[78] Analyt. 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.
[79] Ibid. 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.
[80] Ibid. 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 often facilitate the setting out of the terms. We must carefully note 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.[81] Nor is it the same proposition to say B is predicable of C (indefinite), and B is predicable of all C (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]
[81] Analyt. 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.
[82] Ibid. 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]
[83] Ibid. 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.)