§14.5εἰ οὖν καὶ τὸ μὴ τιθέναι τὸ ἀγαθὸν ἐν ταῖς ἀρχαῖς καὶ τὸ τιθέναι οὕτως ἀδύνατον, δῆλον ὅτι αἱ ἀρχαὶ οὐκ ὀρθῶς ἀποδίδονται οὐδὲ αἱ πρῶται οὐσίαι.
If, then, both not to posit the good among the principles, and to posit it in this way, are impossible, it is clear that the principles are not correctly assigned, nor are the primary substances.
οὐκ ὀρθῶς δʼ ὑπολαμβάνει οὐδʼ εἴ τις παρεικάζει τὰς τοῦ ὅλου ἀρχὰς τῇ τῶν ζῴων καὶ φυτῶν, ὅτι ἐξ ἀορίστων ἀτελῶν τε ἀεὶ τὰ τελειότερα, διὸ καὶ ἐπὶ τῶν πρώτων οὕτως ἔχειν φησίν, ὥστε μηδὲ ὄν τι εἶναι τὸ ἓν αὐτό.
Nor does anyone conceive correctly if he compares the principles of the whole to those of animals and plants, on the ground that the more perfect always come from indefinite and imperfect things, and therefore says that this is so even in the case of the first things, so that the one itself is not even an existing thing.
εἰσὶ γὰρ καὶ ἐνταῦθα τέλειαι αἱ ἀρχαὶ ἐξ ὧν ταῦτα· ἄνθρωπος γὰρ ἄνθρωπον γεννᾷ, καὶ οὐκ ἔστι τὸ σπέρμα πρῶτον.
For even here the principles from which these things come are perfect; for man generates man, and the seed is not first.
ἄτοπον δὲ καὶ τὸ τόπον ἅμα τοῖς στερεοῖς τοῖς μαθηματικοῖς ποιῆσαι (ὁ μὲν γὰρ τόπος τῶν καθʼ ἕκαστον ἴδιος, διὸ χωριστὰ τόπῳ, τὰ δὲ μαθηματικὰ οὐ πού), καὶ τὸ εἰπεῖν μὲν ὅτι ποὺ ἔσται, τί δέ ἐστιν ὁ τόπος μή.
And it is also absurd to make place along with the mathematical solids (for place is peculiar to individual things, which is why they are separate in place, but mathematical things are not somewhere), and to say that they will be somewhere, but not what place is.
—ἔδει δὲ τοὺς λέγοντας ἐκ στοιχείων εἶναι τὰ ὄντα καὶ τῶν ὄντων τὰ πρῶτα τοὺς ἀριθμούς, διελομένους πῶς ἄλλο ἐξ ἄλλου ἐστίν, οὕτω λέγειν τίνα τρόπον ὁ ἀριθμός ἐστιν ἐκ τῶν ἀρχῶν.
But those who say that existing things are from elements, and that the first of existing things are numbers, ought to have distinguished in what ways one thing is from another, and so to have stated in what manner number is from the principles.
πότερον μίξει;
Is it by mixture?
ἀλλʼ οὔτε πᾶν μικτόν, τό τε γιγνόμενον ἕτερον, οὐκ ἔσται τε χωριστὸν τὸ ἓν οὐδʼ ἑτέρα φύσις· οἱ δὲ βούλονται.
But neither is everything mixable, and the product is different, and the one will not be separate nor a distinct nature; yet they wish it to be.
ἀλλὰ συνθέσει, ὥσπερ συλλαβή;
Or by composition, like a syllable?
ἀλλὰ θέσιν τε ἀνάγκη ὑπάρχειν, καὶ χωρὶς ὁ νοῶν νοήσει τὸ ἓν καὶ τὸ πλῆθος.
But then position must belong to it, and he who thinks of them will think of the one and the multiplicity separately.
τοῦτʼ οὖν ἔσται ὁ ἀριθμός, μονὰς καὶ πλῆθος, ἢ τὸ ἓν καὶ ἄνισον.
This, then, will be number—a unit and multiplicity, or the one and the unequal.
καὶ ἐπεὶ τὸ ἐκ τινῶν εἶναι ἔστι μὲν ὡς ἐνυπαρχόντων ἔστι δὲ ὡς οὔ, ποτέρως ὁ ἀριθμός;
And since being from certain things can mean either that they are inherent or that they are not, in which way is number so?
οὕτως γὰρ ὡς ἐνυπαρχόντων οὐκ ἔστιν ἀλλʼ ἢ ὧν γένεσις ἔστιν.
For in the sense of their being inherent, this is not possible except for things which have generation.
ἀλλʼ ὡς ἀπὸ σπέρματος;
Or is it as from a seed?
ἀλλʼ οὐχ οἷόν τε τοῦ ἀδιαιρέτου τι ἀπελθεῖν.
But it is impossible for anything to be shed from the indivisible.
ἀλλʼ ὡς ἐκ τοῦ ἐναντίου μὴ ὑπομένοντος;
Or is it as from a contrary which does not persist?
ἀλλʼ ὅσα οὕτως ἔστι, καὶ ἐξ ἄλλου τινός ἐστιν ὑπομένοντος.
But all things which are in this way are also from something else which persists.
ἐπεὶ τοίνυν τὸ ἓν ὁ μὲν τῷ πλήθει ὡς ἐναντίον τίθησιν, ὁ δὲ τῷ ἀνίσῳ, ὡς ἴσῳ τῷ ἑνὶ χρώμενος, ὡς ἐξ ἐναντίων εἴη ἂν ὁ ἀριθμός· ἔστιν ἄρα τι ἕτερον ἐξ οὗ ὑπομένοντος καὶ θατέρου ἐστὶν ἢ γέγονεν.
Since, then, one person posits the one as contrary to multiplicity, and another as contrary to the unequal, treating the one as the equal, number would be as if from contraries; there must therefore be some other thing, from which as persisting, and from one of the contraries, it is or has been generated.
ἔτι τί δή ποτε τὰ μὲν ἄλλʼ ὅσα ἐξ ἐναντίων ἢ οἷς ἔστιν ἐναντία φθείρεται κἂν ἐκ παντὸς ᾖ, ὁ δὲ ἀριθμὸς οὔ;
Further, why on earth do all other things which are from contraries or which have contraries perish, even if they are from everything, while number does not?
περὶ τούτου γὰρ οὐθὲν λέγεται.
For nothing is said about this.
καίτοι καὶ ἐνυπάρχον καὶ μὴ ἐνυπάρχον φθείρει τὸ ἐναντίον, οἷον τὸ νεῖκος τὸ μῖγμα (καίτοι γε οὐκ ἔδει· οὐ γὰρ ἐκείνῳ γε ἐναντίον).
And yet, whether inherent or not inherent, the contrary destroys the contrary, for example, strife destroys the mixture (and yet it ought not, for it is not contrary to that).
—οὐθὲν δὲ διώρισται οὐδὲ ὁποτέρως οἱ ἀριθμοὶ αἴτιοι τῶν οὐσιῶν καὶ τοῦ εἶναι, πότερον ὡς ὅροι (οἷον αἱ στιγμαὶ τῶν μεγεθῶν, καὶ ὡς Εὔρυτος ἔταττε τίς ἀριθμὸς τίνος, οἷον ὁδὶ μὲν ἀνθρώπου ὁδὶ δὲ ἵππου, ὥσπερ οἱ τοὺς ἀριθμοὺς ἄγοντες εἰς τὰ σχήματα τρίγωνον καὶ τετράγωνον, οὕτως ἀφομοιῶν ταῖς ψήφοις τὰς μορφὰς τῶν φυτῶν), ἢ ὅτι λόγος ἡ συμφωνία ἀριθμῶν, ὁμοίως δὲ καὶ ἄνθρωπος καὶ τῶν ἄλλων ἕκαστον;
And nothing has been defined, either, as to in which of the two ways numbers are causes of substances and of being—whether as boundaries (as points are of magnitudes, and as Eurytus determined what number belongs to what, e.g. this number to man and that to horse, like those who bring numbers into the figures of triangle and square, thus assimilating with pebbles the forms of plants), or because harmony is a ratio of numbers, and similarly also man and each of the other things?
τὰ δὲ δὴ πάθη πῶς ἀριθμοί, τὸ λευκὸν καὶ γλυκὺ καὶ τὸ θερμόν;
And how indeed are attributes numbers—the white, the sweet, and the hot?
ὅτι δὲ οὐχ οἱ ἀριθμοὶ οὐσία οὐδὲ τῆς μορφῆς αἴτιοι, δῆλον· ὁ γὰρ λόγος ἡ οὐσία, ὁ δʼ ἀριθμὸς ὕλη.
But that numbers are not substance, nor causes of form, is clear; for the ratio is the substance, and number is matter.
οἷον σαρκὸς ἢ ὀστοῦ ἀριθμὸς ἡ οὐσία οὕτω, τρία πυρὸς γῆς δὲ δύο· καὶ ἀεὶ ὁ ἀριθμὸς ὃς ἂν ᾖ τινῶν ἐστιν, ἢ πύρινος ἢ γήϊνος ἢ μοναδικός, ἀλλʼ ἡ οὐσία τὸ τοσόνδʼ εἶναι πρὸς τοσόνδε κατὰ τὴν μῖξιν· τοῦτο δʼ οὐκέτι ἀριθμὸς ἀλλὰ λόγος μίξεως ἀριθμῶν σωματικῶν ἢ ὁποιωνοῦν.
For example, if the substance of flesh or bone is number in this way, three of fire and two of earth; and whatever number it may be, it is always a number of certain things, either of fire or of earth or of units, but the substance is the being of so much to so much in the mixture; and this is no longer a number, but a ratio of a mixture of numbers, whether bodily or of whatever kind.
οὔτε οὖν τῷ ποιῆσαι αἴτιος ὁ ἀριθμός, οὔτε ὅλως ὁ ἀριθμὸς οὔτε ὁ μοναδικός, οὔτε ὕλη οὔτε λόγος καὶ εἶδος τῶν πραγμάτων.
Therefore, number is not a cause by producing—neither number in general, nor that which consists of units—nor is it the matter, nor the ratio and form of things.
ἀλλὰ μὴν οὐδʼ ὡς τὸ οὗ ἕνεκα.
Nor indeed is it a cause as that for the sake of which.