Authors/Aristotle/priora/Liber 1/C21

Chapter 21

Greek	Latin	English
	(PL 64 0663B) CAPUT XX/XXI. Mixtio contingentis et inesse in tertia figura.	21
39b7Ἐὰν δὲ ἡ μὲν ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι σημαίνηι τῶν προτάσεων, τὸ μὲν συμπέρασμα ἔσται ὅτι ἐνδέχεται καὶ οὐχ ὅτι ὑπάρχει, συλλογισμὸς δ᾽ ἔσται τὸν αὐτὸν τρό πον ἐχόντων τῶν ὅρων ὃν καὶ ἐν τοῖς πρότερον. ἔστωσαν γὰρ πρῶτον κατηγορικοί, καὶ τὸ μὲν Α παντὶ τῶι Γ ὑπαρχέτω, τὸ δὲ Β παντὶ ἐνδεχέσθω ὑπάρχειν. ἀντιστραφέντος οὖν τοῦ Β Γ τὸ πρῶτον ἔσται σχῆμα, καὶ τὸ συμπέρασμα ὅτι ἐνδέχεται τὸ Α τινὶ τῶι Β ὑπάρχειν· ὅτε γὰρ ἡ ἑτέρα τῶν προτάσεων ἐν τῶι πρώτωι σχήματι σημαίνοι ἐνδέχεσθαι, καὶ τὸ συμπέρασμα ἦν ἐνδεχόμενον.	(0663C) Si autem haec quidem propositionum inesse, illa autem contingere significet, conclusio quidem erit quoniam contingit, et non quoniam inest, syllogismus autem erit eodem modo se habentibus terminis, quo et in prioribus. Sint enim primum praedicativae, et A quidem omni C insit, B autem omni C contingat, conversa ergo B C erit prima figura, et conclusio quoniam contingit A alicui B inesse, cum enim altera propositionum in prima figura significabit contingere, et conclusio erit contingens.	If one premiss is pure, the other problematic, the conclusion will be problematic, not pure; and a syllogism will be possible under the same arrangement of the terms as before. First let the premisses be affirmative: suppose that A belongs to all C, and B may possibly belong to all C. If the proposition BC is converted, we shall have the first figure, and the conclusion that A may possibly belong to some of the Bs. For when one of the premisses in the first figure is problematic, the conclusion also (as we saw) is problematic.
ὁμοίως δὲ καὶ εἰ τὸ μὲν Β Γ ὑπάρχειν τὸ δὲ Α Γ ἐνδέχεσθαι, καὶ εἰ τὸ μὲν Α Γ στερητικὸν τὸ δὲ Β Γ κατηγορικόν, ὑπάρχοι δ᾽ ὁποτερονοῦν, ἀμφοτέρως ἐνδεχόμενον ἔσται τὸ συμπέρασμα· γίνεται γὰρ πάλιν τὸ πρῶτον σχῆμα, δέδεικται δ᾽ ὅτι τῆς ἑτέρας προτάσεως ἐνδέχεσθαι σημαινούσης ἐν αὐτῶι καὶ τὸ συμπέρασμα ἔσται ἐνδεχόμενον. εἰ δὲ τὸ στερητικὸν τεθείη πρὸς τὸ ἔλαττον ἄκρον, ἢ καὶ ἄμφω ληφθείη στερητικά, δι᾽ αὐτῶν μὲν τῶν κειμένων οὐκ ἔσται συλλογισμός, ἀντιστρα φέντων δ᾽ ἔσται, καθάπερ ἐν τοῖς πρότερον.	Similiter autem et si B C quidem inesse, A C autem contingit inesse. Et si A C quidem privativa, B C autem praedicativa, insit autem alterutra utrinque, contingens erit conclusio, fit enim rursum prima figura. Ostensum est autem quoniam si altera propositio significet contingere in prima figura, et conclusio erit contingens. (0663D) Si autem contingens privativa ponatur ad minorem extremitatem, vel si utraque ponatur privativa, per ea quidem quae posita sunt non erit syllogismus, conversis autem erit, quemadmodum et in prioribus.	Similarly if the proposition BC is pure, AC problematic; or if AC is negative, BC affirmative, no matter which of the two is pure; in both cases the conclusion will be problematic: for the first figure is obtained once more, and it has been proved that if one premiss is problematic in that figure the conclusion also will be problematic. But if the minor premiss BC is negative, or if both premisses are negative, no syllogistic conclusion can be drawn from the premisses as they stand, but if they are converted a syllogism is obtained as before.
Εἰ δ᾽ ἡ μὲν καθόλου τῶν προτάσεων ἡ δ᾽ ἐν μέρει, κατηγορικῶν μὲν οὐσῶν ἀμφοτέρων, ἢ τῆς μὲν καθόλου στερητικῆς τῆς δ᾽ ἐν μέρει καταφατικῆς, ὁ αὐτὸς τρόπος ἔσται τῶν συλλογισμῶν· πάντες γὰρ περαίνονται διὰ τοῦ πρώτου σχήματος. ὥστε φανερὸν ὅτι τοῦ ἐνδέχεσθαι καὶ οὐ τοῦ ὑπάρχειν ἔσται ὁ συλλογισμός. εἰ δ᾽ ἡ μὲν καταφατικὴ καθόλου ἡ δὲ στερητικὴ ἐν μέρει, διὰ τοῦ ἀδυνάτου ἔσται ἡ ἀπόδειξις. ὑπαρχέτω γὰρ τὸ μὲν Β παντὶ τῶι Γ, τὸ δὲ Α ἐνδεχέσθω τινὶ τῶι Γ μὴ ὑπάρχειν· ἀνάγκη δὴ τὸ Α ἐν δέχεσθαι τινὶ τῶι Β μὴ ὑπάρχειν. εἰ γὰρ παντὶ τῶι Β τὸ Α ὑπάρχει ἐξ ἀνάγκης, τὸ δὲ Β παντὶ τῶι Γ κεῖται ὑπάρχειν, τὸ Α παντὶ τῶι Γ ἐξ ἀνάγκης ὑπάρξει· τοῦτο γὰρ δέδεικται πρότερον. ἀλλ᾽ ὑπέκειτο τινὶ ἐνδέχεσθαι μὴ ὑπάρχειν.	Si autem haec quidem propositionum sit universalis, illa vero particularis, utrisque quidem praedicativis, aut universali quidem privativa, particulari autem affirmativa, idem modus erit syllogismorum, omnes enim clauduntur per primam figuram. Quare manifestum quoniam eius quod est contingere, et non eius quod est inesse, erit syllogismus. Si autem affirmativa quidem universalis, privativa autem particularis, per impossibile erit demonstratio. (0664A) Insit enim B quidem omni C, A autem contingat alicui C non inesse, necesse est ergo A alicui B contingere non inesse, nam si omni B inest A ex necessitate, B autem omni C positum est inesse, A omni C ex necessitate inerit. Hoc autem ostensum est prius, sed positum est alicui contingere non inesse.	If one of the premisses is universal, the other particular, then when both are affirmative, or when the universal is negative, the particular affirmative, we shall have the same sort of syllogisms: for all are completed by means of the first figure. So it is clear that we shall have not a pure but a problematic syllogistic conclusion. But if the affirmative premiss is universal, the negative particular, the proof will proceed by a reductio ad impossibile. Suppose that B belongs to all C, and A may possibly not belong to some C: it follows that may possibly not belong to some B. For if A necessarily belongs to all B, and B (as has been assumed) belongs to all C, A will necessarily belong to all C: for this has been proved before. But it was assumed at the outset that A may possibly not belong to some C.
↵ Ὅταν δ᾽ ἀδιόριστοι ἢ ἐν μέρει ληφθῶσιν ἀμφότεραι, οὐκ ἔσται συλλογισμός. ἀπόδειξις δ᾽ ἡ αὐτὴ ἣ καὶ ἐν τοῖς πρότερον, καὶ διὰ τῶν αὐτῶν ὅρων.	Quando autem indefinitae, vel particulares sumuntur utraeque, non erit syllogismus, demonstratio autem eadem quae et in universis et per eosdem terminos.	Whenever both premisses are indefinite or particular, no syllogism will be possible. The demonstration is the same as was given in the case of universal premisses, and proceeds by means of the same terms.