51Analyt. Prior. I. xxvii. p. 43, b. 8: καὶ τούτων ποῖα δοξαστικῶς καὶ ποῖα κατ’ ἀλήθειαν.
51Analyt. Prior. I. xxvii. p. 43, b. 8: καὶ τούτων ποῖα δοξαστικῶς καὶ ποῖα κατ’ ἀλήθειαν.
52Ibid. I. xxvii. p. 43, b. 10-35.
52Ibid. I. xxvii. p. 43, b. 10-35.
53Ibid. b. 36: ἔτι τὰ πᾶσιν ἑπόμενα οὐκ ἐκλεκτέον· 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 realgenera.
53Ibid. b. 36: ἔτι τὰ πᾶσιν ἑπόμενα οὐκ ἐκλεκτέον· 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 realgenera.
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 thelist 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 (inBarbara, Fig. 1), demonstrating that A belongs toallE; 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 tosomeE, by a syllogism (inDarapti, 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 (inCelarent, 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 (inCamestres, Fig. 2), shewing that no A belongs to E.54In 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.55It 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
54Analyt. Prior. I. xxviii. p. 43, b. 39-p. 44, a. 35.
54Analyt. Prior. I. xxviii. p. 43, b. 39-p. 44, a. 35.
55Ibid. 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 Aristotlehereto 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.
55Ibid. 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 Aristotlehereto 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.
56Ibid. p. 44, b. 6-20.
56Ibid. 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 inthe 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
57Analyt. Prior. I. xxviii. p. 44, b. 25-37.
57Analyt. 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
58Ibid. 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.
58Ibid. 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 ofReductio 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 theReductio ad Impossibile, one of the premisses is assumed as true though known to be false, and the conclusion also.59In the other cases of hypothetical syllogism your attention must be directed, not to the originalquæsitum, but to the condition annexed thereto; yet the search for predicates, subjects, and a middle term, must be conducted in the same manner.60Sometimes, by the helpof 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 theonlyones to which E belongs as predicate (this seems to be theextraneousorextra-syllogisticcondition 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.61In 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.
59Ibid. I. xxix. p. 45, a. 25-b. 15.
59Ibid. I. xxix. p. 45, a. 25-b. 15.
60Ibid. I. xxix. p. 45, b. 15-20. This paragraph is very obscure. Neither Alexander, nor Waitz, nor St. Hilaire clears it upcompletely. 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.
60Ibid. I. xxix. p. 45, b. 15-20. This paragraph is very obscure. Neither Alexander, nor Waitz, nor St. Hilaire clears it upcompletely. 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.
61Analyt. Prior. I. xxix. p. 45, b. 21-30.
61Analyt. 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
62Ibid. b. 36-xxx. p. 46, a. 10.
62Ibid. 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,63and to debatein Dialectic. In both, the premisses orprincipiaof 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 orprincipia, which must be searched out and selected in the way above described. Experience alone can furnish theseprincipia, 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.64When 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
63Ibid. p. 46, a. 8:κατὰ μὲν ἀλήθειαν ἐκ τῶν κατ’ ἀλήθειανδιαγεγραμμένωνὑπάρχειν, 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.
63Ibid. p. 46, a. 8:κατὰ μὲν ἀλήθειαν ἐκ τῶν κατ’ ἀλήθειανδιαγεγραμμένωνὑπάρχειν, 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.
64Analyt. 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 ἐπιστήμης· 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.
64Analyt. 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 ἐπιστήμης· 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.
65Analyt. Prior. I. xxx. p. 46, a. 22-27:ὥστε ἂν ληφθῇ τὰ ὑπάρχοντα περὶ ἕκαστον, ἡμέτερον ἤδη τὰς ἀποδείξεις ἑτοίμως ἐμφανίζειν. εἰ γὰρ μηδὲνκατὰ τὴν ἱστορίανπαραλειφθείη 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.
65Analyt. Prior. I. xxx. p. 46, a. 22-27:ὥστε ἂν ληφθῇ τὰ ὑπάρχοντα περὶ ἕκαστον, ἡμέτερον ἤδη τὰς ἀποδείξεις ἑτοίμως ἐμφανίζειν. εἰ γὰρ μηδὲνκατὰ τὴν ἱστορίανπαραλειφθείη 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 futurechapter. 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 intogeneraandspecies; a process much relied upon by other philosophers, and especially by Plato. This logical Division, according to Aristotle, is amere fragment of the syllogistic procedure; nothing better than a feeble syllogism.66Those 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.67Instead 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
66Analyt. 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 Sophistês and Politicus; compare also Philêbus, c. v., p. 15.
66Analyt. 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 Sophistês and Politicus; compare also Philêbus, c. v., p. 15.
67Ibid. 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.
67Ibid. 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.
68Ibid. p. 46, b. 1-12.
68Ibid. 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.69Moreover, 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 respectinggenus, orproprium, oraccidens; thegenusis assumed, and the method proceeds from thence tospeciesanddifferentia. 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
69Ibid. p. 46, b. 1-12.
69Ibid. p. 46, b. 1-12.
70Ibid. b. 26-37. Alexander in Schol. p. 180, b. 1.
70Ibid. 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 whenvalid, often elliptical and disorderly), to the figures of syllogism as above set forth, for the purpose of testing its validity.71In 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
71Analyt. Prior. I. xxxii. p. 47, a. 2: λοιπὸν γὰρ ἔτι τοῦτο τῆς σκέψεως· εἰ γὰρ τήν τε γένεσιν τῶν συλλογισμῶν θεωροῖμεν καὶ τοῦ εὑρίσκειν ἔχοιμεν δύναμιν, ἔτι δὲ τοὺς γεγενημένους ἀναλύοιμεν εἰς τὰ προειρημένα σχήματα, τέλος ἂν ἔχοι ἡ ἐξ ἀρχῆς πρόθεσις.
71Analyt. Prior. I. xxxii. p. 47, a. 2: λοιπὸν γὰρ ἔτι τοῦτο τῆς σκέψεως· εἰ γὰρ τήν τε γένεσιν τῶν συλλογισμῶν θεωροῖμεν καὶ τοῦ εὑρίσκειν ἔχοιμεν δύναμιν, ἔτι δὲ τοὺς γεγενημένους ἀναλύοιμεν εἰς τὰ προειρημένα σχήματα, τέλος ἂν ἔχοι ἡ ἐξ ἀρχῆς πρόθεσις.
72Ibid. a. 8.
72Ibid. 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
73Ibid. a. 10-b. 14.
73Ibid. 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.74Another sourceof 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.75To 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.76When we take the concrete man, we may say with truth that the two contraries, health-sickness, knowledge-ignorance,mayboth alike belong to him; though not to the same individual at the same time.
74Ibid. I. xxxiii. p. 47, b. 16-40: αὕτη μὲν οὖν ἡ ἀπάτη γίνεται ἐν τῷ παρὰ μικρόν· ὠς γὰρ οὐδὲν διαφέρον εἰπεῖντόδε τῷδε ὑπάρχειν, ἢ τόδε τῷδε παντὶ ὑπάρχειν, συγχωροῦμεν.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.â€� Julius Pacius (p. 264) gives the same explanation at greater length; but the example chosen by Aristotle (ὁ Ἀριστομένης ἐστὶ διανοητὸς Ἀριστομένης) appears open to other objections besides.
74Ibid. I. xxxiii. p. 47, b. 16-40: αὕτη μὲν οὖν ἡ ἀπάτη γίνεται ἐν τῷ παρὰ μικρόν· ὠς γὰρ οὐδὲν διαφέρον εἰπεῖντόδε τῷδε ὑπάρχειν, ἢ τόδε τῷδε παντὶ ὑπάρχειν, συγχωροῦμεν.
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.â€� Julius Pacius (p. 264) gives the same explanation at greater length; but the example chosen by Aristotle (ὁ Ἀριστομένης ἐστὶ διανοητὸς Ἀριστομένης) appears open to other objections besides.
75Analyt. Prior. I. xxxiv. p. 48, a. 1-28.
75Analyt. Prior. I. xxxiv. p. 48, a. 1-28.
76Ibid. a. 2-23. See the Scholion of Alexander, p. 181, b. 16-27, Brandis.
76Ibid. 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 triangleper se, and follows from the fundamental properties of the figure.77There 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.
77Ibid. I. xxxv. p. 48, a. 30-39: φανερὸν ὅτι τὸ μέσον οὐχ οὕτως ἀεὶ ληπτέον ὡς τόδε τι, ἀλλ’ ἐνίοτε λόγον, ὅπερ συμβαίνει κἀπὶ τοῦ λεχθέντος. A good Scholion of Philoponus is given, p. 181, b. 28-45, Brand.
77Ibid. I. xxxv. p. 48, a. 30-39: φανερὸν ὅτι τὸ μέσον οὐχ οὕτως ἀεὶ ληπτέον ὡς τόδε τι, ἀλλ’ ἐνίοτε λόγον, ὅπερ συμβαίνει κἀπὶ τοῦ λεχθέντος. 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.78Moreover, 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; predicationsecundum quidis distinguished from predicationsimpliciter, simple from combined or compound, &c. This applies to negatives as well as affirmatives.79There 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 knowledgequatenus bonumorquod bonum est; the three terms of the syllogism must stand thus:—
Major—Bonumis knowable,quatenus bonumorquod bonum est.Minor— The wholesome isbonum.Ergo— The wholesome is knowable,quatenus bonum, &c.
Major—Bonumis knowable,quatenus bonumorquod bonum est.
Minor— The wholesome isbonum.
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
78Analyt. Prior. I. xxxvi. p. 48, a. 40-p. 49, a. 5. ἁπλῶς λέγομεν γὰρ τοῦτο κατὰ πάντων, ὅτι τοὺς μὲν ὅρους ἄει θετέον κατὰ τὰς κλήσεις τῶν ὀνομάτων — τὰς δὲ προτάσεις ληπτέον κατὰ τὰς ἑκάστου πτώσεις. Several examples are given of this precept.
78Analyt. Prior. I. xxxvi. p. 48, a. 40-p. 49, a. 5. ἁπλῶς λέγομεν γὰρ τοῦτο κατὰ πάντων, ὅτι τοὺς μὲν ὅρους ἄει θετέον κατὰ τὰς κλήσεις τῶν ὀνομάτων — τὰς δὲ προτάσεις ληπτέον κατὰ τὰς ἑκάστου πτώσεις. Several examples are given of this precept.
79Ibid. 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, Περὶ Καταφάσεως, not preserved.
79Ibid. 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, Περὶ Καταφάσεως, not preserved.
80Ibid. I. xxxviii. p. 49, a. 11-b. 2. φανερὸν οὖν ὅτι ἐν τοῖς ἐν μέρει συλλογισμοῖς οὕτω ληπτέον τοὺς ὅρους. Alexander explains οἱ ἐν μέρει συλλογισμοί (Schol. p. 183, b. 32, Br.) to be those in which the predicate has a qualifying adjunct tacked to it.
80Ibid. I. xxxviii. p. 49, a. 11-b. 2. φανερὸν οὖν ὅτι ἐν τοῖς ἐν μέρει συλλογισμοῖς οὕτω ληπτέον τοὺς ὅρους. Alexander explains οἱ ἐν μέρει συλλογισμοί (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 oftenfacilitatethe setting out of the terms. We must carefullynote 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.81Nor is it the same proposition to say B is predicable of C (indefinite), and B is predicable ofallC (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
81Analyt. Prior. I. xxxix.-xl. p. 49, b. 3-13. οὐ ταὐτὸν ἐστι τὸ εἶναι τὴν ἡδονὴν ἀγαθὸν καὶ τὸ εἶναι τὴν ἡδονὴν τὸ ἀγαθόν, &c.
81Analyt. Prior. I. xxxix.-xl. p. 49, b. 3-13. οὐ ταὐτὸν ἐστι τὸ εἶναι τὴν ἡδονὴν ἀγαθὸν καὶ τὸ εἶναι τὴν ἡδονὴν τὸ ἀγαθόν, &c.
82Ibid. 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 κατὰ πρόσληψιν, 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.
82Ibid. 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 κατὰ πρόσληψιν, 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
83Ibid. I. xli. p. 50, a. 1: τῷ δ’ ἐκτίθεσθαι οὕτω χρώμεθα ὥσπερ καὶ τῷ αἰσθάνεσθαι τὸν μανθάνοντα λέγοντες· οὐ γὰρ οὕτως ὡς ἄνευ τούτων οὐχ οἷόν τ’ ἀποδειχθῆναι, ὥσπερ ἐξ ὧν ὁ συλλογισμός.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.)
83Ibid. I. xli. p. 50, a. 1: τῷ δ’ ἐκτίθεσθαι οὕτω χρώμεθα ὥσπερ καὶ τῷ αἰσθάνεσθαι τὸν μανθάνοντα λέγοντες· οὐ γὰρ οὕτως ὡς ἄνευ τούτων οὐχ οἷόν τ’ ἀποδειχθῆναι, ὥσπερ ἐξ ὧν ὁ συλλογισμός.
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 threefigures 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.84All 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 byReductio ad Absurdum.85
84Analyt. 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 ofwater) does not convey much instruction.
84Analyt. 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 ofwater) does not convey much instruction.
85Ibid. xlv. p. 50, b. 5-p. 51, b. 2.
85Ibid. 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.86The same is true about the procedure byReductio ad Absurdum, which involves an hypothesis over and above the syllogism. In employing suchReductio 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 knowaliundethat 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; youmust assume it by hypothesis, or depend upon the hearer to grant it.87