§104ΦΑΙΔ. ἆρα μόνον τῶν ὄντων — τοῦτο γὰρ ἐρωτῶ — ἢ καὶ ἄλλο τι ὃ ἔστι μὲν οὐχ ὅπερ τὸ περιττόν, ὅμως δὲ δεῖ αὐτὸ μετὰ τοῦ ἑαυτοῦ ὀνόματος καὶ τοῦτο καλεῖν ἀεὶ διὰ τὸ οὕτω πεφυκέναι ὥστε τοῦ περιττοῦ μηδέποτε ἀπολείπεσθαι;
"Is it the only one among existing things—for this is what I am asking—or is there also some other thing which, though not the same as the odd, nevertheless must always be called by this name along with its own name, because it is so constituted by nature as never to be left behind by the odd?
λέγω δὲ αὐτὸ εἶναι οἷον καὶ ἡ τριὰς πέπονθε καὶ ἄλλα πολλά.
What I mean is that it is such as is the case with the triad and many other things.
σκόπει δὲ περὶ τῆς τριάδος.
Consider the case of the triad.
ἆρα οὐ δοκεῖ σοι τῷ τε αὑτῆς ὀνόματι ἀεὶ προσαγορευτέα εἶναι καὶ τῷ τοῦ περιττοῦ, ὄντος οὐχ ὅπερ τῆς τριάδος;
Do you not think it must always be addressed both by its own name and by that of the odd, even though the odd is not the same as the triad?
ἀλλ’ ὅμως οὕτως πέφυκε καὶ ἡ τριὰς καὶ ἡ πεμπτὰς καὶ ὁ ἥμισυς τοῦ ἀριθμοῦ ἅπας, ὥστε οὐκ ὢν ὅπερ τὸ περιττὸν ἀεὶ ἕκαστος αὐτῶν ἐστι περιττός·
But nevertheless, both the triad and the pentad and the entire half of the number are so constituted by nature, that although each of them is not the same as the odd, it is always odd.
καὶ αὖ τὰ δύο καὶ τέτταρα καὶ ἅπας ὁ ἕτερος αὖ στίχος τοῦ ἀριθμοῦ οὐκ ὢν ὅπερ τὸ ἄρτιον ὅμως ἕκαστος αὐτῶν ἄρτιός ἐστιν ἀεί·
And again, two and four and the entire other row of the number, though not the same as the even, nevertheless each of them is always even.
συγχωρεῖς ἢ οὔ; πῶς γὰρ οὔκ; ἔφη.
Do you agree or not?" "How could I not?" he said.
ὃ τοίνυν, ἔφη, βούλομαι δηλῶσαι, ἄθρει.
"Then look," he said, "at what I wish to show.
ἔστιν δὲ τόδε, ὅτι φαίνεται οὐ μόνον ἐκεῖνα τὰ ἐναντία ἄλληλα οὐ δεχόμενα, ἀλλὰ καὶ ὅσα οὐκ ὄντ’ ἀλλήλοις ἐναντία ἔχει ἀεὶ τἀναντία, οὐδὲ ταῦτα ἔοικε δεχομένοις ἐκείνην τὴν ἰδέαν ἣ ἂν τῇ ἐν αὐτοῖς οὔσῃ ἐναντία ᾖ, ἀλλ’ ἐπιούσης αὐτῆς ἤτοι ἀπολλύμενα ἢ ὑπεκχωροῦντα.
It is this: that not only those opposites do not seem to admit one another, but also all those things which, though not being opposites to one another, always have the opposites in them; these also do not seem to admit that form which is opposite to the one that is in them, but when it approaches, they either perish or withdraw.
ἢ οὐ φήσομεν τὰ τρία καὶ ἀπολεῖσθαι πρότερον καὶ ἄλλο ὁτιοῦν πείσεσθαι, πρὶν ὑπομεῖναι ἔτι τρία ὄντα ἄρτια γενέσθαι; πάνυ μὲν οὖν, ἔφη ὁ Κέβης.
Or shall we not say that three will perish first and suffer anything else whatever, before enduring, while still being three, to become even?" "Certainly indeed," said Cebes.
οὐδὲ μήν, ἦ δ’ ὅς, ἐναντίον γέ ἐστι δυὰς τριάδι. οὐ γὰρ οὖν. οὐκ ἄρα μόνον τὰ εἴδη τὰ ἐναντία οὐχ ὑπομένει ἐπιόντα ἄλληλα, ἀλλὰ καὶ ἄλλ’ ἄττα τὰ ἐναντία οὐχ ὑπομένει ἐπιόντα. ἀληθέστατα, ἔφη, λέγεις.
"And yet," he said, "the dyad is not the opposite to the triad." "Indeed not." "Therefore, not only the opposite forms do not endure the approach of one another, but also certain other things do not endure the approach of the opposites." "You speak most truly," he said.
βούλει οὖν, ἦ δ’ ὅς, ἐὰν οἷοί τ’ ὦμεν, ὁρισώμεθα ὁποῖα ταῦτά ἐστιν; πάνυ γε. ἆρ’ οὖν, ἔφη, ὦ Κέβης, τάδε εἴη ἄν, ἃ ὅτι ἂν κατάσχῃ μὴ μόνον ἀναγκάζει τὴν αὑτοῦ ἰδέαν αὐτὸ ἴσχειν, ἀλλὰ καὶ ἐναντίου αὐτῷ ἀεί τινος; πῶς λέγεις; ὥσπερ ἄρτι ἐλέγομεν.
"Do you wish then," he said, "if we are able, that we define what sort of things these are?" "Certainly." "Would they be these, then, Cebes," he said, "which, whatever they occupy, compel it not only to hold their own form, but also always that of something opposite to it?" "How do you mean?" "Just as we were saying.
οἶσθα γὰρ δήπου ὅτι ἃ ἂν ἡ τῶν τριῶν ἰδέα κατάσχῃ, ἀνάγκη αὐτοῖς οὐ μόνον τρισὶν εἶναι ἀλλὰ καὶ περιττοῖς. πάνυ γε. ἐπὶ τὸ τοιοῦτον δή, φαμέν, ἡ ἐναντία ἰδέα ἐκείνῃ τῇ μορφῇ ἣ ἂν τοῦτο ἀπεργάζηται οὐδέποτ’ ἂν ἔλθοι. οὐ γάρ. εἰργάζετο δέ γε ἡ περιττή; ναί. ἐναντία δὲ ταύτῃ ἡ τοῦ ἀρτίου; ναί. ἐπὶ τὰ τρία ἄρα ἡ τοῦ ἀρτίου ἰδέα οὐδέποτε ἥξει. οὐ δῆτα. ἄμοιρα δὴ τοῦ ἀρτίου τὰ τρία. ἄμοιρα. ἀνάρτιος ἄρα ἡ τριάς. ναί.
For you surely know that whatever the form of three occupies, it is necessary for them not only to be three but also to be odd." "Certainly." "Then, we say, the form opposite to that shape which produces this would never come upon such a thing." "No indeed." "But did the odd produce it?" "Yes." "And is the form of the even opposite to this?" "Yes." "Therefore, the form of the even will never come upon the three." "Certainly not." "So three has no share in the even." "No share." "The triad is therefore uneven." "Yes."