Authors/Aristotle/priora/Liber 1/C16

Chapter 16

Greek	Latin	English
	(PL 64 0657B) CAPUT XV. Mixtio necessarii et contingentis in prima figura.	16
35b23 Ὅταν δ᾽ ἡ μὲν ἐξ ἀνάγκης ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι σημαίνηι τῶν προτάσεων, ὁ μὲν συλλογισμὸς ἔσται τὸν αὐτὸν τρόπον ἐχόντων τῶν ὅρων, καὶ τέλειος ὅταν πρὸς τῶι ἐλάττονι ἄκρωι τεθῆι τὸ ἀναγκαῖον· τὸ δὲ συμπέρασμα κατηγορικῶν μὲν ὄντων τῶν ὅρων τοῦ ἐνδέχεσθαι καὶ οὐ τοῦ ὑπάρχειν ἔσται, καὶ καθόλου καὶ μὴ καθόλου τιθεμένων, ἐὰν δ᾽ ἦι τὸ μὲν καταφατικὸν τὸ δὲ στερητικόν, ὅταν μὲν ἦι τὸ καταφατικὸν ἀναγκαῖον, τοῦ ἐνδέχεσθαι καὶ οὐ τοῦ μὴ ὑπάρχειν, ὅταν δὲ τὸ στερητικόν, καὶ τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν καὶ τοῦ μὴ ὑπάρχειν, καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων ὄντων· τὸ δ᾽ ἐνδέχεσθαι ἐν τῶι συμπεράσματι τὸν αὐτὸν τρόπον ληπτέον ὅνπερ καὶ ἐν τοῖς πρότερον. τοῦ δ᾽ ἐξ ἀνάγκης μὴ ὑπάρχειν οὐκ ἔσται συλλογισμός· ἕτερον γὰρ τὸ μὴ ἐξ ἀνάγκης ὑπάρχειν καὶ τὸ ἐξ ἀνάγκης μὴ ὑπάρχειν.	(0657C) Quando autem haec quidem propositionum ex necessitate inesse, vel non inesse, illa vero contingere significat, syllogismus quidem erit hoc modo habentibus se terminis. Et perfectus, quando ad minorem extremitatem ponetur necessaria. Conclusio autem, si praedicativi sunt quidem termini, contingentis, et non inesse erit, sive universaliter, sive non universaliter ponantur, si autem sint hoc quidem affirmativum, illud vero privativum, quando affirmativum quidem fuerit necessarium, et contingentis erit conclusio, et non eius quod est non inesse. Quando autem privativum necessarium, et contingentis non esse, et non inesse, sive universales, sive non universales sint termini. Contingere autem in conclusione eodem modo accipiendum est quo in prioribus. (0657D) Eius autem quod est ex necessitate non inesse, non erit syllogismus, aliud enim est non ex necessitate inesse, et ex necessitate non inesse.	Whenever one premiss is necessary, the other problematic, there will be a syllogism when the terms are related as before; and a perfect syllogism when the minor premiss is necessary. If the premisses are affirmative the conclusion will be problematic, not assertoric, whether the premisses are universal or not: but if one is affirmative, the other negative, when the affirmative is necessary the conclusion will be problematic, not negative assertoric; but when the negative is necessary the conclusion will be problematic negative, and assertoric negative, whether the premisses are universal or not. Possibility in the conclusion must be understood in the same manner as before. There cannot be an inference to the necessary negative proposition: for ‘not necessarily to belong’ is different from ‘necessarily not to belong’.
Ὅτι μὲν οὖν καταφατικῶν ὄντων τῶν ὅρων οὐ γίνεται τὸ συμπέρασμα ἀναγκαῖον, φανερόν. ὑπαρχέτω γὰρ τὸ μὲν Α παντὶ τῶι Β ἐξ ἀνάγκης, τὸ δὲ Β ἐνδεχέσθω παντὶ τῶι Γ. ἔσται δὴ συλλογισμὸς ἀτελὴς ὅτι ἐνδέχεται τὸ Α παντὶ τῶι Γ ↵ ὑπάρχειν. ὅτι δ᾽ ἀτελής, ἐκ τῆς ἀποδείξεως δῆλον· τὸν αὐτὸν γὰρ τρόπον δειχθήσεται ὅνπερ κἀπὶ τῶν πρότερον. πάλιν τὸ μὲν Α ἐνδεχέσθω παντὶ τῶι Β, τὸ δὲ Β παντὶ τῶι Γ ὑπαρχέτω ἐξ ἀνάγκης. ἔσται δὴ συλλογισμὸς ὅτι τὸ Α παντὶ τῶι Γ ἐνδέχεται ὑπάρχειν, ἀλλ᾽ οὐχ ὅτι ὑπάρχει, καὶ τέλειος, ἀλλ᾽ οὐκ ἀτελής· εὐθὺς γὰρ ἐπιτελεῖται διὰ τῶν ἐξ ἀρχῆς προτάσεων.	Quoniam igitur universalibus affirmativis existentibus terminis non fit conclusio necessaria, manifestum: insit enim A omni B ex necessitate, B autem contingat omni C, erit igitur syllogismus imperfectus, quoniam A contingit omni C inesse. Quoniam autem imperfectus, ex demonstratione palam, eodem enim modo ostendetur quo et in prioribus. Rursum A quidem contingat omni B inesse, B autem omni C insit ex necessitate, erit itaque syllogismus, quoniam A contingat omni C inesse, sed non quoniam inest, et perfectus quidem, sed non imperfectus, statim enim perficitur ex principio propositionis.	If the premisses are affirmative, clearly the conclusion which follows is not necessary. Suppose A necessarily belongs to all B, and let B be possible for all C. We shall have an imperfect syllogism to prove that A may belong to all C. That it is imperfect is clear from the proof: for it will be proved in the same manner as above. Again, let A be possible for all B, and let B necessarily belong to all C. We shall then have a syllogism to prove that A may belong to all C, not that A does belong to all C: and it is perfect, not imperfect: for it is completed directly through the original premisses.
Εἰ δὲ μὴ ὁμοιοσχήμονες αἱ προτάσεις, ἔστω πρῶτον ἡ στερητικὴ ἀναγκαία, καὶ τὸ μὲν Α μηδενὶ ἐνδεχέσθω τῶι Β ἐξ ἀνάγκης, , τὸ δὲ Β παντὶ τῶι Γ ἐνδεχέ σθω. ἀνάγκη δὴ τὸ Α μηδενὶ τῶι Γ ὑπάρχειν. κείσθω γὰρ ὑπάρχειν ἢ παντὶ ἢ τινί· τῶι δὲ Β ὑπέκειτο μηδενὶ ἐνδέχεσθαι. ἐπεὶ οὖν ἀντιστρέφει τὸ στερητικόν, οὐδὲ τὸ Β τῶι Α οὐδενὶ ἐνδέχεται· τὸ δὲ Α τῶι Γ ἢ παντὶ ἢ τινὶ κεῖται ὑπάρχειν· ὥστ᾽ οὐδενὶ ἢ οὐ παντὶ τῶι Γ τὸ Β ἐνδέχοιτ᾽ ἂν ὑπάρχειν· ὑπέκειτο δὲ παντὶ ἐξ ἀρχῆς. φανερὸν δ᾽ ὅτι καὶ τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν γίγνεται συλλογισμός, εἴπερ καὶ τοῦ μὴ ὑπάρχειν.	(0658A) Si autem non similis figurae sint propositiones, sit primum privativa necessaria, et A quidem nulli contingat B ex necessitate, B autem contingat omni C, necesse est igitur A nulli C inesse. Ponatur enim A inesse aut omni, aut alicui, positum autem est A nulli contingere B, quoniam ergo convertitur privativa, et B nulli A contingit, A autem positum est inesse C aut omni, aut alicui, quare nulli, aut non omni C continget B inesse, sed supponebatur omni ex principio. Manifestum autem quoniam et eius quod est contingere non inesse fit syllogismus, siquidem non inesse.	But if the premisses are not similar in quality, suppose first that the negative premiss is necessary, and let necessarily A not be possible for any B, but let B be possible for all C. It is necessary then that A belongs to no C. For suppose A to belong to all C or to some C. Now we assumed that A is not possible for any B. Since then the negative proposition is convertible, B is not possible for any A. But A is supposed to belong to all C or to some C. Consequently B will not be possible for any C or for all C. But it was originally laid down that B is possible for all C. And it is clear that the possibility of belonging can be inferred, since the fact of not belonging is inferred.
πάλιν ἔστω ἡ καταφατικὴ πρότασις ἀναγκαία, καὶ τὸ μὲν Α ἐνδεχέσθω μηδενὶ τῶι Β ὑπάρχειν, τὸ δὲ Β παντὶ τῶι Γ ὑπαρχέτω ἐξ ἀνάγκης. ὁ μὲν οὖν συλλογισμὸς ἔσται τέλειος, ἀλλ᾽ οὐ τοῦ μὴ ὑπάρχειν ἀλλὰ τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν· ἥ τε γὰρ πρότασις οὕτως ἐλήφθη ἡ ἀπὸ τοῦ μείζονος ἄκρου, καὶ εἰς τὸ ἀδύνατον οὐκ ἔστιν ἀγαγεῖν· εἰ γὰρ ὑποτεθείη τὸ Α τῶι Γ τινὶ ὑπάρχειν, κεῖται δὲ καὶ τῶι Β ἐνδέχεσθαι μηδενὶ ὑπάρχειν, οὐδὲν συμβαίνει διὰ τούτων ἀδύνατον.	Rursum sit affirmativa quidem propositio necessaria, et A quidem contingat nulli B inesse, B autem insit omni C ex necessitate. Ergo fit syllogismus quidem perfectus, sed non eius quod est non inesse, sed eius quod est contingere non inesse. (0658B) Nam et propositio sic sumpta est, quae ad maiorem est extremitatem, et ad impossibile non est ducere: nam si ponatur A inesse ulli C, positum est autem et A B contingere nulli inesse, nihil accidit per haec impossibile.	Again, let the affirmative premiss be necessary, and let A possibly not belong to any B, and let B necessarily belong to all C. The syllogism will be perfect, but it will establish a problematic negative, not an assertoric negative. For the major premiss was problematic, and further it is not possible to prove the assertoric conclusion per impossibile. For if it were supposed that A belongs to some C, and it is laid down that A possibly does not belong to any B, no impossible relation between B and C follows from these premisses.
ἐὰν δὲ πρὸς τῶι ἐλάττονι ἄκρωι τεθῆι τὸ στερητικόν, ὅταν μὲν ἐνδέχεσθαι σημαίνηι, συλλογισμὸς ἔσται διὰ τῆς ἀντιστροφῆς, καθάπερ ἐν τοῖς πρότερον, ὅταν δὲ μὴ ἐνδέχεσθαι, οὐκ ἔσται. οὐδ᾽ ὅταν ἄμφω μὲν τεθῆι στερητικά, μὴ ἦι δ᾽ ἐνδεχόμενον τὸ πρὸς τὸ ἔλαττον. ὅροι δ᾽ οἱ αὐτοί, τοῦ μὲν ὑπάρχειν λευκόν – ζῶιον – χιών, τοῦ δὲ μὴ ὑπάρχειν λευκόν – ζῶιον – πίττα.	Si autem ad minorem extremitatem ponatur privativum quando contingere quidem significaverit, syllogismus erit per conversionem, quemadmodum in prioribus. Quando autem non contingere, non erit ex necessitate, nec quando utraque quidem propositio privativa, non est autem contingens quod ad minorem est. Termini autem inesse quidem, album, animal, nix; non inesse quidem, album, animal, pix.	But if the minor premiss is negative, when it is problematic a syllogism is possible by conversion, as above; but when it is necessary no syllogism can be formed. Nor again when both premisses are negative, and the minor is necessary. The same terms as before serve both for the positive relation-white-animal-snow, and for the negative relation-white-animal-pitch.
Τὸν αὐτὸν δὲ τρόπον ἕξει κἀπὶ τῶν ἐν μέρει συλλογισμῶν. ὅταν μὲν γὰρ ἦι τὸ στερητικὸν ἀναγκαῖον, καὶ τὸ συμπέρασμα ἔσται τοῦ μὴ ὑπάρχειν. οἷον εἰ τὸ μὲν Α μηδενὶ τῶι Β ἐνδέχεται ὑπάρ χειν, τὸ δὲ Β τινὶ τῶι Γ ἐνδέχεται ὑπάρχειν, ἀνάγκη τὸ Α τινὶ τῶι Γ μὴ ὑπάρχειν. εἰ γὰρ παντὶ ὑπάρχει, τῶι δὲ Β μηδενὶ ἐνδέχεται, οὐδὲ τὸ Β οὐδενὶ τῶι Α ἐνδέχεται ὑπάρχειν. ὥστ᾽ εἰ τὸ Α παντὶ τῶι Γ ὑπάρχει, οὐδενὶ τῶι Γ τὸ Β ἐνδέχεται. ἀλλ᾽ ὑπέκειτό τινι ἐνδέχεσθαι. ὅταν δὲ τὸ ἐν μέρει καταφατικὸν ἀναγκαῖον ἦι, τὸ ἐν τῶι στερητικῶι συλλογισμῶι, οἷον τὸ Β Γ, ἢ τὸ κα ↵ θόλου τὸ ἐν τῶι κατηγορικῶι, οἷον τὸ Α Β, οὐκ ἔσται τοῦ ὑπάρχειν συλλογισμός. ἀπόδειξις δ᾽ ἡ αὐτὴ ἣ καὶ ἐπὶ τῶν πρότερον. ἐὰν δὲ τὸ μὲν καθόλου τεθῆι πρὸς τὸ ἔλαττον ἄκρον, ἢ καταφατικὸν ἢ στερητικόν, ἐνδεχόμενον, τὸ δ᾽ ἐν μέρει ἀναγ καῖον [πρὸς τῶι μείζονι ἄκρωι], οὐκ ἔσται συλλογισμός	Eodem autem modo se habebit, et in particularibus syllogismis. (0658C) Quando enim fuerit privativa necessaria, et conclusio erit eius quod est non inesse, ut si A quidem nulli B contingit inesse ex necessitate, B autem alicui C contingat inesse, necesse est A alicui eorum quae sunt C non inesse. Si enim A omni C inest, nulli autem contingit B, et B nulli A contingit inesse: quare si omni C inest A, nulli C contingit B, sed positum erat alicui contingere. Quando autem particularis affirmativa necessaria fuerit, quae in privativo est syllogismo, ut B C, aut universalis in affirmativo, ut A B, non erit inesse syllogismus. Demonstratio autem eadem quae in prioribus. Si autem universale quidem ponatur ad minorem extremitatem vel affirmativum vel privativum contingens, particulare autem necessarium, non erit syllogismus.	The same relation will obtain in particular syllogisms. Whenever the negative proposition is necessary, the conclusion will be negative assertoric: e.g. if it is not possible that A should belong to any B, but B may belong to some of the Cs, it is necessary that A should not belong to some of the Cs. For if A belongs to all C, but cannot belong to any B, neither can B belong to any A. So if A belongs to all C, to none of the Cs can B belong. But it was laid down that B may belong to some C. But when the particular affirmative in the negative syllogism, e.g. BC the minor premiss, or the universal proposition in the affirmative syllogism, e.g. AB the major premiss, is necessary, there will not be an assertoric conclusion. The demonstration is the same as before. But if the minor premiss is universal, and problematic, whether affirmative or negative, and the major premiss is particular and necessary, there cannot be a syllogism.
(ὅροι δὲ τοῦ μὲν ὑπάρχειν ἐξ ἀνάγκης ζῶιον – λευκόν – ἄνθρωπος, τοῦ δὲ μὴ ἐνδέχεσθαι ζῶιον – λευκόν – ἱμάτιον)· ὅταν δ᾽ ἀναγκαῖον ἦι τὸ καθόλου, τὸ δ᾽ ἐν μέρει ἐνδεχόμενον, στερητικοῦ μὲν ὄντος τοῦ καθόλου τοῦ μὲν ὑπάρχειν ὅροι ζῶιον – λευκόν – κόραξ, τοῦ δὲ μὴ ὑπάρχειν ζῶιον – λευκόν – πίττα, καταφατικοῦ δὲ τοῦ μὲν ὑπάρχειν ζῶιον – λευκόν – κύκνος, τοῦ δὲ μὴ ἐνδέχεσθαι ζῶιον – λευκόν – χιών.	Termini autem inesse quidem ex necessitate, animal, album, homo; non contingere autem, animal, album, tunica. (0658D) Quando similiter universale quidem est necessarium, particulare autem contingens, cum privativum quidem est universale, inesse quidem termini, animal, album, corvus; non inesse, animal, album, pix. Cum autem affirmativum, inesse quidem, animal, album, cygnus; non contingere autem, animal, album, nix.	Premisses of this kind are possible both where the relation is positive and necessary, e.g. animal-white-man, and where it is necessary and negative, e.g. animal-white-garment. But when the universal is necessary, the particular problematic, if the universal is negative we may take the terms animal-white-raven to illustrate the positive relation, or animal-white-pitch to illustrate the negative; and if the universal is affirmative we may take the terms animal-white-swan to illustrate the positive relation, and animal-white-snow to illustrate the negative and necessary relation.
οὐδ᾽ ὅταν ἀδιόριστοι ληφθῶσιν αἱ προτάσεις ἢ ἀμφότεραι κατὰ μέρος, οὐδ᾽ οὕτως ἔσται συλλογισμός. ὅροι δὲ κοινοὶ τοῦ μὲν ὑπάρχειν ζῶιον – λευκόν – ἄνθρωπος, τοῦ δὲ μὴ ὑπάρχειν ζῶιον – λευκόν – ἄψυχον. καὶ γὰρ τὸ ζῶιον τινὶ λευκῶι καὶ τὸ λευκὸν ἀψύχωι τινὶ καὶ ἀναγκαῖον ὑπάρ- χειν καὶ οὐκ ἐνδέχεται ὑπάρχειν. κἀπὶ τοῦ ἐνδέχεσθαι ὁμοίως, ὥστε πρὸς ἅπαντα χρήσιμοι οἱ ὅροι.	Nec quando indefinitae sumuntur propositiones, aut utraeque particulares, non sic erit syllogismus. Termini autem communes, inesse quidem, animal, album, homo; non inesse autem, animal, album, inanimatum. Nam et animal alicui albo, et album inanimato alicui est necessarium inesse, et non contingit inesse, et in contingenti similiter, quare ad omnia utiles sunt termini.	Nor again is a syllogism possible when the premisses are indefinite, or both particular. Terms applicable in either case to illustrate the positive relation are animal-white-man: to illustrate the negative, animal-white-inanimate. For the relation of animal to some white, and of white to some inanimate, is both necessary and positive and necessary and negative. Similarly if the relation is problematic: so the terms may be used for all cases.
Φανερὸν οὖν ἐκ τῶν εἰρημένων ὅτι ὁμοίως ἐχόντων τῶν ὅρων ἔν τε τῶι ὑπάρχειν καὶ ἐν τοῖς ἀναγκαίοις γίνεταί τε καὶ οὐ γίνεται συλλογισμός, πλὴν κατὰ μὲν τὸ ὑπάρχειν τιθεμένης τῆς στερητικῆς προτάσεως τοῦ ἐνδέχεσθαι ἦν ὁ συλλογισμός, κατὰ δὲ τὸ ἀναγκαῖον τῆς στερητικῆς καὶ τοῦ ἐνδέχεσθαι καὶ τοῦ μὴ ὑπάρχειν. [δῆλον δὲ καὶ ὅτι πάντες ἀτελεῖς οἱ συλ λογισμοὶ καὶ ὅτι τελειοῦνται διὰ τῶν προειρημένων σχημάτων.]	(0659A) Manifestum ergo ex iis quae dicta sunt, quoniam similiter habentibus se terminis, et in eo quod est inesse, et in necessariis, et fit, et non fit syllogismus, verumtamen secundum inesse quidem posita privativa propositione, eius quod est contingere erat syllogismus, secundum necessarium autem privativa, et contingere, et non inesse. Palam autem et quoniam omnes imperfecti syllogismi, et quomodo perficiuntur per praedictas figuras.	Clearly then from what has been said a syllogism results or not from similar relations of the terms whether we are dealing with simple existence or necessity, with this exception, that if the negative premiss is assertoric the conclusion is problematic, but if the negative premiss is necessary the conclusion is both problematic and negative assertoric. [It is clear also that all the syllogisms are imperfect and are perfected by means of the figures above mentioned.]