Authors/Aristotle/priora/Liber 2/C22

Chapter 22

Greek	Latin	English
	(PL 64 0707C) CAPUT XXII. De conversionibus terminorum.	22
67b27 Ὅταν δ᾽ ἀντιστρέφηι τὰ ἄκρα, ἀνάγκη καὶ τὸ μέσον ἀντιστρέφειν πρὸς ἄμφω. εἰ γὰρ τὸ Α κατὰ τοῦ Γ διὰ τοῦ Β ὑπάρχει, εἰ ἀντιστρέφει καὶ ὑπάρχει, ὧι τὸ Α, παντὶ τὸ Γ, καὶ τὸ Β τῶι Α ἀντιστρέψει καὶ ὑπάρξει, ὧι τὸ Α, παντὶ τὸ Β διὰ μέσου τοῦ Γ· καὶ τὸ Γ τῶι Β ἀντιστρέψει διὰ μέσου τοῦ Α. καὶ ἐπὶ τοῦ μὴ ὑπάρχειν ὡσαύτως, οἷον εἰ τὸ Β τῶι Γ ὑπάρχει, τῶι δὲ Β τὸ Α οὐχ ὑπάρχει, οὐδὲ τὸ Α τῶι Γ οὐχ ὑπάρξει. εἰ δὴ τὸ Β τῶι Α ἀντιστρέφει, καὶ τὸ Γ τῶι Α ἀντιστρέψει. ἔστω γὰρ τὸ Β μὴ ὑπάρχον τῶι Α· οὐδ᾽ ἄρα τὸ Γ· παντὶ γὰρ τῶι Γ τὸ Β ὑπῆρχεν. καὶ εἰ τῶι Β τὸ Γ ἀντιστρέφει, καὶ τὸ Α ἀντιστρέψει· καθ᾽ οὗ γὰρ ἅπαντος τὸ Β, καὶ τὸ Γ. καὶ εἰ τὸ Γ καὶ› πρὸς τὸ Α ἀντιστρέφει, καὶ τὸ Β ἀντιστρέψει. ὧι γὰρ τὸ Β, ↵ τὸ Γ· ὧι δὲ τὸ Α, τὸ Γ οὐχ ὑπάρχει. καὶ μόνον τοῦτο ἀπὸ τοῦ συμπεράσματος ἄρχεται, τὰ δ᾽ ἄλλα οὐχ ὁμοίως καὶ ἐπὶ τοῦ κατηγορικοῦ συλλογισμοῦ.	Quando vero convertuntur extremitates, necesse est et medium converti ad utramque; si enim A de C per B est, si convertitur et inest cui A omni, C et B A convertitur, et inest cui A omni, B per medium C, et C B convertitur per medium A. Et in non esse itidem, ut si B inest C, A vero non inest B, neque A inerit C. (0707D) Si ergo B convertatur ad A, et C ad A convertetur: sit enim B nulli A inexistens, ergo neque C, omni enim C inerat B, et si B convertitur ad C, et A convertetur ad C; nam de quocunque omnino B, et C. Et si C ad A convertitur, et B convertetur ad A: cui enim B inest, et C; cui autem C, A non inest; et solum hoc A conclusione incipit, alia autem non similiter, ut in praedicativo syllogismo.	Whenever the extremes are convertible it is necessary that the middle should be convertible with both. For if A belongs to C through B, then if A and C are convertible and C belongs everything to which A belongs, B is convertible with A, and B belongs to everything to which A belongs, through C as middle, and C is convertible with B through A as middle. Similarly if the conclusion is negative, e.g. if B belongs to C, but A does not belong to B, neither will A belong to C. If then B is convertible with A, C will be convertible with A. Suppose B does not belong to A; neither then will C: for ex hypothesi B belonged to all C. And if C is convertible with B, B is convertible also with A, for C is said of that of all of which B is said. And if C is convertible in relation to A and to B, B also is convertible in relation to A. For C belongs to that to which B belongs: but C does not belong to that to which A belongs. And this alone starts from the conclusion; the preceding moods do not do so as in the affirmative syllogism.
Πάλιν εἰ τὸ Α καὶ τὸ Β ἀντιστρέφει, καὶ τὸ Γ καὶ τὸ Δ ὡσαύτως, ἅπαντι δ᾽ ἀνάγκη τὸ Α ἢ τὸ Γ ὑπάρχειν, καὶ τὸ Β καὶ Δ οὕτως ἕξει ὥστε παντὶ θάτερον ὑπάρχειν. ἐπεὶ γὰρ ὧι τὸ Α, τὸ Β, καὶ ὧι τὸ Γ, τὸ Δ, παντὶ δὲ τὸ Α ἢ τὸ Γ καὶ οὐχ ἅμα, φανερὸν ὅτι καὶ τὸ Β ἢ τὸ Δ παντὶ καὶ οὐχ ἅμα [οἷον εἰ τὸἀγένητον ἄφθαρτον καὶ τὸ ἄφθαρτον ἀγένητον, ἀνάγκη τὸγένομενον φθαρτὸν καὶ τὸ φθαρτὸν γεγονέναι]· δύο γὰρ συλλογισμοὶ σύγκεινται.	(0708A) Rursum si A et B convertuntur, et C et D similiter, omni autem necesse est A aut C inesse, et B et D sic se habebunt, ut omni alterum insit; quoniam enim cui A B, E cui C D, omni autem A aut C, et non simul, manifestum quoniam et B aut D omni, et non simul, ut si ingenitum, incorruptibile, et incorruptibile ingenitum, necesse est quod factum est corruptibile et corruptibile factum esse, duo enim syllogismi constituti sunt.	Again if A and B are convertible, and similarly C and D, and if A or C must belong to anything whatever, then B and D will be such that one or other belongs to anything whatever. For since B belongs to that to which A belongs, and D belongs to that to which C belongs, and since A or C belongs to everything, but not together, it is clear that B or D belongs to everything, but not together. For example if that which is uncreated is incorruptible and that which is incorruptible is uncreated, it is necessary that what is created should be corruptible and what is corruptible should have been created. For two syllogisms have been put together.
πάλιν εἰ παντὶ μὲν τὸ Α ἢ τὸ Β καὶ τὸ Γ ἢ τὸ Δ, ἅμα δὲ μὴ ὑπάρχει, εἰ ἀντιστρέφει τὸ Α καὶ τὸ Γ, καὶ τὸ Β καὶ τὸ Δ ἀντιστρέφει. εἰ γὰρ τινὶ μὴ ὑπάρχει τὸ Β, ὧι τὸ Δ, δῆλον ὅτι τὸ Α ὑπάρχει. εἰ δὲ τὸ Α, καὶ τὸ Γ· ἀντιστρέφει γάρ. ὥστε ἅμα τὸ Γ καὶ τὸ Δ. τοῦτο δ᾽ ἀδύνατον. οἷον εἰ τὸ ἀγένητον ἄφθαρτον καὶ τὸ ἄφθαρτον ἀγένητον, ἀνάγκη τὸ γενόμενον φθαρτὸν καὶ τὸ φθαρτὸν γεγονέναι›. Ὅταν δὲ τὸ Α ὅλωι τῶι Β καὶ τῶι Γ ὑπάρχηι καὶ μηδενὸς ἄλλου κατηγορῆται, ὑπάρχηι δὲ καὶ τὸ Β παντὶ τῶι Γ, ἀνάγκη τὸ Α καὶ Β ἀντιστρέφειν· ἐπεὶ γὰρ κατὰ μόνων τῶν Β Γ λέγεται τὸ Α, κατηγορεῖται δὲ τὸ Β καὶ αὐτὸ αὑτοῦ καὶ τοῦ Γ, φανερὸν ὅτι καθ᾽ ὧν τὸ Α, καὶ τὸ Β λεχθήσεται πάντων πλὴν αὐτοῦ τοῦ Α. πάλιν ὅταν τὸ Α καὶ τὸ Β ὅλωι τῶι Γ ὑπάρχηι, ἀντιστρέφηι δὲ τὸ Γ τῶι Β, ἀνάγκη τὸ Α παντὶ τῶι Β ὑπάρχειν· ἐπεὶ γὰρ παντὶ τῶι Γ τὸ Α, τὸ δὲ Γ τῶι Β διὰ τὸ ἀντιστρέφειν, καὶ τὸ Α παντὶ τῶι Β ὑπάρξει.	Rursum si omni quidem, A vel B, et C vel D, simul autem non insunt, si convertitur A et C, et B et D convertetur. Nam si alicui non inest B, cui D, palam quoniam A inest; si autem A, et C, convertuntur enim; quare simul C et D, hoc autem impossibile. Quando autem A toti B et C inest, et de nullo alio praedicatur, inest autem et B omni C, necesse est A et B converti, quoniam enim de solis B C dicitur A, praedicatur autem B et idem dese et de C, manifestum quoniam de quibus A, et B dicetur omnibus, verum et de A. Rursum quando A et B, toti C insunt convertitur autem C B, necesse est A omni B inesse, quoniam enim omni C A, C autem B, eo quod convertuntur, et A omni B inerit. (0708B)	Again if A or B belongs to everything and if C or D belongs to everything, but they cannot belong together, then when A and C are convertible B and D are convertible. For if B does not belong to something to which D belongs, it is clear that A belongs to it. But if A then C: for they are convertible. Therefore C and D belong together. But this is impossible. When A belongs to the whole of B and to C and is affirmed of nothing else, and B also belongs to all C, it is necessary that A and B should be convertible: for since A is said of B and C only, and B is affirmed both of itself and of C, it is clear that B will be said of everything of which A is said, except A itself. Again when A and B belong to the whole of C, and C is convertible with B, it is necessary that A should belong to all B: for since A belongs to all C, and C to B by conversion, A will belong to all B.
Ὅταν δὲ δυοῖν ὄντοιν τὸ Α τοῦ Β αἱρετώτερον ἦι, ὄντων ἀντικειμένων, καὶ τὸ Δ τοῦ Γ ὡσαύτως, εἰ αἱρετώτερα τὰ Α Γ τῶν Β Δ, τὸ Α τοῦ Δ αἱρετώτερον. ὁμοίως γὰρ διωκτὸν τὸ Α καὶ φευκτὸν τὸ Β (ἀντικείμενα γάρ), καὶ τὸ Γ τῶι Δ (καὶ γὰρ ταῦτα ἀντίκειται). εἰ οὖν τὸ Α τῶι Δ ὁμοίως αἱρετόν, καὶ τὸ Β τῶι Γ φευκτόν· ἑκά- τερον γὰρ ἑκατέρωι ὁμοίως, φευκτὸν διωκτῶι. ὥστε καὶ τὰ ἄμφω τὰ Α Γ τοῖς Β Δ. ἐπεὶ δὲ μᾶλλον, οὐχ οἷόν τε ὁμοίως· καὶ γὰρ ἂν τὰ Β Δ ὁμοίως ἦσαν.	Quando autem duo fuerint opposita, ut A magis eligendum sit quam B, cum sint opposita, et D quam C similiter, si magis eligenda sunt A C quam B D, A magis eligendum quam D. Similiter enim sequendum A, et fugiendum B, opposita enim, et C ei quod est D, nam et haec opponuntur; si ergo A ei quod est D similiter eligendum, et B ei quod est C fugiendum, utrumque enim utrique similiter fugiendum eligendo; quare et haec ambo A C iis quae sunt B D, quoniam autem magis, non possibile similiter, nam et B D similiter erunt.	When, of two opposites A and B, A is preferable to B, and similarly D is preferable to C, then if A and C together are preferable to B and D together, A must be preferable to D. For A is an object of desire to the same extent as B is an object of aversion, since they are opposites: and C is similarly related to D, since they also are opposites. If then A is an object of desire to the same extent as D, B is an object of aversion to the same extent as C (since each is to the same extent as each-the one an object of aversion, the other an object of desire). Therefore both A and C together, and B and D together, will be equally objects of desire or aversion. But since A and C are preferable to B and D, A cannot be equally desirable with D; for then B along with D would be equally desirable with A along with C.
εἰ δὲ τὸ Δ τοῦ Α αἱρετώτερον, καὶ τὸ Β τοῦ Γ ἧττον φευκτόν· τὸ γὰρ ἔλαττον τῶι ἐλάττονι ἀντίκειται. αἱρετώτερον δὲ τὸ μεῖζον ἀγαθὸν καὶ ἔλαττον κακὸν ἢ τὸ ἔλαττον ἀγαθὸν καὶ μεῖζον κακόν· καὶ τὸ ἅπαν ἄρα, τὸ Β Δ, αἱρετώτερον τοῦ Α Γ. νῦν δ᾽ οὐκ ἔστιν. τὸ Α ἄρα αἱρετώτερον τοῦ Δ, καὶ τὸ Γ ἄρα τοῦ Β ἧττον φευκτόν.	Si autem D magis eligendum quam A, et B quam C minus fugiendum; nam quod minus est minori opponitur; magis autem eligendum est maius bonum et minus malum quam minus bonum et maius malum. (0708C) Universum igitur B D magis eligendum quam A C, nunc autem non est, ergo magis A eligendum quam D, et C ergo minus fugiendum quam B.	But if D is preferable to A, then B must be less an object of aversion than C: for the less is opposed to the less. But the greater good and lesser evil are preferable to the lesser good and greater evil: the whole BD then is preferable to the whole AC. But ex hypothesi this is not so. A then is preferable to D, and C consequently is less an object of aversion than B.
εἰ δὴ ἕλοιτο πᾶς ὁ ἐρῶν κατὰ τὸν ἔρωτα τὸ Α τὸ οὕτως ἔχειν ὥστε χαρίζεσθαι, καὶ τὸ μὴ χαρίζεσθαι τὸ ἐφ᾽ οὗ Γ, ἢ τὸ χαρίζεσθαι τὸ ἐφ᾽ οὗ Δ, καὶ ↵ τὸ μὴ τοιοῦτον εἶναι οἷον χαρίζεσθαι τὸ ἐφ᾽ οὗ Β, δῆλον ὅτι τὸ Α τὸ τοιοῦτον εἶναι αἱρετώτερόν ἐστιν ἢ τὸ χαρίζεσθαι. τὸ ἄρα φιλεῖσθαι τῆς συνουσίας αἱρετώτερον κατὰ τὸν ἔρωτα. μᾶλλον ἄρα ὁ ἔρως ἐστὶ τῆς φιλίας ἢ τοῦ συνεῖναι.	Si ergo eligat omnis amans secundum amorem A sic se habere, ut concedere, et non concedere in quo C, aut concedere in quo D, et non tale esse ut concedere in quo B, manifestum quoniam A huiusmodi esse, magis eligendum est quam concedere; ergo diligi quam conventio magis eligendum secundum amorem; magis ergo amor est in amicitia quam convenire.	If then every lover in virtue of his love would prefer A, viz. that the beloved should be such as to grant a favour, and yet should not grant it (for which C stands), to the beloved’s granting the favour (represented by D) without being such as to grant it (represented by B), it is clear that A (being of such a nature) is preferable to granting the favour. To receive affection then is preferable in love to sexual intercourse. Love then is more dependent on friendship than on intercourse.
εἰ δὲ μάλιστα τούτου, καὶ τέλος τοῦτο. τὸ ἄρα συνεῖναι ἢ οὐκ ἔστιν ὅλως ἢ τοῦ φιλεῖσθαι ἕνεκεν· καὶ γὰρ αἱ ἄλλαι ἐπιθυμίαι καὶ τέχναι οὕτως. Πῶς μὲν οὖν ἔχουσιν οἱ ὅροι κατὰ τὰς ἀντιστροφὰς καὶ τὸ αἱρετώτεροι ἢ φευκτότεροι εἶναι, φανερόν·	Si autem maxime huius, et finis haec, ergo convenire aut non est omnino, aut diligendi gratia, nam et aliae concupiscentiae et artes sic fiunt. Quomodo ergo se habent termini secundum conversiones, et in eo quod magis fugiendum vel magis eligendum sit, manifestum est.	And if it is most dependent on receiving affection, then this is its end. Intercourse then either is not an end at all or is an end relative to the further end, the receiving of affection. And indeed the same is true of the other desires and arts.