[27] Analyt. Prior. I. iv. p. 26, a. 2, seq.
This mode of reasoning plainly depends upon an appeal to prior experience. The validity or invalidity of each mode of the First figure is tested by applying it to different particular cases, each of which is familiar and known to the learner aliunde; in one case, the conjunction of the major and minor terms in the third proposition makes an universal Affirmative which he knows to be true; in another case, the like conjunction makes an universal Negative, which he also knows to be true; so that there is no one necessary (i.e. no one uniform and trustworthy) conclusion derivable from such premisses.[28] In other words, these modes of the First figure are not valid or available in form; the negation being sufficiently proved by one single undisputed example.
[28] Though M. Barthélemy St. Hilaire (note, p. 19) declares Aristotle’s exposition to be a model of analysis, it appears to me that the grounds for disallowing this invalid mode of the First figure (A — E — A, or A — E — E) are not clearly set forth by Aristotle himself, while they are rendered still darker by some of his best commentators. Thus Waitz says (p. 381): “Per exempla allata probat (Aristoteles) quod demonstrare debebat ex ipsâ ratione quam singuli termini inter se habeant: est enim proprium artis logicæ, ut terminorum rationem cognoscat, dum res ignoret. Num de Caio prædicetur animal nescit, scit de Caio prædicari animal, si animal de homine et homo de Caio prædicetur.�
This comment of Waitz appears to me founded in error. Aristotle had no means of shewing the invalidity of the mode A E in the First figure, except by an appeal to particular examples. The invalidity of the invalid modes, and the validity of the valid modes, rest alike upon this ultimate reference to examples of propositions known to be true or false, by prior experience of the learner. The valid modes are those which will stand this trial and verification; the invalid modes are those which will not stand it. Not till such verification has been made, is one warranted in generalizing the result, and enunciating a formula applicable to unknown particulars (rationem terminorum cognoscere, dum res ignoret). It was impossible for Aristotle to do what Waitz requires of him. I take the opposite ground, and regret that he did not set forth the fundamental test of appeal to example and experience, in a more emphatic and unmistakeable manner.
M. Barthélemy St. Hilaire (in the note to his translation, p. 14) does not lend any additional clearness, when he talks of the “conclusion� from the propositions A and E in the First figure. Julius Pacius says (p. 134): “Si tamen conclusio dici debet, quæ non colligitur ex propositionibus,� &c. Moreover, M. St. Hilaire (p. 19) slurs over the legitimate foundation, the appeal to experience, much as Aristotle himself does: “Puis prenant des exemples où la conclusion est de toute évidence, Aristote les applique successivement à chacune de ces combinaisons; celles qui donnent la conclusion fournie d’ailleurs par le bon sens, sont concluantes ou syllogistiques, les autres sont asyllogistiques.�
We are now introduced to the Second figure, in which each of the two premisses has the middle term as Predicate.[29] To give a legitimate conclusion in this figure, one or other of the premisses must be negative, and the major premiss must be universal; moreover no affirmative conclusions can ever be obtained in it — none but negative conclusions, universal or particular. In this Second figure too, Aristotle recognizes four valid modes; setting aside the other possible modes as invalid[30] (in the same way as he had done in the First figure), because the third proposition or conjunction of the major term with the minor, might in some cases be a true universal affirmative, in other cases a true universal negative. As to the third and fourth of the valid modes, he demonstrates them by assuming the contradictory of the conclusion, together with the major premiss, and then showing that these two premisses form a new syllogism, which leads to a conclusion contradicting the minor premiss. This method, called Reductio ad Impossibile, is here employed for the first time; and employed without being ushered in or defined, as if it were familiarly known.[31]
[29] Analyt. Prior. I. v. p. 26, b. 34. As Aristotle enunciates a proposition by putting the predicate before the subject, he says that in this Second figure the middle term comes πρῶτον τῇ θέσει. In the Third figure, for the same reason, he calls it ἔσχατον τῇ θέσει, vi. p. 28, a. 15.
[30] Analyt. Prior. I. v. p. 27, a. 18. In these invalid modes, Aristotle says there is no syllogism; therefore we cannot properly speak of a conclusion, but only of a third proposition, conjoining the major with the minor.
[31] Ibid. p. 27, a. 15, 26, seq. It is said to involve ὑπόθεσις, p. 28, a. 7; to be ἐξ ὑποθέσεως xxiii. p. 41, a. 25; to be τοῦ ἐξ ὑποθέσεως, as opposed to δεικτικός, xxiii. p. 40, b. 25.
M. B. St. Hilaire remarks justly, that Aristotle might be expected to define or explain what it is, on first mentioning it (note, p. 22).