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39 Ibid. xxiii. p. 40, b. 20, p. 41, a. 4–20.

40 Ibid. p. 40, b. 25: ἔτι ἢ δεικτικῶς ἢ ἐξ ὑποθέσεωςˇ τοῦ δ ἐξ ὑποθέσεως μέρος τὸ διὰ τοῦ ἀδυνάτου.

41 Ibid. p. 41, b. 23: πάντες γὰρ οἱ διὰ τοῦ ἀδυνάτου περαίνοντες τὸ μὲν ψεῦδος συλλογίζονται, τὸ δ ἐξ ἀρχῆς ἐξ ὑποθέσεως δεικνύουσιν, ὅταν ἀδύνατόν τι συμβαίνῃ τῆς ἀντιφάσεως τεθείσης.

It deserves to be remarked that Aristotle uses the phrase συλλογισμὸς ἐξ ὑποθέσεως, not συλλογισμὸς ὑποθετικός. This bears upon the question as to his views upon what subsequently received the title of hypothetical syllogisms; a subject to which I shall advert in a future note.

Aristotle here again enforces what he had before urged that in every valid syllogism, one premiss at least must be affirmative, and one premiss at least must be universal. If the conclusion be universal, both premisses must be so likewise; if it be particular, one of the premisses may not be universal. But without one universal premiss at least, there can be no syllogistic proof. If you have a thesis to support, you cannot assume (or ask to be conceded to you) that very thesis, without committing petitio principii, (i.e. qućsiti or probandi); you must assume (or ask to have conceded to you) some universal proposition containing it and more besides; under which universal you may bring the subject of your thesis as a minor, and thus the premisses necessary for supporting it will be completed. Aristotle illustrates this by giving a demonstration that the angles at the base of an isosceles triangle are equal; justifying every step in the reasoning by an appeal to some universal proposition.42

42 Analyt. Prior. I. xxiv. p. 41, b. 6–31. The demonstration given (b. 13–22) is different from that which we read in Euclid, and is not easy to follow. It is more clearly explained by Waitz (p. 434) than either by Julius Pacius or by M. Barth. St. Hilaire (p. 108).

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

43 Ibid. I. xxv. p. 41, b. 36, seq.

44 Ibid. xxv. p. 42, a. 23: μάτην ἔσται εἰλημμένα, εἰ μὴ ἐπαγωγῆς ἢ κρύψεως ἤ τινος ἄλλου τῶν τοιούτων χάριν. Ib. a. 38: οὗτος ὁ λόγος ἢ οὐ συλλελόγισται ἢ πλείω τῶν ἀναγκαίων ἠρώτηκε πρὸς τὴν θέσιν.

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.

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

47 Ibid. I. xxvii. p. 43, a. 20: πῶς δ εὐπορήσομεν αὐτοὶ πρὸς τὸ τιθέμενον ἀεὶ συλλογισμῶν, καὶ διὰ ποίας ὁδοῦ ληψόμεθα τὰς περὶ ἕκαστον ἀρχάς, νῦν ἤδη λεκτέονˇ οὐ γὰρ μόνον ἴσως δεῖ τὴν γένεσιν θεωρεῖν τῶν συλλογισμῶν, ἀλλὰ καὶ τὴν δύναμιν ἔχειν τοῦ ποιεῖν. 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 Categorić.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

48 Ibid. I. xxvii. p. 43, a. 25, seq.

49 Ibid. p. 43, a. 39: πλὴν εἰ μὴ κατὰ δόξαν. Cf. Schol. of Alexander, p. 175, a. 44, Br.: ἐνδόξως καὶ διαλεκτικῶς, ὥσπερ εἶπεν ἐν τοῖς Τοπικοῖς, that even the principia of science may be debated; for example, in book B. of the Metaphysica. Aristotle does not recognize either τὸ ὄν or τὸ ἕν as true genera, but only as predicates.

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 predicable53 both of the predicate and subject; for no valid affirmative conclusion can be obtained from them.

51 Analyt. Prior. I. xxvii. p. 43, b. 8: καὶ τούτων ποῖα δοξαστικῶς καὶ ποῖα κατ ἀλήθειαν.

52 Ibid. I. xxvii. p. 43, b. 10–35.

53 Ibid. b. 36: ἔτι τὰ πᾶσιν ἑπόμενα οὐκ ἐκλεκτέονˇ οὐ γὰρ ἔσται συλλογισμὸς ἐξ αὐτῶν. The phrase τὰ πᾶσιν ἑπόμενα, 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 τὰ πᾶσιν ἑπόμενα 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 οἷον εἰ τὰ ἑπόμενα ἑκατέρῳ ταὐτά ἐστιν in which the same meaning as that which the commentators ascribe to τὰ πᾶσιν ἑπόμενα is given in its own special and appropriate terms, and thus the same supposition unnecessarily repeated I cannot help suspecting that Aristotle intends τὰ πᾶσιν ἑπόμενα to mean something different; to mean such wide and universal predicates as τὸ ἓν and τὸ ὄν 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

54 Analyt. Prior. I. xxviii. p. 43, b. 39-p. 44, a. 35.

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. Alexanders 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 (τὸ καθόλου Ζ) is to be preferred to the indefinite or indeterminate (simply Z, ἀδιόριστον), also KΓ (τὸ καθόλου Γ) to simple Γ (ἀδιόριστον). This appears to me not inconsistent with the recommendation which Aristotle had given before.

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

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

58 Ibid. p. 44, b. 38-p. 45, a. 22. συμβαίνει δὴ τοῖς οὕτως ἐπισκοποῦσι προσεπιβλέπειν ἄλλην ὁδὸν τῆς ἀναγκαίας, διὰ τὸ λανθάνειν τὴν ταὐτότητα τῶν Β καὶ τῶν Θ.

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 qućsitum, 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 Aristotles 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.

59 Ibid. I. xxix. p. 45, a. 25-b. 15.

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 ἐπισκέψασθαι δὲ δεῖ καὶ διελεῖν ποσαχῶς οἱ ἐξ ὑποθέσεως (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.

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

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

63 Ibid. p. 46, a. 8: κατὰ μὲν ἀλήθειαν ἐκ τῶν κατ ἀλήθειαν διαγεγραμμένων ὑπάρχειν, εἰς δὲ τοὺς διαλεκτικοὺς συλλογισμοὺς ἐκ τῶν κατὰ δόξαν προτάσεων.

Julius Pacius (p. 257) remarks upon the word διαγεγραμμένων 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.

64 Analyt. Prior. I. xxx. p. 46, a. 10–20: αἱ δ ἀρχαὶ τῶν συλλογισμῶν καθόλου μὲν εἴρηνται ἴδιαι δὲ καθ ἑκάστην αἱ πλεῖσται. διὸ τὰς μὲν ἀρχὰς τὰς περὶ ἕκαστον ἐμπειρίας ἔστι παραδοῦναι. λέγω δ οἷον τὴν ἀστρολογικὴν μὲν ἐμπειρίαν τῆς ἀστρολογικῆς ἐπιστήμηςˇ ληφθέντων γὰρ ἱκανῶς τῶν φαινομένων οὕτως εὑρέθησαν αἱ ἀστρολογικαὶ ἀποδείξεις. ὁμοίως δὲ καὶ περὶ ἄλλην ὁποιανοῦν ἔχει τέχνην τε καὶ ἐπιστήμην.

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. Λ. p. 1073, a. 6, seq., with the commentary of Bonitz, p. 506.

65 Analyt. Prior. I. xxx. p. 46, a. 22–27: ὥστε ἂν ληφθῇ τὰ ὑπάρχοντα περὶ ἕκαστον, ἡμέτερον ἤδη τὰς ἀποδείξεις ἑτοίμως ἐμφανίζειν. εἰ γὰρ μηδὲν κατὰ τὴν ἱστορίαν παραλειφθείη τῶν ἀληθῶς ὑπαρχόντων τοῖς πράγμασιν, ἕξομεν περὶ ἅπαντος οὗ μὲν ἔστιν ἀπόδειξις, ταύτην εὑρεῖν καὶ ἀποδεικνύναι, οὗ δὲ μὴ πέφυκεν ἀπόδειξις, τοῦτο ποιεῖν φανερόν.

Respecting the word ἱστορία 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 Aristotles 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

66 Analyt. Prior. I. xxxi. p. 46, a. 33. Alexander, in Scholia, p. 180, a. 14. The Platonic method of διαίρεσις is exemplified in the dialogues called Sophistęs and Politicus; compare also Philębus, c. v., p. 15.

67 Ibid. p. 46, a. 34: πρῶτον δ αὐτὸ τοῦτο ἐλελήθει τοὺς χρωμένους αὐτῇ πάντας, καὶ πείθειν ἐπεχείρουν ὡς ὄντος δυνατοῦ περὶ οὐσίας ἀπόδειξιν γίνεσθαι καὶ τοῦ τί ἐστιν.

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

69 Ibid. p. 46, b. 1–12.

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