Authors/Aristotle/priora/Liber 1/C19

Chapter 19

Greek	Latin	English
	(PL 64 0661A) CAPUT XVIII/XIX. Mixtio necessarii et contingentis in secunda figura.	19
38a13 Ἐὰν δ᾽ ἡ μὲν ἐξ ἀνάγκης ἡ δ᾽ ἐνδέχεσθαι σημαίνηι τῶν προτάσεων, τῆς μὲν στερητικῆς ἀναγκαίας οὔσης ἔσται συλλογισμός, οὐ μόνον ὅτι ἐνδέχεται μὴ ὑπάρχειν, ἀλλὰ καὶ ὅτι οὐχ ὑπάρχει, τῆς δὲ καταφατικῆς οὐκ ἔσται.	(0661B) Si autem haec quidem propositionum ex necessitate, illa vero contingere significat, privativa quidem necessaria, erit syllogismus, non solum quoniam contingit non inesse, sed et quoniam non inest, affirmativa autem non erit.	If one of the premisses is necessary, the other problematic, then if the negative is necessary a syllogistic conclusion can be drawn, not merely a negative problematic but also a negative assertoric conclusion; but if the affirmative premiss is necessary, no conclusion is possible.
κείσθω γὰρ τὸ Α τῶι μὲν Β ἐξ ἀνάγκης μηδενὶ ὑπάρχειν, τῶι δὲ Γ παντὶ ἐνδέχεσθαι. ἀντιστραφείσης οὖν τῆς στερητικῆς οὐδὲ τὸ Β τῶι Α οὐδενὶ ὑπάρξει· τὸ δὲ Α παντὶ τῶι Γ ἐνεδέχετο· γίνεται δὴ πάλιν διὰ τοῦ πρώτου σχήματος ὁ συλλογισμὸς ὅτι τὸ Β τῶι Γ ἐνδέχεται μηδενὶ ὑπάρχειν. ἅμα δὲ δῆλον ὅτι οὐδ᾽ ὑπάρξει τὸ Β οὐδενὶ τῶι Γ. κείσθω γὰρ ὑπάρχειν· οὐκοῦν εἰ τὸ Α τῶι Β μηδενὶ ἐνδέχεται, τὸ δὲ Β ὑπάρχει τινὶ τῶι Γ, τὸ Α τῶι Γ τινὶ οὐκ ἐνδέχεται· ἀλλὰ παντὶ ὑπέ κειτο ἐνδέχεσθαι. τὸν αὐτὸν δὲ τρόπον δειχθήσεται καὶ εἰ πρὸς τῶι Γ τεθείη τὸ στερητικόν.	Ponatur autem A B quidem nulli inesse ex necessitate, C autem omni contingere, conversa ergo privativa, et B nulli A inerit, A autem omni E contingebat. Fit igitur rursum per primam figuram syllogismus, quoniam B contingit nulli C inesse. Simul autem manifestum quoniam neque inest B nulli C, ponatur enim inesse, ergo si A nulli B contingit, B autem inest alicui C, A alicui C non contingit, sed omni ponebatur contingere. (0661C) Eodem autem modo ostendetur, et si ad C ponatur privativum.	Suppose that A necessarily belongs to no B, but may belong to all C. If the negative premiss is converted B will belong to no A: but A ex hypothesi is capable of belonging to all C: so once more a conclusion is drawn by the first figure that B may belong to no C. But at the same time it is clear that B will not belong to any C. For assume that it does: then if A cannot belong to any B, and B belongs to some of the Cs, A cannot belong to some of the Cs: but ex hypothesi it may belong to all. A similar proof can be given if the minor premiss is negative.
Πάλιν ἔστω τὸ κατηγορικὸν ἀναγκαῖον, θάτερον δ᾽ ἐνδεχόμενον, καὶ τὸ Α τῶι μὲν Β ἐν- δεχέσθω μηδενί, τῶι δὲ Γ παντὶ ὑπαρχέτω ἐξ ἀνάγκης. οὕτως οὖν ἐχόντων τῶν ὅρων οὐδεὶς ἔσται συλλογισμός. συμ βαίνει γὰρ τὸ Β τῶι Γ ἐξ ἀνάγκης μὴ ὑπάρχειν.	Rursum. Sit praedicativa quidem necessaria, altera autem privativa, et contingens, et A B contingat nulli, C autem omni insit ex necessitate, sic ergo habentibus se terminis, nullus erit syllogismus, accidit enim B ex necessitate non inesse.	Again let the affirmative proposition be necessary, and the other problematic; i.e. suppose that A may belong to no B, but necessarily belongs to all C. When the terms are arranged in this way, no syllogism is possible. For (1) it sometimes turns out that B necessarily does not belong to C.
ἔστω γὰρ τὸ μὲν Α λευκόν, ἐφ᾽ ὧι δὲ τὸ Β ἄνθρωπος, ἐφ᾽ ὧι δὲ τὸ Γ κύκνος. τὸ δὴ λευκὸν κύκνωι μὲν ἐξ ἀνάγκης ὑπάρχει, ἀνθρώπωι δ᾽ ἐνδέχεται μηδενί· καὶ ἄνθρωπος οὐδενὶ κύκνωι ἐξ ἀνάγκης. ὅτι μὲν οὖν τοῦ ἐνδέχεσθαι οὐκ ἔστι συλλογισμός, φανερόν· τὸ γὰρ ἐξ ἀνάγκης οὐκ ἦν ἐνδεχόμενον.	Sit enim A quidem album, in quo autem B, homo, in quo vero C, cygnus, ergo album cygno quidem ex necessitate inest, homini autem contingit nulli, et homo nulli cygno ex necessitate. Quoniam igitur eius quod est contingere non est syllogismus, manifestum est, nam ex necessitate non erat contingens.	Let A be white, B man, C swan. White then necessarily belongs to swan, but may belong to no man; and man necessarily belongs to no swan; Clearly then we cannot draw a problematic conclusion; for that which is necessary is admittedly distinct from that which is possible.
ἀλλὰ μὴν οὐδὲ τοῦ ἀναγκαίου· τὸ γὰρ ἀναγκαῖον ἢ ἐξ ἀμφοτέρων ἀναγκαίων ἢ ἐκ τῆς στερητικῆς συνέβαινεν. ἔτι δὲ καὶ ἐγχωρεῖ τούτων κειμένων τὸ Β τῶι Γ ὑπάρχειν· οὐδὲν γὰρ κωλύει τὸ μὲν Γ ὑπὸ τὸ Β εἶναι, τὸ δὲ Α τῶι μὲν Β παντὶ ἐνδέχεσθαι, τῶι δὲ Γ ἐξ ἀνάγκης ὑπάρχειν, οἷον εἰ τὸ μὲν Γ εἴη ἐγρηγορός, τὸ δὲ Β ζῶιον, τὸ δ᾽ ἐφ᾽ ὧι τὸ Α κίνησις. τῶι μὲν γὰρ ἐγρηγορότι ἐξ ἀνάγ ↵ κης κίνησις, ζώιωι δὲ παντὶ ἐνδέχεται· καὶ πᾶν τὸ ἐγρηγορὸς ζῶιον. φανερὸν οὖν ὅτι οὐδὲ τοῦ μὴ ὑπάρχειν, εἴπερ οὕτως ἐχόντων ἀνάγκη ὑπάρχειν. οὐδὲ δὴ τῶν ἀντικειμένων καταφάσεων, ὥστ᾽ οὐδεὶς ἔσται συλλογισμός. ὁμοίως δὲ δειχθήσεται καὶ ἀνάπαλιν τεθείσης τῆς καταφατικῆς.	Sed tamen non necessarii, nam necessarium aut ex utrisque necessariis, aut ex privativa necessaria contingebat. Amplius et possibile est iis positis B inesse C. (0661D) Nihil enim prohibet C quidem sub B esse, A autem B quidem omni contingere, C vero ex necessitate inesse, ut sit quidem C vigilia, B autem animal, in quo autem A motus. Nam vigilanti quidem ex necessitate inest motus, animali autem nulli contingit, et omne vigilans animal. Manifestum ergo quoniam non eius quod est non inesse, siquidem sic se habentibus terminis, necesse est inesse, neque autem oppositarum affirmationum, quare nullus erit syllogismus. Similiter autem ostendetur, et e converso posita affirmativa.	(2) Nor again can we draw a necessary conclusion: for that presupposes that both premisses are necessary, or at any rate the negative premiss. (3) Further it is possible also, when the terms are so arranged, that B should belong to C: for nothing prevents C falling under B, A being possible for all B, and necessarily belonging to C; e.g. if C stands for ‘awake’, B for ‘animal’, A for ‘motion’. For motion necessarily belongs to what is awake, and is possible for every animal: and everything that is awake is animal. Clearly then the conclusion cannot be the negative assertion, if the relation must be positive when the terms are related as above. Nor can the opposite affirmations be established: consequently no syllogism is possible. A similar proof is possible if the major premiss is affirmative.
Ἐὰν δ᾽ ὁμοιοσχήμονες ὦσιν αἱ προτάσεις, στερητικῶν μὲν οὐσῶν ἀεὶ γίνεται συλλογισμὸς ἀντιστραφείσης τῆς κατὰ τὸ ἐνδέχεσθαι προτάσεως καθάπερ ἐν τοῖς πρότερον. εἰλήφθω γὰρ τὸ Α τῶι μὲν Β ἐξ ἀνάγκης μὴ ὑπάρχειν, τῶι δὲ Γ ἐνδέχεσθαι μὴ ὑπάρχειν· ἀντιστραφεισῶν οὖν τῶν προτάσεων τὸ μὲν Β τῶι Α οὐδενὶ ὑπάρχει, τὸ δὲ Α παντὶ τῶι Γ ἐνδέχεται· γίνεται δὴ τὸ πρῶτον σχῆμα. κἂν εἰ πρὸς τῶι Γ τεθείη τὸ στερητικόν, ὡσαύτως. ἐὰν δὲ κατηγορικαὶ τεθῶσιν, οὐκ ἔσται συλλογισμός. τοῦ μὲν γὰρ μὴ ὑπάρχειν ἢ τοῦ ἐξ ἀνάγκης μὴ ὑπάρχειν φανερὸν ὅτι οὐκ ἔσται διὰ τὸ μὴ εἰλῆφθαι στερητικὴν πρότασιν μήτ᾽ ἐν τῶι ὑπάρχειν μήτ᾽ ἐν τῶι ἐξ ἀνάγκης ὑπάρχειν. ἀλλὰ μὴν οὐδὲ τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν· ἐξ ἀνάγκης γὰρ οὕτως ἐχόντων τὸ Β τῶι Γ οὐχ ὑπάρξει, οἷον εἰ τὸ μὲν Α τε θείη λευκόν, ἐφ᾽ ὧι δὲ τὸ Β κύκνος, τὸ δὲ Γ ἄνθρωπος. οὐδέ γε τῶν ἀντικειμένων καταφάσεων, ἐπεὶ δέδεικται τὸ Β τῶι Γ ἐξ ἀνάγκης οὐχ ὑπάρχον. οὐκ ἄρα γίνεται συλλογισμὸς ὅλως.	Si autem similis figurae sint propositiones, cum privativae sint, semper fit syllogismus, conversa secundum contingere propositione, quemadmodum in prioribus. (0662A) Si sumatur enim A B quidem ex necessitate non inesse, C autem contingere non inesse, conversis autem propositionibus, B quidem nulli inesse A, A autem omni C contingit, fit igitur prima figura, et si ad C ponatur privativum similiter. Si autem praedicativae ponantur, non erit syllogismus, nam eius quod est non inesse, aut eius quod est ex necessitate non inesse, manifestum quoniam non erit, eo quod non sumpta sit privativa propositio, neque in eo quod est inesse, neque in eo quod est ex necessitate inesse, sed neque eius quod est contingere non inesse, ex necessitate enim sic se habentibus, B non inerit C, ut si A quidem ponatur album, in quo autem B cygnus, in quo autem C homo, neque oppositarum affirmationum, quoniam ostensum est B ex necessitate non inesse C, non ergo fit syllogismus omnino.	But if the premisses are similar in quality, when they are negative a syllogism can always be formed by converting the problematic premiss into its complementary affirmative as before. Suppose A necessarily does not belong to B, and possibly may not belong to C: if the premisses are converted B belongs to no A, and A may possibly belong to all C: thus we have the first figure. Similarly if the minor premiss is negative. But if the premisses are affirmative there cannot be a syllogism. Clearly the conclusion cannot be a negative assertoric or a negative necessary proposition because no negative premiss has been laid down either in the assertoric or in the necessary mode. Nor can the conclusion be a problematic negative proposition. For if the terms are so related, there are cases in which B necessarily will not belong to C; e.g. suppose that A is white, B swan, C man. Nor can the opposite affirmations be established, since we have shown a case in which B necessarily does not belong to C. A syllogism then is not possible at all.
Ὁμοίως δ᾽ ἕξει κἀπὶ τῶν ἐν μέρει συλλογισμῶν· ὅταν μὲν γὰρ ἦι τὸ στερητικὸν καθόλου τε καὶ ἀναγκαῖον, ἀεὶ συλλογισμὸς ἔσται καὶ τοῦ ἐνδέχεσθαι καὶ τοῦ μὴ ὑπάρχειν (ἀπόδειξις δὲ διὰ τῆς ἀντιστροφῆσ), ὅταν δὲ τὸ καταφατικόν, οὐδέποτε· τὸν αὐτὸν γὰρ τρόπον δειχθήσεται ὃν καὶ ἐν τοῖς καθόλου, καὶ διὰ τῶν αὐτῶν ὅρων. οὐδ᾽ ὅταν ἀμφότεραι ληφθῶσι καταφατικαί· καὶ γὰρ τούτου ἡ αὐτὴ ἀπόδειξις ἣ καὶ πρότερον. ὅταν δὲ ἀμφότεραι μὲν στερητικαί, καθόλου δὲ καὶ ἀναγκαία ἡ τὸ μὴ ὑπάρχειν σημαίνουσα, δι᾽ αὐτῶν μὲν τῶν εἰλημμένων οὐκ ἔσται τὸ ἀναγκαῖον, ἀντιστραφείσης δὲ τῆς κατὰ τὸ ἐνδέχεσθαι προτά σεως ἔσται συλλογισμός, καθάπερ ἐν τοῖς πρότερον. ἐὰν δ᾽ ἀμφότεραι ἀδιόριστοι ἢ ἐν μέρει τεθῶσιν, οὐκ ἔσται συλλογισμός. ἀπόδειξις δ᾽ ἡ αὐτὴ καὶ διὰ τῶν αὐτῶν ὅρων.	Similiter autem se habebit et in particularibus syllogismis. (0662B) Quando autem fuerit privativa, et universalis, et necessaria, semper erit syllogismus, et eius quod est contingere non inesse, et eius quod est non inesse, demonstratio autem per conversionem. Quando autem affirmativa, nunquam, eodem autem modo ostendetur quo et in universalibus, et per eosdem terminos. Nec quando utraeque sumuntur affirmative, nam et huius eadem demonstratio, quae et prius. Quando utraeque quidem privativae, universalis autem et necessaria, quae non inesse significat, per ea quidem quae sumpta sunt, non erit necessarium, conversa autem secundum contingere propositione, erit syllogismus, quemadmodum in prioribus. (0662C) Si autem utraeque indefinitae, vel particulares sumantur, non erit syllogismus, demonstratio autem eadem, et per eosdem terminos.	Similar relations will obtain in particular syllogisms. For whenever the negative proposition is universal and necessary, a syllogism will always be possible to prove both a problematic and a negative assertoric proposition (the proof proceeds by conversion); but when the affirmative proposition is universal and necessary, no syllogistic conclusion can be drawn. This can be proved in the same way as for universal propositions, and by the same terms. Nor is a syllogistic conclusion possible when both premisses are affirmative: this also may be proved as above. But when both premisses are negative, and the premiss that definitely disconnects two terms is universal and necessary, though nothing follows necessarily from the premisses as they are stated, a conclusion can be drawn as above if the problematic premiss is converted into its complementary affirmative. But if both are indefinite or particular, no syllogism can be formed. The same proof will serve, and the same terms.
Φανερὸν οὖν ἐκ τῶν εἰρημένων ὅτι τῆς μὲν στερητικῆς τῆς καθόλου τιθεμένης ἀναγκαίας ἀεὶ γίνεται συλλογι σμὸς οὐ μόνον τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν, ἀλλὰ καὶ τοῦ μὴ ὑπάρχειν, τῆς δὲ καταφατικῆς οὐδέποτε. καὶ ὅτι τὸν αὐτὸν τρόπον ἐχόντων ἔν τε τοῖς ἀναγκαίοις καὶ ἐν τοῖς ↵ ὑπάρχουσι γίνεταί τε καὶ οὐ γίνεται συλλογισμός. δῆλον δὲ καὶ ὅτι πάντες ἀτελεῖς οἱ συλλογισμοί, καὶ ὅτι τελειοῦνται διὰ τῶν προειρημένων σχημάτων.	Manifestum igitur ex praedictis quoniam privativa quidem universalis posita necessaria, semper fit syllogismus, non solum eius, quod est contingere non inesse, sed et non inesse, affirmativa autem nunquam. Et quoniam eodem modo se habentibus, et in necessariis, et in iis quae insunt, fit et non fit syllogismus Palam et quoniam imperfecti omnes sunt syllogismi, et quoniam omnes perficiuntur per praedictas figuras.	It is clear then from what has been said that if the universal and negative premiss is necessary, a syllogism is always possible, proving not merely a negative problematic, but also a negative assertoric proposition; but if the affirmative premiss is necessary no conclusion can be drawn. It is clear too that a syllogism is possible or not under the same conditions whether the mode of the premisses is assertoric or necessary. And it is clear that all the syllogisms are imperfect, and are completed by means of the figures mentioned.