formularized under the intellectual habitus called Noûs. By Demonstration Aristotle means deduction in its most perfect form, beginning from these [Greek: a)rchai\] which are inductively known but not demonstrable (i. e. not knowable deductively). And in this view the very able and instructive treatise of M. Delboeuf mainly coincides, assigning even greater preponderance to the inductive process, and approximating in this respect to the important improvements in logical theory advanced by Mr. John Stuart Mill.

Among the universal propositions which are not derived from Induction, but which serve as [Greek: a)rchai\] for Deduction and Demonstration, we may reckon the religious, ethical, æsthetical, social, political, &c., beliefs received in each different community, and impressed upon all newcomers born into it by the force of precept, example, authority. Here the major premiss is felt by each individual as carrying an authority of its own, stamped and enforced by the sanction of society, and by the disgrace or other penalties in store for those who disobey it. It is ready to be interpreted and diversified by suitable minor premisses in all inferential applications. But these [Greek: a)rchai\] for deduction, differing widely at different times and places, though generated in the same manner and enforced by the same sanction, would belong more properly to the class which Aristotle terms [Greek: ta\ e)/ndoxa].]

We have thus recognized that there exist immediate (ultimate or primary) propositions, wherein the conjunction between predicate and subject is such that no intermediate term can be assigned between them. When A is predicated both of B and C, this may perhaps be in consequence of some common property possessed by B and C, and such common property will form a middle term. For example, equality of angles to two right angles belongs both to an isosceles and to a scalene triangle, and it belongs to them by reason of their common property--triangular figure; which last is thus the middle term. But this need not be always the case.[66] It is possible that the two propositions--A predicated of B, A predicated of C--may both of them be immediate propositions; and that there may be no community of nature between B and C. Whenever a middle term can be found, demonstration is possible; but where no middle term can be found, demonstration is impossible. The proposition, whether affirmative or negative, is then an immediate or indivisible one. Such propositions, and the terms of which they are composed, are the ultimate elements or principia of Demonstration. Predicate and subject are brought constantly into closer and closer conjunction, until at last they become one and indivisible.[67] Here we reach the unit or element of the syllogizing process. In all scientific calculations there is assumed an unit to start from, though in each branch of science it is a different unit; e.g. in barology, the pound-weight; in harmonics, the quarter-tone; in other branches of science, other units.[68] Analytical research teaches us that the corresponding unit in Syllogism is the affirmative or negative proposition which is primary, immediate, indivisible. In Demonstration and Science it is the Noûs or Intellect.[69]

[Footnote 66: Analyt. Post. I. xxiii. p. 84, b. 3-18. [Greek: tou=to d' ou)k a)ei\ ou(/tôs e)/chei.]]

[Footnote 67: Ibid. b. 25-37. [Greek: a)ei\ to\ me/son puknou=tai, e(/ôs a)diai/reta ge/nêtai kai\ e(/n. e)/sti d' e(/n, o(/tan a)/meson ge/nêtai kai\ mi/a pro/tasis a(plô=s ê( a)/mesos.]]

[Footnote 68: Analyt. Post. I. xxiii. p. 84, b. 37: [Greek: kai\ ô(/sper e)n toi=s a)/llois ê( a)rchê\ a(plou=n, tou=to d' ou) tau)to\ pantachou=, a)ll' e)n barei= me\n mna=, e)n de\ me/lei di/esis, a)/llo d' e)n a)/llô|, ou(/tôs e)n sullogismô=| to\ e(\n pro/tasis a)/mesos, e)n d' a)podei/xei kai\ e)pistê/mê| o( nou=s.]]

[Footnote 69: Ibid. b. 35-p. 85, a. 1.]

Having thus, in the long preceding reasoning, sought to prove that all demonstration must take its departure from primary undemonstrable principia--from some premisses, affirmative and negative, which are directly true in themselves, and not demonstrable through any middle term or intervening propositions, Aristotle now passes to a different enquiry. We have some demonstrations in which the conclusion is Particular, others in which it is Universal: again, some Affirmative, some Negative, Which of the two, in each of these alternatives, is the best? We have also demonstrations Direct or Ostensive, and demonstrations Indirect or by way of Reductio ad Absurdum. Which of these two is the best? Both questions appear to have been subjected to debate by contemporary philosophers.[70]

[Footnote 70: Ibid. xxiv. p. 85, a. 13-18. [Greek: a)mphisbêtei=tai pote/ra belti/ôn; ô(s d' au(/tôs kai\ peri\ tê=s a)podeiknu/nai legome/nês kai\ tê=s ei)s to\ a)du/naton a)gou/sês a)podei/xeôs.]]

Aristotle discusses these points dialectically (as indeed he points out in the Topica that the comparison of two things generally, as to better and worse, falls under the varieties of **dialectical enquiry[71]), first stating and next refuting the arguments on the weaker side. Some persons may think (he says) that demonstration of the Particular is better than demonstration of the Universal: first, because it conducts to fuller cognition of that which the thing is in itself, and not merely that which it is quatenus member of a class; secondly, because demonstrations of the Universal are apt to generate an illusory belief, that the Universal is a distinct reality apart from and independent of all its particulars (i.e., that figure in general has a real existence apart from all particular figures, and number in general apart from all particular numbers, &c.), while demonstrations of the Particular do not lead to any such illusion.[72]

[Footnote 71: Aristot. Topic. III. i. p. 116, a. 1, seq.]

[Footnote 72: Analyt. Post. I. xxiv. p. 85, a. 20-b. 3. Themistius, pp. 58-59, Spengel: [Greek: ou) ga\r o(mô/numon to\ katho/lou e)sti/n, ou)de\ phônê\ mo/non, a)ll' u(po/stasis, ou) chôristê\ me\n ô(/sper ou)de\ ta\ sumbebêko/ta, e)nargô=s d' ou)=n emphainome/nê toi=s pra/gmasin.] The Scholastic doctrine of Universalia in re is here expressed very clearly by Themistius.]

To these arguments Aristotle replies:--1. It is not correct to say that cognition of the Particular is more complete, or bears more upon real existence, than cognition of the Universal. The reverse would be nearer to the truth. To know that the isosceles, quatenus triangle, has its three angles equal to two right angles, is more complete cognition than knowing simply that the isosceles has its three angles equal to two right angles. 2. If the Universal be not an equivocal term--if it represents one property and one definition common to many particulars, it then has a real existence as much or more than any one or any number of the particulars. For all these particulars are perishable, but the class is imperishable. 3. He who believes that the universal term has one meaning in all the particulars, need not necessarily believe that it has any meaning apart from all particulars; he need not believe this about Quiddity, any more than he believes it about Quality or Quantity. Or if he does believe so, it is his own individual mistake, not imputable to the demonstration. 4. We have shown that a complete demonstration is one in which the middle term is the cause or reason of the conclusion. Now the Universal is most of the nature of Cause; for it represents the First Essence or the Per Se, and is therefore its own cause, or has no other cause behind it. The demonstration of the Universal has thus more of the Cause or the Why, and is therefore better than the demonstration of the Particular. 5. In the Final Cause or End of action, there is always some ultimate end for the sake of which the intermediate ends are pursued, and which, as it is better than they, yields, when it is known, the only complete explanation of the action. So it is also with the Formal Cause: there is one highest form which contains the Why of the subordinate forms, and the knowledge of which is therefore better; as when, for example, the exterior angles of a given isosceles triangle are seen to be equal to four right angles, not because it is isosceles or triangle, but because it is a rectilineal figure. 6. Particulars, as such, fall into infinity of number, and are thus unknowable; the Universal tends towards oneness and simplicity, and is thus essentially knowable, more fully demonstrable than the infinity of particulars. The demonstration thereof is therefore better. 7. It is also better, on another ground; for he that knows the Universal does in a certain sense know also the Particular;[73] but he that knows the Particular cannot be said in any sense to know the Universal. 8. The principium or perfection of cognition is to be found in the immediate proposition, true per se. When we demonstrate, and thus employ a middle term, the nearer the middle term approaches to that principium, the better the demonstration is. The demonstration of the Universal is thus better and more accurate than that of the Particular.[74]

[Footnote 73: Compare Analyt. Post. I. i. p. 71, a. 25; also Metaphys. A. p. 981, a. 12.]

[Footnote 74: Analyt. Post. I. xxiv. p. 85, b. 4-p. 86, a. 21. Schol. p. 233, b. 6: [Greek: o(moi/ôs de\ o)/ntôn gnôri/môn, ê( di' e)latto/nôn me/sôn ai(retôte/ra; ma=llon ga\r e)ggute/rô tê=s tou= nou= e)nergei/as.]]

Such are the several reasons enumerated by Aristotle in refutation of the previous opinion stated in favour of the Particular. Evidently he does not account them all of equal value: he intimates that some are purely dialectical ([Greek: logika/]); and he insists most upon the two following:--1. He that knows the Universal knows in a certain sense the Particular; if he knows that every triangle has its three angles equal to two right angles, he knows potentially that the isosceles has its three angles equal to the same, though he may not know as yet that the isosceles is a triangle. But he that knows the Particular does not in any way know the Universal, either actually or potentially.[75] 2. The Universal is apprehended by Intellect or Noûs, the highest of all cognitive powers; the Particular terminates in sensation. Here, I presume, he means, that, in demonstration of the Particular, the conclusion teaches you nothing more than you might have learnt from a direct observation of sense; whereas in that of the Universal the conclusion teaches you more than you could have learnt from direct sensation, and comes into correlation with the highest form of our intellectual nature.[76]

[Footnote 75: Analyt. Post. I. xxiv. p. 86**, a. 22: [Greek: a)lla\ tô=n me\n ei)rême/nôn e)/nia logika/ e)sti; ma/lista de\ dê=lon o(/ti ê( katho/lou kuriôte/ra, o(/ti--o( de\ tau/tên e)/chôn tê\n pro/tasin] (the Particular) [Greek: to\ katho/lou ou)damô=s oi)=den, ou)/te duna/mei ou)/t' e)nergei/a|.]]

[Footnote 76: Ibid. a. 29: [Greek: kai\ ê( me\n katho/lou noêtê/, ê( de\ kata\ me/ros ei)s ai)/sthêsin teleuta=|.] Compare xxiii. p. 84, b. 39, where we noticed the doctrine that [Greek: Nou=s] is the unit of scientific demonstration.]

Next, Aristotle compares the Affirmative with the Negative demonstration, and shows that the Affirmative is the better. Of two demonstrations (he lays it down) that one which proceeds upon a smaller number of postulates, assumptions, or propositions, is better than the other; for, to say nothing of other reasons, it conducts you more speedily to knowledge than the other, and that is an advantage. Now, both in the affirmative and in the negative syllogism, you must have three terms and two propositions; but in the affirmative you assume only that something is; while in the negative you assume both that something is, and that something is not. Here is a double assumption instead of a single; therefore the negative is the worse or inferior of the two.[77] Moreover, for the demonstration of a negative conclusion, you require one affirmative premiss (since from two negative premisses nothing whatever can be concluded); while for the demonstration of an affirmative conclusion, you must have two affirmative premisses, and you cannot admit a negative. This, again, shows that the affirmative is logically prior, more trustworthy, and better than the negative.[78] The negative is only intelligible and knowable through the affirmative, just as Non-Ens is knowable only through Ens. The affirmative demonstration therefore, as involving better principles, is, on this ground also, better than the negative.[79] A fortiori, it is also better than the demonstration by way of Reductio ad Absurdum, which was the last case to be considered. This, as concluding only indirectly and from impossibility of the contradictory, is worse even than the negative; much more therefore is it worse than the direct affirmative.[80]

[Footnote 77: Analyt. Post. I. xxv. p. 86, a. 31-b. 9.]

[Footnote 78: Ibid. b. 10-30.]

[Footnote 79: Ibid. b. 30-39.]

[Footnote 80: Ibid. I. xxvi. p. 87, a. 2-30. Waitz (II. p. 370), says: "deductio (ad absurdum), quippe quæ per ambages cogat, post ponenda, est demonstrationi rectæ."

Philoponus says (Schol. pp. 234-235**, Brand.) that the Commentators all censured Aristotle for the manner in which he here laid out the Syllogism [Greek: di' a)duna/tou]. I do not, however, find any such censure in Themistius. Philoponus defends Aristotle from the censure.]

If we next compare one Science with another, the prior and more accurate of the two is, (1) That which combines at once the [Greek: o(/ti] and the [Greek: dio/ti]; (2) That which is abstracted from material conditions, as compared with that which is immersed therein--for example, arithmetic is more accurate than harmonics; (3) The more simple as compared with the more complex: thus, arithmetic is more accurate than geometry, a monad or unit is a substance without position, whereas a point (more concrete) is a substance with position.[81] One and the same science is that which belongs to one and the same generic subject-matter. The premisses of a demonstration must be included in the same genus with the conclusion; and where the ultimate premisses are heterogeneous, the cognition derived from them must be considered as not one but a compound of several.[82] You may find two or more distinct middle terms for demonstrating the same conclusion; sometimes out of the same logical series or table, sometimes out of different tables.[83]

[Footnote 81: Analyt. Post. I. xxvii. p. 87, a. 31-37. Themistius, Paraphras. p. 60, ed. Speng.: [Greek: kat' a)/llon de\ (tro/pon), e)a\n ê( me\n peri\ u(pokei/mena/ tina kai\ ai)sthêta\ pragmateu/êtai, ê( de\ peri\ noêta\ kai\ katho/lou.]

Philoponus illustrates this (Schol. p. 235, b. 41, Br.): [Greek: oi(=on ta\ Theodosi/ou sphairika\ a)kribe/stera/ e)stin e)pistê/mê| tê=s tô=n Au)tolu/kou peri\ kinoume/nês sphai/ras.] &c.]

[Footnote 82: Analyt. Post. I. xxviii. p. 87, a. 38-b. 5. Themistius, p. 61: [Greek: dê=lon de\ tou=to gi/netai proi+ou=sin e)pi\ ta\s a)napodei/ktous a)rcha/s; au(=tai ga\r ei) mêdemi/an e)/choien sugge/neian, e(/terai ai( e)pistê=mai.]]

[Footnote 83: Analyt. Post. I. xxix. p. 87, b. 5-18. Aristotle gives an example to illustrate this general doctrine: [Greek: ê(/desthai, to\ kinei=sthai, to\ ê)remi/zesthai, to\ metaba/llein]. As he includes these terms und this subject among the topics for demonstration, it is difficult to see where he would draw a distinct line between topics for Demonstration and topics for Dialectic.]

There cannot be demonstrative cognition of fortuitous events,[84] for all demonstration is either of the necessary or of the customary. Nor can there be demonstrative cognition through sensible perception. For though by sense we perceive a thing as such and such (through its sensible qualities), yet we perceive it inevitably as hoc aliquid, hic, et nunc. But the Universal cannot be perceived by sense; for it is neither hic nor nunc, but semper et ubique.[85] Now demonstrations are all accomplished by means of the Universal, and demonstrative cognition cannot therefore be had through sensible perception. If the equality of the three angles of a triangle to two right angles were a fact directly perceivable by sense, we should still have looked out for a demonstration thereof: we should have no proper scientific cognition of it (though some persons contend for this): for sensible perception gives us only particular cases, and Cognition or Science proper comes only through knowing the Universal.[86] If, being on the surface of the moon, we had on any one occasion seen the earth between us and the sun, we could not have known from that single observation that such interposition is the cause universally of eclipses. We cannot directly by sense perceive the Universal, though sense is the principium of the Universal. By multiplied observation of sensible particulars, we can hunt out and elicit the Universal, enunciate it clearly and separately, and make it serve for demonstration.[87] The Universal is precious, because it reveals the Cause or [Greek: dio/ti], and is therefore more precious, not merely than sensible observation, but also than intellectual conception of the [Greek: o(/ti] only, where the Cause or [Greek: dio/ti] lies apart, and is derived from a higher genus. Respecting First Principles or Summa Genera, we must speak elsewhere.[88] It is clear, therefore, that no demonstrable matter can be known, properly speaking, from direct perception of sense; though there are cases in which nothing but the impossibility of direct observation drives us upon seeking for demonstration. Whenever we can get an adequate number of sensible observations, we can generalize the fact; and in some instances we may perhaps not seek for any demonstrative knowledge (i.e. to explain it by any higher principle). If we could see the pores in glass and the light passing through them, we should learn through many such observations why combustion arises on the farther side of the glass; each of our observations would have been separate and individual, but we should by intellect generalize the result that all the cases fall under the same law.[89]

[Footnote 84: Analyt. Post. I. xxx. p. 87, b. 19-27.]

[Footnote 85: Ibid. xxxi. p. 87, b. 28: [Greek: ei) ga\r kai\ e)/stin ê( ai)/sthêsis tou= toiou=de kai\ mê\ tou=de/ tinos, a)ll' ai)stha/nesthai/ ge a)nagkai=on to/de ti kai\ pou= kai\ nu=n.]]

[Footnote 86: Ibid. b. 35: [Greek: dê=lon o(/ti kai\ ei) ê)=n ai)stha/nesthai to\ tri/gônon o(/ti dusi\n o)rthai=s i)/sas e)/chei ta\s gôni/as, e)zêtou=men a)\n a)po/deixin, kai\ ou)ch (ô(/sper phasi/ tines) ê)pista/metha; ai)stha/nesthai me\n ga\r a)na/gkê kath' e(/kaston, ê( d' e)pistê/mê tô=| to\ katho/lou gnôri/zein e)sti/n.]

Euclid, in the 20th Proposition of his first Book, demonstrates that any two sides of a triangle are together greater than the third side. According to Proklus, the Epikureans derided the demonstration of such a point as absurd; and it seems that some contemporaries of Aristotle argued in a similar way, judging by the phrase [Greek: ô(/sper phasi/ tines].]

[Footnote 87: Analyt. Post. I. xxxi. p. 88, a. 2: [Greek: ou) mê\n a)ll' e)k tou= theôrei=n tou=to polla/kis sumbai=non, to\ katho/lou a)\n thêreu/santes a)po/deixin ei)/chomen; e)k ga\r tô=n kath' e(/kasta pleio/nôn to\ katho/lou dê=lon.] Themistius, p. 62, Sp.: [Greek: a)rchê\ me\n ga\r a)podei/xeôs ai)/sthêsis, kai\ to\ katho/lou e)nnoou=men dia\ to\ polla/kis ai)sthe/sthai.]]

[Footnote 88: Analyt. Post. I. xxxi. p. 88, a. 6: [Greek: to\ de\ katho/lou ti/mion, o(/ti dêloi= to\ ai)/tion; ô(/ste peri\ tô=n toiou/tôn ê( katho/lou timiôte/ra tô=n ai)sthê/seôn kai\ tê=s noê/seôs, o(/sôn e(/teron to\ ai)/tion; peri\ de\ tô=n prô/tôn a)/llos lo/gos.]

By [Greek: ta\ prô=ta], he means the [Greek: a)rchai\] of Demonstration, which are treated especially in II. xix. See Biese, Die Philos. des Aristoteles, p. 277.]

[Footnote 89: Analyt. Post. I. xxxi. p. 88, a. 9-17. [Greek: e)/sti me/ntoi e)/nia a)nago/mena ei)s ai)sthê/seôs e)/kleipsin e)n toi=s problê/masin; e)/nia ga\r ei) e(ô/rômen, ou)k a)\n e)zêtou=men, ou)ch ô(s ei)do/tes tô=| o(ra=|n, a)ll' ô(s e)/chontes to\ katho/lou e)k tou= o(ra=|n.]

The text of this and the succeeding words seems open to doubt, as well as that of Themistius (p. 63). Waitz in his note (p. 374) explains the meaning clearly:--"non ita quidem ut ipsa sensuum perceptio scientiam afferat; sed ita ut quod in singulis accidere videamus, idem etiam in omnibus accidere coniicientes universe intelligamus."]

Aristotle next proceeds to refute, at some length, the supposition, that the principia of all syllogisms are the same. We see at once that this cannot be so, because some syllogisms are true, others false. But, besides, though there are indeed a few Axioms essential to the process of demonstration, and the same in all syllogisms, yet these are not sufficient of themselves for demonstration. There must farther be other premisses or matters of evidence--propositions immediately true (or established by prior demonstrations) belonging to each branch of Science specially, as distinguished from the others. Our demonstration relates to these special matters or premisses, though it is accomplished out of or by means of the common Axioms.[90]

[Footnote 90: Analyt. Post. I. xxxii. p. 88, a. 18-b. 29. [Greek: ai( ga\r a)rchai\ dittai/, e)x ô(=n te kai\ peri\ o(\; ai( me\n ou)=n e)x ô(=n koinai/, ai( de\ peri\ o(/ i)/diai, oi(=on a)rithmo/s, me/gethos.] Compare xi. p. 77, a. 27. See Barthélemy St. Hilaire, Plan Général des Derniers Analytiques, p. lxxxi.]

Science or scientific Cognition differs from true Opinion, and the cognitum from the opinatum, herein, that Science is of the Universal, and through necessary premisses which cannot be otherwise; while Opinion relates to matters true, yet which at the same time may possibly be false. The belief in a proposition which is immediate (i. e., undemonstrable) yet not necessary, is Opinion; it is not Science, nor is it Noûs or Intellect--the principium of Science or scientific Cognition. Such beliefs are fluctuating, as we see every day; we all distinguish them from other beliefs, which we cannot conceive not to be true and which we call cognitions.[91] But may there not be Opinion and Cognition respecting the same matters? There may be (says Aristotle) in different men, or in the same man at different times; but not in the same man at the same time. There may also be, respecting the same matter, true opinion in one man's mind, and false opinion in the mind of another.[92]

[Footnote 91: Analyt. Post. I. xxxiii. p. 88, b. 30-p. 89, a. 10.]

[Footnote 92: Ibid. p. 89, a. 11-b. 6. That eclipse of the sun is caused by the interposition of the moon was to the astronomer Hipparchos scientific Cognition; for he saw that it could not be otherwise. To the philosopher Epikurus it was Opinion; for he thought that it might be otherwise (Themistius, p. 66, Spengel).]

With some remarks upon Sagacity, or the power of divining a middle term in a time too short for reflection (as when the friendship of two men is on the instant referred to the fact of their having a common enemy), the present book is brought to a close.[93]

[Footnote 93: Ibid. xxxiv. p. 89, b. 10-20.]

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VI. ANALYTICA PRIORA II…

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VI. ANALYTICA PRIORA II

VII. ANALYTICA POSTERIORA I