Chapter V: Analytica Priora I (2)

Again, every demonstration is effected by two propositions (an _even_ number) and by three terms (an _odd_ number); though the same proposition may perhaps be demonstrable by more than one pair of premisses, or through more than one middle term;[43] that is, by two or more distinct syllogisms. If there be more than three terms and two propositions, either the syllogism will no longer be one but several; or there must be particulars introduced for the purpose of obtaining an universal by induction; or something will be included, superfluous and not essential to the demonstration, perhaps for the purpose of concealing from the respondent the real inference meant.[44] In the case (afterwards called _Sorites_) where the ultimate conclusion is obtained through several mean terms in continuous series, the number of terms will always exceed by one the number of propositions; but the numbers may be odd or even, according to circumstances. As terms are added, the total of intermediate conclusions, if drawn out in form, will come to be far greater than that of the terms or propositions, multiplying as it will do in an increasing ratio to them.[45]

[Footnote 43: Ibid. I. xxv. p. 41, b. 36, seq.]

[Footnote 44: Ibid. xxv. p. 42, a. 23: [Greek: ma/tên e)/stai ei)lêmme/na, ei) mê\ e)pagôgê=s ê)\ kru/pseôs ê)/ tinos a)/llou tô=n toiou/tôn cha/rin.] Ib. a. 38: [Greek: ou(=tos o( lo/gos ê)\ ou) sullelo/gistai ê)\ plei/ô tô=n a)nagkai/ôn ê)rô/têke pro\s tê\n the/sin.]]

[Footnote 45: Ibid. p. 42, b. 5-26.]

It will be seen clearly from the foregoing remarks that there is a great difference between one thesis and another as to facility of attack or defence in Dialectic. If the thesis be an Universal Affirmative proposition, it can be demonstrated only in the First figure, and only by one combination of premisses; while, on the other hand, it can be impugned either by an universal negative, which can be demonstrated both in the First and Second figures, or by a particular negative, which can be demonstrated in all the three figures. Hence an Universal Affirmative thesis is at once the hardest to defend and the easiest to oppugn: more so than either a Particular Affirmative, which can be proved both in the First and Third figures; or a Universal Negative, which can be proved either in First or Second.[46] To the opponent, an universal thesis affords an easier victory than a particular thesis; in fact, speaking generally, his task is easier than that of the defendant.

[Footnote 46: Analyt. Prior. I. xxvi. p. 42, b. 27, p. 43, a. 15.]

In the Analytica Priora, Aristotle proceeds to tell us that he contemplates not only theory, but also practice and art. The reader must be taught, not merely to understand the principles of Syllogism, but likewise where he can find the matter for constructing syllogisms readily, and how he can obtain the principles of demonstration pertinent to each thesis propounded.[47]

[Footnote 47: Ibid. I. xxvii. p. 43, a. 20: [Greek: pô=s d' eu)porê/somen au)toi\ pro\s to\ tithe/menon a)ei\ sullogismô=n, kai\ dia\ poi/as o(dou= lêpso/metha ta\s peri\ e(/kaston a)rcha/s, nu=n ê)/dê lekte/on; ou) ga\r mo/non i)/sôs dei= tê\n ge/nesin theôrei=n tô=n sullogismô=n, a)lla\ kai\ tê\n du/namin e)/chein tou= poiei=n.] The second section of Book I. here begins.]

A thesis being propounded in appropriate terms, with subject and predicate, how are you the propounder to seek out arguments for its defence? In the first place, Aristotle reverts to the distinction already laid down at the beginning of the Categoriæ.[48] Individual things or persons are subjects only, never appearing as predicates--this is the lowest extremity of the logical scale: at the opposite extremity of the scale, there are the highest generalities, predicates only, and not subjects of any predication, though sometimes supposed to be such, as matters of dialectic discussion.[49] Between the lowest and highest we have intermediate or graduate generalities, appearing sometimes as subjects, sometimes as predicates; and it is among these that the materials both of problems for debate, and of premisses for proof, are usually found.[50]

[Footnote 48: Ibid. I. xxvii. p. 43, a. 25, seq.]

[Footnote 49: Ibid. p. 43, a. 39: [Greek: plê\n ei) mê\ kata\ do/xan]. Cf. Schol. of Alexander, p. 175, a. 44, Br.: [Greek: e)ndo/xôs kai\ dialektikô=s, ô(/sper ei)=pen e)n toi=s Topikoi=s], that even the _principia_ of science may be debated; for example, in book B. of the Metaphysica. Aristotle does not recognize either [Greek: to\ o)/n] or [Greek: to\ e(/n] as true genera, but only as predicates.]

[Footnote 50: Ibid. a. 40-43.]

You must begin by putting down, along with the matter in hand itself, its definition and its _propria_; after that, its other predicates; next, those predicates which _cannot_ belong to it; lastly, those other subjects, of which it may itself be predicated. You must classify its various predicates distinguishing the essential, the _propria_, and the accidental; also distinguishing the true and unquestionable, from the problematical and hypothetical.[51] You must look out for those predicates which belong to it as subject universally, and not to certain portions of it only; since universal propositions are indispensable in syllogistic proof, and indefinite propositions can only be reckoned as particular. When a subject is included in some larger genus--as, for example, man in animal--you must not look for the affirmative or negative predicates which belong to animal universally (since all these will of course belong to man also) but for those which distinguish man from other animals; nor must you, in searching for those lower subjects of which man is the predicate, fix your attention on the higher genus animal; for animal will of course be predicable of all those of which man is predicable. You must collect what pertains to man specially, either as predicate or subject; nor merely that which pertains to him necessarily and universally, but also usually and in the majority of cases; for most of the problems debated belong to this latter class, and the worth of the conclusion will be co-ordinate with that of the premisses.[52]** Do not select predicates that are predicable[53] both of the predicate and subject; for no valid affirmative conclusion can be obtained from them.

[Footnote 51: Analyt. Prior. I. xxvii. p. 43, b. 8: [Greek: kai\ tou/tôn poi=a doxastikô=s kai\ poi=a kat' a)lê/theian.]]

[Footnote 52: Ibid. I. xxvii. p. 43, b. 10-35.]

[Footnote 53: Ibid. b. 36: [Greek: e)/ti ta\ pa=sin e(po/mena ou)k e)klekte/on; ou) ga\r e)/stai sullogismo\s e)x au)tô=n.] The phrase [Greek: ta\ pa=sin e(po/mena], as denoting predicates applicable both to the predicate and to the subject, is curious. We should hardly understand it, if it were not explained a little further on, p. 44, b. 21. Both the Scholiast and the modern commentators understand [Greek: ta\ pa=sin e(po/mena] in this sense; and I do not venture to depart from them. At the same time, when I read six lines afterwards (p. 44, b. 26) the words [Greek: oi(=on ei) ta\ e(po/mena e(kate/rô| tau)ta/ e)stin]--in which the same meaning as that which the commentators ascribe to [Greek: ta\ pa=sin e(po/mena] is given in its own special and appropriate terms, and thus the same supposition unnecessarily repeated--I cannot help suspecting that Aristotle intends [Greek: ta\ pa=sin e(po/mena] to mean something different; to mean such wide and universal predicates as [Greek: to\ e(\n] and [Greek: to\ o)/n] which soar above the Categories and apply to every thing, but denote no real _genera_.]

Thus, when the thesis to be maintained is an universal affirmative (_e.g._ A is predicable of all E), you will survey all the subjects to which A will apply as predicate, and all the predicates applying to E as subject. If these two lists coincide in any point, a middle term will be found for the construction of a good syllogism in the First figure. Let B represent the list of predicates belonging universally to A; D, the list of predicates which cannot belong to it; C, the list of subjects to which A pertains universally as predicate. Likewise, let F represent the list of predicates belonging universally to E; H, the list of predicates that cannot belong to E; G, the list of subjects to which E is applicable as predicate. If, under these suppositions, there is any coincidence between the list C and the list F, you can construct a syllogism (in _Barbara_, Fig. 1), demonstrating that A belongs to _all_ E; since the predicate in F belongs to all E, and A universally to the subject in C. If the list C coincides in any point with the list G, you can prove that A belongs to _some_ E, by a syllogism (in _Darapti_, Fig. 3). If, on the other hand, the list F coincides in any point with the list D, you can prove that A cannot belong to any E: for the predicate in D cannot belong to any A, and therefore (by converting simply the universal negative) A cannot belong as predicate to any D; but D coincides with F, and F belongs to all E; accordingly, a syllogism (in _Celarent_, Fig. 1) may be constructed, shewing that A cannot belong to any E. So also, if B coincides in any point with H, the same conclusion can be proved; for the predicate in B belongs to all A, but B coincides with H, which belongs to no E; whence you obtain a syllogism (in _Camestres_, Fig. 2), shewing that no A belongs to E.[54] In collecting the predicates and subjects both of A and of E, the highest and most universal expression of them is to be preferred, as affording the largest grasp for the purpose of obtaining a suitable middle term.[55] It will be seen (as has been declared already) that every syllogism obtained will have three terms and two propositions; and that it will be in one or other of the three figures above described.[56]

[Footnote 54: Analyt. Prior. I. xxviii. p. 43, b. 39-p. 44, a. 35.]

[Footnote 55: Ibid. p. 44, a. 39. Alexander and Philoponus (Scholia, p. 177, a. 19, 39, Brandis) point out an inconsistency between what Aristotle says here and what he had said in one of the preceding paragraphs, dissuading the inquirer from attending to the highest generalities, and recommending him to look only at both subject and predicate in their special place on the logical scale. Alexander's way of removing the inconsistency is not successful: I doubt if there be an inconsistency. I understand Aristotle _here_ to mean only that the universal expression KZ ([Greek: to\ katho/lou Z]) is to be preferred to the indefinite or indeterminate (simply Z, [Greek: a)dio/riston]), also K[Greek: G] ([Greek: to\ katho/lou G]) to simple [Greek: G (a)dio/riston)]. This appears to me not inconsistent with the recommendation which Aristotle had given before.]

[Footnote 56: Ibid. p. 44, b. 6-20.]

The way just pointed out is the only way towards obtaining a suitable middle term. If, for example, you find some predicate applicable both to A and E, this will not conduct you to a valid syllogism; you will only obtain a syllogism in the Second figure with two affirmative premisses, which will not warrant any conclusion. Or if you find some predicate which cannot belong either to A or to E, this again will only give you a syllogism in the Second figure with two negative premisses, which leads to nothing. So also, if you have a term of which A can be predicated, but which cannot be predicated of E, you derive from it only a syllogism in the First figure, with its minor negative; and this, too, is invalid. Lastly, if you have a subject, of which neither A nor E can be predicated, your syllogism constructed from these conditions will have both its premisses negative, and will therefore be worthless.[57]

[Footnote 57: Analyt. Prior. I. xxviii. p. 44, b. 25-37.]

In the survey prescribed, nothing is gained by looking out for predicates (of A and E) which are different or opposite: we must collect such as are identical, since our purpose is to obtain from them a suitable middle term, which must be the same in both premisses. It is true that if the list B (containing the predicates universally belonging to A) and the list F (containing the predicates universally belonging to E) are incompatible or contrary to each other, you will arrive at a syllogism proving that no A can belong to E. But this syllogism will proceed, not so much from the fact that B and F are incompatible, as from the other fact, distinct though correlative, that B will to a certain extent coincide with H (the list of predicates which cannot belong to E). The middle term and the syllogism constituted thereby, is derived from the coincidence between B and H, not from the opposition between B and F. Those who derive it from the latter, overlook or disregard the real source, and adopt a point of view merely incidental and irrelevant.[58]

[Footnote 58: Ibid. p. 44, b. 38-p. 45, a. 22. [Greek: sumbai/nei dê\ toi=s ou(/tôs e)piskopou=si prosepible/pein a)/llên o(do\n tê=s a)nagkai/as, dia\ to\ lantha/nein tê\n tau)to/têta tô=n B kai\ tô=n Th.]]

The precept here delivered--That in order to obtain middle terms and good syllogisms, you must study and collect both the predicates and the subjects of the two terms of your thesis--Aristotle declares to be equally applicable to all demonstration, whether direct or by way of _Reductio ad Impossibile_. In both the process of demonstration is the same--involving two premisses, three terms, and one of the three a suitable middle term. The only difference is, that in the direct demonstration, both premisses are propounded as true, while in the _Reductio ad Impossibile_, one of the premisses is assumed as true though known to be false, and the conclusion also.[59] In the other cases of hypothetical syllogism your attention must be directed, not to the original _quæsitum_, but to the condition annexed thereto; yet the search for predicates, subjects, and a middle term, must be conducted in the same manner.[60] Sometimes, by the help of a condition extraneous to the premisses, you may demonstrate an universal from a particular: _e.g._, Suppose C (the list of subjects to which A belongs as predicate) and G (the list of subjects to which E belongs as predicate) to be identical; and suppose farther that the subjects in G are the _only_ ones to which E belongs as predicate (this seems to be the _extraneous_ or _extra-syllogistic_ condition assumed, on which Aristotle's argument turns); then, A will be applicable to all E. Or if D (the list of predicates which cannot belong to A) and G (the list of subjects to which E belongs as predicate) are identical; then, assuming the like extraneous condition, A will not be applicable to any E.[61] In both these cases, the conclusion is more universal than the premisses; but it is because we take in an hypothetical assumption, in addition to the premisses.

[Footnote 59: Ibid. I. xxix. p. 45, a. 25-b. 15.]

[Footnote 60: Ibid. I. xxix. p. 45, b. 15-20. This paragraph is very obscure. Neither Alexander, nor Waitz, nor St. Hilaire clears it up **completely. See Schol. pp. 178, b., 179, a. Brandis.

Aristotle concludes by saying that syllogisms from an hypothesis ought to be reviewed and classified into varieties--[Greek: e)piske/psasthai de\ dei= kai\ dielei=n posachô=s oi( e)x u(pothe/seôs] (b. 20). But it is doubtful whether he himself ever executed this classification. It was done in the Analytica of his successor Theophrastus (Schol. p. 179, a. 6, 24). Compare the note of M. Barthélemy St. Hilaire, p. 140.]

[Footnote 61: Analyt. Prior. I. xxix. p. 45, b. 21-30.]

Aristotle has now shown a method of procedure common to all investigations and proper for the solution of all problems, wherever soluble. He has shown, first, all the conditions and varieties of probative Syllogism, two premisses and three terms, with the place required for the middle term in each of the three figures; next, the quarter in which we are to look for all the materials necessary or suitable for constructing valid syllogisms. Having the two terms of the thesis given, we must study the predicates and subjects belonging to both, and must provide a large list of them; out of which list we must make selection according to the purpose of the moment. Our selection will be different, according as we wish to prove or to refute, and according as the conclusion that we wish to prove is an universal or a particular. The lesson here given will be most useful in teaching the reasoner to confine his attention to the sort of materials really promising, so that he may avoid wasting his time upon such as are irrelevant.[62]

[Footnote 62: Ibid. b. 36-xxx. p. 46, a. 10.]

This method of procedure is alike applicable to demonstration in Philosophy or in any of the special sciences,[63] and to debate in Dialectic. In both, the premisses or _principia_ of syllogisms must be put together in the same manner, in order to make the syllogism valid. In both, too, the range of topics falling under examination is large and varied; each topic will have its own separate premisses or _principia_, which must be searched out and selected in the way above described. Experience alone can furnish these _principia_, in each separate branch or department. Astronomical experience--the observed facts and phenomena of astronomy--have furnished the data for the scientific and demonstrative treatment of astronomy. The like with every other branch of science or art.[64] When the facts in each branch are brought together, it will be the province of the logician or analytical philosopher to set out the demonstrations in a manner clear and fit for use. For if nothing in the way of true matter of fact has been omitted from our observation, we shall be able to discover and unfold the demonstration, on every point where demonstration is possible; and, wherever it is not possible, to make the impossibility manifest.[65]

[Footnote 63: Ibid. p. 46, a. 8**: [Greek: kata\ me\n a)lê/theian e)k tô=n kat' a)lê/theian _diagegramme/nôn_ u(pa/rchein, ei)s de\ tou\s dialektikou\s sullogismou\s e)k tô=n kata\ do/xan prota/seôn.]

Julius Pacius (p. 257) remarks upon the word [Greek: diagegramme/nôn] as indicating that Aristotle, while alluding to special sciences distinguishable from philosophy on one side, and from dialectic on the other, had in view geometrical demonstrations.]

[Footnote 64: Analyt. Prior. I. xxx. p. 46, a. 10-20**: [Greek: ai( d' a)rchai\ tô=n sullogismô=n katho/lou me\n ei)/rêntai--i)/diai de\ kath' e(ka/stên ai( plei=stai. dio\ ta\s me\n a)rcha\s ta\s peri\ e(/kaston e)mpeiri/as e)/sti paradou=nai. le/gô d' oi(=on tê\n a)strologikê\n me\n e)mpeiri/an tê=s a)strologikê=s e)pistê/mês; lêphthe/ntôn ga\r i(kanô=s tô=n phainome/nôn ou(/tôs eu(re/thêsan ai( a)strologikai\ a)podei/xeis. o(moi/ôs de\ kai\ peri\ a)/llên o(poianou=n e)/chei te/chnên te kai\ e)pistê/mên.]

What Aristotle says here--of astronomical observation and experience as furnishing the basis for astronomical science--stands in marked contrast with Plato, who rejects this basis, and puts aside, with a sort of contempt, astronomical observation (Republic, vii. pp. 530-531); treating acoustics also in a similar way. Compare Aristot. Metaphys. [Greek: L]. p. 1073, a. 6, seq., with the commentary of Bonitz, p. 506.]

[Footnote 65: Analyt. Prior. I. xxx. p. 46, a. 22-27**: [Greek: ô(/ste a)\n lêphthê=| ta\ u(pa/rchonta peri\ e(/kaston, ê(me/teron ê)/dê ta\s a)podei/xeis e(toi/môs e)mphani/zein. ei) ga\r mêde\n _kata\ tê\n i(stori/an_ paraleiphthei/ê tô=n a)lêthô=s u(parcho/ntôn toi=s pra/gmasin, e(/xomen peri\ a(/pantos ou(= me\n e)/stin a)po/deixis, tau/tên eu(rei=n kai\ a)podeiknu/nai, ou(= de\ mê\ pe/phuken a)po/deixis, tou=to poiei=n phanero/n.]

Respecting the word [Greek: i(stori/a]--investigation and record of matters of fact--the first sentence of Herodotus may be compared with Aristotle, Histor. Animal. p. 491, a. 12; also p. 757, b. 35; Rhetoric. p. 1359, b. 32.]

For the fuller development of these important principles, the reader is referred to the treatise on Dialectic, entitled Topica, which we shall come to in a future chapter. There is nothing in all Aristotle's writings more remarkable than the testimony here afforded, how completely he considered all the generalities of demonstrative science and deductive reasoning to rest altogether on experience and inductive observation.

We are next introduced to a comparison between the syllogistic method, as above described and systematized, and the process called logical Division into _genera_ and _species_; a process much relied upon by other philosophers, and especially by Plato. This logical Division, according to Aristotle, is a mere fragment of the syllogistic procedure; nothing better than a feeble syllogism.[66] Those who employed it were ignorant both of Syllogism and of its conditions. They tried to demonstrate--what never can be demonstrated--the essential constitution of the subject.[67] Instead of selecting a middle term, as the Syllogism requires, more universal than the subject but less universal (or not more so) than the predicate, they inverted the proper order, and took for their middle term the highest universal. What really requires to be demonstrated, they never demonstrated but assume.[68]

[Footnote 66: Analyt. Prior. I. xxxi. p. 46, a. 33. Alexander, in Scholia, p. 180, a. 14. The Platonic method of [Greek: diai/resis] is exemplified in the dialogues called Sophistês and Politicus; compare also Philêbus, c. v., p. 15.]

[Footnote 67: Ibid. p. 46, a. 34: [Greek: prô=ton d' au)to\ tou=to e)lelê/thei tou\s chrôme/nous au)tê=| pa/ntas, kai\ pei/thein e)pechei/roun ô(s o)/ntos dunatou= peri\ ou)si/as a)po/deixin gi/nesthai kai\ tou= ti/ e)stin.]]

[Footnote 68: Ibid. p. 46, b. 1-12.]

Thus, they take the subject man, and propose to prove that man is mortal. They begin by laying down that man is an animal, and that every animal is either mortal or immortal. Here, the most universal term, animal, is selected as middle or as medium of proof; while after all, the conclusion demonstrated is, not that man is mortal, but that man is either mortal or immortal. The position that man is mortal, is assumed but not proved.[69] Moreover, by this method of logical division, all the steps are affirmative and none negative; there cannot be any refutation of error. Nor can any proof be given thus respecting _genus_, or _proprium_, or _accidens_; the _genus_ is assumed, and the method proceeds from thence to _species_ and _differentia_. No doubtful matter can be settled, and no unknown point elucidated by this method; nothing can be done except to arrange in a certain order what is already ascertained and unquestionable. To many investigations, accordingly, the method is altogether inapplicable; while even where it is applicable, it leads to no useful conclusion.[70]

[Footnote 69: Ibid. p. 46, b. 1-12.]

[Footnote 70: Ibid. b. 26-37. Alexander in Schol. p. 180, b. 1.]

We now come to that which Aristotle indicates as the third section of this First Book of the Analytica Priora. In the first section he explained the construction and constituents of Syllogism, the varieties of figure and mode, and the conditions indispensable to a valid conclusion. In the second section he tells us where we are to look for the premisses of syllogisms, and how we may obtain a stock of materials, apt and ready for use when required. There remains one more task to complete his plan--that he should teach the manner of reducing argumentation as it actually occurs (often invalid, and even when valid, often elliptical and disorderly), to the figures of syllogism as above set forth, for the purpose of testing its validity.[71] In performing this third part (Aristotle says) we shall at the same time confirm and illustrate the two preceding parts; for truth ought in every way to be consistent with itself.[72]

[Footnote 71: Analyt. Prior. I. xxxii. p. 47, a. 2: [Greek: loipo\n ga\r e)/ti tou=to tê=s ske/pseôs; ei) ga\r tê/n te ge/nesin tô=n sullogismô=n theôroi=men kai\ tou= eu(ri/skein e)/choimen du/namin, e)/ti de\ tou\s gegenême/nous a)nalu/oimen ei)s ta\ proeirême/na schê/mata, te/los a)\n e)/choi ê( e)x a)rchê=s pro/thesis.]]

[Footnote 72: Ibid. a. 8.]

When a piece of reasoning is before us, we must first try to disengage the two syllogistic premisses (which are more easily disengaged than the three terms), and note which of them is universal or particular. The reasoner, however, may not have set out both of them clearly: sometimes he will leave out the major, sometimes the minor, and sometimes, even when enunciating both of them, he will join with them irrelevant matter. In either of these cases we must ourselves supply what is wanting and strike out the irrelevant. Without this aid, reduction to regular syllogism is impracticable; but it is not always easy to see what the exact deficiency is. Sometimes indeed the conclusion may follow necessarily from what is implied in the premisses, while yet the premisses themselves do not form a correct syllogism; for though every such syllogism carries with it necessity, there may be necessity without a syllogism. In the process of reduction, we must first disengage and set down the two premisses, then the three terms; out of which three, that one which appears twice will be the middle term. If we do not find one term twice repeated, we have got no middle and no real syllogism. Whether the syllogism when obtained will be in the first, second, or third figure, will depend upon the place of the middle term in the two premisses. We know by the nature of the conclusion which of the three figures to look for, since we have already seen what conclusions can be demonstrated in each.[73]

[Footnote 73: Ibid. a. 10-b. 14.]

Sometimes we may get premisses which look like those of a true syllogism, but are not so in reality; the major proposition ought to be an universal, but it may happen to be only indefinite, and the syllogism will not in all cases be valid; yet the distinction between the two often passes unnoticed.[74] Another source of fallacy is, that we may set out the terms incorrectly; by putting (in modern phrase) the abstract instead of the concrete, or abstract in one premiss and concrete in the other.[75] To guard against this, we ought to use the concrete term in preference to the abstract. For example, let the major proposition be, Health cannot belong to any disease; and the minor. Disease can belong to any man; _Ergo_, Health cannot belong to any man. This conclusion seems valid, but is not really so. We ought to substitute concrete terms to this effect:--It is impossible that the sick can be well; Any man may be sick; _Ergo_, It is impossible that any man can be well. To the syllogism, now, as stated in these concrete terms, we may object, that the major is not true. A person who is at the present moment sick may at a future time become well. There is therefore no valid syllogism.[76] When we take the concrete man, we may say with truth that the two contraries, health-sickness, knowledge-ignorance, _may_ both alike belong to him; though not to the same individual at the same time.

[Footnote 74: Ibid. I. xxxiii. p. 47, b. 16-40: [Greek: au(/tê me\n ou)=n ê( a)pa/tê gi/netai e)n tô=| para\ mikro/n; ôs ga\r ou)de\n diaphe/ron ei)pei=n _to/de tô=|de u(pa/rchein, ê)\ to/de tô=|de panti\ u(pa/rchein_, sugchôrou=men.]

M. B. St. Hilaire observes in his note (p. 155): "L'erreur vient uniquement de ce qu'on confond l'universel et l'indeterminé séparés par une nuance très faible d'expression, qu'on ne doit pas cependant negliger." Julius Pacius (p. 264) gives the same explanation at greater length; but the example chosen by Aristotle ([Greek: o( A)ristome/nês e)sti\ dianoêto\s A)ristome/nês]) appears open to other objections besides.]

[Footnote 75: Analyt. Prior. I. xxxiv. p. 48, a. 1-28.]

[Footnote 76: Ibid. a. 2-23. See the Scholion of Alexander, p. 181, b. 16-27, Brandis.]

Again, we must not suppose that we can always find one distinct and separate name belonging to each term. Sometimes one or all of the three terms can only be expressed by an entire phrase or proposition. In such cases it is very difficult to reduce the reasoning into regular syllogism. We may even be deceived into fancying that there are syllogisms without any middle term at all, because there is no single word to express it. For example, let A represent equal to two right angles; B, triangle; C, isosceles. Then we have a regular syllogism, with an explicit and single-worded middle term; A belongs first to B, and then to C through B as middle term (triangle). But how do we know that A belongs to B? We know it by demonstration; for it is a demonstrable truth that every triangle has its three angles equal to two right angles. Yet there is no other more general truth about triangles from which it is a deduction; it belongs to the triangle _per se_, and follows from the fundamental properties of the figure.[77] There is, however, a middle term in the demonstration, though it is not single-worded and explicit; it is a declaratory proposition or a fact. We must not suppose that there can be any demonstration without a middle term, either single-worded or many-worded.

[Footnote 77: Ibid. I. xxxv. p. 48, a. 30-39: [Greek: phanero\n o(/ti to\ me/son ou)ch ou(/tôs a)ei\ lêpte/on ô(s to/de ti, a)ll' e)ni/ote lo/gon, o(/per sumbai/nei ka)pi\ tou= lechthe/ntos.] A good Scholion of Philoponus is given, p. 181, b. 28-45, Brand.]

When we are reducing any reasoning to a syllogistic form, and tracing out the three terms of which it is composed, we must expose or set out these terms in the nominative case; but when we actually construct the syllogism or put the terms into propositions, we shall find that one or other of the oblique cases, genitive, dative, &c., is required.[78] Moreover, when we say, 'this belongs to that,' or 'this may be truly predicated of that,' we must recollect that there are many distinct varieties in the relation of predicate to subject. Each of the Categories has its own distinct relation to the subject; predication _secundum quid_ is distinguished from predication _simpliciter_, simple from combined or compound, &c. This applies to negatives as well as affirmatives.[79] There will be a material difference in setting out the terms of the syllogism, according as the predication is qualified (_secundum quid_) or absolute (_simpliciter_). If it be qualified, the qualification attaches to the predicate, not to the subject: when the major proposition is a qualified predication, we must consider the qualification as belonging, not to the middle term, but to the major term, and as destined to re-appear in the conclusion. If the qualification be attached to the middle term, it cannot appear in the conclusion, and any conclusion that embraces it will not be proved. Suppose the conclusion to be proved is. The wholesome is knowledge _quatenus bonum_ or _quod bonum est_; the three terms of the syllogism must stand thus:--

_Major_--_Bonum_ is knowable, _quatenus bonum_ or _quod bonum est_.

_Minor_--The wholesome is _bonum_.

_Ergo_--The wholesome is knowable, _quatenus bonum_, &c.

For every syllogism in which the conclusion is qualified, the terms must be set out accordingly.[80]

[Footnote 78: Analyt. Prior. I. xxxvi. p. 48, a. 40-p. 49, a. 5. [Greek: a(plô=s le/gomen ga\r tou=to kata\ pa/ntôn, o(/ti tou\s me\n o(/rous a)/ei thete/on kata\ ta\s klê/seis tô=n o)noma/tôn--ta\s de\ prota/seis lêpte/on kata\ ta\s e(ka/stou ptô/seis.] Several examples are given of this precept.]

[Footnote 79: Ibid. I. xxxvii. p. 49, a. 6-10. Alexander remarks in the Scholia (p. 183, a. 2) that the distinction between simple and compound predication has already been adverted to by Aristotle in De Interpretatione (see p. 20, b. 35); and that it was largely treated by Theophrastus in his work, [Greek: Peri\ Katapha/seôs], not preserved.]

[Footnote 80: Ibid. I. xxxviii. p. 49, a. 11-b. 2. [Greek: phanero\n ou)=n o(/ti e)n toi=s e)n me/rei sullogismoi=s ou(/tô lêpte/on tou\s o(/rous.] Alexander explains [Greek: oi( e)n me/rei sullogismoi/] (Schol. p. 183, b. 32, Br.) to be those in which the predicate has a qualifying adjunct tacked to it.]

We are permitted, and it is often convenient, to exchange one phrase or term for another of equivalent signification, and also one word against any equivalent phrase. By doing this, we often **facilitate the setting out of the terms. We must carefully note the different meanings of the same substantive noun, according as the definite article is or is not prefixed. We must not reckon it the same term, if it appears in one premiss with the definite article, and in the other without the definite article.[81] Nor is it the same proposition to say B is predicable of C (indefinite), and B is predicable of _all_ C (universal). In setting out the syllogism, it is not sufficient that the major premiss should be indefinite; the major premiss must be universal; and the minor premiss also, if the conclusion is to be universal. If the major premiss be universal, while the minor premiss is only affirmative indefinite, the conclusion cannot be universal, but will be no more than indefinite, that is, counting as particular.[82]

[Footnote 81: Analyt. Prior. I. xxxix.-xl. p. 49, b. 3-13. [Greek: ou) tau)to\n e)sti to\ ei)=nai tê\n ê(donê\n a)gatho\n kai\ to\ ei)=nai tê\n ê(donê\n to\ a)gatho/n], &c.]

[Footnote 82: Ibid. I. xli. p. 49, b. 14-32. The Scholion of Alexander (Schol. p. 184, a. 22-40) alludes to the peculiar mode, called by Theophrastus [Greek: kata\ pro/slêpsin], of stating the premisses of the syllogism: two terms only, the major and the middle, being enunciated, while the third or minor was included potentially, but not enunciated. Theophrastus, however, did not recognize the distinction of meaning to which Aristotle alludes in this chapter. He construed as an universal minor, what Aristotle treats as only an indefinite minor. The liability to mistake the Indefinite for an Universal is here again adverted to.]

There is no fear of our being misled by setting out a particular case for the purpose of the general demonstration; for we never make reference to the specialties of the particular case, but deal with it as the geometer deals with the diagram that he draws. He calls the line A B, straight, a foot long, and without breadth, but he does not draw any conclusion from these assumptions. All that syllogistic demonstration either requires or employs, is, terms that are related to each other either as whole to part or as part to whole. Without this, no demonstration can be made: the exposition of the particular case is intended as an appeal to the senses, for facilitating the march of the student, but is not essential to demonstration.[83]

[Footnote 83: Ibid. I. xli. p. 50, a. 1: [Greek: tô=| d' e)kti/thesthai ou(/tô chrô/metha ô(/sper kai\ tô=| ai)stha/nesthai to\n mantha/nonta le/gontes; ou) ga\r ou(/tôs ô(s a)/neu tou/tôn ou)ch oi(=o/n t' a)podeichthê=nai, ô(/sper e)x ô(=n o( sullogismo/s.]

This chapter is a very remarkable statement of the Nominalistic doctrine; perceiving or conceiving all the real specialties of a particular case, but attending to, or reasoning upon, only a portion of them.

Plato treats it as a mark of the inferior scientific value of Geometry, as compared with true and pure Dialectic, that the geometer cannot demonstrate through Ideas and Universals alone, but is compelled to help himself by visible particular diagrams or illustrations. (Plato, Repub. vi. pp. 510-511, vii. p. 533, C.)]

Aristotle reminds us once more of what he had before said, that in the Second and Third figures, not all varieties of conclusion are possible, but only some varieties; accordingly, when we are reducing a piece of reasoning to the syllogistic form, the nature of the conclusion will inform us which of the three figures we must look for. In the case where the question debated relates to a definition, and the reasoning which we are trying to reduce turns upon one part only of that definition, we must take care to look for our three terms only in regard to that particular part, and not in regard to the whole definition.[84] All the modes of the Second and Third figures can be reduced to the First, by conversion of one or other of the premisses; except the fourth mode (_Baroco_) of the Second, and the fifth mode (_Bocardo_) of the Third, which can be proved only by _Reductio ad Absurdum_.[85]

[Footnote 84: Analyt. Prior. I. xlii., xliii. p. 50, a. 5-15. I follow here the explanation given by Philoponus and Julius Pacius, which M. Barthélemy St. Hilaire adopts. But the illustrative example given by Aristotle himself (the definition of _water_) does not convey much instruction.]

[Footnote 85: Ibid. xlv. p. 50, b. 5-p. 51, b. 2.]

No syllogisms from an Hypothesis, however, are reducible to any of the three figures; for they are not proved by syllogism alone: they require besides an extra-syllogistic assumption granted or understood between speaker and hearer. Suppose an hypothetical proposition given, with antecedent and consequent: you may perhaps prove or refute by syllogism either the antecedent separately, or the consequent separately, or both of them separately; but you cannot directly either prove or refute by syllogism the conjunction of the two asserted in the hypothetical. The speaker must ascertain beforehand that this will be granted to him; otherwise he cannot proceed.[86] The same is true about the procedure by _Reductio ad Absurdum_, which involves an hypothesis over and above the syllogism. In employing such _Reductio ad Absurdum_, you prove syllogistically a certain conclusion from certain premisses; but the conclusion is manifestly false; therefore, one at least of the premisses from which it follows must be false also. But if this reasoning is to have force, the hearer must know _aliunde_ that the conclusion is false; your syllogism has not shown it to be false, but has shown it to be hypothetically true; and unless the hearer is prepared to grant the conclusion to be false, your purpose is not attained. Sometimes he will grant it without being expressly asked, when the falsity is glaring: _e.g._ you prove that the diagonal of a square is incommensurable with the side, because if it were taken as commensurable, an odd number might be shown to be equal to an even number. Few disputants will hesitate to grant that this conclusion is false, and therefore that its contradictory is true; yet this last (viz. that the contradictory is true) has not been proved syllogistically; you must assume it by hypothesis, or depend upon the hearer to grant it.[87]

[Footnote 86: Ibid. xliv. p. 50, a. 16-28.]

[Footnote 87: Analyt. Prior. I. xliv. p. 50, a. 29-38. See above, xxiii. p. 40, a. 25.

M. Barthélemy St. Hilaire remarks in the note to his translation of the Analytica Priora (p. 178): "Ce chapitre suffit à prouver qu'Aristote a distingué très-nettement les syllogismes par l'absurde, des syllogismes hypothétiques. Cette dernière dénomination est tout à fait pour lui ce qu'elle est pour nous." Of these two statements, I think the _latter_ is more than we can venture to affirm, considering that the general survey of hypothetical syllogisms, which Aristotle intended to draw up, either never was really completed, or at least has perished: the _former_ appears to me incorrect. Aristotle decidedly reckons the _Reductio ad Impossibile_ among hypothetical proofs. But he understands by _Reductio ad Impossibile_ something rather wider than what the moderns understand by it. It now means only, that you take the contradictory of the conclusion together with one of the premisses, and by means of these two demonstrate a conclusion contradictory or contrary to the other premiss. But Aristotle understood by it this, and something more besides, namely, whenever, by taking the contradictory of the conclusion, together with some other incontestable premiss, you demonstrate, by means of the two, some new conclusion notoriously false. What I here say, is illustrated by the very example which he gives in this chapter. The incommensurability of the diagonal (with the side of the square) is demonstrated by _Reductio ad Impossibile_; because if it be supposed commensurable, you may demonstrate that an odd number is equal to an even number; a conclusion which every one will declare to be inadmissible, but which is not the contradictory of either of the premisses whereby the true proposition was demonstrated.]

Here Aristotle expressly reserves for separate treatment the general subject of Syllogisms from Hypothesis.[88]

[Footnote 88: The expressions of Aristotle here are remarkable, Analyt. Prior. I. xliv. p. 50, a. 39-b. 3: [Greek: polloi\ de\ kai\ e(/teroi perai/nontai e)x u(pothe/seôs, ou(\s e)piske/psasthai dei= kai\ diasêmê=nai katharô=s. ti/nes me\n ou)=n ai( diaphorai\ tou/tôn, kai\ posachô=s gi/netai to\ e)x u(pothe/seôs, u(/steron e)rou=men; nu=n de\ tosou=nton ê(mi=n e)/stô phanero/n, o(/ti ou)k e)/stin a)nalu/ein ei)s ta\ schê/mata tou\s toiou/tous sullogismou/s. kai\ di' ê(\n ai)ti/an, ei)rê/kamen.]

Syllogisms from Hypothesis were many and various, and Aristotle intended to treat them in a future treatise; but all that concerns the present treatise, in his opinion, is, to show that none of them can be reduced to the three Figures. Among the Syllogisms from Hypothesis, two varieties recognized by Aristotle (besides [Greek: oi) dia\ tou= a)duna/tou]) were [Greek: oi( kata\ meta/lêpsin] and [Greek: oi( kata\ poio/têta]. The same proposition which Aristotle entitles [Greek: kata\ meta/lêpsin], was afterwards designated by the Stoics [Greek: kata\ pro/slêpsin] (Alexander ap. Schol. p. 178, b. 6-24).

It seems that Aristotle never realized this intended future treatise on Hypothetical Syllogisms; at least Alexander did not know it. The subject was handled more at large by Theophrastus and Eudêmus after Aristotle (Schol. p. 184, b. 45. Br.; Boethius, De Syllog. Hypothetico, pp. 606-607); and was still farther expanded by Chrysippus and the Stoics.

Compare Prantl, Geschichte der Logik, I. pp. 295, 377, seq. He treats the Hypothetical Syllogism as having no logical value, and commends Aristotle for declining to develop or formulate it; while Ritter (Gesch. Phil. iii. p. 93), and, to a certain extent, Ueberweg (System der Logik, sect. 121, p. 326), consider this to be a defect in Aristotle.]

In the last chapter of the first book of the Analytica Priora, Aristotle returns to the point which we have already considered in the treatise De Interpretatione, viz. what is really a _negative_ proposition; and how the adverb of negation must be placed in order to constitute one. We must place this adverb immediately before the copula and in conjunction with the copula: we must not place it after the copula and in conjunction with the predicate; for, if we do so, the proposition resulting will not be negative but affirmative ([Greek: e)k metathe/seôs], by transposition, according to the technical term introduced afterwards by Theophrastus). Thus of the four propositions:

1. Est bonum. 2. Non est bonum.
4. Non est non bonum. 3. Est non bonum.

No. 1 is affirmative; No. 3 is affirmative ([Greek: e)k metathe/seôs]); Nos. 2 and 4 are negative. Wherever No. 1 is predicable, No. 4 will be predicable also; wherever No. 3 is predicable, No. 2 will be predicable also--but in neither case _vice versâ_.[89] Mistakes often flow from incorrectly setting out the two contradictories.

[Footnote 89: Analyt. Prior. I. xlvi. p. 51, b. 5, ad finem. See above, Chap. IV. p. 118, seq.]