Authors/Aristotle/priora/Liber 2/C13

Chapter 13

Greek	Latin	English
	(PL 64 0699C) CAPUT XIII. De ostensione per impossibile in tertia figura.	13
62b5 Ὁμοίως δὲ καὶ διὰ τοῦ ἐσχάτου. κείσθω γὰρ τὸ Α τινὶ τῶι Β μὴ ὑπάρχειν, τὸ δὲ Γ παντί· τὸ ἄρα Α τινὶ τῶι Γ οὐχ ὑπάρχει. εἰ οὖν τοῦτ᾽ ἀδύνατον, ψεῦδος τὸ τινὶ μὴ ὑπάρχειν, ὥστ᾽ ἀληθὲς τὸ παντί. ἐὰν δ᾽ ὑποτεθῆι μηδενὶ ὑπάρχειν, συλλογισμὸς μὲν ἔσται καὶ τὸ ἀδύνατον, οὐ δείκνυται δὲ τὸ προτεθέν· ἐὰν γὰρ τὸ ἐναντίον ὑποτεθῆι, ταὐτ᾽ ἔσται ἅπερ ἐπὶ τῶν πρότερον. ἀλλὰ πρὸς τὸ τινὶ ὑπάρχειν αὕτη ληπτέα ἡ ὑπόθεσις.	Similiter autem et per ultimam. Ponatur enim A alicui B non inesse, C autem omni B, ergo A alicui C non inerit; si ergo hoc impossibile, falsum alicui non inesse, quare verum est omni. Si vero supponatur nulli inesse, syllogismus quidem erit, et impossibile, non ostendit autem quod propositum est; si enim contrarium supponatur, eadem erunt quae in prioribus.	Similarly they can all be formed in the last figure. Suppose that A does not belong to some B, but C belongs to all B: then A does not belong to some C. If then this is impossible, it is false that A does not belong to some B; so that it is true that A belongs to all B. But if it is supposed that A belongs to no B, we shall have a syllogism and a conclusion which is impossible: but the problem in hand is not proved: for if the contrary is supposed, we shall have the same results as before.
εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τὸ δὲ Γ τινὶ τῶι Β, τὸ Α οὐ παντὶ τῶι Γ. εἰ οὖν τοῦτο ψεῦδος, ἀληθὲς τὸ Α τινὶ τῶι Β ὑπάρχειν. ὅτι δ᾽ οὐδενὶ τῶι Β ὑπάρχει τὸ Α, ὑποκείσθω τινὶ ὑπάρχειν, εἰλήφθω δὲ καὶ τὸ Γ παντὶ τῶι Β ὑπάρχον.	Sed ad ostendendum alicui inesse, eadem sumenda est hypothesis, nam si A nulli B, C autem alicui B, A non omni C; si ergo hoc falsum, verum est A alicui B inesse. (0699D)	But to prove that A belongs to some B, this hypothesis must be made. If A belongs to no B, and C to some B, A will belong not to all C. If then this is false, it is true that A belongs to some B.
οὐκοῦν ἀνάγκη τῶι Γ τινὶ τὸ Α ὑπάρχειν. ἀλλ᾽ οὐδενὶ ὑπῆρχεν, ὥστε ψεῦδος τὸ τινὶ τῶι Β ὑπάρχειν τὸ Α. ἐὰν δ᾽ ὑποτεθῆι παντὶ τῶι Β ὑπάρχειν τὸ Α, οὐ δείκνυται τὸ προτεθέν, ἀλλὰ πρὸς τὸ μὴ παντὶ ὑπάρχειν αὕτη ληπτέα ἡ ὑπόθεσις.	Quando autem nulli B inest A, supponatur alicui inesse, sumptum sit autem et C omni B inesse, ergo necesse est A alicui C inesse; sed nulli inerat, quare falsum est alicui B inesse A. Si autem supponatur omni B inesse A, non ostenditur propositum:	When A belongs to no B, suppose A belongs to some B, and let it have been assumed that C belongs to all B. Then it is necessary that A should belong to some C. But ex hypothesi it belongs to no C, so that it is false that A belongs to some B. But if it is supposed that A belongs to all B, the problem is not proved.
εἰ γὰρ τὸ Α παντὶ τῶι Β καὶ τὸ Γ παντὶ τῶι Β, τὸ Α ὑπάρχει τινὶ τῶι Γ. τοῦτο δὲ οὐκ ἦν, ὥστε ψεῦδος τὸ παντὶ ὑπάρχειν. εἰ δ᾽ οὕτως, ἀληθὲς τὸ μὴ παντί. ἐὰν δ᾽ ὑποτεθῆι τινὶ ὑπάρχειν, ταὐτ᾽ ἔσται ἃ καὶ ἐπὶ τῶν προειρημένων.	sed ad ostendendum non omni inesse, eadem sumenda hypothesis, nam si A omni B, et C alicui B, A inest alicui C; hoc autem non fuit, quare falsum est omni inesse, si autem sic, verum non omni. Si autem supponatur alicui inesse, eadem erunt quae et in iis quae prius dicta sunt.	But this hypothesis must be made if we are prove that A belongs not to all B. For if A belongs to all B and C to some B, then A belongs to some C. But this we assumed not to be so, so it is false that A belongs to all B. But in that case it is true that A belongs not to all B. If however it is assumed that A belongs to some B, we shall have the same result as before.
Φανερὸν οὖν ὅτι ἐν ἅπασι τοῖς διὰ τοῦ ἀδυνάτου συλλογισμοῖς τὸ ἀντικείμενον ὑποθετέον. δῆλον δὲ καὶ ὅτι ἐν τῶι μέσωι σχήματι δείκνυταί πως τὸ καταφατικὸν καὶ ἐν τῶι ἐσχάτωι τὸ καθόλου.	Manifestum ergo quoniam in omnibus per impossibile syllogismis oppositum supponendum. Palam autem et quoniam in media figura ostenditur quodammodo affirmativum, et in postrema universale.	It is clear then that in all the syllogisms which proceed per impossibile the contradictory must be assumed. And it is plain that in the middle figure an affirmative conclusion, and in the last figure a universal conclusion, are proved in a way.