Authors/Aristotle/priora/Liber 2/C9

Chapter 9

Greek	Latin	English
	(PL 64 0695D) CAPUT IX. De syllogismo conversivo in secunda figura.	9
60a15 Ἐν δὲ τῶι δευτέρωι σχήματι τὴν μὲν πρὸς τῶι μείζονι ἄκρωι πρότασιν οὐκ ἔστιν ἀνελεῖν ἐναντίως, ὁποτερωσοῦν τῆς ἀντιστροφῆς γινομένης· ἀεὶ γὰρ ἔσται τὸ συμπέρασμα ἐν τῶι τρίτωι σχήματι, καθόλου δ᾽ οὐκ ἦν ἐν τούτωι συλλογισμός. τὴν δ᾽ ἑτέραν ὁμοίως ἀναιρήσομεν τῆι ἀντιστροφῆι. λέγω δὲ τὸ ὁμοίως, εἰ μὲν ἐναντίως ἀντιστρέφεται, ἐναντίως, εἰ δ᾽ ἀντικειμένως, ἀντικειμένως.	(0696A) In secunda autem figura, eam quidem quae est ad maiorem extremitatem propositionem, non est interimere contrarie, quolibet modo conversione facta, semper erit conclusio in tertia figura, universalis autem non fuit in hac syllogismus, alteram autem in hac interimemus, similiter conversione. Dico autem similiter: si contrarie quidem convertitur, contrarie; si opposite, opposite.	In the second figure it is not possible to refute the premiss which concerns the major extreme by establishing something contrary to it, whichever form the conversion of the conclusion may take. For the conclusion of the refutation will always be in the third figure, and in this figure (as we saw) there is no universal syllogism. The other premiss can be refuted in a manner similar to the conversion: I mean, if the conclusion of the first syllogism is converted into its contrary, the conclusion of the refutation will be the contrary of the minor premiss of the first, if into its contradictory, the contradictory.
ὑπαρχέτω γὰρ τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μηδενί· συμπέρασμα Β Γ. ἐὰν οὖν ληφθῆι τὸ Β παντὶ τῶι Γ ὑπάρχειν καὶ τὸ Α Β μένηι, τὸ Α παντὶ τῶι Γ ὑπάρξει· γίνεται γὰρ τὸ πρῶτον σχῆμα. εἰ δὲ τὸ Β παντὶ τῶι Γ, τὸ δὲ Α μηδενὶ τῶι Γ, τὸ Α οὐ παντὶ τῶι Β· σχῆμα τὸ ἔσχατον. ἐὰν δ᾽ ἀντικειμένως ἀντιστραφῆι τὸ Β Γ, ἡ μὲν Α Β ὁμοίως δειχθήσεται, ἡ δὲ Α Γ ἀντικειμένως. εἰ γὰρ τὸ Β τινὶ τῶι Γ, τὸ δὲ Α μηδενὶ τῶι Γ, τὸ Α τινὶ τῶι Β οὐχ ὑπάρξει. πάλιν εἰ τὸ Β τινὶ τῶι Γ, τὸ δὲ Α παντὶ τῶι Β, τὸ Α τινὶ τῶι Γ, ὥστ᾽ ἀντικείμενος γίνεται ὁ συλλογισμός. ὁμοίως δὲ δειχθήσεται καὶ εἰ ἀνάπαλιν ἔχοιεν αἱ προτάσεις.	Insit enim A omni B, C autem nulli, conclusio B C. Si ergo sumatur B omni C inesse, et A B maneat, A omni C inerit, fit enim prima figura. Si autem B omni C, A autem nulli C, A non omni B, figura postrema. (0696B) Si autem opposite convertatur B C, A B quidem similiter ostendetur, A C autem opposite: nam si B alicui C, A autem nulli C, A alicui B non inerit; rursum si B alicui C, A autem omni B, A alicui C, quare oppositus fit syllogismus. Similiter autem ostendetur et si e converso se habeant propositiones.	Let A belong to all B and to no C: conclusion BC. If then it is assumed that B belongs to all C, and the proposition AB stands, A will belong to all C, since the first figure is produced. If B belongs to all C, and A to no C, then A belongs not to all B: the figure is the last. But if the conclusion BC is converted into its contradictory, the premiss AB will be refuted as before, the premiss, AC by its contradictory. For if B belongs to some C, and A to no C, then A will not belong to some B. Again if B belongs to some C, and A to all B, A will belong to some C, so that the syllogism results in the contradictory of the minor premiss. A similar proof can be given if the premisses are transposed in respect of their quality.
εἰ δ᾽ ἐστὶν ἐπὶ μέρους ὁ συλλογισμός, ἐναντίως μὲν ἀντιστρεφομένου τοῦ συμπεράσματος οὐδετέρα τῶν προτάσεων ἀναιρεῖται, καθάπερ οὐδ᾽ ἐν τῶι πρώτωι σχήματι, ἀντικειμένως δ᾽ ἀμφότεραι. κείσθω γὰρ τὸ Α τῶι μὲν Β μηδενὶ ὑπάρχειν, τῶι δὲ Γ τινί· συμπέρασμα Β Γ. ἐὰν οὖν τεθῆι τὸ Β τινὶ τῶι Γ ὑπάρχειν καὶ τὸ Α Β μένηι, συμπέρασμα ἔσται ὅτι τὸ Α τινὶ τῶι Γ οὐχ ὑπάρχει, ἀλλ᾽ οὐκ ἀνήιρηται τὸ ἐξ ἀρχῆς· ἐνδέχεται γὰρ τινὶ ὑπάρχειν καὶ μὴ ὑπάρχειν. πάλιν εἰ τὸ Β τινὶ τῶι Γ καὶ τὸ Α τινὶ τῶι Γ, οὐκ ἔσται συλλογισμός· οὐδέτερον γὰρ καθόλου τῶν εἰλημμένων. ↵ ὥστ᾽ οὐκ ἀναιρεῖται τὸ Α Β. ἐὰν δ᾽ ἀντικειμένως ἀντιστρέφηται, ἀναιροῦνται ἀμφότεραι. εἰ γὰρ τὸ Β παντὶ τῶι Γ, τὸ δὲ Α μηδενὶ τῶι Β, οὐδενὶ τῶι Γ τὸ Α· ἦν δὲ τινί. πάλιν εἰ τὸ Β παντὶ τῶι Γ, τὸ δὲ Α τινὶ τῶι Γ, τινὶ τῶι Β τὸ Α. ἡ αὐτὴ δ᾽ ἀπόδειξις καὶ εἰ τὸ καθόλου κατηγορικόν.	Si autem particularis est syllogismus, contrarie quidem conversa conclusione neutra propositionum interimitur, quemadmodum nec in prima figura, opposite autem, utraeque. Ponatur enim A B quidem nulli inesse, C autem alicui, conclusio B C. Si igitur ponatur B alicui C inesse, et A B maneat, conclusio erit quoniam A alicui C non inest, sed non interimitur quod ex principio, contingit enim alicui inesse et non inesse. Rursum si B alicui C, et A alicui C, non erit syllogismus, neutrum enim universale eorum quae sumpta sunt, quare non interimitur A B. (0696C) Si autem opposite convertatur, interimuntur utraeque, non si B omni C, A autem nulli B, nulli C, A erit autem alicui. Rursum si B omni C, A autem alicui C, alicui B, A . Eadem autem demonstratio et si universalis sit praedicativa.	If the syllogism is particular, when the conclusion is converted into its contrary neither premiss can be refuted, as also happened in the first figure,’ if the conclusion is converted into its contradictory, both premisses can be refuted. Suppose that A belongs to no B, and to some C: the conclusion is BC. If then it is assumed that B belongs to some C, and the statement AB stands, the conclusion will be that A does not belong to some C. But the original statement has not been refuted: for it is possible that A should belong to some C and also not to some C. Again if B belongs to some C and A to some C, no syllogism will be possible: for neither of the premisses taken is universal. Consequently the proposition AB is not refuted. But if the conclusion is converted into its contradictory, both premisses can be refuted. For if B belongs to all C, and A to no B, A will belong to no C: but it was assumed to belong to some C. Again if B belongs to all C and A to some C, A will belong to some B. The same proof can be given if the universal statement is affirmative.