Authors/Aristotle/priora/Liber 2/C8

Chapter 8

Greek	Latin	English
	(PL 64 0695A) CAPUT VIII. De syllogismo conversivo.	8
↵ Τὸ δ᾽ ἀντιστρέφειν ἐστὶ τὸ μετατιθέντα τὸ συμπέρασμα ποιεῖν τὸν συλλογισμὸν ὅτι ἢ τὸ ἄκρον τῶι μέσωι οὐχ ὑπάρξει ἢ τοῦτο τῶι τελευταίωι. ἀνάγκη γὰρ τοῦ συμπεράσματος ἀντιστραφέντος καὶ τῆς ἑτέρας μενούσης προτάσεως ἀναιρεῖσθαι τὴν λοιπήν· εἰ γὰρ ἔσται, καὶ τὸ συμπέρασμα ἔσται. διαφέρει δὲ τὸ ἀντικειμένως ἢ ἐναντίως ἀντιστρέφειν τὸ συμπέρασμα· οὐ γὰρ ὁ αὐτὸς γίνεται συλλογισμὸς ἑκατέρως ἀντιστραφέντος· δῆλον δὲ τοῦτ᾽ ἔσται διὰ τῶν ἑπομένων. λέγω δ᾽ ἀντικεῖσθαι μὲν τὸ παντὶ τῶι οὐ παντὶ καὶ τὸ τινὶ τῶι οὐδενί, ἐναντίως δὲ τὸ παντὶ τῶι οὐδενὶ καὶ τὸ τινὶ τῶι οὐ τινὶ ὑπάρχειν.	Convertere autem est transponentem conclusionem facere syllogismum, quoniam vel extremum medio non inerit, vel hoc postremo; necesse est enim conclusione conversa, et altera remanente propositione, interimi reliquam; nam si erit, et conclusio erit: differt autem opposite aut contrarie convertere conclusionem, non enim fit idem syllogismus utrolibet conversa; palam autem hoc erit per sequentia. (0695B) Dico autem opponi quidem omni inesse non omni, et alicui nulli, contrarie autem omni nulli, et alicui non alicui inesse.	To convert a syllogism means to alter the conclusion and make another syllogism to prove that either the extreme cannot belong to the middle or the middle to the last term. For it is necessary, if the conclusion has been changed into its opposite and one of the premisses stands, that the other premiss should be destroyed. For if it should stand, the conclusion also must stand. It makes a difference whether the conclusion is converted into its contradictory or into its contrary. For the same syllogism does not result whichever form the conversion takes. This will be made clear by the sequel. By contradictory opposition I mean the opposition of ‘to all’ to ‘not to all’, and of ‘to some’ to ‘to none’; by contrary opposition I mean the opposition of ‘to all’ to ‘to none’, and of ‘to some’ to ‘not to some’.
ἔστω γὰρ δεδειγμένον τὸ Α κατὰ τοῦ Γ διὰ μέσου τοῦ Β. εἰ δὴ τὸ Α ληφθείη μηδενὶ τῶι Γ ὑπάρχειν, τῶι δὲ Β παντί, οὐδενὶ τῶι Γ ὑπάρξει τὸ Β. καὶ εἰ τὸ μὲν Α μηδενὶ τῶι Γ, τὸ δὲ Β παντὶ τῶι Γ, τὸ Α οὐ παντὶ τῶι Β καὶ οὐχ ἁπλῶς οὐδενί· οὐ γὰρ ἐδείκνυτο τὸ καθόλου διὰ τοῦ ἐσχάτου σχήματος. ὅλως δὲ τὴν πρὸς τῶι μείζονι ἄκρωι πρότασιν οὐκ ἔστιν ἀνασκευάσαι καθόλου διὰ τῆς ἀντιστροφῆς· ἀεὶ γὰρ ἀναιρεῖται διὰ τοῦ τρίτου σχήματος· ἀνάγκη γὰρ πρὸς τὸ ἔσχατον ἄκρον ἀμφοτέρας λαβεῖν τὰς προτάσεις. καὶ εἰ στερητικὸς ὁ συλλογισμός, ὡσαύτως. δεδείχθω γὰρ τὸ Α μηδενὶ τῶι Γ ὑπάρχον διὰ τοῦ Β. οὐκοῦν ἂν ληφθῆι τὸ Α τῶι Γ παντὶ ὑπάρχειν, τῶι δὲ Β μηδενί, οὐδενὶ τῶι Γ τὸ Β ὑπάρξει. καὶ εἰ τὸ Α καὶ τὸ Β παντὶ τῶι Γ, τὸ Α τινὶ τῶι Β· ἀλλ᾽ οὐδενὶ ὑπῆρχεν.	Sit enim ostensum A de C per medium B; si igitur sumatur A nulli C inesse, omni autem B, nulli C inerit B, et si A quidem nulli C, B autem omni C, A non omni B, et non omnino nulli, non enim ostendebatur universale per tertiam figuram. Omnino autem eam quae est ad maiorem extremitatem propositionem non est destruere universaliter per conversionem, semper enim interimitur per tertiam figuram, necesse enim ad postremam extremitatem utrasque sumere propositiones. Et si privativus sit syllogismus, similiter: ostendatur, enim A nulli C inesse per B, ergo si sumatur A omni C inesse, nulli autem B, nulli C inerit B. Et si A et B omni C, A alicui B, sed nulli inerat.	Suppose that A been proved of C, through B as middle term. If then it should be assumed that A belongs to no C, but to all B, B will belong to no C. And if A belongs to no C, and B to all C, A will belong, not to no B at all, but not to all B. For (as we saw) the universal is not proved through the last figure. In a word it is not possible to refute universally by conversion the premiss which concerns the major extreme: for the refutation always proceeds through the third since it is necessary to take both premisses in reference to the minor extreme. Similarly if the syllogism is negative. Suppose it has been proved that A belongs to no C through B. Then if it is assumed that A belongs to all C, and to no B, B will belong to none of the Cs. And if A and B belong to all C, A will belong to some B: but in the original premiss it belonged to no B.
Ἐὰν δ᾽ ἀντικειμένως ἀντιστραφῆι τὸ συμπέρασμα, καὶ οἱ συλλογισμοὶ ἀντικείμενοι καὶ οὐ καθόλου ἔσονται. γίνεται γὰρ ἡ ἑτέρα πρότασις ἐν μέρει, ὥστε καὶ τὸ συμπέρασμα ἔσται κατὰ μέρος. ἔστω γὰρ κατηγορικὸς ὁ συλλογισμός, καὶ ἀντιστρεφέσθω οὕτως. οὐκοῦν εἰ τὸ Α οὐ παντὶ τῶι Γ, τῶι δὲ Β παντί, τὸ Β οὐ παντὶ τῶι Γ· καὶ εἰ τὸ μὲν Α μὴ παντὶ τῶι Γ, τὸ δὲ Β παντί, τὸ Α οὐ παντὶ τῶι Β. ὁμοίως δὲ καὶ εἰ στερητικὸς ὁ συλλογισμός. εἰ γὰρ τὸ Α τινὶ τῶι Γ ὑπάρχει, τῶι δὲ Β μηδενί, τὸ Β τινὶ τῶι Γ οὐχ ὑπάρξει, οὐχ ἁπλῶς οὐδενί· καὶ εἰ τὸ μὲν Α τῶι Γ τινί, τὸ δὲ Β παντί, ὥσπερ ἐν ἀρχῆι ἐλήφθη, τὸ Α τινὶ τῶι Β ὑπάρξει.	(0695C) Si autem opposite convertatur conclusio, et alii syllogismi oppositi, et non universales erunt, fit enim altera propositio particularis, quare conclusio erit particularis. Sit enim praedicativus syllogismus, et convertatur sic, ergo si A non omni C, B autem omni B, non omni C. Et si A quidem non omni C, B autem omni A, non omni B. Similiter autem et si privativus sit syllogismus, nam si A alicui C inest, B autem nulli, B alicui C non inerit, et non simpliciter nulli, et si A quidem alicui C, B autem omni, quemadmodum in principio sumptum est, A alicui B inerit.	If the conclusion is converted into its contradictory, the syllogisms will be contradictory and not universal. For one premiss is particular, so that the conclusion also will be particular. Let the syllogism be affirmative, and let it be converted as stated. Then if A belongs not to all C, but to all B, B will belong not to all C. And if A belongs not to all C, but B belongs to all C, A will belong not to all B. Similarly if the syllogism is negative. For if A belongs to some C, and to no B, B will belong, not to no C at all, but-not to some C. And if A belongs to some C, and B to all C, as was originally assumed, A will belong to some B.
Ἐπὶ δὲ τῶν ἐν μέρει συλλογισμῶν ὅταν μὲν ἀντικειμένως ἀντιστρέφηται τὸ συμπέρασμα, ἀναιροῦνται ἀμφότεραι αἱ προτάσεις, ὅταν δ᾽ ἐναντίως, οὐδετέρα. οὐ γὰρ ἔτι συμβαίνει, καθάπερ ἐν τοῖς καθόλου, ἀναιρεῖν ἐλλείποντος τοῦ συμπεράσματος κατὰ τὴν ἀντιστροφήν, ἀλλ᾽ οὐδ᾽ ὅλως ↵ ἀναιρεῖν.	In particularibus autem syllogismis quando opposite convertitur conclusio, interimuntur utraeque propositiones, quando vero contrariae, neutra; non enim iam accidit quemadmodum in universalibus interimere deficiente conclusione secundum conversionem, sed nec omnino interimere.	In particular syllogisms when the conclusion is converted into its contradictory, both premisses may be refuted, but when it is converted into its contrary, neither. For the result is no longer, as in the universal syllogisms, refutation in which the conclusion reached by O, conversion lacks universality, but no refutation at all.
δεδείχθω γὰρ τὸ Α κατὰ τινὸς τοῦ Γ. οὐκοῦν ἂν ληφθῆι τὸ Α μηδενὶ τῶι Γ ὑπάρχειν, τὸ δὲ Β τινί, τὸ Α τῶι Β τινὶ οὐχ ὑπάρξει· καὶ εἰ τὸ Α μηδενὶ τῶι Γ, τῶι δὲ Β παντί, οὐδενὶ τῶι Γ τὸ Β. ὥστ᾽ ἀναιροῦνται ἀμφότεραι. ἐὰν δ᾽ ἐναντίως ἀντιστραφῆι, οὐδετέρα. εἰ γὰρ τὸ Α τινὶ τῶι Γ μὴ ὑπάρχει, τῶι δὲ Β παντί, τὸ Β τινὶ τῶι Γ οὐχ ὑπάρξει, ἀλλ᾽ οὔπω ἀναιρεῖται τὸ ἐξ ἀρχῆς· ἐνδέχεται γὰρ τινὶ ὑπάρχειν καὶ τινὶ μὴ ὑπάρχειν. τῆς δὲ καθόλου, τῆς Α Β, ὅλως οὐδὲ γίνεται συλλογισμός· εἰ γὰρ τὸ μὲν Α τινὶ τῶι Γ μὴ ὑπάρχει, τὸ δὲ Β τινὶ ὑπάρχει, οὐδετέρα καθόλου τῶν προτάσεων. ὁμοίως δὲ καὶ εἰ στερητικὸς ὁ συλλογισμός· εἰ μὲν γὰρ ληφθείη τὸ Α παντὶ τῶι Γ ὑπάρχειν, ἀναιροῦνται ἀμφότεραι, εἰ δὲ τινί, οὐδετέρα. ἀπόδειξις δ᾽ ἡ αὐτή.	(0695D) Ostendatur enim A de aliquo C per B; ergo si sumatur A nulli C inesse, B autem alicui C, A alicui B non inerit, et si A nulli C, B autem omni, nulli C inerit B; quare interimentur utraeque. Si autem contrarie convertantur, neutra; nam si A alicui C non inest, B autem omni, B alicui C non inerit, sed nondum interimitur quod ex principio, contingit, enim alicui inesse, et alicui non inesse: universali autem sublato A B, omnino non fit syllogismus. Si enim A quidem alicui C non inest, B autem alicui inest, neutra propositionum universalis est. Similiter autem et si privativus sit syllogismus, si enim sumatur A omni C inesse, interimuntur utraeque; si autem alicui, neutra; demonstratio autem eadem.	Suppose that A has been proved of some C. If then it is assumed that A belongs to no C, and B to some C, A will not belong to some B: and if A belongs to no C, but to all B, B will belong to no C. Thus both premisses are refuted. But neither can be refuted if the conclusion is converted into its contrary. For if A does not belong to some C, but to all B, then B will not belong to some C. But the original premiss is not yet refuted: for it is possible that B should belong to some C, and should not belong to some C. The universal premiss AB cannot be affected by a syllogism at all: for if A does not belong to some of the Cs, but B belongs to some of the Cs, neither of the premisses is universal. Similarly if the syllogism is negative: for if it should be assumed that A belongs to all C, both premisses are refuted: but if the assumption is that A belongs to some C, neither premiss is refuted. The proof is the same as before.