Authors/Aristotle/priora/Liber 2/C10

Chapter 10

Greek	Latin	English
	(PL 64 0696C) CAPUT X. De syllogismo conversivo in tertia figura.	10
60b6 Ἐπὶ δὲ τοῦ τρίτου σχήματος ὅταν μὲν ἐναντίως ἀντιστρέφηται τὸ συμπέρασμα, οὐδετέρα τῶν προτάσεων ἀναιρεῖται κατ᾽ οὐδένα τῶν συλλογισμῶν, ὅταν δ᾽ ἀντικειμένως, ἀμφότεραι καὶ ἐν ἅπασιν. δεδείχθω γὰρ τὸ Α τινὶ τῶι Β ὑπάρχον, μέσον δ᾽ εἰλήφθω τὸ Γ, ἔστωσαν δὲ καθόλου αἱ προτάσεις. οὐκοῦν ἐὰν ληφθῆι τὸ Α τινὶ τῶι Β μὴ ὑπάρχειν, τὸ δὲ Β παντὶ τῶι Γ, οὐ γίνεται συλλογισμὸς τοῦ Α καὶ τοῦ Γ. οὐδ᾽ εἰ τὸ Α τῶι μὲν Β τινὶ μὴ ὑπάρχει, τῶι δὲ Γ παντί, οὐκ ἔσται τοῦ Β καὶ τοῦ Γ συλλογισμός.	In tertia vero figura quando contrarie quidem convertitur conclusio, neutra propositionum interimitur secundum nullum syllogismorum; quando autem opposite, utraeque in omnibus. Si enim ostensum A alicui B inesse, medium autem sumptum C, et sint universales propositiones, si ergo sumatur A alicui B non inesse, B autem omni C, non fit syllogismus eius quod est A de C. Neque si A B alicui non inest, C autem omni, non erit eius quod est B C syllogismus.	In the third figure when the conclusion is converted into its contrary, neither of the premisses can be refuted in any of the syllogisms, but when the conclusion is converted into its contradictory, both premisses may be refuted and in all the moods. Suppose it has been proved that A belongs to some B, C being taken as middle, and the premisses being universal. If then it is assumed that A does not belong to some B, but B belongs to all C, no syllogism is formed about A and C. Nor if A does not belong to some B, but belongs to all C, will a syllogism be possible about B and C.
ὁμοίως δὲ δειχθήσεται καὶ εἰ μὴ καθόλου αἱ προτάσεις. ἢ γὰρ ἀμφοτέρας ἀνάγκη κατὰ μέρος εἶναι διὰ τῆς ἀντιστροφῆς, ἢ τὸ καθόλου πρὸς τῶι ἐλάττονι ἄκρωι γίνεσθαι· οὕτω δ᾽ οὐκ ἦν συλλογισμὸς οὔτ᾽ ἐν τῶι πρώτωι σχήματι οὔτ᾽ ἐν τῶι μέσωι. ἐὰν δ᾽ ἀντικειμένως ἀντιστρέφηται, αἱ προτάσεις ἀναιροῦνται ἀμφότεραι. εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ, τὸ Α οὐδενὶ τῶι Γ· πάλιν εἰ τὸ Α τῶι μὲν Β μηδενί, τῶι δὲ Γ παντί, τὸ Β οὐδενὶ τῶι Γ. καὶ εἰ ἡ ἑτέρα μὴ καθόλου, ὡσαύτως. εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ, τὸ Α τινὶ τῶι Γ οὐχ ὑπάρξει· εἰ δὲ τὸ Α τῶι μὲν Β μηδενί, τῶι δὲ Γ παντί, οὐδενὶ τῶι Γ τὸ Β.	(0696D) Similiter autem ostendetur et si non universales sint propositiones, aut enim utrasque necesse est particulares esse per conversionem, aut universalem ad minorem extremitatem fieri, sic autem non fiet syllogismus, nec in prima figura, nec in media. Si autem opposite convertantur propositiones, interimuntur utraeque, nam si A nulli B, B autem omni C, A nulli C. Rursum si A B quidem nulli, C autem omni, B nulli C. Et si altera non sit universalis, similiter; si enim A nulli B, B autem alicui C, A alicui C non inerit. Si autem A quidem nulli, C autem omni, nulli C, B.	A similar proof can be given if the premisses are not universal. For either both premisses arrived at by the conversion must be particular, or the universal premiss must refer to the minor extreme. But we found that no syllogism is possible thus either in the first or in the middle figure. But if the conclusion is converted into its contradictory, both the premisses can be refuted. For if A belongs to no B, and B to all C, then A belongs to no C: again if A belongs to no B, and to all C, B belongs to no C. And similarly if one of the premisses is not universal. For if A belongs to no B, and B to some C, A will not belong to some C: if A belongs to no B, and to C, B will belong to no C.
Ὁμοίως δὲ καὶ εἰ στερητικὸς ὁ συλλογισμός. δεδείχθω γὰρ τὸ Α τινὶ τῶι Β μὴ ὑπάρχον, ἔστω δὲ κατηγορικὸν μὲν τὸ Β Γ, ἀποφατικὸν δὲ τὸ Α Γ· οὕτω γὰρ ἐγίνετο ὁ συλλογισμός. ὅταν μὲν οὖν τὸ ἐναντίον ληφθῆι τῶι συμπεράσματι, οὐκ ἔσται συλλογισμός. εἰ γὰρ τὸ Α τινὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ, οὐκ ἦν συλλογισμὸς τοῦ Α καὶ τοῦ Γ. οὐδ᾽ εἰ τὸ Α τινὶ τῶι Β, τῶι δὲ Γ μηδενί, οὐκ ἦν τοῦ Β καὶ τοῦ Γ συλλογισμός. ὥστε οὐκ ἀναιροῦνται αἱ προτάσεις.	(0697A) Similiter et si privativus sit syllogismus; ostendatur enim A alicui B non inesse; si autem praedicativa quidem B C, A C autem negativa, sic enim fiebat syllogismus. Quando igitur contrarium sumitur conclusioni, non erit syllogismus, nam si A alicui B, B autem omni C, non fit syllogismus eius quod est A et C. Neque si A alicui B, nulli autem C, non fuit eius quod est A B et C syllogismus, quare non interimuntur propositiones.	Similarly if the original syllogism is negative. Suppose it has been proved that A does not belong to some B, BC being affirmative, AC being negative: for it was thus that, as we saw, a syllogism could be made. Whenever then the contrary of the conclusion is assumed a syllogism will not be possible. For if A belongs to some B, and B to all C, no syllogism is possible (as we saw) about A and C. Nor, if A belongs to some B, and to no C, was a syllogism possible concerning B and C. Therefore the premisses are not refuted.
ὅταν δὲ τὸ ἀντικείμενον, ἀναιροῦνται. εἰ γὰρ τὸ Α παντὶ τῶι Β καὶ τὸ Β τῶι Γ, τὸ Α παντὶ τῶι Γ· ἀλλ᾽ οὐδενὶ ὑπῆρχεν. πάλιν εἰ τὸ Α παντὶ τῶι Β, τῶι δὲ Γ μηδενί, τὸ Β οὐδενὶ τῶι Γ· ἀλλὰ παντὶ ὑπῆρχεν. ὁμοίως δὲ δείκνυται καὶ εἰ μὴ καθόλου εἰσὶν αἱ προτάσεις. γίνεται γὰρ τὸ Α Γ καθόλου τε καὶ στερητικόν, θάτερον δ᾽ ἐπὶ μέρους καὶ κατηγορικόν. εἰ μὲν οὖν τὸ Α παντὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ, τὸ Α τινὶ τῶι Γ συμβαίνει· ἀλλ᾽ οὐδενὶ ὑπῆρχεν. πάλιν εἰ τὸ Α παντὶ τῶι Β, τῶι δὲ Γ ↵ μηδενί, τὸ Β οὐδενὶ τῶι Γ· ἔκειτο δὲ τινί. εἰ δὲ τὸ Α τινὶ τῶι Β καὶ τὸ Β τινὶ τῶι Γ, οὐ γίνεται συλλογισμός· οὐδ᾽ εἰ τὸ Α τινὶ τῶι Β, τῶι δὲ Γ μηδενί, οὐδ᾽ οὕτως. ὥστ᾽ ἐκείνως μὲν ἀναιροῦνται, οὕτω δ᾽ οὐκ ἀναιροῦνται αἱ προτάσεις.	Quando vero oppositum, interimuntur; nam si A omni B, et B omni C, A omni C, sed nulli inerat. Rursum si A omni B, nulli autem C, B nulli C, sed omni inerat. Similiter autem monstratur, et si non universales sint propositiones: sit enim A C universalis et privativa, altera autem particularis et praedicativa, ergo si A quidem omni B, B autem alicui C, A alicui C accidit, sed nulli inerat. Rursum si A omni B, nulli autem C, et B nulli C. (0697B) Si autem A alicui B, et B alicui C, non fit syllogismus. Neque si A alicui B, et nulli C, nec sic. Quare illo quidem modo interimuntur, sic autem non interimuntur propositiones.	But when the contradictory of the conclusion is assumed, they are refuted. For if A belongs to all B, and B to C, A belongs to all C: but A was supposed originally to belong to no C. Again if A belongs to all B, and to no C, then B belongs to no C: but it was supposed to belong to all C. A similar proof is possible if the premisses are not universal. For AC becomes universal and negative, the other premiss particular and affirmative. If then A belongs to all B, and B to some C, it results that A belongs to some C: but it was supposed to belong to no C. Again if A belongs to all B, and to no C, then B belongs to no C: but it was assumed to belong to some C. If A belongs to some B and B to some C, no syllogism results: nor yet if A belongs to some B, and to no C. Thus in one way the premisses are refuted, in the other way they are not.
Φανερὸν οὖν διὰ τῶν εἰρημένων πῶς ἀντιστρεφομένου τοῦ συμπεράσματος ἐν ἑκάστωι σχήματι γίνεται συλλογισμός, καὶ πότ᾽ ἐναντίος τῆι προτάσει καὶ πότ᾽ ἀντικείμενος, καὶ ὅτι ἐν μὲν τῶι πρώτωι σχήματι διὰ τοῦ μέσου καὶ τοῦ ἐσχάτου γίνονται οἱ συλλογισμοί, καὶ ἡ μὲν πρὸς τῶι ἐλάττονι ἄκρωι ἀεὶ διὰ τοῦ μέσου ἀναιρεῖται, ἡ δὲ πρὸς τῶι μείζονι διὰ τοῦ ἐσχάτου· ἐν δὲ τῶι δευτέρωι διὰ τοῦ πρώτου καὶ τοῦ ἐσχάτου, ἡ μὲν πρὸς τῶι ἐλάττονι ἄκρωι ἀεὶ διὰ τοῦ πρώτου σχήματος, ἡ δὲ πρὸς τῶι μείζονι διὰ τοῦ ἐσχάτου· ἐν δὲ τῶι τρίτωι διὰ τοῦ πρώτου καὶ διὰ τοῦ μέσου, καὶ ἡ μὲν πρὸς τῶι μείζονι διὰ τοῦ πρώτου ἀεί, ἡ δὲ πρὸς τῶι ἐλάττονι διὰ τοῦ μέσου.	(0697C) Manifestum est ergo ex iis quae dicta sunt quomodo conversa conclusione in unaquaque figura fit syllogismus, et quando contrarie propositioni, et quando opposite; et quoniam in prima quidem figura per mediam et postremam fiunt syllogismi, et quae quidem ad minorem extremitatem semper per mediam interimitur, quae vero ad maiorem per postremam; in secunda autem, per primam et postremam, quae quidem ad minorem extremitatem semper per primam figuram, quae vero ad maiorem, per postremam; in tertia vero, per primam et per mediam, et quae quidem ad maiorem per primam semper, quae vero ad minorem per mediam semper.	From what has been said it is clear how a syllogism results in each figure when the conclusion is converted; when a result contrary to the premiss, and when a result contradictory to the premiss, is obtained. It is clear that in the first figure the syllogisms are formed through the middle and the last figures, and the premiss which concerns the minor extreme is alway refuted through the middle figure, the premiss which concerns the major through the last figure. In the second figure syllogisms proceed through the first and the last figures, and the premiss which concerns the minor extreme is always refuted through the first figure, the premiss which concerns the major extreme through the last. In the third figure the refutation proceeds through the first and the middle figures; the premiss which concerns the major is always refuted through the first figure, the premiss which concerns the minor through the middle figure.