§1.1.2Ἐπεὶ δὲ πᾶσα πρότασίς ἐστιν ἢ τοῦ ὑπάρχειν ἢ τοῦ ἐξ ἀνάγκης ὑπάρχειν ἢ τοῦ ἐνδέχεσθαι ὑπάρχειν, τούτων· δὲ αἱ μὲν καταφατικαὶ αἱ δὲ ἀποφατικαὶ καθʼ ἑκάστην πρόσρησιν, πάλιν δὲ τῶν καταφατικῶν καὶ ἀποφατικῶν αἱ μὲν καθόλου αἱ δὲ ἐν μέρει αἱ δὲ ἀδιόριστοι, τὴν μὲν ἐν τῷ ὑπάρχειν καθόλου στερητικὴν ἀνάγκη τοῖς ὅροις ἀντιστρέφειν, οἷον εἰ μηδεμία ἡδονὴ ἀγαθόν, οὐδʼ ἀγαθὸν οὐδὲν ἔσται ἡδονή·
Since every premise is either of belonging, or of belonging of necessity, or of being possible to belong, and of these some are affirmative and some negative in respect of each prefix, and again of the affirmative and negative some are universal, some particular, and some indefinite, it is necessary for the universal privative premise of belonging to convert in its terms; for example, if no pleasure is a good, neither will any good be a pleasure.
τὴν δὲ κατηγορικὴν ἀντιστρέφειν μὲν ἀναγκαῖον, οὐ μὴν καθόλου ἀλλʼ ἐν μέρει, οἷον εἰ πᾶσα ἡδονή ἀγαθόν, καὶ ἀγαθόν τι εἶναι ἡδονήν·
But the affirmative premise must convert necessarily, not indeed universally but particularly; for example, if every pleasure is a good, some good must also be a pleasure.
τῶν δὲ ἐν μέρει τὴν μὲν καταφατικὴν ἀντιστρέφειν ἀνάγκη κατὰ μέρος (εἰ γὰρ ἡδονή τις ἀγαθόν, καὶ ἀγαθόν τι ἔσται ἡδονή), τὴν δὲ στερητικὴν οὐκ ἀναγκαῖον· (οὐ γὰρ εἰ ἄνθρωπος μὴ ὑπάρχει τινὶ ζῴῳ, καὶ ζῷον οὐχ ὑπάρχει τινὶ ἀνθρώπῳ).
Of particular premises, the affirmative must convert particularly (for if some pleasure is a good, some good will also be a pleasure), but the privative does not convert necessarily (for if man does not belong to some animal, it is not necessary that animal does not belong to some man).
Πρῶτον μὲν οὖν ἔστω στερητικὴ καθόλου ἡ Α Β πρότασις.
First, then, let the premise AB be a universal privative.
εἰ οὖν μηδενὶ τῷ Β τὸ Α ὑπάρχει, οὐδὲ τῷ Α οὐδενὶ ὑπάρξει τὸ Β·
If, then, A belongs to no B, neither will B belong to any A.
εἰ γάρ τινι, οἷον τῷ Γ, οὐκ ἀληθὲς ἔσται τὸ μηδενὶ τῷ Β τὸ Α ὑπάρχειν· τὸ γὰρ Γ τῶν Β τί ἐστιν.
For if it belongs to some, for instance to C, it will not be true that A belongs to no B, since C is one of the Bs.
εἰ δὲ παντὶ τὸ Α τῷ Β, καὶ τὸ Β τινὶ τῷ Α ὑπάρξει· εἰ γὰρ μηδενί, οὐδὲ τὸ Α οὐδενὶ τῷ Β ὑπάρξει· ἀλλʼ ὑπέκειτο παντὶ ὑπάρχειν.
And if A belongs to every B, B will also belong to some A; for if to none, neither will A belong to any B, but it was assumed to belong to every B.
ὁμοίως δὲ καὶ εἰ κατά μέρος ἐστὶν ἡ πρότασις.
Similarly also if the premise is particular.
εἰ γὰρ τὸ Α τινὶ τῷ Β, καὶ τὸ Β τινὶ τῷ Α ἀνάγκη ὑπάρχειν·
For if A belongs to some B, B must also belong to some A; for if to none, neither will A belong to any B.
εἰ γὰρ μηδενί, οὐδὲ τὸ Α οὐδενὶ τῷ Β. εἰ δέ γε τὸ Α τινὶ τῷ Β μὴ ὑπάρχει, οὐκ ἀνάγκη καὶ τὸ Β τινὶ τῷ Α μὴ ὑπάρχειν, οἷον εἰ τὸ μὲν ἐστὶ ζῷον, τὸ δὲ Α ἄνθρωπος· ἄνθρωπος μὲν γὰρ οὐ παντὶ ζῴῳ, ζῷον δὲ παντὶ ἀνθρώπῳ ὑπάρχει.
But if A does not belong to some B, it is not necessary that B also does not belong to some A, as for example if one is animal and A is man; for man does not belong to every animal, but animal belongs to every man.
§1.1.3Τὸν αὐτὸν δὲ τρόπον ἕξει καὶ ἐπὶ τῶν ἀναγκαίων προτάσεων.
It will be the same way also in the case of necessary premises.
ἡ μὲν γὰρ καθόλου στερητικὴ καθόλου ἀντιστρέφει, τῶν δὲ καταφατικῶν ἐκατέρα κατὰ μέρος.
For the universal privative converts universally, but each of the affirmatives converts particularly.
εἰ μὲν γὰρ ἀνάγκη τὸ τῷ Β μηδενὶ ὑπάρχειν, ἀνάγκη καὶ τὸ Β τῷ Α μηδενὶ ὑπάρχειν· εἰ γὰρ τινὶ ἐνδέχεται, καὶ τὸ τῷ Β τινὶ ἐνδέχοιτο ἄν.
For if it is necessary for A to belong to no B, it is necessary also for B to belong to no A; for if it is possible for it to belong to some, A would also be possible to belong to some B.
εἰ δὲ ἐξ ἀνάγκης τὸ παντὶ ἢ τινὶ τῷ Β ὑπάρχει, καὶ τὸ Β τινὶ τῷ Α ἀνάγκη ὑπάρχειν· εἰ γὰρ μὴ ἀνάγκη, οὐδʼ ἂν τὸ Α τινὶ τῷ Β ἐξ ἀνάγκης ὑπάρχοι.
And if A belongs to every or some B of necessity, B must also belong to some A; for if it were not necessary, neither would A belong to some B of necessity.
τὸ δʼ ἐν μέρει στερητικὸν οὐκ ἀντιστρέφει, διὰ τὴν αὐτὴν αἰτίαν διʼ ἣν καὶ πρότερον ἔφαμεν.
But the particular privative does not convert, for the same reason which we stated before.
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.
In the case of possible premises, since "to be possible" is said in many ways (for we say that the necessary, the non-necessary, and the capable are possible), in all the affirmative premises it will be similar in respect of conversion.
εἰ γὰρ τὸ Α παντὶ ἢ τινὶ τῷ Β ἐνδέχεται, καὶ τὸ Β τινὶ τῷ Α ἐνδέχοιτο ἄν· εἰ γὰρ μηδενί, οὐδʼ ἂν τὸ Α οὐδενὶ τῷ Β· δέδεικται γὰρ τοῦτο πρότερον.
For if A is possible to belong to every or some B, B also would be possible to belong to some A; for if to none, neither would A belong to any B, for this has been shown before.
ἐν δὲ τοῖς ἀποφατικοῖς οὐχ ὡσαύτως, ἀλλʼ 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·
But in the negative premises it is not the same, but those which are said to be possible either because they belong of necessity or because they do not of necessity not belong, are similar; for example, if someone should say that it is possible for a man not to be a horse, or for white to belong to no cloak (for of these, the one does not belong of necessity, and the other does not belong of necessity, and the premise converts similarly; for if it is possible for a horse to belong to no man, it is also admissible for a man to belong to no horse; and if white is admissible to belong to no cloak, a cloak is also admissible to belong to no white; for if to some of necessity, white also will belong to some cloak of necessity, for this has been shown before), and similarly also in the case of the particular negative.
ὅσα δὲ τῷ ὡς ἐπὶ τὸ πολὺ καὶ τῷ πεφυκέναι λέγεται ἐνδέχεσθαι, καθʼ ὃν τρόπον διορίζομεν τὸ ἐνδεχόμενον, οὐχ ὁμοίως ἕξει ἐν ταῖς στερητικαῖς ἀντιστροφαῖς, ἀλλʼ ἡ μὲν καθόλου στερητικὴ πρότασις οὐκ ἀντιστρέφει, ἡ δὲ ἐν μέρει ἀντιστρέφει.
But those which are said to be possible as happening for the most part and by nature, which is the way we define the possible, will not be similar in negative conversions, but the universal negative premise does not convert, whereas the particular converts.
τοῦτο δὲ ἔσται φανερὸν ὅταν περὶ τοῦ ἐνδεχομένου λέγωμεν.
This will be clear 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.
For now, let this much be plain to us in addition to what has been said, that to be possible to belong to none or not to some has an affirmative form (for "is possible" is arranged similarly to "is", and "is", whenever it is predicated in addition, always and in every way makes an affirmation, as for example "is not-good" or "is not-white" or simply "is not-this"; and this also will be shown in what follows), and in respect of conversions they will be in the same case as the others.