§13.2#2εἰ δὲ ταῦτα, καὶ ζῷα ἔσονται, εἴπερ καὶ αἰσθήσεις.
And if these exist, there will also be animals, since there are also senses.
ἔτι γράφεται ἔνια καθόλου ὑπὸ τῶν μαθηματικῶν παρὰ ταύτας τὰς οὐσίας.
Furthermore, some universal propositions are proved by mathematicians, which extend beyond these substances.
ἔσται οὖν καὶ αὕτη τις ἄλλη οὐσία μεταξὺ κεχωρισμένη τῶν τʼ ἰδεῶν καὶ τῶν μεταξύ, ἣ οὔτε ἀριθμός ἐστιν οὔτε στιγμαὶ οὔτε μέγεθος οὔτε χρόνος.
There will therefore be some other separate substance between the Ideas and the intermediates, which is neither number nor points nor magnitude nor time.
εἰ δὲ τοῦτο ἀδύνατον, δῆλον ὅτι κἀκεῖνα ἀδύνατον εἶναι κεχωρισμένα τῶν αἰσθητῶν.
But if this is impossible, it is clear that those too cannot exist separated from sensible things.
ὅλως δὲ τοὐναντίον συμβαίνει καὶ τοῦ ἀληθοῦς καὶ τοῦ εἰωθότος ὑπολαμβάνεσθαι, εἴ τις θήσει οὕτως εἶναι τὰ μαθηματικὰ ὡς κεχωρισμένας τινὰς φύσεις.
In general, the opposite of the truth and of what is usually believed happens if one posits the objects of mathematics to exist in this way as certain separate natures.
ἀνάγκη γὰρ διὰ τὸ μὲν οὕτως εἶναι αὐτὰς προτέρας εἶναι τῶν αἰσθητῶν μεγεθῶν, κατὰ τὸ ἀληθὲς δὲ ὑστέρας· τὸ γὰρ ἀτελὲς μέγεθος γενέσει μὲν πρότερόν ἐστι, τῇ οὐσίᾳ δʼ ὕστερον, οἷον ἄψυχον ἐμψύχου.
For it is necessary, on the account of their existing in this way, that they should be prior to sensible magnitudes, whereas in truth they are posterior; for the incomplete magnitude is prior in generation, but posterior in substance, as the inanimate is to the animate.
ἔτι τίνι καὶ πότʼ ἔσται ἓν τὰ μαθηματικὰ μεγέθη;
Furthermore, by what and when will mathematical magnitudes be one?
τὰ μὲν γὰρ ἐνταῦθα ψυχῇ ἢ μέρει ψυχῆς ἢ ἄλλῳ τινί, εὐλόγως (εἰ δὲ μή, πολλά, καὶ διαλύεται), ἐκείνοις δὲ διαιρετοῖς καὶ ποσοῖς οὖσι τί αἴτιον τοῦ ἓν εἶναι καὶ συμμένειν;
For the things here are one by soul or a part of soul or some other thing, reasonably enough (and if not, they are many and are dissolved); but for those things, which are divisible and are quantities, what is the cause of their being one and holding together?
ἔτι αἱ γενέσεις δηλοῦσιν.
Furthermore, generations show this.
πρῶτον μὲν γὰρ ἐπὶ μῆκος γίγνεται, εἶτα ἐπὶ πλάτος, τελευταῖον δʼ εἰς βάθος, καὶ τέλος ἔσχεν.
For first it comes to be in length, then in breadth, and finally in depth, and has its limit.
εἰ οὖν τὸ τῇ γενέσει ὕστερον τῇ οὐσίᾳ πρότερον, τὸ σῶμα πρότερον ἂν εἴη ἐπιπέδου καὶ μήκους·
If, then, that which is posterior in generation is prior in substance, body would be prior to plane and length.
καὶ ταύτῃ καὶ τέλειον καὶ ὅλον μᾶλλον, ὅτι ἔμψυχον γίγνεται· γραμμὴ δὲ ἔμψυχος ἢ ἐπίπεδον πῶς ἂν εἴη;
And in this way it is also more complete and a whole, because it becomes animate; but how could there be an animate line or plane?
ὑπὲρ γὰρ τὰς αἰσθήσεις τὰς ἡμετέρας ἂν εἴη τὸ ἀξίωμα.
For the assumption would be beyond our senses.
ἔτι τὸ μὲν σῶμα οὐσία τις (ἤδη γὰρ ἔχει πως τὸ τέλειον), αἱ δὲ γραμμαὶ πῶς οὐσίαι;
Furthermore, body is a kind of substance (for it already has completeness in a way), but how are lines substances?
οὔτε γὰρ ὡς εἶδος καὶ μορφή τις, οἷον εἰ ἄρα ἡ ψυχὴ τοιοῦτον, οὔτε ὡς ἡ ὕλη, οἷον τὸ σῶμα· οὐθὲν γὰρ ἐκ γραμμῶν οὐδʼ ἐπιπέδων οὐδὲ στιγμῶν φαίνεται συνίστασθαι δυνάμενον, εἰ δʼ ἦν οὐσία τις ὑλική, τοῦτʼ ἂν ἐφαίνετο δυνάμενα πάσχειν.
For they are neither like a form and a kind of shape, as the soul is if indeed it is such, nor like matter, as body is; for nothing appears to be able to be composed of lines or planes or points, whereas if they were some kind of material substance, they would appear to be capable of undergoing this.
τῷ μὲν οὖν λόγῳ ἔστω πρότερα, ἀλλʼ οὐ πάντα ὅσα τῷ λόγῳ πρότερα καὶ τῇ οὐσίᾳ πρότερα.
Let them, then, be prior in definition, but not everything that is prior in definition is also prior in substance.
τῇ μὲν γὰρ οὐσίᾳ πρότερα ὅσα χωριζόμενα τῷ εἶναι ὑπερβάλλει, τῷ λόγῳ δὲ ὅσων οἱ λόγοι ἐκ τῶν λόγων· ταῦτα δὲ οὐχ ἅμα ὑπάρχει.
For those things are prior in substance which, when separated, excel in being; and those are prior in definition whose definitions are made up of the definitions of others; and these two do not belong together.
εἰ γὰρ μὴ ἔστι τὰ πάθη παρὰ τὰς οὐσίας, οἷον κινούμενόν τι ἢ λευκόν, τοῦ λευκοῦ ἀνθρώπου τὸ λευκὸν πρότερον κατὰ τὸν λόγον ἀλλʼ οὐ κατὰ τὴν οὐσίαν· οὐ γὰρ ἐνδέχεται εἶναι κεχωρισμένον ἀλλʼ ἀεὶ ἅμα τῷ συνόλῳ ἐστίν (σύνολον δὲ λέγω τὸν ἄνθρωπον τὸν λευκόν), ὥστε φανερὸν ὅτι οὔτε τὸ ἐξ ἀφαιρέσεως πρότερον οὔτε τὸ ἐκ προσθέσεως ὕστερον· ἐκ προσθέσεως γὰρ τῷ λευκῷ ὁ λευκὸς ἄνθρωπος λέγεται.
For if attributes do not exist apart from substances, as for example a moving thing or a white thing, 'white' is prior in definition to 'white man', but not prior in substance; for it cannot exist separated, but is always together with the concrete whole (and by 'concrete whole' I mean the 'white man'), so that it is clear that neither is that which is by abstraction prior, nor that which is by addition posterior; for 'white man' is said of 'white' by addition.
ὅτι μὲν οὖν οὔτε οὐσίαι μᾶλλον τῶν σωμάτων εἰσὶν οὔτε πρότερα τῷ εἶναι τῶν αἰσθητῶν ἀλλὰ τῷ λόγῳ μόνον, οὔτε κεχωρισμένα που εἶναι δυνατόν, εἴρηται ἱκανῶς·
That they are, then, neither substances to a greater degree than bodies, nor prior in being to sensible things, but only in definition, nor is it possible for them to exist separated anywhere, has been sufficiently stated.
ἐπεὶ δʼ οὐδʼ ἐν τοῖς αἰσθητοῖς ἐνεδέχετο αὐτὰ εἶναι, φανερὸν ὅτι ἢ ὅλως οὐκ ἔστιν ἢ τρόπον τινὰ ἔστι καὶ διὰ τοῦτο οὐχ ἁπλῶς ἔστιν· πολλαχῶς γὰρ τὸ εἶναι λέγομεν.
But since they could not exist in sensible things either, it is clear that they either do not exist at least at all, or they exist in a certain way, and therefore do not exist in an unqualified sense; for we speak of being in many ways.