[18] Aristot. Analyt. Post. I. v. p. 74, a. 4-23. ἀλλὰ διὰ τὸ μὴ εἶναι ὠνομασμένον τι πάντα ταῦτα ἕν, ἀριθμοί, μήκη, χρόνος, στερεά, καὶ εἴδει διαφέρειν ἀλλήλων, χωρὶς ἐλαμβάνετο. What these four have in common is that which he himself expresses by Ποσόν — Quantum — in the Categoriæ and elsewhere. (Categor. p. 4, b. 20, seq.; Metaph. Δ. p. 1020, a. 7, seq.)
[19] Aristot. Analyt. Post. I. v. p. 74, a. 27: οὔπω οἶδε τὸ τρίγωνον ὅτι δύο ὀρθαῖς, εἰ μὴ τὸν σοφιστικὸν τρόπον οὐδὲ καθόλου τρίγωνον, οὔδ’ εἰ μηδέν ἐστι παρὰ ταῦτα τρίγωνον ἕτερον. The phrase τὸν σοφιστικὸν τρόπον is equivalent to τὸν σοφιστικὸν τρόπον τὸν κατὰ συμβεβηκός, p. 71, b. 10. I see nothing in it connected with Aristotle’s characteristic of a Sophist (special professional life purpose — τοῦ βίου τῇ προαιρέσει, Metaphys. Γ. p. 1004, b. 24): the phrase means nothing more than unscientific.
[20] Aristot. Analyt. Post. I. v. p. 74, a. 32-b. 4.
In every demonstration the principia or premisses must be not only true, but necessarily true; the conclusion also will then be necessarily true, by reason of the premisses, and this constitutes Demonstration. Wherever the premisses are necessarily true, the conclusion will be necessarily true; but you cannot say, vice versâ, that wherever the conclusion is necessarily true, the syllogistic premisses from which it follows must always be necessarily true. They may be true without being necessarily true, or they may even be false: if, then, the conclusion be necessarily true, it is not so by reason of these premisses; and the syllogistic proof is in this case no demonstration. Your syllogism may have true premisses and may lead to a conclusion which is true by reason of them; but still you have not demonstrated, since neither premisses nor conclusion are necessarily true.[21] When an opponent contests your demonstration, he succeeds if he can disprove the necessity of your conclusion; if he can show any single case in which it either is or may be false.[22] It is not enough to proceed upon a premiss which is either probable or simply true: it may be true, yet not appropriate to the case: you must take your departure from the first or highest universal of the genus about which you attempt to demonstrate.[23] Again, unless you can state the why of your conclusion; that is to say, unless the middle term, by reason of which the conclusion is necessarily true, be itself necessarily true, — you have not demonstrated it, nor do you know it absolutely. Your middle term not being necessary may vanish, while the conclusion to which it was supposed to lead abides: in truth no conclusion was known through that middle.[24] In the complete demonstrative or scientific syllogism, the major term must be predicable essentially or per se of the middle, and the middle term must be predicable essentially or per se of the minor; thus alone can you be sure that the conclusion also is per se or necessary. The demonstration cannot take effect through a middle term which is merely a Sign; the sign, even though it be a constant concomitant, yet being not, or at least not known to be, per se, will not bring out the why of the conclusion, nor make the conclusion necessary. Of non-essential concomitants altogether there is no demonstration; wherefore it might seem to be useless to put questions about such; yet, though the questions cannot yield necessary premisses for a demonstrative conclusion, they may yield premisses from which a conclusion will necessarily follow.[25]
[21] Ibid. vi. p. 74, b. 5-18. ἐξ ἀληθῶν μὲν γὰρ ἔστι καὶ μὴ ἀποδεικνύντα συλλογίσθαι, ἐξ ἀναγκαίων δ’ οὐκ ἔστιν ἀλλ’ ἢ ἀποδεικνύντα· τοῦτο γὰρ ἤδη ἀποδείξεώς ἐστιν. Compare Analyt. Prior. I. ii. p. 53, b. 7-25.
[22] Aristot. Analyt. Post. I. vi. p. 74, b. 18: σημεῖον δ’ ὅτι ἡ ἀπόδειξις ἐξ ἀναγκαίων, ὅτι καὶ τὰς ἐνστάσεις οὕτω φέρομεν πρὸς τοὺς οἰομένους ἀποδεικνύναι, ὅτι οὐκ ἀνάγκη, &c.
[23] Ibid. vi. p. 74, b. 21-26: δῆλον δ’ ἐκ τούτων καὶ ὅτι εὐήθεις οἱ λαμβάνειν οἰόμενοι καλῶς τὰς ἀρχάς, ἐὰν ἔνδοξος ᾖ ἡ πρότασις καὶ ἀληθής, οἷον οἱ σοφισταὶ ὅτι τὸ ἐπίστασθαι τὸ ἐπιστήμην ἔχειν·, &c.
[24] Aristot. Analyt. Post. I. vi. p. 74, b. 26-p. 75, a. 17.
[25] Ibid. vi. p. 75, a. 8-37.
On the point last mentioned, M. Barthélemy St. Hilaire observes in his note, p. 41: “Dans les questions de dialectique, la conclusion est nécessaire en ce sens, qu’elle suit nécessairement des prémisses; elle n’est pas du tout nécessaire en ce sens, que la chose qu’elle exprime soit nécessaire. Ainsi il faut distinguer la nécessité de la forme et la nécessité de la matière: ou comme disent les scholastiques, necessitas illationis et necessitas materiæ. La dialectique se contente de la première, mais la demonstration a essentiellement besoin des deux.�