§1.12#112 Διωρισμένων δὲ τούτων λεκτέον τὸ ἐφεξῆς.
12 These things having been defined, we must speak of what follows next.
εἰ δή ἐστιν ἔνια δυνατὰ καὶ εἶναι καὶ μή, ἀνάγκη χρόνον τινὰ ὡρίσθαι τὸν πλεῖστον καὶ τοῦ εἶναι καὶ τοῦ μή, λέγω δʼ ὃν δυνατὸν τὸ πρᾶγμα εἶναι καὶ ὃν δυνατὸν μὴ εἶναι καθʼ ὁποιανοῦν κατηγορίαν, οἷον ἄνθρωπον ἢ λευκὸν ἢ τρίπηχυ ἢ ἄλλ᾿ ὁτιοῦν τῶν τοιούτων.
If indeed there are some things capable of both being and not being, it is necessary that some maximum time should be defined both for their being and for their not being; I mean, the time during which the thing is capable of being and that during which it is capable of not being, according to any category whatsoever, such as man, or white, or three cubits long, or any other such thing.
εἰ γὰρ μὴ ἔσται ποσός τις, ἀλλ᾿ ἀεὶ πλείων τοῦ προτεθέντος καὶ οὐκ ἔστιν οὗ ἐλάττων, ἄπειρον ἔσται χρόνον τὸ αὐτὸ δυνατὸν εἶναι καὶ μὴ εἶναι ἄλλον ἄπειρον.
For if it is not of some definite quantity, but is always greater than any pre-established time and there is none shorter than which it is, the same thing will be capable of being for an infinite time, and of not being for another infinite time.
ἀλλά τοῦτʼ ἀδύνατον.
But this is impossible.
ἀρχὴ δʼ ἔστω ἐντεῦθεν· τὸ γὰρ ἀδύνατον καὶ τὸ ψεῦδος οὐ ταὐτὸ σημαίνει.
Let the starting point be from here: for 'impossible' and 'false' do not signify the same thing.
ἔστι δὲ τὸ ἀδύνατον καὶ τὸ δυνατὸν καὶ τὸ ψεῦδος καὶ τὸ ἀληθὲς τὸ μὲν ἐξ ὑποθέσεως (λέγω δ᾿, οἷον καὶ τὸ τρίγωνον ἀδύνατον δύο ὀρθὰς ἔχειν, εἰ τάδε, καὶ ἡ διάμετρος σύμμετρος, εἰ τάδε), ἔστι δʼ ἀπλῶς καὶ δυνατὰ καὶ ἀδύνατα καὶ ψευδῆ καὶ ἀληθῇ.
Now, the impossible, the possible, the false, and the true are in one way by hypothesis (I mean, as for instance, that it is impossible for a triangle to have two right angles if such-and-such is the case, and the diagonal is commensurable if such-and-such is the case), and in another way they are absolutely possible, impossible, false, and true.
οὐ δὴ ταὐτόν ἐστι ψεῦδός τέ τι εἶναι ἀπλῶς καὶ ἀδύνατον ἁπλῶς.
Therefore, it is not the same thing for something to be absolutely false and absolutely impossible.
τὸ γάρ σε μὴ ἑστῶτα φάναι ἑστάναι ψεῦδος μέν, οὐκ ἀδύνατον δέ.
For to say that you, who are not standing, are standing is indeed false, but not impossible.
ὁμοίως δὲ τὸν κιθαρίζοντα μὲν μὴ ᾄδοντα δὲ ᾄδειν φάναι ψεῦδος, ἀλλʼ οὐκ ἀδύνατον.
And similarly, to say that one who is playing the cithara but not singing is singing is false, but not impossible.
τὸ δʼ ἅμα ἑστάναι καὶ καθῆσθαι, καὶ τὴν διάμετρον σύμμετρον εἶναι, οὐ μόνον ψεῦδος ἀλλὰ καὶ ἀδύνατον, οὐ δὴ ταὐτόν ἐστιν ὑποθέσθαι ψεῦδος καὶ ἀδύνατον. συμβαίνει δʼ ἀδύνατον ἐξ ἀδυνάτου.
But to stand and to sit at the same time, and for the diagonal to be commensurable, is not only false but also impossible. Thus, to hypothesize what is false is not the same as to hypothesize what is impossible; and from the impossible, the impossible follows.
τοῦ μὲν οὖν καθῆσθαι καὶ ἑστάναι ἅμα ἔχει τὴν δύναμιν, ὅτι ὅτε ἔχει ἐκείνην, καὶ τὴν ἑτέραν· ἀλλʼ οὐχ ὥστε ἅμα καθῆσθαι καὶ ἑστάναι, ἀλλ᾿ ἐν ἄλλῳ χρόνῳ.
Now, a man has the capacity for both sitting and standing at the same time, because when he has the former, he also has the latter; but not so as to sit and stand at the same time, but at another time.
εἰ δή τι ἄπειρον χρόνον ἔχει πλειόνων δύναμιν, οὐκ ἔστιν ἐν ἄλλῳ χρόνῳ, ἀλλὰ τοῦθʼ ἅμα.
If indeed something has the capacity for more than one thing for an infinite time, it is not at another time, but this must be at the same time.
ὥστʼ εἴ τι ἄπειρον χρόνον ὂν φθαρτόν ἐστι, δύναμιν ἔχοι ἄν τοῦ μὴ εἶναι.
Consequently, if something which exists for an infinite time is corruptible, it would have the capacity of not being.
εἰ δὴ ἄπειρον χρόνον ἐστίν, ἔσται ὑπάρχον ὁ δύναται.
If indeed it is for an infinite time, that which it is capable of being will be actual.
ἅμα ἄῤ ἔσται τε καὶ οὐκ ἔσται κατʼ ἐνέργειαν.
Therefore, at the same time it will both be and not be in actuality.
ψεῦδος μὲν οὖν συμβαίνοι ἄν, ὅτι ψεῦδος ἐτέθη.
A falsehood would indeed follow, because a falsehood was assumed.
ἀλλʼ εἰ μὴ ἀδύνατον ἦν, οὐκ ἂν καὶ ἀδύνατον ἦν τὸ συμβαῖνον.
But if it were not impossible, that which follows would not be impossible either.
ἅπαν ἄρα τὸ ἀεὶ ὂν ἀπλῶς ἄφθαρτον.
Therefore, everything that is absolutely always is incorruptible.
ὁμοίως δὲ καὶ ἀγένητον· εἰ γὰρ γενητόν, ἔσται δυνατὸν χρόνον τινὰ μὴ εἶναι.
And similarly also ungenerated; for if it is generated, it will be capable of not being for some time.
φθαρτὸν μὲν γάρ ἐστι τὸ πρότερον μὲν ὄν, νῦν δὲ μὴ ὂν ἢ ἐνδεχόμενόν ποτε ὕστερον μὴ εἶναι· γενητὸν δὲ ὃ ἐνδέχεται πρότερον μὴ εἶναι, ἀλλʼ οὐκ ἔστιν ἐν ᾧ χρόνῳ δυνατὸν τὸ ἀεὶ ὄν.
For the corruptible is that which was previously being, but now is not, or is capable of not being at some time afterwards; and the generated is that which is capable of not being previously; but there is no time in which that which always is can possibly not be, so as to not be either for an infinite or for a finite time.
ὥστε μὴ εἶναι οὔτʼ ἄπειρον οὔτε πεπερασμένον· καὶ γὰρ τὸν πεπερασμένον χρόνον δύναται εἶναι, εἴπερ καὶ τὸν ἄπειρον.
For it is capable of being for a finite time, since indeed it is capable of being for an infinite time.
οὐκ ἄρα ἐνδέχεται τὸ αὐτὸ καὶ ἓν ἀεί τε δύνασθαι εἶναι καὶ μὴ εἶναι.
Therefore, it is not possible for the same and one thing to be capable of always being and always not being.
ἀλλὰ μὴν οὐδὲ τὴν ἀπόφασιν, οἷον λέγω μὴ ἀεὶ εἶναι.
And indeed, neither can it be capable of its negation, as for instance, I mean, of not always being.
ἀδύνατον ἄρα καὶ ἀεὶ μέν τι εἶναι, φθαρτὸν δʼ εἶναι.
Therefore, it is impossible for something both to be always and to be corruptible.
ὁμοίως δʼ οὐδὲ γενητόν.
And similarly, neither can it be generated.
δυοῖν γὰρ ὅροιν εἰ ἀδύνατον τὸ ὕστερον ἄνευ τοῦ προτέρου ὑπάρξαι, ἐκεῖνο δʼ ἀδύνατον ὑπάρξαι, καὶ τὸ ὕστερον.
For of two terms, if it is impossible for the latter to exist without the former, and it is impossible for the former to exist, it is also impossible for the latter.
ὥστʼ εἰ τὸ ἀεὶ ὂν μὴ ἐνδέχεταί ποτε μὴ εἶναι, ἀδύνατον καὶ γενητὸν εἶναι.
So that if that which always is cannot possibly not be at some time, it is also impossible for it to be generated.
ἐπεὶ δʼ ἡ ἀπόφασις τοῦ μὲν ἀεὶ δυναμένου εἶναι τὸ μὴ ἀεὶ δυνάμενον εἶναι, τὸ δʼ ἀεὶ δυνάμενον μὴ εἶναι ἐναντίον, οὗ ἀπόφασις τὸ μὴ ἀεὶ δυνάμενον μὴ εἶναι, ἀνάγκη τὰς ἀποφάσεις ἀμφοῖν τῷ αὐτῷ ὑπάρχειν, καὶ εἶναι μέσον τοῦ ἀεὶ ὄντος καὶ τοῦ ἀεὶ μὴ ὄντος τὸ δυνάμενον εἶναι καὶ μὴ εἶναι·
And since the negation of 'that which is always capable of being' is 'that which is not always capable of being', while 'that which is always capable of not being' is the contrary, whose negation is 'that which is not always capable of not being', it is necessary that the negations of both should belong to the same thing, and that there should be an intermediate between that which always is and that which always is not, namely, that which is capable of being and of not being.
ἡ γὰρ ἑκατέρου ἀπόφασίς ποτε ὑπάρξει, εἰ μὴ εἴη ἀεί.
For the negation of each will belong to it at some time, if it is not always.
ὥστε καὶ τὸ μὴ ἀεὶ μὴ ὂν ἔσται ποτὲ καὶ οὐκ ἔσται, καὶ τὸ μὴ ἀεὶ δυνάμενον εἶναι δηλονότι, ἀλλά ποτε ὄν· ὥστε καὶ μὴ εἶναι.
Consequently, that which is not always non-being will at some time be and not be, and clearly also that which is not always capable of being, but is at some time; so that it also is not.
τὸ αὐτὸ ἄῤ ἔσται δυνατὸν εἶναι καὶ μή, καὶ τοῦτʼ ἔστιν ἀμφοῖν μέσον.
Therefore, the same thing will be capable of being and not being, and this is the intermediate between both.
λόγος δὲ καθόλου ὅδε.
And the universal argument is as follows.