§13#1Καὶ αἱ ἀκολουθήσεις δὲ κατὰ λόγον γίνονται οὕτω τιθεμένοις· τῷ μὲν γὰρ δυνατὸν εἶναι τὸ ἐνδέχεσθαι εἶναι, καὶ τοῦτο ἐκείνῳ ἀντιστρέφει, καὶ τὸ μὴ ἀδύνατον εἶναι καὶ τὸ μὴ ἀναγκαῖον εἶναι· τῷ δὲ δυνατὸν μὴ εἶναι καὶ ἐνδεχόμενον μὴ εἶναι τὸ μὴ ἀναγκαῖον μὴ εἶναι καὶ τὸ οὐκ ἀδύνατον μὴ εἶναι, τῷ δὲ μὴ δυνατὸν εἶναι καὶ μὴ ἐνδεχόμενον εἶναι τὸ ἀναγκαῖον μὴ εἶναι καὶ τὸ ἀδύνατον εἶναι, τῷ δὲ μὴ δυνατὸν μὴ εἶναι καὶ μὴ ἐνδεχόμενον μὴ εἶναι τὸ ἀναγκαῖον εἶναι καὶ τὸ ἀδύνατον μὴ εἶναι.
And followings also occur in a logical order for those who place them in this way: for with 'to be possible' there follows 'to be contingent', and this reciprocates with that, and also 'not to be impossible' and 'not to be necessary'; and with 'to be possible not to be' and 'to be contingent not to be' there follows 'not to be necessary not to be' and 'not to be impossible not to be'; and with 'not to be possible' and 'not to be contingent' there follows 'to be necessary not to be' and 'to be impossible'; and with 'not to be possible not to be' and 'not to be contingent not to be' there follows 'to be necessary' and 'to be impossible not to be'.
Θεωρείσθω δὲ ἐκ τῆς ὑπογραφῆς ὡς λέγομεν. δυνατὸν εἶναι οὐ δυνατὸν εἶναι
ἐνδεχόμενον εἶναι οὐκ ἐνδεχόμενον εἶναι
οὐκ ἀδύνατον εἶναι ἀδύνατον εἶναι
οὐκ ἀναγκαῖον εἶναι ἀναγκαῖον μὴ εἶναι
δυνατὸν μὴ εἶναι οὐ δυνατὸν μὴ εἶναι
ἐνδεχόμενον μὴ εἶναι οὐκ ἐνδεχόμενον μὴ εἶναι
οὐκ ἀδύνατον μὴ εἶναι ἀδύνατον μὴ εἶναι
οὐκ ἀναγκαῖον μὴ εἶναι ἀναγκαῖον εἶναι
Τὸ μὲν οὖν ἀδύνατον καὶ οὐκ ἀδύνατον τῷ ἐνδεχομένῳ καὶ δυνατῷ καὶ οὐκ ἐνδεχομένῳ καὶ μὴ δυνατῷ ἀκολουθεῖ μὲν ἀντιφατικῶς, ἀντεστραμμένως δέ·
Let it be viewed from the diagram as we say: to be possible | not to be possible to be contingent | not to be contingent not to be impossible | to be impossible not to be necessary | to be necessary not to be to be possible not to be | not to be possible not to be to be contingent not to be | not to be contingent not to be not to be impossible not to be | to be impossible not to be not to be necessary not to be | to be necessary Now the 'impossible' and the 'not impossible' follow 'contingent' and 'possible', and 'not contingent' and 'not possible', in a contradictory but reciprocal way.
τῷ μὲν γὰρ δυνατὸν εἶναι ἡ ἀπόφασις τοῦ ἀδυνάτου ἀκολουθεῖ, τῇ δὲ ἀποφάσει ἡ κατάφασις· τῷ γὰρ οὐ δυνατὸν εἶναι τὸ ἀδύνατον εἶναι· κατάφασις γὰρ τὸ ἀδύνατον εἶναι, τὸ δ᾿ οὐκ ἀδύνατον εἶναι ἀπόφασις.
For to 'to be possible' the negation of the 'impossible' follows, and to the negation the affirmation follows; for to 'not to be possible' there follows 'to be impossible'; for 'to be impossible' is an affirmation, and 'not to be impossible' is a negation.
Τὸ δ᾿ ἀναγκαῖον πῶς, ὀπτέον.
But how the 'necessary' stands must be seen.
Φανερὸν δὴ ὅτι οὐχ οὕτως ἔχει, ἀλλ᾿ αἱ ἐναντίαι ἕπονται· αἱ δ᾿ ἀντιφάσεις χωρίς.
It is clear, indeed, that it is not so, but rather the contraries follow, while the contradictions follow separately.
Οὐ γάρ ἐστιν ἀπόφασις τοῦ ἀνάγκη μὴ εἶναι τὸ οὐκ ἀνάγκη εἶναι· ἐνδέχεται γὰρ ἀληθεύεσθαι ἐπὶ τοῦ αὐτοῦ ἀμφοτέρας· τὸ γὰρ ἀναγκαῖον μὴ εἶναι οὐκ ἀναγκαῖον εἶναι.
For the negation of 'necessary not to be' is not 'not necessary to be'; for it is possible for both to be true of the same thing; for that which is necessary not to be is not necessary to be.
Αἴτιον δὲ τοῦ μὴ ἀκολουθεῖν τὸ ἀναγκαῖον ὁμοίως τοῖς ἑτέροις, ὅτι ἐναντίως τὸ ἀδύνατον τῷ ἀναγκαίῳ ἀποδίδοται, τὸ αὐτὸ δυνάμενον.
And the reason why the 'necessary' does not follow in the same way as the others is that the 'impossible' is applied contrariwise to the 'necessary', though having the same force.
Εἰ γὰρ ἀδύνατον εἶναι, ἀναγκαῖον τοῦτο οὐκ εἶναι ἀλλὰ μὴ εἶναι· εἰ δὲ ἀδύνατον μὴ εἶναι, τοῦτο ἀνάγκη εἶναι· ὥστε εἰ ἐκεῖνα ὁμοίως τῷ δυνατῷ καὶ μή, ταῦτα ἐξ ἐναντίας, ἐπεὶ οὐ σημαίνει γε ταὐτὸν τό τε ἀνάγκαῖον καὶ τὸ ἀδύνατον, ἀλλ᾿ ὥσπερ εἴρηται, ἀντεστραμμένως.
For if it is impossible to be, it is necessary not to be, but to not be; and if it is impossible not to be, it is necessary to be; so that if those follow in the same way as 'possible' and its negation, these follow in the opposite way, since the 'necessary' and the 'impossible' do not signify the same thing, but, as has been said, in a reciprocal way.
Ἣ ἀδύνατον οὕτως κεῖσθαι τὰς τοῦ ἀναγκαίου ἀντιφάσεις;
Or is it impossible for the contradictions of the 'necessary' to be placed in this way?
τὸ μὲν γὰρ ἀναγκαῖον εἶναι δυνατὸν εἶναι· εἰ γὰρ μή, ἡ ἀπόφασις ἀκολουθήσει· ἀνάγκη γὰρ ἢ φάναι ἢ ἀποφάναι·
For to 'be necessary to be' there follows 'to be possible to be'; for if not, the negation will follow, since it is necessary either to affirm or to deny.
ὥστ᾿ εἰ μὴ δυνατὸν εἶναι, ἀδύνατον εἶναι· ἀδύνατον ἄρα εἶναι τὸ ἀναγκαῖον εἶναι, ὅπερ ἄτοπον.
Consequently, if it is not possible to be, it is impossible to be; therefore, for that which is necessary to be, it is impossible to be, which is absurd.
Ἀλλὰ μὴν τῷ γε δυνατὸν εἶναι τὸ οὐκ ἀδύνατον εἶναι ἀκολουθεῖ, τούτῳ δὲ τὸ μὴ ἀναγκαῖον εἶναι· ὥστε συμβαίνει τὸ ἀναγκαῖον εἶναι μὴ ἀναγκαῖον εἶναι, ὅπερ ἄτοπον.
But indeed, to 'to be possible' there follows 'not to be impossible', and to this follows 'not to be necessary to be'; so that it results that to be necessary to be is not to be necessary to be, which is absurd.
Ἀλλὰ μὴν οὐδὲ τὸ ἀναγκαῖον εἶναι ἀκολουθεῖ τῷ δυνατὸν εἶναι, οὐδὲ τὸ ἀναγκαῖον μὴ εἶναι· τῷ μὲν γὰρ ἄμφω ἐνδέχεται συμβαίνειν, τούτων δὲ ὁπότερον ἂν ἀληθὲς ᾖ, οὐκέτι ἔσται ἐκεῖνα ἀληθῆ.
But indeed, neither does 'to be necessary to be' follow 'to be possible to be', nor 'to be necessary not to be'; for to the latter both are contingent to happen, but whichever of these is true, those will no longer be true.
Ἄμα γὰρ δυνατὸν εἶναι καὶ μὴ εἶναι· εἰ δ᾿ ἀνάγκη εἶναι ἢ μὴ εἶναι, οὐκ ἔσται δυνατὸν ἄμφω.
For at the same time it is possible to be and not to be; but if it is necessary to be or not to be, both will not be possible.
Λείπεται τοίνυν τὸ οὐκ ἀναγκαῖον μὴ εἶναι ἀκολουθεῖν τῷ δυνατὸν εἶναι. Τοῦτο γὰρ ἀληθὲς καὶ κατὰ τοῦ ἀναγκαῖον εἶναι.
It remains, therefore, that 'not to be necessary not to be' follows 'to be possible to be'; for this is true also of 'to be necessary to be'.
Καὶ γὰρ αὕτη γίνεται ἀντίφασις τῇ ἑπομένῃ τῷ οὐ δυνατὸν εἶναι· ἐκείνῳ γὰρ ἀκολουθεῖ τὸ ἀδύνατον εἶναι καὶ ἀναγκαῖον μὴ εἶναι, οὗ ἡ ἀπόφασις τὸ οὐκ ἀναγκαῖον μὴ εἶναι.
For this becomes the contradiction of that which follows 'not to be possible to be'; for to that there follows 'to be impossible' and 'to be necessary not to be', of which the negation is 'not to be necessary not to be'.
Ἀκολουθοῦσί τε ἄρα καὶ αὗται αἱ ἀντιφάσεις κατὰ τὸν εἰρημένον τρόπον, καὶ οὐδὲν ἀδύνατον συμβαίνει τιθεμένων οὕτως.
Therefore, these contradictions also follow in the manner described, and no impossible consequence results when they are placed thus.