Authors/Aristotle/priora/Liber 1/C3

Chapter 3

Greek	Latin	English
	(PL 64 0640D) CAPUT III. De conversione propositionum de modo	3
25a27 Τὸν αὐτὸν δὲ τρόπον ἕξει καὶ ἐπὶ τῶν ἀναγκαίων προτάσεων. ἡ μὲν γὰρ καθόλου στερητικὴ καθόλου ἀντιστρέφει, τῶν δὲ καταφατικῶν ἑκατέρα κατὰ μέρος. εἰ μὲν γὰρ ἀνάγκη τὸ Α τῶι Β μηδενὶ ὑπάρχειν, ἀνάγκη καὶ τὸ Β τῶι Α μηδενὶ ὑπάρχειν· εἰ γὰρ τινὶ ἐνδέχεται, καὶ τὸ Α τῶι Β τινὶ ἐνδέχοιτο ἄν. εἰ δὲ ἐξ ἀνάγκης τὸ Α παντὶ ἢ τινὶ τῶι Β ὑπάρχει, καὶ τὸ Β τινὶ τῶι Α ἀνάγκη ὑπάρχειν· εἰ γὰρ μὴ ἀνάγκη, οὐδ᾽ ἂν τὸ Α τινὶ τῶι Β ἐξ ἀνάγκης ὑπάρχοι. τὸ δ᾽ ἐν μέρει στερητικὸν οὐκ ἀντιστρέφει, διὰ τὴν αὐτὴν αἰτίαν δι᾽ ἣν καὶ πρότερον ἔφαμεν.	Eodem autem modo se habebit in necessariis propositionibus, nam universalis quidem privativa universaliter convertitur. Affirmativarum autem utraque particulariter. Nam si necesse est A nulli B inesse, necesse est et B nulli A inesse; si enim alicui contingit, et A alicui B continget. (0641A) Si autem ex necessitate A omni vel alicui B inest, et B alicui A necesse est inesse, nam si non ex necessitate inest, neque A alicui B ex necessitate inerit. Particularis vero privativa non convertitur, propter eamdem causam, propter quam et supra diximus.	The same manner of conversion will hold good also in respect of necessary premisses. The universal negative converts universally; each of the affirmatives converts into a particular. If it is necessary that no B is A, it is necessary also that no A is B. For if it is possible that some A is B, it would be possible also that some B is A. If all or some B is A of necessity, it is necessary also that some A is B: for if there were no necessity, neither would some of the Bs be A necessarily. But the particular negative does not convert, for the same reason which we have already stated.
Ἐπὶ δὲ τῶν ἐνδεχομένων, ἐπειδὴ πολλαχῶς λέγεται τὸ ἐνδέχεσθαι (καὶ γὰρ τὸ ἀναγκαῖον καὶ τὸ μὴ ἀναγκαῖον καὶ τὸ δυνατὸν ἐνδέχεσθαι λέγομεν), ἐν μὲν τοῖς καταφατικοῖς ὁμοίως ἕξει κατὰ τὴν ἀντιστροφὴν ἐν ἅπασιν. εἰ γὰρ τὸ Α ↵ παντὶ ἢ τινὶ τῶι Β ἐνδέχεται, καὶ τὸ Β τινὶ τῶι Α ἐνδέχοιτο ἄν· εἰ γὰρ μηδενί, οὐδ᾽ ἂν τὸ Α οὐδενὶ τῶι Β· δέδεικται γὰρ τοῦτο πρότερον. ἐν δὲ τοῖς ἀποφατικοῖς οὐχ ὡσαύτως, ἀλλ᾽ ὅσα μὲν ἐνδέχεσθαι λέγεται τῶι ἐξ ἀνάγκης ὑπάρχειν ἢ τῶι μὴ ἐξ ἀνάγκης μὴ ὑπάρχειν, ὁμοίως, οἷον εἴ τις φαίη τὸν ἄνθρωπον ἐνδέχεσθαι μὴ εἶναι ἵππον ἢ τὸ λευκὸν μηδενὶ ἱματίωι ὑπάρχειν (τούτων γὰρ τὸ μὲν ἐξ ἀνάγκης οὐχ ὑπάρχει, τὸ δὲ οὐκ ἀνάγκη ὑπάρχειν, καὶ ὁμοίως ἀντιστρέφει ἡ πρότασις· εἰ γὰρ ἐνδέχεται μηδενὶ ἀνθρώπωι ἵππον, καὶ ἄνθρωπον ἐγχωρεῖ μηδενὶ ἵππωι· καὶ εἰ τὸ λευκὸν ἐγχωρεῖ μηδενὶ ἱματίωι, καὶ τὸ ἱμάτιον ἐγχωρεῖ μηδενὶ λευκῶι· εἰ γάρ τινι ἀνάγκη, καὶ τὸ λευκὸν ἱματίωι τινὶ ἔσται ἐξ ἀνάγκης· τοῦτο γὰρ δέδεικται πρότερον), ὁμοίως δὲ καὶ ἐπὶ τῆς ἐν μέρει ἀποφατικῆς· ὅσα δὲ τῶι ὡς ἐπὶ τὸ πολὺ καὶ τῶι πεφυκέναι λέγεται ἐνδέχεσθαι, καθ᾽ ὃν τρόπον διορίζομεν τὸ ἐνδεχόμενον, οὐχ ὁμοίως ἕξει ἐν ταῖς στερητικαῖς ἀντιστροφαῖς, ἀλλ᾽ ἡ μὲν καθόλου στερητικὴ πρότασις οὐκ ἀντιστρέφει, ἡ δὲ ἐν μέρει ἀντιστρέφει. τοῦτο δὲ ἔσται φανερὸν ὅταν περὶ τοῦ ἐνδεχομένου λέγωμεν.	In contingentibus vero, quoniam multipliciter dicitur contingere, nam et necessarium, et non necessarium, et possibile contingere dicimus; in affirmativis quidem, similiter se habebit secundum conversionem in omnibus. Nam si A omni aut alicui B contingit, et B alicui A contingit, si enim nulli, nec A nulli B, ostensum est enim hoc prius. In negativis vero non similiter, sed quaecunque quidem contingere dicuntur, ex eo quod ex necessitate non insunt, vel in eo quod non ex necessitate insunt similiter. Ut si quis dicat hominem contingere non esse equum, aut album nulli tunicae inesse. (0641B) Horum enim hoc quidem ex necessitate inest, illud vero non ex necessitate inest, et similiter convertitur propositio. Nam si contingit nulli homini equum inesse, et hominem contingit nulli equo inesse, et si album contingit nulli tunicae, et tunica contingit nulli albo, si enim alicui necessario, et album tunicae alicui inerit ex necessitate, hoc enim ostensum est prius. Similiter autem et in particulari negativa. Quaecunque vero ut in pluribus, et in eo quod nata sunt dicuntur contingere secundum quem modum determinamus contingens, non similiter se habebit in privativis conversionibus. Sed et universalis quidem privativa propositio non convertitur, particularis vero convertitur. Hoc autem erit manifestum quando de contingenti dicemus.	In respect of possible premisses, since possibility is used in several senses (for we say that what is necessary and what is not necessary and what is potential is possible), affirmative statements will all convert in a manner similar to those described. For if it is possible that all or some B is A, it will be possible that some A is B. For if that were not possible, then no B could possibly be A. This has been already proved. But in negative statements the case is different. Whatever is said to be possible, either because B necessarily is A, or because B is not necessarily A, admits of conversion like other negative statements, e.g. if one should say, it is possible that man is not horse, or that no garment is white. For in the former case the one term necessarily does not belong to the other; in the latter there is no necessity that it should: and the premiss converts like other negative statements. For if it is possible for no man to be a horse, it is also admissible for no horse to be a man; and if it is admissible for no garment to be white, it is also admissible for nothing white to be a garment. For if any white thing must be a garment, then some garment will necessarily be white. This has been already proved. The particular negative also must be treated like those dealt with above. But if anything is said to be possible because it is the general rule and natural (and it is in this way we define the possible), the negative premisses can no longer be converted like the simple negatives; the universal negative premiss does not convert, and the particular does. This will be plain when we speak about the possible.
νῦν δὲ τοσοῦτον ἡμῖν ἔστω πρὸς τοῖς εἰρημένοις δῆλον, ὅτι τὸ ἐνδέχεσθαι μηδενὶ ἢ τινὶ μὴ ὑπάρχειν καταφατικὸν ἔχει τὸ σχῆμα (τὸ γὰρ ἐνδέχεται τῶι ἔστιν ὁμοίως τάττεται, τὸ δὲ ἔστιν, οἷς ἂν προσκατηγορῆται, κατάφασιν ἀεὶ ποιεῖ καὶ πάντως, οἷον τὸ ἔστιν οὐκ ἀγαθόν ἢ ἔστιν οὐ λευκόν ἢ ἁπλῶς τὸ ἔστιν οὐ τοῦτο· δειχθήσεται δὲ καὶ τοῦτο διὰ τῶν ἑπομένων), κατὰ δὲ τὰς ἀντιστροφὰς ὁμοίως ἕξουσι ταῖς ἄλλαις.	(0641C) Nunc autem nobis tantum sit cum iis quae dicta sunt, manifestum, quoniam contingere nulli aut alicui non inesse affirmativam habet figuram, nam et contingit ipsi est similiter ordinatur. Est autem, quibuscunque adiacens praedicatur, affirmationem semper facit, et omnino, ut: est non bonum, vel est non album, vel simpliciter, est non hoc. Ostendetur autem et hoc per sequentia, secundum conversiones autem similiter se habebunt in aliis.	At present we may take this much as clear in addition to what has been said: the statement that it is possible that no B is A or some B is not A is affirmative in form: for the expression ‘is possible’ ranks along with ‘is’, and ‘is’ makes an affirmation always and in every case, whatever the terms to which it is added, in predication, e.g. ‘it is not-good’ or ‘it is not-white’ or in a word ‘it is not-this’. But this also will be proved in the sequel. In conversion these premisses will behave like the other affirmative propositions.