Chapter XVI: Book II: ch. iii. sect 2:--"It must be granted, that in every (1)

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 57: Ibid. II. xxiv. p. 68, b. 38: [Greek: paradei=gma d' e)sti\n o(/tan tô=| me/sô| to\ a)/kron u(pa/rchon deichthê=| dia\ tou= o(moi/ou tô=| tri/tô|.]]

[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.]