[1] This is the remark of the ancient Scholiasts. See Schol. p. 188, a. 44, b. 11.
[2] Analyt. Prior. II. i. p. 53, a. 3-14.
[3] Analyt. Prior. II. i. p. 53, a. 14-35. M. Barthélemy St. Hilaire, following Pacius, justly remarks (note, p. 203 of his translation) that the rule as to particulars breaks down in the cases of Baroco, Disamis, and Bocardo.
On the chapter in general he remarks (note, p. 204):— “Cette théorie des conclusions diverses, soit patentes soit cachées, d’un même syllogisme, est surtout utile en dialectique, dans la discussion; où il faut faire la plus grande attention à ce qu’on accorde à l’adversaire, soit explicitement, soit implicitement.� This illustrates the observation cited in the preceding note from the Scholiasts.
Aristotle has hitherto regarded the Syllogism with a view to its formal characteristics: he now makes an important observation which bears upon its matter. Formally speaking, the two premisses are always assumed to be true; but in any real case of syllogism (form and matter combined) it is possible that either one or both may be false. Now, Aristotle remarks that if both the premisses are true (the syllogism being correct in form), the conclusion must of necessity be true; but that if either or both the premisses are false, the conclusion need not necessarily be false likewise. The premisses being false, the conclusion may nevertheless be true; but it will not be true because of or by reason of the premisses.[4]
[4] Analyt. Prior. II. ii. p. 53, b. 5-10: ἐξ ἀληθῶν μὲν οὖν οὐκ ἔστι ψεῦδος συλλογίσασθαι, ἐκ ψευδῶν δ’ ἔστιν ἀληθές, πλὴν οὐ διότι ἀλλ’ ὅτι· τοῦ γὰρ διότι οὐκ ἔστιν ἐκ ψευδῶν συλλογισμός· δι’ ἣν δ’ αἰτίαν, ἐν τοῖς ἑπομένοις λεχθήσεται.
The true conclusion is not true by reason of these false premisses, but by reason of certain other premisses which are true, and which may be produced to demonstrate it. Compare Analyt. Poster. I. ii. p. 71, b. 19.
First, he would prove that if the premisses be true, the conclusion must be true also; but the proof that he gives does not seem more evident than the probandum itself. Assume that if A exists, B must exist also: it follows from hence (he argues) that if B does not exist, neither can A exist; which he announces as a reductio ad absurdum, seeing that it contradicts the fundamental supposition of the existence of A.[5] Here the probans is indeed equally evident with the probandum, but not at all more evident; one who disputes the latter, will dispute the former also. Nothing is gained in the way of proof by making either of them dependent on the other. Both of them are alike self-evident; that is, if a man hesitates to admit either of them, you have no means of removing his scruples except by inviting him to try the general maxim upon as many particular cases as he chooses, and to see whether it does not hold good without a single exception.
[5] Ibid. II. ii. p. 53, b. 11-16.
In regard to the case here put forward as illustration, Aristotle has an observation which shows his anxiety to maintain the characteristic principles of the Syllogism; one of which principles he had declared to be — That nothing less than three terms and two propositions, could warrant the inferential step from premisses to conclusion. In the present case he assumed, If A exists, then B must exist; giving only one premiss as ground for the inference. This (he adds) does not contravene what has been laid down before; for A in the case before us represents two propositions conceived in conjunction.[6] Here he has given the type of hypothetical reasoning; not recognizing it as a variety per se, nor following it out into its different forms (as his successors did after him), but resolving it into the categorical syllogism.[7] He however conveys very clearly the cardinal principle of all hypothetical inference — That if the antecedent be true, the consequent must be true also, but not vice versâ; if the consequent be false, the antecedent must be false also, but not vice versâ.