Authors/Aristotle/priora/Liber 2/C12

Chapter 12

Greek	Latin	English
	(PL 64 0699A) CAPUT XII. De syllogismo per impossibile in secunda figura.	12
62a20 Φανερὸν οὖν ὅτι ἐν τῶι πρώτωι σχήματι τὰ μὲν ἄλλα προβλήματα πάντα δείκνυται διὰ τοῦ ἀδυνάτου, τὸ δὲ καθόλου καταφατικὸν οὐ δείκνυται. ἐν δὲ τῶι μέσωι καὶ τῶι ἐσχάτωι καὶ τοῦτο δείκνυται. κείσθω γὰρ τὸ Α μὴ παντὶ τῶι Β ὑπάρχειν, εἰλήφθω δὲ τῶι Γ παντὶ ὑπάρχειν τὸ Α. οὐκοῦν εἰ τῶι μὲν Β μὴ παντί, τῶι δὲ Γ παντί, οὐ παντὶ τῶι Β τὸ Γ. τοῦτο δ᾽ ἀδύνατον· ἔστω γὰρ φανερὸν ὅτι παντὶ τῶι Β ὑπάρχει τὸ Γ, ὥστε ψεῦδος τὸ ὑποκείμενον. ἀληθὲς ἄρα τὸ παντὶ ὑπάρχειν. ἐὰν δὲ τὸ ἐναντίον ὑποτεθῆι, συλλογισμὸς μὲν ἔσται καὶ τὸ ὀδύνατον, οὐ μὴν δείκνυται τὸ προτεθέν. εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τῶι δὲ Γ παντί, οὐδενὶ τῶι Β τὸ Γ. τοῦτο δ᾽ ἀδύνατον, ὥστε ψεῦδος τὸ μηδενὶ ὑπάρχειν. ἀλλ᾽ οὐκ εἰ τοῦτο ψεῦδος, τὸ παντὶ ἀληθές.	In media autem figura et postrema et hoc ostenditur. Ponatur enim A non omni B inesse, sumptum sit autem omni C inesse A ; ergo si B quidem non omni inest A, C autem omni, non omni B inest C, hoc autem impossibile. Sit enim manifestum quoniam omni B inest C, quare falsum quod suppositum est, verum est ergo omni inesse. (0699B) Si autem contrarium supponatur, syllogismus quidem erit ad impossibile, non tamen ostenditur quod propositum est. Si enim A nulli B, omni autem C, nulli B, C, hoc autem impossibile, quare falsum est, nulli inesse, sed non si hoc falsum, verum omni.	It is clear then that in the first figure all problems except the universal affirmative are proved per impossibile. But in the middle and the last figures this also is proved. Suppose that A does not belong to all B, and let it have been assumed that A belongs to all C. If then A belongs not to all B, but to all C, C will not belong to all B. But this is impossible (for suppose it to be clear that C belongs to all B): consequently the hypothesis is false. It is true then that A belongs to all B. But if the contrary is supposed, we shall have a syllogism and a result which is impossible: but the problem in hand is not proved. For if A belongs to no B, and to all C, C will belong to no B. This is impossible; so that it is false that A belongs to no B. But though this is false, it does not follow that it is true that A belongs to all B.
ὅτι δὲ τινὶ τῶι Β ὑπάρχει τὸ Α, ὑποκείσθω τὸ Α μηδενὶ τῶι Β ὑπάρχειν, τῶι δὲ Γ παντὶ ὑπαρχέτω. ἀνάγκη οὖν τὸ Γ μηδενὶ τῶι Β. ὥστ᾽ εἰ τοῦτ᾽ ἀδύνατον, ἀνάγκη τὸ Α τινὶ τῶι Β ὑπάρχειν. ἐὰν δ᾽ ὑποτεθῆι τινὶ μὴ ὑπάρχειν, ταὐτ᾽ ἔσται ἅπερ ἐπὶ τοῦ πρώτου σχήματος.	Quando autem alicui B inest A, supponatur A nulli B inesse, C autem omni insit, necesse est ergo C nulli B inesse, quare si hoc impossibile, necesse est A alicui B inesse. Si autem supponatur alicui non esse, eadem erunt quae in prima figura.	When A belongs to some B, suppose that A belongs to no B, and let A belong to all C. It is necessary then that C should belong to no B. Consequently, if this is impossible, A must belong to some B. But if it is supposed that A does not belong to some B, we shall have the same results as in the first figure.
πάλιν ὑποκείσθω τὸ Α τινὶ τῶι Β ὑπάρχειν, τῶι δὲ Γ μηδενὶ ὑπαρχέτω. ἀνάγκη οὖν τὸ Γ τινὶ τῶι Β μὴ ὑπάρχειν. ἀλλὰ παντὶ ὑπῆρχεν, ὥστε ψεῦδος τὸ ὑποτεθέν· οὐδενὶ ἄρα τῶι Β τὸ Α ὑπάρξει.	Rursum supponatur A alicui B inesse, C autem nulli insit, necesse est igitur C alicui B non inesse; sed omni inerat, quare falsum quod suppositum est, nulli ergo B inerat A.	Again suppose that A belongs to some B, and let A belong to no C. It is necessary then that C should not belong to some B. But originally it belonged to all B, consequently the hypothesis is false: A then will belong to no B.
ὅτι δ᾽ οὐ παντὶ τὸ Α τῶι Β, ὑποκείσθω παντὶ ὑπάρχειν, τῶι ↵ δὲ Γ μηδενί. ἀνάγκη οὖν τὸ Γ μηδενὶ τῶι Β ὑπάρχειν. τοῦτο δ᾽ ἀδύνατον, ὥστ᾽ ἀληθὲς τὸ μὴ παντὶ ὑπάρχειν. φανερὸν οὖν ὅτι πάντες οἱ συλλογισμοὶ γίνονται διὰ τοῦ μέσου σχήματος.	(0699C) Quando autem non omni B inest A, supponatur omni inesse: C autem nulli, necesse est ergo C nulli B inesse, hoc autem impossibile, quare verum est non omni inesse. Manifestum ergo quoniam omnes syllogismi fiunt per mediam figuram.	When A does not belong to an B, suppose it does belong to all B, and to no C. It is necessary then that C should belong to no B. But this is impossible: so that it is true that A does not belong to all B. It is clear then that all the syllogisms can be formed in the middle figure.