§1.1111 Πρῶτον δὲ διαιρετέον πῶς ἀγένητα καὶ γενητά φαμεν καὶ φθαρτὰ καὶ ἄφθαρτα· πολλαχῶς γὰρ λεγομένων, κἂν μηδὲν διαφέρῃ πρὸς τὸν λόγον, ἀνάγκη τὴν διάνοιαν ἀορίστως ἔχειν, ἄν τις τῷ διαιρουμένῳ πολλαχῶς ὡς ἀδιαιρέτῳ χρῆται· ἄδηλον γὰρ κατὰ ποίαν φύσιν αὐτῷ συμβαίνει τὸ λεχθέν.
11 First, we must distinguish in what ways we speak of 'ungenerated' and 'generated', and 'corruptible' and 'incorruptible'; for since they are spoken of in many ways, even if it makes no difference to the argument, the mind must be in an indefinite state if anyone uses that which is spoken of in many ways as if it were undivided; for it is unclear according to which nature the stated thing belongs to it.
λέγεται δʼ ἀγένητον ἕνα μὲν τρόπον ἐὰν ᾖ τι νῦν πρότερον μὴ ὂν ἄνευ γενέσεως καὶ μεταβολῆς, καθάπερ ἔνιοι τὸ ἅπτεσθαι καὶ τὸ κινεῖσθαι λέγουσιν· οὐ γὰρ εἶναι γίνεσθαί φασιν ἁπτόμενον, οὐδὲ κινούμενον.
Now, 'ungenerated' is spoken of in one way if something now is, which was not before, without generation and change, just as some say concerning 'touching' and 'being moved'; for they say there is no coming to be of touching, nor of being moved.
ἕνα δʼ εἴ τι ἐνδεχόμενον γίνεσθαι ἢ γενέσθαι μή ἐστιν· ὁμοίως γὰρ καὶ τοῦτο ἀγένητον, ὅτι ἐνδέχεται γενέσθαι.
In another way, if something capable of coming to be or having come to be, is not; for in like manner this too is 'ungenerated', because it is capable of coming to be.
ἕνα δʼ εἴ τι ὅλως ἀδύνατον γενέσθαι, ὥσθʼ ὁτὲ μὲν εἶναι ὁτὲ δὲ μή.
In another way, if it is completely impossible for something to come to be, so as to be at one time and not at another.
τὸ δʼ ἀδύνατον λέγεται διχῶς. ἢ γὰρ τῷ μὴ ἀληθὲς εἶναι εἰπεῖν ὅτι γένοιτʼ ἄν, ἢ τῷ μὴ ῥᾳδίως μηδὲ ταχὺ ἢ καλῶς.
And 'impossible' is spoken of in two ways: either because it is not true to say that it could come to be, or because it cannot do so easily, quickly, or well.
τὸν αὐτὸν δὲ τρόπον καὶ τὸ γενητὸν ἕνα μὲν εἰ μὴ ὂν πρότερον ὕστερον ἔστιν, εἴτε γενόμενον εἴτʼ ἄνευ τοῦ γίνεσθαι, ὁτὲ μὲν μὴ ὄν, πάλιν δʼ ὄν· ἕνα δʼ εἰ δυνατόν, εἴτε τῷ ἀληθεῖ διορισθέντος τοῦ δυνατοῦ εἴτε τῷ ῥᾳδίως· ἕνα δ᾿ ἐὰν ἡ γένεσις αὐτοῦ ἐκ τοῦ μὴ ὄντος εἰς τὸ ὄν, εἴτʼ ἤδη ὄντος, διὰ τοῦ γίνεσθαι δʼ ὄντος, εἴτε καὶ μήπω ὄντος, ἀλλ᾿ ἐνδεχομένου.
In the same way, 'generated' also is spoken of in one way if, not being previously, it is afterwards, whether having come to be or without coming to be, at one time not being, and again being; in another way if it is possible, whether 'possible' is defined by truth or by 'easily'; in another way, if its generation is from non-being into being, whether it is already being through the process of coming to be, or is not yet being but is possible.
καὶ φθαρτὸν δὲ καὶ ἄφθαρτον ὡσαύτως· εἴτε γὰρ πρότερόν τι ὂν ὕστερον ἢ μή ἐστιν ἢ ἐνδέχεται με` εἶναι, φθαρτὸν εἶναί φαμεν, εἴτε φθειρόμενόν ποτε καὶ μεταβάλλον, εἴτε μή.
And 'corruptible' and 'incorruptible' likewise: for if something being previously is afterwards either not or capable of not being, we say it is corruptible, whether it is being destroyed at some time and changing, or not.
ἔστι δʼ ὅτε καὶ τὸ διὰ τοῦ φθείρεσθαι ἐνδεχόμενον μὴ εἶναι φθαρτὸν εἶναί φαμεν, καὶ ἔτι ἄλλως τὸ ῥᾳδίως φθειρόμενον, ὃ εἴποι ἄν τις εὔφθαρτον.
And sometimes we also say that what is capable of not being through being destroyed is corruptible, and in yet another way what is easily destroyed, which one might call 'easily corruptible'.
καὶ περὶ τοῦ ἀφθάρτου ὁ αὐτὸς λόγος· ἢ γὰρ τὸ ἄνευ φθορᾶς ὁτὲ μὲν ὂν ὁτὲ δὲ μὴ ὄν, οἷον τὰς ἁφάς, ὅτι ἄνευ τοῦ φθείρεσθαι πρότερον οὖσαι ὕστερον οὐκ εἰσίν, ἢ τὸ ὂν μὲν δυνατὸν δὲ μὴ εἶναι, ἢ οὐκ ἐσόμενόν ποτε, νῦν δʼ ὄν· σὺ γὰρ εἶ, καὶ ἡ ἁφὴ νῦν· ἀλλʼ ὅμως φθαρτόν, ὅτι ἔσται ποτὲ ὅτε οὐκ ἀληθές σε εἰπεῖν ὅτι εἶ, οὐδὲ ταῦτα ἅπτεσθαι.
And concerning 'incorruptible' the same argument holds: for either that which without destruction is at one time being and at another non-being, like contacts, because having been before they are not afterwards without being destroyed, or that which is being but is capable of not being, or that which will never not be, but is now being; for you are, and the contact is now; but nevertheless it is corruptible, because there will be a time when it is not true to say that you are, nor that these things touch.
τὸ δὲ μάλιστα κυρίως, τὸ ὂν μέν, ἀδύνατον δὲ φθαρῆναι οὕτως ὥστε νῦν ὂν ὕστερον μὴ εἶναι ἢ ἐνδέχεσθαι μὴ εἶναι, ἢ καὶ τὸ μήπω ἐφθαρμένον, οὐκ ἐνδεχόμενον δʼ ὕστερον μὴ εἶναι.
But in the most proper sense, that which is indeed, but which is impossible to be destroyed in such a way that, being now, it is not afterwards or is capable of not being, or also that which is not yet destroyed, and is not capable of not being afterwards.
λέγεται δʼ ἄφθαρτον καὶ τὸ μὴ ῥᾳδίως φθειρόμενον.
And that which is not easily destroyed is also called incorruptible.
εἰ δὴ ταῦθʼ οὕτως ἔχει, σκεπτέον πῶς λέγομεν τὸ δυνατὸν καὶ ἀδύνατον· τό τε γὰρ κυριώτατα λεγόμενον ἄφθαρτον τῷ μὴ δύνασθαι φθαρῆναι ἄν, μηδʼ ὁτὲ μὲν εἶναι ὁτὲ δὲ μή· λέγεται δὲ καὶ τὸ ἀγένητον τὸ ἀδύνατον, καὶ τὸ μὴ δυνάμενον γενέσθαι οὕτως ὥστε πρότερον μὲν μὴ εἶναι ὕστερον δὲ εἶναι, οἷον τὴν διάμετρον σύμμετρον.
If indeed these things are so, we must consider how we speak of the 'possible' and the 'impossible'; for the most properly called 'incorruptible' is so by not being able to be destroyed, nor being at one time and not at another; and the 'ungenerated' is also spoken of as the 'impossible', namely that which is not able to come to be in such a way as not to be previously and to be afterwards, like the diagonal being commensurable.
εἰ δὴ τι δύναται κινηθῆναι στάδια ἑκατὸν ἢ ἆραι βάρος, ἀεὶ πρὸς τὸ πλεῖστον λέγομεν, οἷον τάλαντα ἆραι ἑκατὸν ἂ στάδια βαδίσαι ἑκατόν (καίτοι καὶ τὰ μόρια δύναται τὰ ἐντός, εἴπερ καὶ τὴν ὑπεροχήν), ὡς δέον ὁρίζεσθαι πρὸς τὸ τέλος καὶ τὴν ὑπεροχὴν τὴν δύναμιν.
If indeed something is able to move a hundred stades or lift a weight, we always speak with reference to the maximum, as for example to lift a hundred talents or to walk a hundred stades (although it is also able to do the parts within, since indeed it can do the excess), on the ground that the power must be defined with reference to the end and the excess.
ἀνάγκη μὲν οὖν τὸ δυνατὸν καθʼ ὑπεροχὴν τοσαδὶ καὶ τὰ ἐντὸς δύνασθαι, οἷον εἰ τάλαντα ἑκατὸν ἆραι, καὶ δύο, κἀν εἰ στάδια ἑκατόν, καὶ δύο δύνασθαι βαδίσαι.
Therefore, it is necessary that what is capable according to the excess of so much is also capable of the things within, as for example if it is capable of lifting a hundred talents, it is also capable of two, and if a hundred stades, it is also capable of walking two.
ἡ δὲ δύναμις τῆς ὑπεροχῆς ἐστίν· κἂν εἴ τι ἀδύνατον τοσονδὶ καθʼ ὑπερβαλὴν εἰπόντων, καὶ τὰ πλείω ἀδύνατον, οἷον ὁ χίλια βαδίσαι στάδια μὴ δυνάμενος δῆλον ὅτι καὶ χίλια καὶ ἕν.
But the power is of the excess; and if something is impossible of so much when we speak according to the excess, it is also impossible of the greater, as for example he who is not able to walk a thousand stades is clearly not able to walk a thousand and one.
μηδὲν δʼ ἡμᾶς παρενοχλείτω· διωρίσθω γὰρ κατὰ τῆς ὑπεροχῆς τὸ τέλος λεγόμενον τὸ κυρίως δυνατόν.
And let nothing trouble us; for let the end spoken of in accordance with the excess be defined as the properly 'possible'.
τάχα γὰρ ἐνσταίη τις ἂν ὡς οὐκ ἀνάγκη τὸ λεχθέν· ὁ γὰρ ὁρῶν στάδιον οὐ καὶ τὰ ἐντὸς ὄψεται μεγέθη, ἀλλά τοὐναντίον μᾶλλον ὁ δυνάμενος ἰδεῖν στιγμὴν ἢ ἀκοῦσαι μικροῦ ψόφου καὶ τῶν μειζόνων ἕξει αἴσθησιν.
For perhaps someone might object that what has been said is not necessary: for he who sees a stade will not also see the magnitudes within, but on the contrary, rather he who is able to see a point or to hear a small sound will also have perception of the greater things.
ἀλλʼ οὐδὲν διαφέρεὶ πρὸς τὸν λόγον· διωρίσθω γὰρ ἤτοι ἐπὶ τῆς δυνάμεως ἢ ἐπὶ τοῦ πράγματος ἡ ὑπερβολή.
But it makes no difference to the argument; for let the excess be defined either in respect of the power or in respect of the thing.
τὸ γὰρ λεγόμενον δῆλον· ἡ μὲν γὰρ ὄψις ἡ τοῦ ἐλάττονος ὑπερέχει, ἡ δὲ ταχυτὴς ἡ τοῦ πλείονος.
For what is said is clear: for sight is superior in respect of the smaller, but speed in respect of the greater.