Authors/Aristotle/priora/Liber 1/C18

Chapter 18

Greek	Latin	English
	(PL 64 0660C) CAPUT XVII/ XVIII. Mixtio absoluti et contingentis in secunda figura	18
37b19 Εἰ δ᾽ ἡ μὲν ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι σημαίνει, τῆς μὲν κατηγορικῆς ὑπάρχειν τεθείσης τῆς δὲ στερητικῆς ἐνδέχεσθαι οὐδέποτ᾽ ἔσται συλλογισμός, οὔτε καθόλου τῶν ὅρων οὔτ᾽ ἐν μέρει λαμβανομένων (ἀπόδειξις δ᾽ ἡ αὐτὴ καὶ διὰ τῶν αὐτῶν ὅρων)· ὅταν δ᾽ ἡ μὲν καταφατικὴ ἐνδέχεσθαι ἡ δὲ στερητικὴ ὑπάρχειν, ἔσται συλλογισμός. εἰλήφθω γὰρ τὸ Α τῶι μὲν Β μηδενὶ ὑπάρχειν, τῶι δὲ Γ παντὶ ἐνδέχεσθαι. ἀντιστραφέντος οὖν τοῦ στερητικοῦ τὸ Β τῶι Α οὐδενὶ ὑπάρξει· τὸ δὲ Α παντὶ τῶι Γ ἐνεδέχετο· γίνεται δὴ συλλογισμὸς ὅτι ἐνδέχεται τὸ Β μηδενὶ τῶι Γ διὰ τοῦ πρώτου σχήματος. ὁμοίως δὲ καὶ εἰ πρὸς τῶι Γ τεθείη τὸ στερητικόν.	Si autem altera quidem inesse, altera vero contingere significat, praedicativa quidem inesse posita, privativa vero contingere, nunquam erit syllogismus, sive universaliter, sive particulariter sumantur termini, demonstratio autem eadem, et per eosdem terminos. Quando autem affirmativa quidem contingere, privativa inesse, erit syllogismus. (0660D) Sumatur enim A B quidem nulli inesse, C vero omnia contingere, conversa ergo privativa, B inest nulli A, A autem omni C contingebat, fit ergo syllogismus, quoniam B contingit nulli C, per primam figuram. Similiter autem et si ad C ponatur privativa.	But if one premiss is assertoric, the other problematic, if the affirmative is assertoric and the negative problematic no syllogism will be possible, whether the premisses are universal or particular. The proof is the same as above, and by means of the same terms. But when the affirmative premiss is problematic, and the negative assertoric, we shall have a syllogism. Suppose A belongs to no B, but can belong to all C. If the negative proposition is converted, B will belong to no A. But ex hypothesi can belong to all C: so a syllogism is made, proving by means of the first figure that B may belong to no C. Similarly also if the minor premiss is negative.
ἐὰν δ᾽ ἀμ φότεραι μὲν ὦσι στερητικαί, σημαίνηι δ᾽ ἡ μὲν μὴ ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι, δι᾽ αὐτῶν μὲν τῶν εἰλημμένων οὐδὲν συμβαίνει ἀναγκαῖον, ἀντιστραφείσης δὲ τῆς κατὰ τὸ ἐνδέχεσθαι προτάσεως γίγνεται συλλογισμὸς ὅτι τὸ Β τῶι Γ ἐνδέχεται μηδενὶ ὑπάρχειν, καθάπερ ἐν τοῖς πρότερον· ἔσται γὰρ πάλιν τὸ πρῶτον σχῆμα. ἐὰν δ᾽ ἀμφότεραι τεθῶσι κατηγορικαί, οὐκ ἔσται συλλογισμός. ὅροι τοῦ μὲν ὑπάρχειν ὑγίεια – ζῶιον – ἄνθρωπος, τοῦ δὲ μὴ ὑπάρχειν ὑγίεια – ἵππος – ἄνθρωπος.	Si autem utraeque sint privativae, significet autem haec quidem non inesse, illa vero contingere non inesse, per ea quidem quae sumpta sunt nihil accidit necessarium, conversa autem secundum contingere propositione fit syllogismus, quoniam B contingit nulli C inesse, quemadmodum in prioribus, erit enim rursum prima figura. Si autem utraeque ponantur praedicativae, non erit syllogismus. Termini quidem inesse sanitas, equus, homo.	But if both premisses are negative, one being assertoric, the other problematic, nothing follows necessarily from these premisses as they stand, but if the problematic premiss is converted into its complementary affirmative a syllogism is formed to prove that B may belong to no C, as before: for we shall again have the first figure. But if both premisses are affirmative, no syllogism will be possible. This arrangement of terms is possible both when the relation is positive, e.g. health, animal, man, and when it is negative, e.g. health, horse, man.
Τὸν αὐτὸν δὲ τρόπον ἕξει κἀπὶ τῶν ἐν μέρει συλλογισμῶν. ὅταν μὲν γὰρ ἦι τὸ καταφατικὸν ὑπάρχον, εἴτε κα ↵ θόλου εἴτ᾽ ἐν μέρει ληφθέν, οὐδεὶς ἔσται συλλογισμός (τοῦτο δ᾽ ὁμοίως καὶ διὰ τῶν αὐτῶν ὅρων δείκνυται τοῖς πρότερον), ὅταν δὲ τὸ στερητικόν, ἔσται διὰ τῆς ἀντιστροφῆς, καθάπερ ἐν τοῖς πρότερον.	Eodem autem modo se habebit et in particularibus syllogismis. (0661A) Quando autem erit affirmativa inesse, sive universaliter, sive particulariter sumpta, nullus erit syllogismus; hoc autem similiter, et per eosdem terminos demonstratur, quibus et prius. Quando autem et privativa, erit per conversionem, quemadmodum in prioribus.	The same will hold good if the syllogisms are particular. Whenever the affirmative proposition is assertoric, whether universal or particular, no syllogism is possible (this is proved similarly and by the same examples as above), but when the negative proposition is assertoric, a conclusion can be drawn by means of conversion, as before.
πάλιν ἐὰν ἄμφω μὲν τὰ διαστήματα στερη τικὰ ληφθῆι, καθόλου δὲ τὸ μὴ ὑπάρχειν, ἐξ αὐτῶν μὲν τῶν προτάσεων οὐκ ἔσται τὸ ἀναγκαῖον, ἀντιστραφέντος δὲ τοῦ ἐνδέχεσθαι καθάπερ ἐν τοῖς πρότερον ἔσται συλλογισμός. ἐὰν δὲ ὑπάρχον μὲν ἦι τὸ στερητικόν, ἐν μέρει δὲ ληφθῆι, οὐκ ἔσται συλλογισμός, οὔτε καταφατικῆς οὔτε στερητικῆς οὔσης τῆς ἑτέρας προτάσεως. οὐδ᾽ ὅταν ἀμφότεραι ληφθῶσιν ἀδιόριστοι – ἢ καταφατικαὶ ἢ ἀποφατικαί – ἢ κατὰ μέρος. ἀπόδειξις δ᾽ ἡ αὐτὴ καὶ διὰ τῶν αὐτῶν ὅρων.	Rursum si ambo quidem intervalla privativa sumantur, universaliter autem quod non inesse, ex ipsis quidem propositionibus non erit necessarium, conversa autem contingenti sicut in prioribus, erit syllogismus. Si autem inesse quidem sit privativa, particulariter quidem sumpta, non erit syllogismus, neque praedicativa, neque privativa existente altera propositione. Nec quando utraeque ponuntur indefinitae, vel affirmativae, vel negativae, aut particulares; demonstratio autem eadem et per eosdem terminos.	Again if both the relations are negative, and the assertoric proposition is universal, although no conclusion follows from the actual premisses, a syllogism can be obtained by converting the problematic premiss into its complementary affirmative as before. But if the negative proposition is assertoric, but particular, no syllogism is possible, whether the other premiss is affirmative or negative. Nor can a conclusion be drawn when both premisses are indefinite, whether affirmative or negative, or particular. The proof is the same and by the same terms.