Authors/Aristotle/priora/Liber 2/C6

Chapter 6

Greek	Latin	English
	(PL 64 0693C) CAPUT VI. De eadem cyclica circulari ostensione in secunda figura.	6
58b13 Ἐν δὲ τῶι δευτέρωι σχήματι τὸ μὲν καταφατικὸν οὐκ ἔστι δεῖξαι διὰ τούτου τοῦ τρόπου, τὸ δὲ στερητικὸν ἔστιν. τὸ μὲν οὖν κατηγορικὸν οὐ δείκνυται διὰ τὸ μὴ ἀμφοτέρας εἶναι τὰς προτάσεις καταφατικάς· τὸ γὰρ συμπέρασμα στερητικόν ἐστι, τὸ δὲ κατηγορικὸν ἐξ ἀμφοτέρων ἐδείκνυτο καταφατικῶν. τὸ δὲ στερητικὸν ὧδε δείκνυται. ὑπαρχέτω τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μηδενί· συμπέρασμα τὸ Β οὐδενὶ τῶι Γ. ἐὰν οὖν ληφθῆι τὸ Β παντὶ τῶι Α ὑπάρχον, [τῶι δὲ Γ μηδενί,] ἀνάγκη τὸ Α μηδενὶ τῶι Γ ὑπάρχειν· γίνεται γὰρ τὸ δεύτερον σχῆμα· μέσον τὸ Β. εἰ δὲ τὸ Α Β στερητικὸν ἐλήφθη, θάτερον δὲ κατηγορικόν, τὸ πρῶτον ἔσται σχῆμα. τὸ μὲν γὰρ Γ παντὶ τῶι Α, τὸ δὲ Β οὐδενὶ τῶι Γ, ὥστ᾽ οὐδενὶ τῶι Α τὸ Β· οὐδ᾽ ἄρα τὸ Α τῶι Β. διὰ μὲν οὖν τοῦ συμπεράσματος καὶ τῆς μιᾶς προτάσεως οὐ γίνεται συλλογισμός, προσληφθείσης δ᾽ ἑτέρας ἔσται.	In secunda autem figura affirmativam quidem non est ostendere per hunc modum, privativam autem est; ergo praedicativa quidem non ostenditur, eo quod non sunt utraeque propositiones affirmativae, nam conclusio privativa, praedicativa autem ex utrisque ostendebatur affirmativis. (0693D) Privativa autem sic ostenditur: insit enim A omni B, C autem nulli, conclusio quoniam B nulli C; si ergo sumatur B omni A inesse, et nulli C, necesse est A nulli C inesse, fit enim secunda figura, medium B. Si autem A B privativa sumpta sit, altera vero praedicativa, prima erit figura, nam C quidem omni A, B autem nulli C, quare B nulli A, ergo nec A B, medium C; ergo per conclusionem quidem et unam propositionem non fit syllogismus, assumpta autem altera erit.	In the second figure it is not possible to prove an affirmative proposition in this way, but a negative proposition may be proved. An affirmative proposition is not proved because both premisses of the new syllogism are not affirmative (for the conclusion is negative) but an affirmative proposition is (as we saw) proved from premisses which are both affirmative. The negative is proved as follows. Let A belong to all B, and to no C: we conclude that B belongs to no C. If then it is assumed that B belongs to all A, it is necessary that A should belong to no C: for we get the second figure, with B as middle. But if the premiss AB was negative, and the other affirmative, we shall have the first figure. For C belongs to all A and B to no C, consequently B belongs to no A: neither then does A belong to B. Through the conclusion, therefore, and one premiss, we get no syllogism, but if another premiss is assumed in addition, a syllogism will be possible.
εἰ δὲ μὴ καθόλου ὁ συλλογισμός, ἡ μὲν ἐν ὅλωι πρότασις οὐ δείκνυται διὰ τὴν αὐτὴν αἰτίαν ἥνπερ εἴπομεν καὶ πρότερον, ἡ δ᾽ ἐν μέρει δείκνυται, ὅταν ἦι τὸ καθόλου κατηγορικόν· ὑπαρχέτω γὰρ τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μὴ παντί· συμπέρασμα Β Γ. ἐὰν οὖν ληφθῆι τὸ Β παντὶ τῶι Α, τῶι δὲ Γ οὐ παντί, τὸ Α τινὶ τῶι Γ οὐχ ὑπάρξει· μέσον Β. εἰ δ᾽ ἐστὶν ἡ καθόλου στερητική, οὐ δειχθήσεται ἡ Α Γ πρότασις ἀντιστραφέντος τοῦ Α Β· συμβαίνει γὰρ ἢ ἀμφοτέρας ἢ τὴν ἑτέραν πρότασιν γίνεσθαι ἀποφατικήν, ὥστ᾽ οὐκ ἔσται συλλογισμός. ἀλλ᾽ ὁμοίως δειχθήσεται ὡς καὶ ἐπὶ τῶν καθόλου, ἐὰν ληφθῆι, ὧι τὸ Β τινὶ μὴ ὑπάρχει, τὸ Α τινὶ ὑπάρχειν.	Si autem non universalis sit syllogismus, quae in toto quidem est propositio non ostenditur, propter eamdem causam quam quidem diximus et prius, quae autem in parte, ostenditur quando universalis sit praedicativa. (0694A) Insit enim A omni B, C autem non omni, conclusio B C; si ergo sumatur B omni A, C autem non omni, conclusio A alicui C non inerit medium B. Si autem est universalis privativa, non ostenditur A propositio, conversa A B, accidit enim utrasque aut alteram propositionem fieri negativam: quare non erit syllogismus; sed similiter ostendetur quemadmodum et in universalibus, si sumatur, cui B alicui non inest, A alicui inesse.	But if the syllogism not universal, the universal premiss cannot be proved, for the same reason as we gave above, but the particular premiss can be proved whenever the universal statement is affirmative. Let A belong to all B, and not to all C: the conclusion is BC. If then it is assumed that B belongs to all A, but not to all C, A will not belong to some C, B being middle. But if the universal premiss is negative, the premiss AC will not be demonstrated by the conversion of AB: for it turns out that either both or one of the premisses is negative; consequently a syllogism will not be possible. But the proof will proceed as in the universal syllogisms, if it is assumed that A belongs to some of that to some of which B does not belong.