§1.12#2ἔστω γὰρ τὸ Α καὶ τὸ Β μηδενὶ τῷ αὐτῷ δυνάμενα ὑπάρχειν, ἅπαντι δὲ τὸ Α τὸ Γ καὶ τὸ Β ἢ τὸ Δ. ἀνάγκη δὴ μήτε τὸ Α ὑπάρχει μήτε τὸ Β, παντὶ ὑπάρχειν τὰ ΓΔ. ἔστω δὴ τὸ Ε τὸ μεταξὺ τῶν ΑΒ· ἐναντίων γὰρ τὸ μηθέτερον μέσον.
For let us assume that A and B can belong to nothing that is the same, but that to everything either A or C belongs, and either B or D. It is necessary then that to everything to which neither A nor B belongs, both C and D belong. Let E be the intermediate between A and B; for the intermediate is that which is neither of the contraries.
τούτῳ δὴ ἀνάγκη ἄμφω ὑπάρχειν τό τε Γ καὶ τὸ Δ. παντὶ γὰρ ἢ τὸ Α ἢ τὸ Γ, ὥστε καὶ τῷ Ε· ἐπεὶ οὖν τὸ Α ἀδύνατον, τὸ Γ ὑπάρξει.
To this, then, it is necessary that both C and D belong. For to everything belongs either A or C, and consequently to E as well; since then it is impossible for A to belong, C will belong.
ὁ δʼ αὐτὸς λόγος καὶ ἐπὶ τοῦ Δ. οὔτε δὴ τὸ ἀεὶ ὂν γενητὸν οὐδὲ φθαρτόν, οὔτε τὸ ἀεὶ μὴ ὄν.
And the same argument applies to D as well. Therefore, neither that which always is is generated or corruptible, nor that which always is not.
δῆλον δʼ ὅτι καὶ εἰ γενητὸν ἢ φθαρτόν, οὐκ ἀΐδιον.
And it is clear that even if something is generated or corruptible, it is not eternal.
ἅμα γὰρ ἔσται δυνάμενον ἀεὶ εἶναι καὶ δυνάμενον μὴ ἀεί εἶναι· τοῦτο δʼ ὅτι ἀδύνατον, δέδεικται πρότερον.
For it will at the same time have the capacity of always being and the capacity of not always being; and that this is impossible has been shown before.
ἆῤ οὖν εἰ καὶ ἀγένητον, ὂν δέ, τοῦτʼ ἀνάγκη ἀΐδιον εἶναι;
Is it then necessary that if something is ungenerated, and is existing, it is eternal?
ὁμοίως δὲ καὶ εἰ ἄφθαρτον, ὂν δέ.
And similarly if it is incorruptible, and is existing.
λέγω δὲ τὸ ἀγένητον καὶ ἄφθαρτον τὰ κυρίως λεγόμενα, ἀγένητον μὲν ὃ ἔστι νῦν, καὶ πρότερον οὐκ ἀληθὲς ἦν εἰπεῖν τὸ μὴ εἶναι, ἄφθαρτον δὲ ὃ νῦν ὃν ὕστερον μὴ ἀληθὲς ἔσται εἰπεῖν μὴ εἶναι.
I mean by 'ungenerated' and 'incorruptible' those which are so called in the strict sense: ungenerated, that which is now, and of which it was not true to say formerly that it was not; incorruptible, that which is now, and of which it will not be true to say afterwards that it is not.
ἢ εἰ μὲν ταῦτα ἀλλήλοις ἀκολουθεῖ καὶ τό τε ἀγένητον ἄφθαρτον καὶ τὸ ἄφθαρτον ἀγένητον, ἀνάγκη καὶ τὸ ἀΐδιον ἑκατέρῳ ἀκολουθεῖν, καὶ εἴτε ἀγένητον, ἀΐδιον, εἴτε ἄφθαρτον, ἀΐδιον.
Or, if these follow each other, and that which is ungenerated is incorruptible and that which is incorruptible is ungenerated, it is necessary that the eternal also follows each of them, and whether it is ungenerated, it is eternal, or whether incorruptible, it is eternal.
δῆλον δὲ καὶ ἐκ τοῦ ὁρισμοῦ αὐτῶν· καὶ γὰρ ἀνάγκη, εἰ φθαρτόν, γενητόν.
This is also clear from their definition; for it is necessary, if it is corruptible, that it is generated.
ἢ γὰρ ἀγένητον ἢ γενητόν· εἰ δὲ ἀγένητον, ἄφθαρτον ὑπόκειται.
For it is either ungenerated or generated; but if it is ungenerated, it is assumed to be incorruptible.
καὶ εἰ γενητὸν δή, φθαρτὸν ἀνάγκη· ἢ γὰρ φθαρτὸν ἢ ἄφθαρτον· ἀλλʼ εἰ ἄφθαρτον, ἀγένητον ὑπέκειτο.
And if indeed it is generated, it is necessary that it is corruptible; for it is either corruptible or incorruptible; but if it is incorruptible, it was assumed to be ungenerated.
εἰ δὲ μὴ ἀκολουθοῦσιν ἀλλήλοις τὸ ἄφθαρτον καὶ τὸ ἀγένητον, οὐκ ἀνάγκη οὔτε τὸ ἀγένητον οὔτε τὸ ἄφθαρτον ἀΐδιον εἶναι.
But if the incorruptible and the ungenerated do not follow each other, it is not necessary that either the ungenerated or the incorruptible is eternal.
ὅτι δʼ ἀνάγκη ἀκολουθεῖν, ἐκ τῶνδε φανερόν.
But that it is necessary that they follow each other is clear from the following.
τὸ γὰρ γενητὸν καὶ τὸ φθαρτὸν ἀκολουθοῦσιν ἀλλήλοις.
For the generated and the corruptible follow each other.
δῆλον δὲ καὶ τοῦτο ἐκ τῶν πρότερον· τοῦ γὰρ ἀεὶ ὄντος καὶ τοῦ ἀεὶ μὴ ὄντος ἐστὶ μεταξὺ ᾧ μηδέτερον ἀκολουθεῖ, τοῦτο δʼ ἐστὶ τὸ γενητὸν καὶ φθαρτόν.
And this is also clear from what was said before; for between that which always is and that which always is not there is an intermediate which neither of them follows, and this is the generated and corruptible.
δυνατὸν γὰρ καὶ εἶναι καὶ μὴ εἶναι ὡρισμένον χρόνον ἑκάτερον· λέγω δʼ ἑκάτερον καὶ εἶναι ποσόν τινα χρόνον καὶ μὴ εἶναι.
For it is possible for each to be and not to be for a defined time; and by 'each' I mean both to be for some quantity of time and not to be.
εἰ τοίνυν ἐστί τι γενητὸν ἢ φθαρτόν, ἀνάγκη τοῦτο μεταξύ εἶναι.
If then there is something generated or corruptible, it is necessary that this is the intermediate.
ἔστω γὰρ τὸ Α τὸ ἀεὶ ὄν, τὸ δὲ Β τὸ ἀεὶ μὴ ὄν, τὸ δὲ Γ γενητόν, τὸ δὲ Δ φθαρτόν.
For let A be that which always is, B that which always is not, C that which is generated, and D that which is corruptible.
ἀνάγκη δὴ τὸ Γ μεταξύ εἶναι τοῦ Α καὶ τοῦ Β. τῶν μὲν γὰρ οὐκ ἔστι χρόνος ἐπʼ οὐδέτερον τὸ πέρας ἐν ᾧ ἢ τὸ Α οὐκ ἦν ἢ τὸ Β ἦν· τῷ δὲ γενητῷ ἀνάγκη ἢ ἐνεργείᾳ εἶναι δυνάμει, τοῖς δὲ ΑΒ οὐδετέρως.
It is necessary then that C is intermediate between A and B. For as for A and B, there is no limit of time on either side in which either A was not or B was; but for that which is generated, it is necessary that it is either in actuality or in capacity, whereas for A and B in neither way.
ποσὸν ἄρα τινὰ καὶ ὡρισμένον χρόνον καὶ ἔσται καὶ πάλιν οὐκ ἔσται τὸ Γ. ὁμοίως δὲ καὶ ἐπὶ τοῦ Δ φθαρτοῦ.
Therefore, C both will be and again will not be for some definite and defined quantity of time. And similarly also for the corruptible D.
γενητὸν ἄρα καὶ φθαρτὸν ἑκάτερον.
Therefore, each is both generated and corruptible.
ἀκολουθοῦσιν ἄρα ἀλλήλοις τὸ γενητὸν καὶ τὸ φθαρτόν.
Therefore, the generated and the corruptible follow each other.
ἔστω δὴ τὸ ἐφʼ ᾧ Ε ἀγένητον, τὸ δʼ ἐφʼ ᾧ Ζ γενητόν, τὸ δʼ ἐφʼ ᾧ Η ἄφθαρτον, τὸ δʼ ἐφʼ ᾧ Θ φθαρτόν.
Let then E be ungenerated, Z generated, H incorruptible, and Theta corruptible.
τὰ δὴ ΖΘ δέδεικται ὅτι ἀκολουθεῖ ἀλλήλοις.
It has been shown that Z and Theta follow each other.
ὅταν δʼ ᾖ οὕτω κείμενα ὡς ταῦτα, οἷον τὸ μὲν Ζ καὶ τὸ Θ ἀκολουθοῦντα, τὸ δὲ Ε καὶ τὸ Ζ μηθενὶ τῷ αὐτῷ, ἅπαντι δὲ θάτερον, ὁμοίως δὲ καὶ τὰ ΗΘ, ἀνάγκη καὶ τὰ ΕΗ ἀκολουθεῖν ἀλλήλοις.
And when they are so situated as these, namely, that Z and Theta follow each other, while E and Z belong to nothing that is the same but to everything one of the two belongs, and similarly also H and Theta, it is necessary that E and H also follow each other.
ἔστω γὰρ τῷ Η τὸ Ε μὴ ἀκολουθοῦν.
For let us assume that E does not follow H.
τὸ ἄρα Ζ ἀκολουθήσει· παντὶ γὰρ τὸ Ε ἢ τὸ Ζ. ἀλλὰ μὴν ᾧ τὸ Ζ, καὶ τὸ Θ. τῷ ἄρα Η τὸ Θ ἀκολουθήσει.
Therefore Z will follow; for to everything belongs either E or Z. But indeed, to whatever Z belongs, Theta also belongs. Therefore, Theta will follow H.
ἀλλʼ ὑπέκειτο ἀδύνατον εἶναι.
But this was assumed to be impossible.