Authors/Aristotle/priora/Liber 1/C8

Chapter 8

Greek	Latin	English
	(PL 64 0648A) CAPUT VIII. De syllogismis ex necessario in tribus figuris.	8
29b29 Ἐπεὶ δ᾽ ἕτερόν ἐστιν ὑπάρχειν τε καὶ ἐξ ἀνάγκης ὑπάρχειν καὶ ἐνδέχεσθαι ὑπάρχειν (πολλὰ γὰρ ὑπάρχει μέν, οὐ μέντοι ἐξ ἀνάγκης· τὰ δ᾽ οὔτ᾽ ἐξ ἀνάγκης οὔθ᾽ ὑπάρχει ὅλως, ἐνδέχεται δ᾽ ὑπάρχειν), δῆλον ὅτι καὶ συλλογισμὸς ἑκάστου τούτων ἕτερος ἔσται, καὶ οὐχ ὁμοίως ἐχόντων τῶν ὅρων, ἀλλ᾽ ὁ μὲν ἐξ ἀναγκαίων, ὁ δ᾽ ἐξ ὑπαρχόντων, ὁ δ᾽ ἐξ ἐνδεχομένων.	Quoniam autem diversum est inesse, et ex necessitate inesse, et contingere inesse (nam multa insunt quidem, non tamen ex necessitate, alia vero neque ex necessitate, neque insunt omnino, contingit autem inesse), manifestum quoniam et syllogismus in unoquoque horum diversus est, et non similiter habentibus se terminis, sed hic quidem ex necessariis, ille vero ex iis quae simpliciter insunt, ille autem ex contingentibus.	Since there is a difference according as something belongs, necessarily belongs, or may belong to something else (for many things belong indeed, but not necessarily, others neither necessarily nor indeed at all, but it is possible for them to belong), it is clear that there will be different syllogisms to prove each of these relations, and syllogisms with differently related terms, one syllogism concluding from what is necessary, another from what is, a third from what is possible.
Ἐπὶ μὲν οὖν τῶν ἀναγκαίων σχεδὸν ὁμοίως ἔχει καὶ ἐπὶ τῶν ὑπαρχόντων· ὡσαύτως γὰρ τιθεμένων τῶν ὅρων ἔν τε τῶι ὑπάρχειν καὶ τῶι ἐξ ἀνάγκης ὑπάρχειν ἢ μὴ ὑπάρχειν ἔσται τε καὶ οὐκ ἔσται συλλογισμός, πλὴν διοίσει τῶι ↵ προσκεῖσθαι τοῖς ὅροις τὸ ἐξ ἀνάγκης ὑπάρχειν ἢ μὴ ὑπάρχειν. τό τε γὰρ στερητικὸν ὡσαύτως ἀντιστρέφει, καὶ τὸ ἐν ὅλωι εἶναι καὶ τὸ κατὰ παντὸς ὁμοίως ἀποδώσομεν.	Ergo in necessariis quidem fere similiter se habet, et in iis qui insunt. (0648B) Similiter enim positis terminis, et in iis quae insunt, et in iis quae ex necessitate insunt vel non insunt, et erit, et non erit syllogismus. Verum distabit in eo quod adiacet terminis ex necessitate inesse, vel non inesse, nam et privativum similiter convertitur, et in toto esse, et de omni similiter assignabimus.	There is hardly any difference between syllogisms from necessary premisses and syllogisms from premisses which merely assert. When the terms are put in the same way, then, whether something belongs or necessarily belongs (or does not belong) to something else, a syllogism will or will not result alike in both cases, the only difference being the addition of the expression ‘necessarily’ to the terms. For the negative statement is convertible alike in both cases, and we should give the same account of the expressions ‘to be contained in something as in a whole’ and ‘to be predicated of all of something’.
ἐν μὲν οὖν τοῖς ἄλλοις τὸν αὐτὸν τρόπον δειχθήσεται διὰ τῆς ἀντιστροφῆς τὸ συμπέρασμα ἀναγκαῖον, ὥσπερ ἐπὶ τοῦ ὑπάρχειν· ἐν δὲ τῶι μέσωι σχήματι, ὅταν ἦι τὸ καθόλου καταφατικὸν τὸ δ᾽ ἐν μέρει στερητικόν, καὶ πάλιν ἐν τῶι τρίτωι, ὅταν τὸ μὲν καθόλου κατηγορικὸν τὸ δ᾽ ἐν μέρει στερητικόν, οὐχ ὁμοίως ἔσται ἡ ἀπόδειξις, ἀλλ᾽ ἀνάγκη ἐκθεμένους ὧι τινὶ ἑκάτερον μὴ ὑπάρχει, κατὰ τούτου ποιεῖν τὸν συλλογισμόν· ἔσται γὰρ ἀναγκαῖος ἐπὶ τούτων· εἰ δὲ κατὰ τοῦ ἐκτεθέντος ἐστὶν ἀναγκαῖος, καὶ κατ᾽ ἐκείνου τινός· τὸ γὰρ ἐκτεθὲν ὅπερ ἐκεῖνό τί ἐστιν. γίνεται δὲ τῶν συλλογισμῶν ἑκάτερος ἐν τῶι οἰκείωι σχήματι.	Ergo in aliis quidem eodem modo ostendetur per conversionem, quoniam conclusio necessaria, quomodo in eo quod est inesse. In media autem figura quando fuerit universalis affirmativa, particularis vero privativa, et rursum in tertia quando universalis quidem praedicativa, particularis vero privativa, non similiter erit demonstratio, sed necesse est exponentes, cui alicui utrumque non inest, de hoc facere syllogismum. Erit enim necessarius in hoc. Si autem de exposito est necessarius, erit et de illo aliquo. (0648C) Nam hoc quod est expositum, ipsum quidem illud aliquid est. Fit autem uterque syllogismus in propria figura.	With the exceptions to be made below, the conclusion will be proved to be necessary by means of conversion, in the same manner as in the case of simple predication. But in the middle figure when the universal statement is affirmative, and the particular negative, and again in the third figure when the universal is affirmative and the particular negative, the demonstration will not take the same form, but it is necessary by the ‘exposition’ of a part of the subject of the particular negative proposition, to which the predicate does not belong, to make the syllogism in reference to this: with terms so chosen the conclusion will necessarily follow. But if the relation is necessary in respect of the part taken, it must hold of some of that term in which this part is included: for the part taken is just some of that. And each of the resulting syllogisms is in the appropriate figure.