Authors/Aristotle/priora/Liber 1/C22

Chapter 22

Greek	Latin	English
	(PL 64 0664A) CAPUT XXI/ XXII.Mixtio necessarii et contingentis in tertia figura.	22
40a4 Εἰ δ᾽ ἐστὶν ἡ μὲν ἀναγκαία τῶν προτάσεων ἡ δ᾽ ἐν δεχομένη, κατηγορικῶν μὲν ὄντων τῶν ὅρων ἀεὶ τοῦ ἐνδέχεσθαι ἔσται συλλογισμός, ὅταν δ᾽ ἦι τὸ μὲν κατηγορικὸν τὸ δὲ στερητικόν, ἐὰν μὲν ἦι τὸ καταφατικὸν ἀναγκαῖον, τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν, ἐὰν δὲ τὸ στερητικόν, καὶ τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν καὶ τοῦ μὴ ὑπάρχειν. τοῦ δ᾽ ἐξ ἀνάγ κης μὴ ὑπάρχειν οὐκ ἔσται συλλογισμός, ὥσπερ οὐδ᾽ ἐν τοῖς ἑτέροις σχήμασιν.	Si autem est haec quidem propositionum necessaria, illa vero contingens, si praedicativi quidem sunt termini, semper eius quod est contingere erit syllogismus. (0664B) Quando autem fuerit hic quidem praedicativus, ille autem privativus, si sit affirmativus quidem necessarius, eius erit quod est contingere non inesse, si autem privativus, et eius quod est contingere non inesse, et eius quod est non inesse; eius autem quod est ex necessitate non inesse non erit syllogismus, quemadmodum et in aliis figuris.	If one of the premisses is necessary, the other problematic, when the premisses are affirmative a problematic affirmative conclusion can always be drawn; when one proposition is affirmative, the other negative, if the affirmative is necessary a problematic negative can be inferred; but if the negative proposition is necessary both a problematic and a pure negative conclusion are possible. But a necessary negative conclusion will not be possible, any more than in the other figures.
Ἔστωσαν δὴ κατηγορικοὶ πρῶτον οἱ ὅροι, καὶ τὸ μὲν Α παντὶ τῶι Γ ὑπαρχέτω ἐξ ἀνάγκης, τὸ δὲ Β παντὶ ἐνδεχέσθω ὑπάρχειν. ἐπεὶ οὖν τὸ μὲν Α παντὶ τῶι Γ ἀνάγκη, τὸ δὲ Γ τινὶ τῶι Β ἐνδέχεται, καὶ τὸ Α τινὶ τῶι Β ἐνδεχόμενον ἔσται καὶ οὐχ ὑπάρχον· οὕτω γὰρ συνέπιπτεν ἐπὶ τοῦ πρώτου σχήματος. ὁμοίως δὲ δειχθήσεται καὶ εἰ τὸ μὲν Β Γ τεθείη ἀναγκαῖον, τὸ δὲ Α Γ ἐνδεχόμενον.	Sint ergo praedicativi termini primum, et A C quidem omni insit ex necessitate, B autem omni C contingat inesse, quoniam ergo A omni C necessario inest, C autem alicui B contingit, et A alicui B contingens erit, et non inerit, sic enim accidit in prima figura. Similiter autem ostendetur, et si B C quidem ponatur necessaria, A C autem contingens.	Suppose first that the premisses are affirmative, i.e. that A necessarily belongs to all C, and B may possibly belong to all C. Since then A must belong to all C, and C may belong to some B, it follows that A may (not does) belong to some B: for so it resulted in the first figure. A similar proof may be given if the proposition BC is necessary, and AC is problematic.
πάλιν ἔστω τὸ μὲν κατηγορικὸν τὸ δὲ στερητικόν, ἀναγκαῖον δὲ τὸ κατηγορικόν· καὶ τὸ μὲν Α ἐνδεχέσθω μη δενὶ τῶι Γ ὑπάρχειν, τὸ δὲ Β παντὶ ὑπαρχέτω ἐξ ἀνάγκης. ἔσται δὴ πάλιν τὸ πρῶτον σχῆμα· καὶ γὰρ ἡ στερητικὴ πρότασις ἐνδέχεσθαι σημαίνει· φανερὸν οὖν ὅτι τὸ συμπέρασμα ἔσται ἐνδεχόμενον· ὅτε γὰρ οὕτως ἔχοιεν αἱ προτάσεις ἐν τῶι πρώτωι σχήματι, καὶ τὸ συμπέρασμα ἦν ἐνδεχόμενον. εἰ δ᾽ ἡ στερητικὴ πρότασις ἀναγκαία, τὸ συμπέρασμα ἔσται καὶ ὅτι ἐνδέχεται τινὶ μὴ ὑπάρχειν καὶ ὅτι οὐχ ὑπάρχει.	Rursum sit hoc quidem praedicativum, illud vero privativum, necessarium autem praedicativum, et A quidem contingat nulli C inesse, B autem omni insit ex necessitate C, erit ergo rursum prima figura, et conclusio contingens, sed non inesse. Nam privativa propositio contingere significat. (0664C) Manifestum est igitur quoniam conclusio erit contingens; cum enim sic se habebant propositiones in prima figura, et conclusio erat contingens. Si autem privativa sit propositio necessaria, et conclusio erit, quoniam contingit alicui non inesse, et quoniam non inesse.	Again suppose one proposition is affirmative, the other negative, the affirmative being necessary: i.e. suppose A may possibly belong to no C, but B necessarily belongs to all C. We shall have the first figure once more: and-since the negative premiss is problematic-it is clear that the conclusion will be problematic: for when the premisses stand thus in the first figure, the conclusion (as we found) is problematic. But if the negative premiss is necessary, the conclusion will be not only that A may possibly not belong to some B but also that it does not belong to some B.
κείσθω γὰρ τὸ Α τῶι Γ μὴ ὑπάρχειν ἐξ ἀνάγκης, τὸ δὲ Β παντὶ ἐνδέχεσθαι. ἀντιστραφέντος οὖν τοῦ Β Γ καταφατικοῦ τὸ πρῶτον ἔσται σχῆμα, καὶ ἀναγκαία ἡ στερητικὴ πρότασις. ὅτε δ᾽ οὕτως ἔχοιεν αἱ προτάσεις, συνέβαινε τὸ Α τῶι Γ καὶ ἐνδέχεσθαι τινὶ μὴ ὑπάρχειν καὶ μὴ ὑπάρχειν, ὥστε καὶ τὸ Α τῶι Β ἀνάγκη τινὶ μὴ ὑπάρχειν. ὅταν δὲ τὸ στερητικὸν τεθῆι πρὸς τὸ ἔλαττον ἄκρον, ἐὰν μὲν ἐνδεχόμενον, ἔσται συλλογισμὸς μεταληφθείσης τῆς προτά σεως, καθάπερ ἐν τοῖς πρότερον, ἐὰν δ᾽ ἀναγκαῖον, οὐκ ἔσται· καὶ γὰρ παντὶ ἀνάγκη καὶ οὐδενὶ ἐνδέχεται ὑπάρχειν. ὅροι τοῦ παντὶ ὑπάρχειν ὕπνος – ἵππος καθεύδων – ἄνθρωπος, τοῦ μηδενὶ ὕπνος – ἵππος ἐγρηγορώς – ἄνθρωπος.	Ponatur enim A non inesse C, ex necessitate, B autem omni C contingere, conversa ergo B C affirmativa, prima erit figura, et necessaria privativa propositio. Cum autem sic se habebant propositiones, accidebat A et contingere alicui C non inesse, et non inesse, quare et A necesse est alicui B non inesse. Quando autem privativum ponitur ad minorem extremitatem, si contingens quidem, erit syllogismus transsumpta propositione, quemadmodum! et in prioribus. Si autem necessarium, non erit. (0664D) Etenim necesse est omni et nulli contingat inesse. Termini omni inesse, somnus, equus, dormiens homo. Nulli inesse, somnus, equus, vigilans homo.	For suppose that A necessarily does not belong to C, but B may belong to all C. If the affirmative proposition BC is converted, we shall have the first figure, and the negative premiss is necessary. But when the premisses stood thus, it resulted that A might possibly not belong to some C, and that it did not belong to some C; consequently here it follows that A does not belong to some B. But when the minor premiss is negative, if it is problematic we shall have a syllogism by altering the premiss into its complementary affirmative, as before; but if it is necessary no syllogism can be formed. For A sometimes necessarily belongs to all B, and sometimes cannot possibly belong to any B. To illustrate the former take the terms sleep-sleeping horse-man; to illustrate the latter take the terms sleep-waking horse-man.
Ὁμοίως δ᾽ ἕξει καὶ εἰ ὁ μὲν καθόλου τῶν ὅρων ὁ δ᾽ ἐν μέρει πρὸς τὸ μέσον· κατηγορικῶν μὲν γὰρ ὄντων ἀμ ↵ φοτέρων τοῦ ἐνδέχεσθαι καὶ οὐ τοῦ ὑπάρχειν ἔσται συλλογισμός, καὶ ὅταν τὸ μὲν στερητικὸν ληφθῆι τὸ δὲ καταφατικόν, ἀναγκαῖον δὲ τὸ καταφατικόν. ὅταν δὲ τὸ στερητικὸν ἀναγκαῖον, καὶ τὸ συμπέρασμα ἔσται τοῦ μὴ ὑπάρχειν· ὁ γὰρ αὐτὸς τρόπος ἔσται τῆς δείξεως καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων ὄντων.	Similiter autem se habebit, et si hic quidem terminorum sit universalis, ille autem particularis ad medium, nam si utrique sint praedicativi, eius quod est contingere, et non eius quod est inesse erit syllogismus. Et quando hoc quidem privativum sumetur, illud vero affirmativum, necessarium autem affirmativum, huius quod est contingere. Quando autem privativum necessarium, et conclusio erit quod est non inesse, nam idem modus erit demonstrationis, et cum universales et non universales sunt termini.	Similar results will obtain if one of the terms is related universally to the middle, the other in part. If both premisses are affirmative, the conclusion will be problematic, not pure; and also when one premiss is negative, the other affirmative, the latter being necessary. But when the negative premiss is necessary, the conclusion also will be a pure negative proposition; for the same kind of proof can be given whether the terms are universal or not.
ἀνάγκη γὰρ διὰ τοῦ πρώτου σχήματος τελειοῦσθαι τοὺς συλλογισμούς, ὥστε καθάπερ ἐν ἐκείνοις, καὶ ἐπὶ τούτων ἀναγκαῖον συμπίπτειν. ὅταν δὲ τὸ στερητικὸν καθόλου ληφθὲν τεθῆι πρὸς τὸ ἔλαττον ἄκρον, ἐὰν μὲν ἐν δεχόμενον, ἔσται συλλογισμὸς διὰ τῆς ἀντιστροφῆς, ἐὰν δ᾽ ἀναγκαῖον, οὐκ ἔσται. δειχθήσεται δὲ τὸν αὐτὸν τρόπον ὃν καὶ ἐν τοῖς καθόλου, καὶ διὰ τῶν αὐτῶν ὅρων.	(0665A) Necesse est enim per primam figuram perfici syllogismos, quare ut in illis, et in his necessarium accidere. Quando autem privativum universaliter sumptum ponitur ad minorem extremitatem, si contingens quidem, erit syllogismus per conversionem, si autem necessarium sit, non erit, ostendetur autem eodem modo quo et in universalibus, et per eosdem terminos.	For the syllogisms must be made perfect by means of the first figure, so that a result which follows in the first figure follows also in the third. But when the minor premiss is negative and universal, if it is problematic a syllogism can be formed by means of conversion; but if it is necessary a syllogism is not possible. The proof will follow the same course as where the premisses are universal; and the same terms may be used.
φανερὸν οὖν καὶ ἐν τούτωι τῶι σχήματι πότε καὶ πῶς ἔσται συλλογισμός, καὶ πότε τοῦ ἐνδέχεσθαι καὶ πότε τοῦ ὑπάρχειν. δῆλον δὲ καὶ ὅτι πάντες ἀτελεῖς, καὶ ὅτι τελειοῦνται διὰ τοῦ πρώτου σχήματος.	Manifestum ergo et in hac figura quando et quomodo erit syllogismus, et quando eius quod est contingere, et quando eius quod est inesse. Palam autem et quoniam omnes imperfecti, et quoniam perficiuntur per primam figuram.	It is clear then in this figure also when and how a syllogism can be formed, and when the conclusion is problematic, and when it is pure. It is evident also that all syllogisms in this figure are imperfect, and that they are made perfect by means of the first figure.