§24ΣΩ. λέγω τοίνυν τὰ δύο ἃ προτίθεμαι ταὔτʼ εἶναι ἅπερ νυνδή, τὸ μὲν ἄπειρον, τὸ δὲ πέρας ἔχον·
SOCRATES: I say, then, that the two which I propose are the very same as just now, one being the unlimited, and the other having limit.
ὅτι δὲ τρόπον τινὰ τὸ ἄπειρον πόλλʼ ἐστί, πειράσομαι φράζειν.
How the unlimited is in a certain way many, I will try to explain.
τὸ δὲ πέρας ἔχον ἡμᾶς περιμενέτω.
As for that which has limit, let it wait for us.
ΠΡΩ. μένει.
PROTARCHUS: It waits.
ΣΩ. σκέψαι δή.
SOCRATES: Consider, then.
χαλεπὸν μὲν γὰρ καὶ ἀμφισβητήσιμον ὃ κελεύω σε σκοπεῖν, ὅμως δὲ σκόπει.
For what I bid you examine is difficult and disputable, yet examine it.
θερμοτέρου καὶ ψυχροτέρου πέρι πρῶτον ὅρα πέρας εἴ ποτέ τι νοήσαις ἄν, ἢ τὸ μᾶλλόν τε καὶ ἧττον ἐν αὐτοῖς οἰκοῦντε τοῖς γένεσιν, ἕωσπερ ἂν ἐνοικῆτον, τέλος οὐκ ἂν ἐπιτρεψαίτην γίγνεσθαι· γενομένης γὰρ τελευτῆς καὶ αὐτὼ τετελευτήκατον.
See first concerning the hotter and the colder whether you could ever conceive any limit of them, or whether "the more and less" dwelling in these very kinds, as long as they dwell in them, would not permit any end to come about; for once an end has come about, they themselves also have ended.
ΠΡΩ. ἀληθέστατα λέγεις.
PROTARCHUS: You speak most truly.
ΣΩ. ἀεὶ δέ γε, φαμέν, ἔν τε τῷ θερμοτέρῳ καὶ ψυχροτέρῳ τὸ μᾶλλόν τε καὶ ἧττον ἔνι.
SOCRATES: But indeed, we say, "the more and less" is always in the hotter and the colder.
ΠΡΩ. καὶ μάλα.
PROTARCHUS: Very much so.
ΣΩ. ἀεὶ τοίνυν ὁ λόγος ἡμῖν σημαίνει τούτω μὴ τέλος ἔχειν· ἀτελῆ δʼ ὄντε δήπου παντάπασιν ἀπείρω γίγνεσθον.
SOCRATES: Always, then, our argument indicates that these two do not have an end; and being without an end, they surely become altogether unlimited.
ΠΡΩ. καὶ σφόδρα γε, ὦ Σώκρατες.
PROTARCHUS: Most certainly, Socrates.
ΣΩ. ἀλλʼ εὖ γε, ὦ φίλε Πρώταρχε, ὑπέλαβες καὶ ἀνέμνησας ὅτι καὶ τὸ σφόδρα τοῦτο, ὃ σὺ νῦν ἐφθέγξω, καὶ τό γε ἠρέμα τὴν αὐτὴν δύναμιν ἔχετον τῷ μᾶλλόν τε καὶ ἧττον· ὅπου γὰρ ἂν ἐνῆτον, οὐκ ἐᾶτον εἶναι ποσὸν ἕκαστον, ἀλλʼ ἀεὶ σφοδρότερον ἡσυχαιτέρου καὶ τοὐναντίον ἑκάσταις πράξεσιν ἐμποιοῦντε τὸ πλέον καὶ τὸ ἔλαττον ἀπεργάζεσθον, τὸ δὲ ποσὸν ἀφανίζετον.
SOCRATES: Indeed, you have taken it up well, my dear Protarchus, and reminded me that also this "extremely," which you have just uttered, and the "gently" have the same power as "the more and less." For wherever they are present, they do not permit each thing to be a definite quantity, but always by instilling a stronger rather than a quieter, and the opposite, they produce the more and the less in each action, and make the definite quantity disappear.
ὃ γὰρ ἐλέχθη νυνδή, μὴ ἀφανίσαντε τὸ ποσόν, ἀλλʼ ἐάσαντε αὐτό τε καὶ τὸ μέτριον ἐν τῇ τοῦ μᾶλλον καὶ ἧττον καὶ σφόδρα καὶ ἠρέμα ἕδρᾳ ἐγγενέσθαι, αὐτὰ ἔρρει ταῦτα ἐκ τῆς αὑτῶν χώρας ἐν ᾗ ἐνῆν.
For, as was said just now, if they did not make the definite quantity disappear, but allowed both itself and the moderate to come to be in the seat of "the more and less" and "extremely" and "gently," these very things would flow away from their own place in which they were.
οὐ γὰρ ἔτι θερμότερον οὐδὲ ψυχρότερον εἴτην ἂν λαβόντε τὸ ποσόν· προχωρεῖ γὰρ καὶ οὐ μένει τό τε θερμότερον ἀεὶ καὶ τὸ ψυχρότερον ὡσαύτως, τὸ δὲ ποσὸν ἔστη καὶ προϊὸν ἐπαύσατο.
For they would no longer be hotter or colder once they received the definite quantity; for the hotter always goes forward and does not stay, and the colder likewise, whereas the definite quantity has stood still and ceased to go forward.
κατὰ δὴ τοῦτον τὸν λόγον ἄπειρον γίγνοιτʼ ἂν τὸ θερμότερον καὶ τοὐναντίον ἅμα.
According to this argument, then, the hotter and its opposite would become unlimited.
ΠΡΩ. φαίνεται γοῦν, ὦ Σώκρατες·
PROTARCHUS: It appears so indeed, Socrates.
ἔστι δʼ, ὅπερ εἶπες, οὐ ῥᾴδια ταῦτα συνέπεσθαι.
But, as you said, these things are not easy to follow.
τὸ δὲ εἰς αὖθίς τε καὶ αὖθις ἴσως λεχθέντα τόν τε ἐρωτῶντα καὶ τὸν ἐρωτώμενον ἱκανῶς ἂν συμφωνοῦντας ἀποφήναιεν.
However, perhaps if they are spoken of again and again, they might show the questioner and the questioned to be sufficiently in agreement.
ΣΩ. ἀλλʼ εὖ μὲν λέγεις καὶ πειρατέον οὕτω ποιεῖν.
SOCRATES: You speak well, and we must try to do so.
νῦν μέντοι ἄθρει τῆς τοῦ ἀπείρου φύσεως εἰ τοῦτο δεξόμεθα σημεῖον, ἵνα μὴ πάντʼ ἐπεξιόντες μηκύνωμεν.
For now, however, observe whether we shall accept this as the sign of the nature of the unlimited, so that we do not lengthen the discourse by going through everything.
ΠΡΩ. τὸ ποῖον δὴ λέγεις;
PROTARCHUS: What kind of thing do you mean?
§25ΣΩ. ὁπόσʼ ἂν ἡμῖν φαίνηται μᾶλλόν τε καὶ ἧττον γιγνόμενα καὶ τὸ σφόδρα καὶ ἠρέμα δεχόμενα καὶ τὸ λίαν καὶ ὅσα τοιαῦτα πάντα, εἰς τὸ τοῦ ἀπείρου γένος ὡς εἰς ἓν δεῖ πάντα ταῦτα τιθέναι, κατὰ τὸν ἔμπροσθεν λόγον ὃν ἔφαμεν ὅσα διέσπασται καὶ διέσχισται συναγαγόντας χρῆναι κατὰ δύναμιν μίαν ἐπισημαίνεσθαί τινα φύσιν, εἰ μέμνησαι.
SOCRATES: Whatever things appear to us to become "more and less," and receive "extremely" and "gently," and "too much," and all such things, we must place all of them into the kind of the unlimited as into one, according to the previous argument, in which we said we must collect all things that are pulled apart and split, and, as far as possible, mark them as some one nature, if you remember.
ΠΡΩ. μέμνημαι.
PROTARCHUS: I remember.
ΣΩ. οὐκοῦν τὰ μὴ δεχόμενα ταῦτα, τούτων δὲ τὰ ἐναντία πάντα δεχόμενα, πρῶτον μὲν τὸ ἴσον καὶ ἰσότητα, μετὰ δὲ τὸ ἴσον τὸ διπλάσιον καὶ πᾶν ὅτιπερ ἂν πρὸς ἀριθμὸν ἀριθμὸς ἢ μέτρον ᾖ πρὸς μέτρον, ταῦτα σύμπαντα εἰς τὸ πέρας ἀπολογιζόμενοι καλῶς ἂν δοκοῖμεν δρᾶν τοῦτο.
SOCRATES: Then, as for the things that do not receive these, but receive all their opposites—first, the equal and equality, and after the equal, the double, and whatever is number to number or measure to measure—if we reckon all these together into the limit, we would seem to do this well.
ἢ πῶς σὺ φῄς;
Or how do you say?
ΠΡΩ. κάλλιστά γε, ὦ Σώκρατες.
PROTARCHUS: Most excellently, Socrates.
ΣΩ. εἶεν·
SOCRATES: Very well.
τὸ δὲ τρίτον τὸ μεικτὸν ἐκ τούτοιν ἀμφοῖν τίνα ἰδέαν φήσομεν ἔχειν;
But as for the third, the mixture from both of these, what character shall we say it has?
ΠΡΩ. σὺ καὶ ἐμοὶ φράσεις, ὡς οἶμαι.
PROTARCHUS: You will explain to me, as I think.
ΣΩ. θεὸς μὲν οὖν, ἄνπερ γε ἐμαῖς εὐχαῖς ἐπήκοος γίγνηταί τις θεῶν.
SOCRATES: God will, if indeed some one of the gods listens to my prayers.
ΠΡΩ. εὔχου δὴ καὶ σκόπει.
PROTARCHUS: Pray then and consider.
ΣΩ. σκοπῶ· καί μοι δοκεῖ τις, ὦ Πρώταρχε, αὐτῶν φίλος ἡμῖν νυνδὴ γεγονέναι.
SOCRATES: I am considering; and it seems to me, Protarchus, that one of them has just now become our friend.
ΠΡΩ. πῶς λέγεις τοῦτο καὶ τίνι τεκμηρίῳ χρῇ;
PROTARCHUS: How do you mean this, and what evidence do you use?
ΣΩ. φράσω δῆλον ὅτι· σὺ δέ μοι συνακολούθησον τῷ λόγῳ.
SOCRATES: I will explain, clearly of course; and you follow along with me in the argument.
ΠΡΩ. λέγε μόνον.
PROTARCHUS: Speak only.
ΣΩ. θερμότερον ἐφθεγγόμεθα νυνδή πού τι καὶ ψυχρότερον.
SOCRATES: We were just now uttering something, I believe, about the hotter and the colder.
ἦ γάρ;
Were we not?
ΠΡΩ. ναί.
PROTARCHUS: Yes.
ΣΩ. πρόσθες δὴ ξηρότερον καὶ ὑγρότερον αὐτοῖς καὶ πλέον καὶ ἔλαττον καὶ θᾶττον καὶ βραδύτερον καὶ μεῖζον καὶ σμικρότερον καὶ ὁπόσα ἐν τῷ πρόσθεν τῆς τὸ μᾶλλόν τε καὶ ἧττον δεχομένης ἐτίθεμεν εἰς ἓν φύσεως. ΠΡΩ. τῆς τοῦ ἀπείρου λέγεις;
SOCRATES: Add to them then the drier and the wetter, and the more and the less, and the swifter and the slower, and the greater and the smaller, and all those which we previously placed in the one nature that receives "the more and less." PROTARCHUS: Do you mean that of the unlimited?
ΣΩ. ναί.
SOCRATES: Yes.
συμμείγνυ δέ γε εἰς αὐτὴν τὸ μετὰ ταῦτα τὴν αὖ τοῦ πέρατος γένναν.
And mix into it, next, the family of the limit in turn.
ΠΡΩ. ποίαν;
PROTARCHUS: What kind?
ΣΩ. ἣν καὶ νυνδή, δέον ἡμᾶς καθάπερ τὴν τοῦ ἀπείρου συνηγάγομεν εἰς ἕν, οὕτω καὶ τὴν τοῦ περατοειδοῦς συναγαγεῖν, οὐ συνηγάγομεν. ἀλλʼ ἴσως καὶ νῦν ταὐτὸν δράσει, εἰ τούτων ἀμφοτέρων συναγομένων καταφανὴς κἀκείνη γενήσεται.
SOCRATES: The one which just now—when we ought to have collected the family of the limit-form into one, just as we collected that of the unlimited, but we did not collect it—nevertheless perhaps even now will do the same thing, if, as both of these are collected, that one also becomes manifest.
ΠΡΩ. ποίαν καὶ πῶς λέγεις;
PROTARCHUS: What kind and in what way do you mean?
ΣΩ. τὴν τοῦ ἴσου καὶ διπλασίου, καὶ ὁπόση παύει πρὸς ἄλληλα τἀναντία διαφόρως ἔχοντα, σύμμετρα δὲ καὶ σύμφωνα ἐνθεῖσα ἀριθμὸν ἀπεργάζεται.
SOCRATES: That of the equal and the double, and whatever ceases the opposites from being at variance with one another, and by introducing the moderate and the harmonious, produces number.
ΠΡΩ. μανθάνω· φαίνῃ γάρ μοι λέγειν μειγνὺς ταῦτα γενέσεις τινὰς ἐφʼ ἑκάστων αὐτῶν συμβαίνειν.
PROTARCHUS: I understand; for you seem to me to say, in mixing these, that certain generations occur in each case of them.
ΣΩ. ὀρθῶς γὰρ φαίνομαι.
SOCRATES: Yes, for I do seem to say so.
ΠΡΩ. λέγε τοίνυν.
PROTARCHUS: Speak on then.