Authors/Aristotle/priora/Liber 1/C14

Chapter 14

Greek	Latin	English
	CAPUT XIII. De syllogismis ex ambabus contingentibus in prima figura.	14
32b38 Ὅταν οὖν τὸ Α παντὶ τῶι Β ἐνδέχηται καὶ τὸ Β παντὶ τῶι Γ, συλλογισμὸς ἔσται τέλειος ὅτι τὸ Α παντὶ τῶι Γ ἐνδέχεται ὑπάρχειν. τοῦτο δὲ φανερὸν ἐκ τοῦ ὁρισμοῦ· τὸ γὰρ ↵ ἐνδέχεσθαι παντὶ ὑπάρχειν οὕτως ἐλέγομεν. ὁμοίως δὲ καὶ εἰ τὸ μὲν Α ἐνδέχεται μηδενὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ, ὅτι τὸ Α ἐνδέχεται μηδενὶ τῶι Γ·	Quando ergo A contingit omni B, et B omni C, syllogismus erit perfectus, quoniam A contingit omni C inesse. Hoc autem manifestum est ex definitione, nam contingere omni inesse sic dicebamus. Similiter autem et si A quidem contingit nulli B, B autem omni C, quoniam A contingit nulli C.	Whenever A may possibly belong to all B, and B to all C, there will be a perfect syllogism to prove that A may possibly belong to all C. This is clear from the definition: for it was in this way that we explained ‘to be possible for one term to belong to all of another’. Similarly if it is possible for A to belong no B, and for B to belong to all C, then it is possible for A to belong to no C.
τὸ γὰρ καθ᾽ οὗ τὸ Β ἐνδέχεται, τὸ Α μὴ ἐνδέχεσθαι, τοῦτ᾽ ἦν τὸ μηδὲν ἀπολείπειν τῶν ὑπὸ τὸ Β ἐνδεχομένων. ὅταν δὲ τὸ Α παντὶ τῶι Β ἐνδέχηται, τὸ δὲ Β ἐνδέχηται μηδενὶ τῶι Γ, διὰ μὲν τῶν εἰλημμένων προτάσεων οὐδεὶς γίνεται συλλογισμός, ἀντιστραφείσης δὲ τῆς Β Γ κατὰ τὸ ἐνδέχεσθαι γίνεται ὁ αὐτὸς ὅσπερ πρότερον. ἐπεὶ γὰρ ἐνδέχεται τὸ Β μηδενὶ τῶι Γ ὑπάρ χειν, ἐνδέχεται καὶ παντὶ ὑπάρχειν· τοῦτο δ᾽ εἴρηται πρότερον. ὥστ᾽ εἰ τὸ μὲν Β παντὶ τῶι Γ, τὸ δ᾽ Α παντὶ τῶι Β, πάλιν ὁ αὐτὸς γίνεται συλλογισμός.	Nam de quo B contingit, A non contingere, hoc erat nullum dimittere sub B contingentium. (0653B) Quando autem A contingit omni B, B autem nulli C, per sumptas quidem propositiones nullus fit syllogismus, conversa autem B C secundum contingere, fit idem quemadmodum et prius, quoniam enim contingit B nulli C inesse, contingit et omni inesse. Hoc autem dictum prius. Quare si B quidem omni C, A autem omni B, rursum idem fit syllogismus.	For the statement that it is possible for A not to belong to that of which B may be true means (as we saw) that none of those things which can possibly fall under the term B is left out of account. But whenever A may belong to all B, and B may belong to no C, then indeed no syllogism results from the premisses assumed, but if the premiss BC is converted after the manner of problematic propositions, the same syllogism results as before. For since it is possible that B should belong to no C, it is possible also that it should belong to all C. This has been stated above. Consequently if B is possible for all C, and A is possible for all B, the same syllogism again results.
ὁμοίως δὲ καὶ εἰ πρὸς ἀμφοτέρας τὰς προτάσεις ἡ ἀπόφασις τεθείη μετὰ τοῦ ἐνδέχεσθαι. λέγω δ᾽ οἷον εἰ τὸ Α ἐνδέχεται μηδενὶ τῶι Β καὶ τὸ Β μηδενὶ τῶι Γ· διὰ μὲν γὰρ τῶν εἰλημμένων προτάσεων οὐδεὶς γίνεται συλλογισμός, ἀντιστρεφομένων δὲ πάλιν ὁ αὐτὸς ἔσται ὅσπερ καὶ πρότερον. φανερὸν οὖν ὅτι τῆς ἀποφάσεως τιθεμένης πρὸς τὸ ἔλαττον ἄκρον ἢ πρὸς ἀμφοτέρας τὰς προτάσεις ἢ οὐ γίνεται συλλογισμὸς ἢ γίνεται μὲν ἀλλ᾽ οὐ τέλειος· ἐκ γὰρ τῆς ἀντιστροφῆς περαίνεται τὸ ἀναγκαῖον.	Similiter autem etsi ad utrasque propositiones negatio ponatur cum contingere (dico autem ut si A contingit nulli B, et B nulli C ), igitur per sumptas quidem propositiones nullus fit syllogismus, conversis autem rursus idem erit qui et prius. Manifestum est igitur quoniam negatione posita ad minorem extremitatem, vel ad utrasque propositiones, aut non fit syllogismus, aut fit quidem, sed non perfectus, ex conversione enim fit necessarium.	Similarly if in both the premisses the negative is joined with ‘it is possible’: e.g. if A may belong to none of the Bs, and B to none of the Cs. No syllogism results from the assumed premisses, but if they are converted we shall have the same syllogism as before. It is clear then that if the minor premiss is negative, or if both premisses are negative, either no syllogism results, or if one it is not perfect. For the necessity results from the conversion.
Ἐὰν δ᾽ ἡ μὲν καθόλου τῶν προτάσεων ἡ δ᾽ ἐν μέρει ληφθῆι, πρὸς μὲν τὸ μεῖζον ἄκρον κειμένης τῆς καθόλου συλλογισμὸς ἔσται [τέλειοσ]. εἰ γὰρ τὸ Α παντὶ τῶι Β ἐνδέχεται, τὸ δὲ Β τινὶ τῶι Γ, τὸ Α τινὶ τῶι Γ ἐνδέχεται. τοῦτο δὲ φανερὸν ἐκ τοῦ ὁρισμοῦ τοῦ ἐνδέχεσθαι. πάλιν εἰ τὸ Α ἐνδέχεται μηδενὶ τῶι Β, τὸ δὲ Β τινὶ τῶι Γ ἐνδέχεται ὑπάρχειν, ἀνάγκη τὸ Α ἐνδέχεσθαί τινι τῶν Γ μὴ ὑπάρχειν. ἀπόδειξις δ᾽ ἡ αὐτή. ἐὰν δὲ στερητικὴ ληφθῆι ἡ ἐν μέρει πρότασις, ἡ δὲ καθόλου καταφατική, τῆι δὲ θέσει ὁμοίως ἔχωσιν (οἷον τὸ μὲν Α παντὶ τῶι Β ἐνδέ χεται, τὸ δὲ Β τινὶ τῶι Γ ἐνδέχεται μὴ ὑπάρχειν), διὰ μὲν τῶν εἰλημμένων προτάσεων οὐ γίνεται φανερὸς συλλογισμός, ἀντιστραφείσης δὲ τῆς ἐν μέρει καὶ τεθέντος τοῦ Β τινὶ τῶι Γ ἐνδέχεσθαι ὑπάρχειν τὸ αὐτὸ ἔσται συμπέρασμα ὁ καὶ πρότερον, καθάπερ ἐν τοῖς ἐξ ἀρχῆς.	Si autem haec quidem propositionum universalis, illa vero particularis sumatur, ad maiorem quidem extremitatem posita universali, syllogismus erit perfectus. (0653C) Nam si A omni B contingit, B autem alicui C, A alicui C contingit, hoc autem manifestum ex definitione contingentis. Rursum si A contingit nulli B, B autem contingit alicui C inesse, necesse est A contingere alicui C non inesse. Demonstratio autem eadem quae in his. Si autem privativa sumatur particularis propositio, universalis autem affirmativa, positione autem similiter se habeant (ut A quidem omni B contingat, B autem alicui C contingat non inesse), per sumptas quidem propositiones non fit manifestus syllogismus, conversa autem particulari, et posito B alicui C contingere inesse, eadem erit conclusio quae et prius, quemadmodum in iis quae ex principio.	But if one of the premisses is universal, the other particular, when the major premiss is universal there will be a perfect syllogism. For if A is possible for all B, and B for some C, then A is possible for some C. This is clear from the definition of being possible. Again if A may belong to no B, and B may belong to some of the Cs, it is necessary that A may possibly not belong to some of the Cs. The proof is the same as above. But if the particular premiss is negative, and the universal is affirmative, the major still being universal and the minor particular, e.g. A is possible for all B, B may possibly not belong to some C, then a clear syllogism does not result from the assumed premisses, but if the particular premiss is converted and it is laid down that B possibly may belong to some C, we shall have the same conclusion as before, as in the cases given at the beginning.
Ἐὰν δ᾽ ἡ πρὸς τὸ μεῖζον ἄκρον ἐν μέρει ληφθῆι, ἡ δὲ πρὸς τὸ ἔλαττον καθόλου, ἐάν τ᾽ ἀμφότεραι καταφατικαὶ τεθῶσιν ἐάν τε στερητικαὶ ἐάν τε μὴ ὁμοιοσχήμονες, ἐάν τ᾽ ἀμφότεραι ἀδιόριστοι ἢ κατὰ μέρος, οὐδαμῶς ἔσται συλλογισμός· οὐδὲν γὰρ κωλύει τὸ Β ὑπερτείνειν τοῦ Α καὶ μὴ κατηγορεῖσθαι ἐπ᾽ ἴσων· ὧι δ᾽ ὑπερτείνει τὸ Β τοῦ Α, εἰλήφθω τὸ Γ· τούτωι γὰρ οὔτε παντὶ ↵ οὔτε μηδενὶ οὔτε τινὶ οὔτε μή τινι ἐνδέχεται τὸ Α ὑπάρχειν, εἴπερ ἀντιστρέφουσιν αἱ κατὰ τὸ ἐνδέχεσθαι προτάσεις καὶ τὸ Β πλείοσιν ἐνδέχεται ἢ τὸ Α ὑπάρχειν.	(0653D) Si autem quae ad maiorem extremitatem particularis sumatur, quae ad minorem universalis, sive utraeque sumantur affirmativae, sive privativae, sive non similis figurae, sive utraeque indefinitae, vel particulares, nullo modo erit syllogismus. Nihil enim prohibet B transcendere A, et non praedicari de aequis, in quo enim B transcendit A sumat C, huic neque omni, neque nulli, neque alicui, neque non alicui contingit A inesse, siquidem convertuntur secundum contingere propositiones, et B pluribus contingit quam A inesse.	But if the major premiss is the minor universal, whether both are affirmative, or negative, or different in quality, or if both are indefinite or particular, in no way will a syllogism be possible. For nothing prevents B from reaching beyond A, so that as predicates cover unequal areas. Let C be that by which B extends beyond A. To C it is not possible that A should belong-either to all or to none or to some or not to some, since premisses in the mode of possibility are convertible and it is possible for B to belong to more things than A can.
ἔτι δὲ καὶ ἐκ τῶν ὅρων φανερόν· οὕτω γὰρ ἐχουσῶν τῶν προτάσεων τὸ πρῶτον τῶι ἐσχάτωι καὶ οὐδενὶ ἐνδέχεται καὶ παντὶ ὑπάρχειν ἀναγκαῖον. ὅροι δὲ κοινοὶ πάντων τοῦ μὲν ὑπάρχειν ἐξ ἀνάγκης ζῶιον – λευκόν – ἄνθρωπος, τοῦ δὲ μὴ ἐνδέχεσθαι ζῶιον – λευκόν – ἱμάτιον.	Amplius autem ex terminis manifestum est, nam sic se habentibus propositionibus primum postremo et nulli contingit, et omni ex necessitate inesse. Termini autem communes omnium, inesse quidem ex necessitate, animal, album, homo, non contingere vero, animal, album, vestis.	Further, this is obvious if we take terms; for if the premisses are as assumed, the major term is both possible for none of the minor and must belong to all of it. Take as terms common to all the cases under consideration ‘animal’-’white’-’man’, where the major belongs necessarily to the minor; ‘animal’-’white’-’garment’, where it is not possible that the major should belong to the minor.
φανερὸν οὖν τοῦτον τὸν τρόπον ἐχόντων τῶν ὅρων ὅτι οὐδεὶς γίνεται συλλογισμός. ἢ γὰρ τοῦ ὑπάρχειν ἢ τοῦ ἐξ ἀνάγκης ἢ τοῦ ἐνδέχεσθαι πᾶς ἐστὶ συλλογισμός. τοῦ μὲν οὖν ὑπάρχειν καὶ τοῦ ἀναγκαίου φανερὸν ὅτι οὐκ ἔστιν· ὁ μὲν γὰρ καταφατικὸς ἀναιρεῖται τῶι στερητικῶι, ὁ δὲ στερητικὸς τῶι καταφατικῶι. λείπεται δὴ τοῦ ἐνδέχεσθαι εἶναι· τοῦτο δ᾽ ἀδύνατον· δέδεικται γὰρ ὅτι οὕτως ἐχόντων τῶν ὅρων καὶ παντὶ τῶι ἐσχάτωι τὸ πρῶτον ἀνάγκη καὶ οὐδενὶ ἐνδέχεται ὑπάρχειν. ὥστ᾽ οὐκ ἂν εἴη τοῦ ἐνδέχεσθαι συλλογισμός· τὸ γὰρ ἀναγκαῖον οὐκ ἦν ἐνδεχόμενον.	(0654A) Manifestum igitur quoniam hoc modo habentibus se terminis, nullus fit syllogismus, nam omnis syllogismus vel eius quod est inesse est, vel ex necessitate vel contingere, non est autem eius quod est inesse, neque necessarii, manifestum quoniam non est, nam affirmativus interimitur privativo, et privativus affirmativo, relinquitur ergo eius quod contingere esse, hoc autem impossibile. Ostensum est enim quoniam sic se habentibus terminis, et omni postremo primum necesse inesse, et nulli contingere inesse, quare non erit eius quod est contingere syllogismus, nam necessarium uno [sic] erat contingens.	It is clear then that if the terms are related in this manner, no syllogism results. For every syllogism proves that something belongs either simply or necessarily or possibly. It is clear that there is no proof of the first or of the second. For the affirmative is destroyed by the negative, and the negative by the affirmative. There remains the proof of possibility. But this is impossible. For it has been proved that if the terms are related in this manner it is both necessary that the major should belong to all the minor and not possible that it should belong to any. Consequently there cannot be a syllogism to prove the possibility; for the necessary (as we stated) is not possible.
Φανερὸν δὲ ὅτι καθόλου τῶν ὅρων ὄντων ἐν ταῖς ἐνδεχομέναις προτάσεσιν ἀεὶ γίνεται συλλογισμὸς ἐν τῶι πρώ τωι σχήματι, καὶ κατηγορικῶν καὶ στερητικῶν ὄντων, πλὴν κατηγορικῶν μὲν τέλειος, στερητικῶν δὲ ἀτελής. δεῖ δὲ τὸ ἐνδέχεσθαι λαμβάνειν μὴ ἐν τοῖς ἀναγκαίοις, ἀλλὰ κατὰ τὸν εἰρημένον διορισμόν. ἐνίοτε δὲ λανθάνει τὸ τοιοῦτον.	Manifestum autem et quoniam cum universales sunt termini in contingentibus propositionibus, semper fit syllogismus in prima figura, sive sunt praedicativi, sive privativi. (0654B) Verum ex praedicativis quidem perfectus, ex privativis autem imperfectus. Oportet autem contingere sumere non in necessariis, sed secundum dictam definitionem, aliquoties autem latet huiusmodi.	It is clear that if the terms are universal in possible premisses a syllogism always results in the first figure, whether they are affirmative or negative, only a perfect syllogism results in the first case, an imperfect in the second. But possibility must be understood according to the definition laid down, not as covering necessity. This is sometimes forgotten.