§1.9#2ἐνδέχεταί τε καὶ εἶναι καὶ γίγνεσθαι ὅμοιον ὁτιοῦν καὶ μὴ εἰκαζόμενον πρὸς ἐκεῖνο, ὥστε καὶ ὄντος Σωκράτους καὶ μὴ ὄντος γένοιτʼ ἂν οἷος Σωκράτης· ὁμοίως δὲ δῆλον ὅτι κἂν εἰ ἦν ὁ Σωκράτης ἀΐδιος.
It is possible for anything to be or to become like something else without being modeled after it, so that whether Socrates exists or does not exist, a man like Socrates might arise; and it is clear that the same would hold even if Socrates were eternal.
ἔσται τε πλείω παραδείγματα τοῦ αὐτοῦ, ὥστε καὶ εἴδη, οἷον τοῦ ἀνθρώπου τὸ ζῷον καὶ τὸ δίπουν, ἅμα δὲ καὶ τὸ αὐτοάνθρωπος.
And there will be several patterns of the same thing, and therefore several Forms; for example, of 'man', 'animal' and 'two-footed', and at the same time 'man-himself'.
ἔτι οὐ μόνον τῶν αἰσθητῶν παραδείγματα τὰ εἴδη ἀλλὰ καὶ αὐτῶν, οἷον τὸ γένος, ὡς γένος εἰδῶν· ὥστε τὸ αὐτὸ ἔσται παράδειγμα καὶ εἰκών.
Further, the Forms will be patterns not only of sensible things but of themselves also—for example, the genus, as genus of forms; so that the same thing will be both pattern and image.
ἔτι δόξειεν ἂν ἀδύνατον εἶναι χωρὶς τὴν οὐσίαν καὶ οὗ ἡ οὐσία· ὥστε πῶς ἂν αἱ ἰδέαι οὐσίαι τῶν πραγμάτων οὖσαι χωρὶς εἶεν;
Further, it would seem impossible for the substance and that of which it is the substance to exist apart; how then, if the Ideas are the substances of things, could they exist apart?
ἐν δὲ τῷ Φαίδωνι οὕτω λέγεται, ὡς καὶ τοῦ εἶναι καὶ τοῦ γίγνεσθαι αἴτια τὰ εἴδη ἐστίν·
But in the Phaedo it is said in this way, that the Forms are causes both of being and of becoming.
καίτοι τῶν εἰδῶν ὄντων ὅμως οὐ γίγνεται τὰ μετέχοντα ἂν μὴ ᾖ τὸ κινῆσον, καὶ πολλὰ γίγνεται ἕτερα, οἷον οἰκία καὶ δακτύλιος, ὧν οὔ φαμεν εἴδη εἶναι·
And yet, though the Forms exist, the things that participate in them do not come into being unless there is something to impart motion; and many other things come into being, such as a house and a ring, of which we say there are no Forms.
ὥστε δῆλον ὅτι ἐνδέχεται καὶ τἆλλα καὶ εἶναι καὶ γίγνεσθαι διὰ τοιαύτας αἰτίας οἵας καὶ τὰ ῥηθέντα νῦν. —ἔτι εἴπερ εἰσὶν ἀριθμοὶ τὰ εἴδη, πῶς αἴτιοι ἔσονται;
So that it is clear that other things also can both be and become through such causes as those of the things just mentioned. — Further, if the Forms are numbers, how will they be causes?
πότερον ὅτι ἕτεροι ἀριθμοί εἰσι τὰ ὄντα, οἷον ὁδὶ μὲν ὁ ἀριθμὸς ἄνθρωπος ὁδὶ δὲ Σωκράτης ὁδὶ δὲ Καλλίας;
Is it because existing things are other numbers, e.g. this number is man, this Socrates, and this Callias?
τί οὖν ἐκεῖνοι τούτοις αἴτιοί εἰσιν;
Why then are those causes of these?
οὐδὲ γὰρ εἰ οἱ μὲν ἀΐδιοι οἱ δὲ μή, οὐδὲν διοίσει.
For even if the former are eternal and the latter are not, it will make no difference.
εἰ δʼ ὅτι λόγοι ἀριθμῶν τἀνταῦθα, οἷον ἡ συμφωνία, δῆλον ὅτι ἐστὶν ἕν γέ τι ὧν εἰσὶ λόγοι.
But if it is because things here are ratios of numbers (e.g. harmony), it is clear that there is some one thing of which they are ratios.
εἰ δή τι τοῦτο, ἡ ὕλη, φανερὸν ὅτι καὶ αὐτοὶ οἱ ἀριθμοὶ λόγοι τινὲς ἔσονται ἑτέρου πρὸς ἕτερον.
If then this is something, namely matter, it is manifest that the numbers themselves will also be certain ratios of one thing to another.
λέγω δʼ οἷον, εἰ ἔστιν ὁ Καλλίας λόγος ἐν ἀριθμοῖς πυρὸς καὶ γῆς καὶ ὕδατος καὶ ἀέρος, καὶ ἄλλων τινῶν ὑποκειμένων ἔσται καὶ ἡ ἰδέα ἀριθμός· καὶ αὐτοάνθρωπος, εἴτʼ ἀριθμός τις ὢν εἴτε μή, ὅμως ἔσται λόγος ἐν ἀριθμοῖς τινῶν καὶ οὐκ ἀριθμός, οὐδʼ ἔσται τις διὰ ταῦτα ἀριθμός.
I mean, for instance, if Callias is a ratio in numbers of fire, earth, water, and air, his Idea also will be a number of certain other underlying things; and 'man-himself', whether it is a certain number or not, will still be a ratio in numbers of certain things and not a number, nor will it be a number because of this.
ἔτι ἐκ πολλῶν ἀριθμῶν εἷς ἀριθμὸς γίγνεται, ἐξ εἰδῶν δὲ ἓν εἶδος πῶς;
Further, one number is formed from many numbers, but how can one Form be formed from Forms?
εἰ δὲ μὴ ἐξ αὐτῶν ἀλλʼ ἐκ τῶν ἐν τῷ ἀριθμῷ, οἷον ἐν τῇ μυριάδι, πῶς ἔχουσιν αἱ μονάδες;
And if it is not from them but from the units in the number (for instance, in the ten thousand), how are the units circumstanced?
εἴτε γὰρ ὁμοειδεῖς, πολλὰ συμβήσεται ἄτοπα, εἴτε μὴ ὁμοειδεῖς, μήτε αὐταὶ ἀλλήλαις μήτε αἱ ἄλλαι πᾶσαι πάσαις·
For if they are of the same kind, many absurdities will follow, and if they are not of the same kind, neither will those in the same number be like one another, nor will all the others be like all.
τίνι γὰρ διοίσουσιν ἀπαθεῖς οὖσαι;
For in what will they differ, being without properties?
οὔτε γὰρ εὔλογα ταῦτα οὔτε ὁμολογούμενα τῇ νοήσει.
For these views are neither reasonable nor consistent with thought.
ἔτι δʼ ἀναγκαῖον ἕτερον γένος ἀριθμοῦ κατασκευάζειν περὶ ὃ ἡ ἀριθμητική, καὶ πάντα τὰ μεταξὺ λεγόμενα ὑπό τινων, ἃ πῶς ἢ ἐκ τίνων ἐστὶν ἀρχῶν;
Further, it is necessary to construct another kind of number, about which arithmetic is concerned, and all the things called 'intermediates' by some; and how or from what principles do these exist?
ἢ διὰ τί μεταξὺ τῶν δεῦρό τʼ ἔσται καὶ αὐτῶν;
Or why will they be intermediate between the things here and those?
ἔτι αἱ μονάδες αἱ ἐν τῇ δυάδι ἑκατέρα ἔκ τινος προτέρας δυάδος· καίτοι ἀδύνατον.
Further, each of the units in the dyad must come from some prior dyad; and yet this is impossible.
ἔτι διὰ τί ἓν ὁ ἀριθμὸς συλλαμβανόμενος;
Further, why is a number, taken collectively, one?
ἔτι δὲ πρὸς τοῖς εἰρημένοις, εἴπερ εἰσὶν αἱ μονάδες διάφοροι, ἐχρῆν οὕτω λέγειν ὥσπερ καὶ ὅσοι τὰ στοιχεῖα τέτταρα ἢ δύο λέγουσιν· καὶ γὰρ τούτων ἕκαστος οὐ τὸ κοινὸν λέγει στοιχεῖον, οἷον τὸ σῶμα, ἀλλὰ πῦρ καὶ γῆν, εἴτʼ ἔστι τι κοινόν, τὸ σῶμα, εἴτε μή.
And besides what has been said, if the units are different, they ought to speak in the same way as those who say the elements are four or two; for each of these speaks not of a common element, e.g. body, but of fire and earth, whether there is a common element, body, or not.
νῦν δὲ λέγεται ὡς ὄντος τοῦ ἑνὸς ὥσπερ πυρὸς ἢ ὕδατος ὁμοιομεροῦς· εἰ δʼ οὕτως, οὐκ ἔσονται οὐσίαι οἱ ἀριθμοί, ἀλλὰ δῆλον ὅτι, εἴπερ ἐστί τι ἓν αὐτὸ καὶ τοῦτό ἐστιν ἀρχή, πλεοναχῶς λέγεται τὸ ἕν·
But as it is, they speak of 'the one' as if it were homogeneous, like fire or water; but if this is so, numbers will not be substances.
ἄλλως γὰρ ἀδύνατον. —βουλόμενοι δὲ τὰς οὐσίας ἀνάγειν εἰς τὰς ἀρχὰς μήκη μὲν τίθεμεν ἐκ βραχέος καὶ μακροῦ, ἔκ τινος μικροῦ καὶ μεγάλου, καὶ ἐπίπεδον ἐκ πλατέος καὶ στενοῦ, σῶμα δʼ ἐκ βαθέος καὶ ταπεινοῦ.
And it is clear that if there is a 'one-itself' and this is a principle, 'the one' is said in many ways; for otherwise it is impossible. — And wishing to reduce substances to their principles, we posit lengths as coming from 'the short and long', from a certain 'small and great', and plane from 'the wide and narrow', and body from 'the deep and shallow'.
καίτοι πῶς ἕξει ἢ τὸ ἐπίπεδον γραμμὴν ἢ τὸ στερεὸν γραμμὴν καὶ ἐπίπεδον;
Yet how will the plane contain a line, or the solid a line and a plane?
ἄλλο γὰρ γένος τὸ πλατὺ καὶ στενὸν καὶ βαθὺ καὶ ταπεινόν·
For the wide and narrow, and the deep and shallow, are another genus.
ὥσπερ οὖν οὐδʼ ἀριθμὸς ὑπάρχει ἐν αὐτοῖς, ὅτι τὸ πολὺ καὶ ὀλίγον ἕτερον τούτων, δῆλον ὅτι οὐδʼ ἄλλο οὐθὲν τῶν ἄνω ὑπάρξει τοῖς κάτω.
Therefore, just as number is not present in them, because the 'many and few' is different from these, it is clear that none of the other higher things will be present in the lower.