Authors/Aristotle/priora/Liber 1/C7

Chapter 7

Greek	Latin	English
	(PL 64 0647A) CAPUT VII. De tribus figuris et indirectis syllogismis ad invicem.	7
29a19 Δῆλον δὲ καὶ ὅτι ἐν ἅπασι τοῖς σχήμασιν, ὅταν μὴ γίνηται συλλογισμός, κατηγορικῶν μὲν ἢ στερητικῶν ἀμφοτέρων ὄντων τῶν ὅρων οὐδὲν ὅλως γίνεται ἀναγκαῖον, κατηγορικοῦ δὲ καὶ στερητικοῦ, καθόλου ληφθέντος τοῦ στερητικοῦ ἀεὶ γίνεται συλλογισμὸς τοῦ ἐλάττονος ἄκρου πρὸς τὸ μεῖζον, οἷον εἰ τὸ μὲν Α παντὶ τῶι Β ἢ τινί, τὸ δὲ Β μηδενὶ τῶι Γ· ἀντιστρεφομένων γὰρ τῶν προτάσεων ἀνάγκη τὸ Γ τινὶ τῶι Α μὴ ὑπάρχειν. ὁμοίως δὲ κἀπὶ τῶν ἑτέρων σχημάτων· ἀεὶ γὰρ γίνεται διὰ τῆς ἀντιστροφῆς συλλογισμός. δῆλον δὲ καὶ ὅτι τὸ ἀδιόριστον ἀντὶ τοῦ κατηγορικοῦ τοῦ ἐν μέρει τιθέμενον τὸν αὐτὸν ποιήσει συλλογισμὸν ἐν ἅπασι τοῖς σχήμασιν.	Palam autem et quoniam in omnibus figuris, aliquando non fit syllogismus. Cum praedicativi quidem, vel privativi sunt utrique termini, et particulares, nihil omnino fit necessarium. (0647B) Cum autem praedicativus, et privativus, et universaliter sumptus privativus, semper fit syllogismus minoris extremitatis ad maiorem, ut si A quidem omni B vel alicui, B autem nulli C; conversis enim propositionibus, necesse est C alicui A non inesse. Similiter autem et in aliis figuris, semper enim fit per conversionem syllogismus. Palam etiam quoniam indefinitum pro praedicativo particulari positum, eumdem faciet syllogismum in omnibus figuris.	It is evident also that in all the figures, whenever a proper syllogism does not result, if both the terms are affirmative or negative nothing necessary follows at all, but if one is affirmative, the other negative, and if the negative is stated universally, a syllogism always results relating the minor to the major term, e.g. if A belongs to all or some B, and B belongs to no C: for if the premisses are converted it is necessary that C does not belong to some A. Similarly also in the other figures: a syllogism always results by means of conversion. It is evident also that the substitution of an indefinite for a particular affirmative will effect the same syllogism in all the figures.
Φανερὸν δὲ καὶ ὅτι πάντες οἱ ἀτελεῖς συλλογισμοὶ τελειοῦνται διὰ τοῦ πρώτου σχήματος. ἢ γὰρ δεικτικῶς ἢ διὰ τοῦ ἀδυνάτου περαίνονται πάντες· ἀμφοτέρως δὲ γίνεται τὸ πρῶτον σχῆμα, δεικτικῶς μὲν τελειουμένων, ὅτι διὰ τῆς ἀντιστροφῆς ἐπεραίνοντο πάντες, ἡ δ᾽ ἀντιστροφὴ τὸ πρῶτον ἐποίει σχῆμα, διὰ δὲ τοῦ ἀδυνάτου δεικνυμένων, ὅτι τεθέντος τοῦ ψεύδους ὁ συλλογισμὸς γίνεται διὰ τοῦ πρώτου σχήματος, οἷον ἐν τῶι τελευταίωι σχήματι, εἰ τὸ Α καὶ τὸ Β παντὶ τῶι Γ ὑπάρχει, ὅτι τὸ Α τινὶ τῶι Β ὑπάρχει· εἰ γὰρ μηδενί, τὸ δὲ Β παντὶ τῶι Γ, οὐδενὶ τῶι Γ τὸ Α· ἀλλ᾽ ἦν παντί. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.	Manifestum autem et quoniam omnes imperfecti syllogismi perficiuntur per primam figuram. Aut enim ostensive, aut per impossibile clauduntur omnes. Utrinque autem fit prima figura. Et ostensive quidem perfectis, quoniam per conversionem claudebantur omnes, conversio autem primam faciebat figuram, per impossibile vero demonstratis, quoniam posito falso syllogismus fit per primam figuram. Ut in postrema figura, si A et B omni C insunt, quoniam A alicui B inest, nam si nulli et B omni C, nulli C inerit A, sed inerat omni. (0647C) Similiter autem in aliis.	It is clear too that all the imperfect syllogisms are made perfect by means of the first figure. For all are brought to a conclusion either ostensively or per impossibile. In both ways the first figure is formed: if they are made perfect ostensively, because (as we saw) all are brought to a conclusion by means of conversion, and conversion produces the first figure: if they are proved per impossibile, because on the assumption of the false statement the syllogism comes about by means of the first figure, e.g. in the last figure, if A and B belong to all C, it follows that A belongs to some B: for if A belonged to no B, and B belongs to all C, A would belong to no C: but (as we stated) it belongs to all C. Similarly also with the rest.
↵ Ἔστι δὲ καὶ ἀναγαγεῖν πάντας τοὺς συλλογισμοὺς εἰς τοὺς ἐν τῶι πρώτωι σχήματι καθόλου συλλογισμούς. οἱ μὲν γὰρ ἐν τῶι δευτέρωι φανερὸν ὅτι δι᾽ ἐκείνων τελειοῦνται, πλὴν οὐχ ὁμοίως πάντες, ἀλλ᾽ οἱ μὲν καθόλου τοῦ στερητικοῦ ἀντιστραφέντος, τῶν δ᾽ ἐν μέρει ἑκάτερος διὰ τῆς εἰς τὸ ἀδύνατον ἀπαγωγῆς. οἱ δ᾽ ἐν τῶι πρώτωι, οἱ κατὰ μέρος, ἐπιτελοῦν- ται μὲν καὶ δι᾽ αὑτῶν, ἔστι δὲ καὶ διὰ τοῦ δευτέρου σχήματος δεικνύναι εἰς ἀδύνατον ἀπάγοντας, οἷον εἰ τὸ Α παντὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ, ὅτι τὸ Α τινὶ τῶι Γ· εἰ γὰρ μηδενί, τῶι δὲ Β παντί, οὐδενὶ τῶι Γ τὸ Β ὑπάρξει· τοῦτο γὰρ ἴσμεν διὰ τοῦ δευτέρου σχήματος.	Est etiam reducere omnes syllogismos ad universales syllogismos primae figurae. Nam qui sunt in secunda figura, manifestum quoniam per illos perficiuntur, verum non similiter omnes, sed universales quidem privativa conversa; particularium autem utraque per ad impossibile reductionem. Qui vero in prima sunt particulares, perficiuntur quidem per se. Est autem et per secundam figuram ostendere ad impossibile ducentes, ut si A omni B, et B alicui C, quoniam A alicui C inerit. Si enim nulli, B autem omni, nulli C inerit B. Hoc enim scimus per secundam figuram.	It is possible also to reduce all syllogisms to the universal syllogisms in the first figure. Those in the second figure are clearly made perfect by these, though not all in the same way; the universal syllogisms are made perfect by converting the negative premiss, each of the particular syllogisms by reductio ad impossibile. In the first figure particular syllogisms are indeed made perfect by themselves, but it is possible also to prove them by means of the second figure, reducing them ad impossibile, e.g. if A belongs to all B, and B to some C, it follows that A belongs to some C. For if it belonged to no C, and belongs to all B, then B will belong to no C: this we know by means of the second figure.
ὁμοίως δὲ καὶ ἐπὶ τοῦ στερητικοῦ ἔσται ἡ ἀπόδειξις. εἰ γὰρ τὸ Α μηδενὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ ὑπάρχει, τὸ Α τινὶ τῶι Γ οὐχ ὑπάρξει· εἰ γὰρ παντί, τῶι δὲ Β μηδενὶ ὑπάρχει, οὐδενὶ τῶι Γ τὸ Β ὑπάρξει· τοῦτο δ᾽ ἦν τὸ μέσον σχῆμα. ὥστ᾽ ἐπεὶ οἱ μὲν ἐν τῶι μέσωι σχήματι συλλογισμοὶ πάντες ἀνάγονται εἰς τοὺς ἐν τῶι πρώτωι καθόλου συλλογισμούς, οἱ δὲ κατὰ μέρος ἐν τῶι πρώτωι εἰς τοὺς ἐν τῶι μέσωι, φανερὸν ὅτι καὶ οἱ κατὰ μέρος ἀναχθήσονται εἰς τοὺς ἐν τῶι πρώτωι σχήματι καθόλου συλλογισμούς.	(0647D) Similiter autem et in privativo erit demonstratio; si enim A nulli B, et B alicui C inest, A alicui C non erit, nam si A omni C, B autem nulli inest, nulli C inerit B. Haec autem fuit media figura; quare quoniam qui in media sunt syllogismi, omnes reducuntur in primae figurae universales syllogismos, qui vero particulares sunt in prima, ad eos qui sunt in media, manifestum est quoniam et particulares reducentur ad eos qui in prima figura sunt universales syllogismos;	Similarly also demonstration will be possible in the case of the negative. For if A belongs to no B, and B belongs to some C, A will not belong to some C: for if it belonged to all C, and belongs to no B, then B will belong to no C: and this (as we saw) is the middle figure. Consequently, since all syllogisms in the middle figure can be reduced to universal syllogisms in the first figure, and since particular syllogisms in the first figure can be reduced to syllogisms in the middle figure, it is clear that particular syllogisms can be reduced to universal syllogisms in the first figure.
οἱ δ᾽ ἐν τῶι τρίτωι καθόλου μὲν ὄντων τῶν ὅρων εὐθὺς ἐπιτελοῦνται δι᾽ ἐκείνων τῶν συλλογισμῶν, ὅταν δ᾽ ἐν μέρει ληφθῶσι, διὰ τῶν ἐν μέρει συλλογισμῶν τῶν ἐν τῶι πρώτωι σχήματι· οὗτοι δὲ ἀνήχθησαν εἰς ἐκείνους, ὥστε καὶ οἱ ἐν τῶι τρίτωι σχήματι, οἱ κατὰ μέρος. φανερὸν οὖν ὅτι πάντες ἀναχθήσονται εἰς τοὺς ἐν τῶι πρώτωι σχήματι καθόλου συλλογισμούς.	qui vero sunt in tertia, cum universales sint quidem termini, statim perficiuntur per illos syllogismos. Si autem particulares, sumuntur per particulares syllogismos primae figurae, sed hi reducti sunt ad illos, quare et tertiae figurae particulares. Manifestum ergo quoniam omnes reducentur in primae figurae universales syllogismos.	Syllogisms in the third figure, if the terms are universal, are directly made perfect by means of those syllogisms; but, when one of the premisses is particular, by means of the particular syllogisms in the first figure: and these (we have seen) may be reduced to the universal syllogisms in the first figure: consequently also the particular syllogisms in the third figure may be so reduced. It is clear then that all syllogisms may be reduced to the universal syllogisms in the first figure.
Οἱ μὲν οὖν τῶν συλλογισμῶν ὑπάρχειν ἢ μὴ ὑπάρχειν δεικνύντες εἴρηται πῶς ἔχουσι, καὶ καθ᾽ ἑαυτοὺς οἱ ἐκ τοῦ αὐτοῦ σχήματος καὶ πρὸς ἀλλήλους οἱ ἐκ τῶν ἑτέρων.	(0648A) Igitur syllogismi inesse vel non inesse ostendentes, dictum est quomodo se habent, et ad eos qui ex eadem sunt figura, et ad invicem, et ad eos qui ex aliis sunt figuris.	We have stated then how syllogisms which prove that something belongs or does not belong to something else are constituted, both how syllogisms of the same figure are constituted in themselves, and how syllogisms of different figures are related to one another.