ΞΕ. εἰ πρὸς μηδὲν ἕτερον τὴν τοῦ μείζονος ἐάσει τις φύσιν ἢ πρὸς τοὔλαττον, οὐκ ἔσται ποτὲ πρὸς τὸ μέτριον· ἦ γάρ;
ΝΕ. ΣΩ. οὕτως.
ΞΕ. οὐκοῦν τὰς τέχνας τε αὐτὰς καὶ τἆργα αὐτῶν σύμπαντα διολοῦμεν τούτῳ τῷ λόγῳ, καὶ δὴ καὶ τὴν ζητουμένην νῦν πολιτικὴν καὶ τὴν ῥηθεῖσαν ὑφαντικὴν ἀφανιοῦμεν; ἅπασαι γὰρ αἱ τοιαῦταί που τὸ τοῦ μετρίου πλέον καὶ ἔλαττον οὐχ ὡς οὐκ ὂν ἀλλʼ ὡς ὂν χαλεπὸν περὶ τὰς πράξεις παραφυλάττουσι, καὶ τούτῳ δὴ τῷ τρόπῳ τὸ μέτρον σῴζουσαι πάντα ἀγαθὰ καὶ καλὰ ἀπεργάζονται.
ΝΕ. ΣΩ. τί μήν;
ΞΕ. οὐκοῦν ἂν τὴν πολιτικὴν ἀφανίσωμεν, ἄπορος ἡμῖν ἡ μετὰ τοῦτο ἔσται ζήτησις τῆς βασιλικῆς ἐπιστήμης;
ΝΕ. ΣΩ. καὶ μάλα.
ΞΕ. πότερον οὖν, καθάπερ ἐν τῷ σοφιστῇ προσηναγκάσαμεν εἶναι τὸ μὴ ὄν, ἐπειδὴ κατὰ τοῦτο διέφυγεν ἡμᾶς ὁ λόγος, οὕτω καὶ νῦν τὸ πλέον αὖ καὶ ἔλαττον μετρητὰ προσαναγκαστέον γίγνεσθαι μὴ πρὸς ἄλληλα μόνον ἀλλὰ καὶ πρὸς τὴν τοῦ μετρίου γένεσιν; οὐ γὰρ δὴ δυνατόν γε οὔτε πολιτικὸν οὔτʼ ἄλλον τινὰ τῶν περὶ τὰς πράξεις ἐπιστήμονα ἀναμφισβητήτως γεγονέναι τούτου μὴ συνομολογηθέντος.
ΝΕ. ΣΩ. οὐκοῦν καὶ νῦν ὅτι μάλιστα χρὴ ταὐτὸν ποιεῖν.
ΞΕ. πλέον, ὦ Σώκρατες, ἔτι τοῦτο τὸ ἔργον ἢ ʼκεῖνο— καίτοι κἀκείνου γε μεμνήμεθα τὸ μῆκος ὅσον ἦν—ἀλλʼ ὑποτίθεσθαι μὲν τὸ τοιόνδε περὶ αὐτῶν καὶ μάλα δίκαιον.
ΝΕ. ΣΩ. τὸ ποῖον;
ΞΕ. ὥς ποτε δεήσει τοῦ νῦν λεχθέντος πρὸς τὴν περὶ αὐτὸ τἀκριβὲς ἀπόδειξιν. ὅτι δὲ πρὸς τὰ νῦν καλῶς καὶ ἱκανῶς δείκνυται, δοκεῖ μοι βοηθεῖν μεγαλοπρεπῶς ἡμῖν οὗτος ὁ λόγος, ὡς ἄρα ἡγητέον ὁμοίως τὰς τέχνας πάσας εἶναι, μεῖζόν τε ἅμα καὶ ἔλαττον μετρεῖσθαι μὴ πρὸς ἄλληλα μόνον ἀλλὰ καὶ πρὸς τὴν τοῦ μετρίου γένεσιν. τούτου τε γὰρ ὄντος ἐκεῖνα ἔστι, κἀκείνων οὐσῶν ἔστι καὶ τοῦτο, μὴ δὲ ὄντος ποτέρου τούτων οὐδέτερον αὐτῶν ἔσται ποτέ.
ΝΕ. ΣΩ. τοῦτο μὲν ὀρθῶς· ἀλλὰ τί δὴ τὸ μετὰ τοῦτο;
ΞΕ. δῆλον ὅτι διαιροῖμεν ἂν τὴν μετρητικήν, καθάπερ ἐρρήθη, ταύτῃ δίχα τέμνοντες, ἓν μὲν τιθέντες αὐτῆς μόριον συμπάσας τέχνας ὁπόσαι τὸν ἀριθμὸν καὶ μήκη καὶ βάθη καὶ πλάτη καὶ ταχυτῆτας πρὸς τοὐναντίον μετροῦσιν, τὸ δὲ ἕτερον, ὁπόσαι πρὸς τὸ μέτριον καὶ τὸ πρέπον καὶ τὸν καιρὸν καὶ τὸ δέον καὶ πάνθʼ ὁπόσα εἰς τὸ μέσον ἀπῳκίσθη τῶν ἐσχάτων.
ΝΕ. ΣΩ. καὶ μέγα γε ἑκάτερον τμῆμα εἶπες, καὶ πολὺ διαφέρον ἀλλήλοιν.
Str. If we assert that the greater has no relation to anything except the less, it will never have any relation to the standard of the mean, will it?
Y. Soc. No.
Str. Will not this doctrine destroy the arts and their works one and all, and do away also with statesmanship, which we are now trying to define, and with weaving, which we did define? For all these are doubtless careful about excess and deficiency in relation to the standard of the mean; they regard them not as non-existent, but as real difficulties in actual practice, and it is in this way, when they preserve the standard of the mean, that all their works are good and beautiful.
Y. Soc. Certainly.
Str. And if we do away with the art of statesmanship, our subsequent search for the kingly art will be hopeless, will it not?
Y. Soc. Certainly.
Str. Then just as in the case of the sophist we forced the conclusion that not-being exists, since that was the point at which we had lost our hold of the argument, so now we must force this second conclusion, that the greater and the less are to be measured in relation, not only to one another, but also to the establishment of the standard of the mean, must we not? For if this is not admitted, neither the statesman nor any other man who has knowledge of practical affairs can be said without any doubt to exist.
Y. Soc. Then we must by all means do now the same that we did then.
Str. This, Socrates, is a still greater task than that was; and yet we remember how long that took us; but it is perfectly fair to make about them some such assumption as this.
Y. Soc. As what?
Str. That sometime we shall need this principle of the mean for the demonstration of absolute precise truth. But our belief that the demonstration is for our present purpose good and sufficient is, in my opinion, magnificently supported by this argument—that we must believe that all the arts alike exist and that the greater and the less are measured in relation not only to one another but also to the establishment of the standard of the mean. For if this exists, they exist also, and if they exist, it exists also, but neither can ever exist if the other does not.
Y. Soc. That is quite right. But what comes next?
Str. We should evidently divide the science of measurement into two parts in accordance with what has been said. One part comprises all the arts which measure number, length, depth, breadth, and thickness in relation to their opposites; the other comprises those which measure them in relation to the moderate, the fitting, the opportune, the needful, and all the other standards that are situated in the mean between the extremes.
Y. Soc. Both of your divisions are extensive, and there is a great difference between them.
ΞΕ. ὃ γὰρ ἐνίοτε, ὦ Σώκρατες, οἰόμενοι δή τι σοφὸν φράζειν πολλοὶ τῶν κομψῶν λέγουσιν, ὡς ἄρα μετρητικὴ περὶ πάντʼ ἐστὶ τὰ γιγνόμενα, τοῦτʼ αὐτὸ τὸ νῦν λεχθὲν ὂν τυγχάνει. μετρήσεως μὲν γὰρ δή τινα τρόπον πάνθʼ ὁπόσα ἔντεχνα μετείληφεν· διὰ δὲ τὸ μὴ κατʼ εἴδη συνειθίσθαι σκοπεῖν διαιρουμένους ταῦτά τε τοσοῦτον διαφέροντα συμβάλλουσιν εὐθὺς εἰς ταὐτὸν ὅμοια νομίσαντες, καὶ τοὐναντίον αὖ τούτου δρῶσιν ἕτερα οὐ κατὰ μέρη διαιροῦντες, δέον, ὅταν μὲν τὴν τῶν πολλῶν τις πρότερον αἴσθηται κοινωνίαν, μὴ προαφίστασθαι πρὶν ἂν ἐν αὐτῇ τὰς διαφορὰς ἴδῃ πάσας ὁπόσαιπερ ἐν εἴδεσι κεῖνται, τὰς δὲ αὖ παντοδαπὰς ἀνομοιότητας, ὅταν ἐν πλήθεσιν ὀφθῶσιν, μὴ δυνατὸν εἶναι δυσωπούμενον παύεσθαι πρὶν ἂν σύμπαντα τὰ οἰκεῖα ἐντὸς μιᾶς ὁμοιότητος ἕρξας γένους τινὸς οὐσίᾳ περιβάληται. ταῦτα μὲν οὖν ἱκανῶς περί τε τούτων καὶ περὶ τῶν ἐλλείψεων καὶ ὑπερβολῶν εἰρήσθω· φυλάττωμεν δὲ μόνον ὅτι δύο γένη περὶ αὐτὰ ἐξηύρηται τῆς μετρητικῆς, καὶ ἅ φαμεν αὔτʼ εἶναι μεμνώμεθα.
ΝΕ. ΣΩ. μεμνησόμεθα.
ΞΕ. μετὰ τοῦτον δὴ τὸν λόγον ἕτερον προσδεξώμεθα περὶ αὐτῶν τε τῶν ζητουμένων καὶ περὶ πάσης τῆς ἐν τοῖς τοιοῖσδε λόγοις διατριβῆς.
ΝΕ. ΣΩ. τὸ ποῖον;
ΞΕ. εἴ τις ἀνέροιτο ἡμᾶς τὴν περὶ γράμματα συνουσίαν τῶν μανθανόντων, ὁπόταν τις ὁτιοῦν ὄνομα ἐρωτηθῇ τίνων ἐστὶ γραμμάτων, πότερον αὐτῷ τότε φῶμεν γίγνεσθαι τὴν ζήτησιν ἑνὸς ἕνεκα μᾶλλον τοῦ προβληθέντος ἢ τοῦ περὶ πάντα τὰ προβαλλόμενα γραμματικωτέρῳ γίγνεσθαι;
ΝΕ. ΣΩ. δῆλον ὅτι τοῦ περὶ ἅπαντα.
ΞΕ. τί δʼ αὖ νῦν ἡμῖν ἡ περὶ τοῦ πολιτικοῦ ζήτησις; ἕνεκα αὐτοῦ τούτου προβέβληται μᾶλλον ἢ τοῦ περὶ πάντα διαλεκτικωτέροις γίγνεσθαι;
ΝΕ. ΣΩ. καὶ τοῦτο δῆλον ὅτι τοῦ περὶ πάντα.
ΞΕ. ἦ που τὸν τῆς ὑφαντικῆς γε λόγον αὐτῆς ταύτης ἕνεκα θηρεύειν οὐδεὶς ἂν ἐθελήσειεν νοῦν ἔχων· ἀλλʼ οἶμαι τοὺς πλείστους λέληθεν ὅτι τοῖς μὲν τῶν ὄντων ῥᾳδίως καταμαθεῖν αἰσθηταί τινες ὁμοιότητες πεφύκασιν, ἃς οὐδὲν χαλεπὸν δηλοῦν, ὅταν αὐτῶν τις βουληθῇ τῷ λόγον αἰτοῦντι περί του μὴ μετὰ πραγμάτων ἀλλὰ χωρὶς λόγου ῥᾳδίως ἐνδείξασθαι· τοῖς δʼ αὖ μεγίστοις οὖσι καὶ τιμιωτάτοις οὐκ ἔστιν εἴδωλον οὐδὲν πρὸς τοὺς ἀνθρώπους εἰργασμένον ἐναργῶς, οὗ δειχθέντος τὴν τοῦ πυνθανομένου ψυχὴν ὁ βουλόμενος ἀποπληρῶσαι, πρὸς τῶν αἰσθήσεών τινα προσαρμόττων, ἱκανῶς πληρώσει.
Str. Yes, for what many clever persons occasionally say, Socrates, fancying that it is a wise remark, namely, that the science of measurement has to do with everything, is precisely the same as what we have just said. For in a certain way all things which are in the province of art do partake of measurement; but because people are not in the habit of considering things by dividing them into classes, they hastily put these widely different relations into the same category, thinking they are alike; and again they do the opposite of this when they fail to divide other things into parts. What they ought to do is this: when a person at first sees only the unity or common quality of many things, he must not give up until he sees all the differences in them, so far as they exist in classes; and conversely, when all sorts of dissimilarities are seen in a large number of objects he must find it impossible to be discouraged or to stop until has gathered into one circle of similarity all the things which are related to each other and has included them in some sort of class on the basis of their essential nature. No more need be said, then, about this or about deficiency and excess; let us only bear carefully in mind that two kinds of measurement which apply to them have been found, and let us remember what those kinds are.
Y. Soc. We will remember.
Str. Now that we have finished this discussion, let us take up another which concerns the actual objects of our inquiry and the conduct of such discussions in general.
Y. Soc. What is it?
Str. Suppose we were asked the following question about a group of pupils learning their letters: “When a pupil is asked of what letters some word or other composed, is the question asked for the sake of the one particular word before him or rather to make him more learned about all words in the lesson?”
Y. Soc. Clearly to make him more learned about them all.
Str. And how about our own investigation of the statesman? Has it been undertaken for the sake of his particular subject or rather to make us better thinkers about all subjects?
Y. Soc. Clearly this also is done with a view to them all.
Str. Of course no man of sense would wish to pursue the discussion of weaving for its own sake; but most people, it seems to me, fail to notice that some things have sensible resemblances which are easily perceived; and it is not at all difficult to show them when anyone wishes, in response to a request for an explanation of some one of them, to exhibit them easily without trouble and really without explanation. But, on the other hand, the greatest and noblest conceptions have no image wrought plainly for human vision, which he who wishes to satisfy the mind of the inquirer can apply to some one of his senses and by mere exhibition satisfy the mind.
ΞΕ. διὸ δεῖ μελετᾶν λόγον ἑκάστου δυνατὸν εἶναι δοῦναι καὶ δέξασθαι· τὰ γὰρ ἀσώματα, κάλλιστα ὄντα καὶ μέγιστα, λόγῳ μόνον ἄλλῳ δὲ οὐδενὶ σαφῶς δείκνυται, τούτων δὲ ἕνεκα πάντʼ ἐστὶ τὰ νῦν λεγόμενα. ῥᾴων δʼ ἐν τοῖς ἐλάττοσιν ἡ μελέτη παντὸς πέρι μᾶλλον ἢ περὶ τὰ μείζω.
ΝΕ. ΣΩ. κάλλιστʼ εἶπες.
ΞΕ. ὧν τοίνυν χάριν ἅπανθʼ ἡμῖν ταῦτʼ ἐρρήθη περὶ τούτων, μνησθῶμεν.
ΝΕ. ΣΩ. τίνων;
ΞΕ. ταύτης τε οὐχ ἥκιστα αὐτῆς ἕνεκα τῆς δυσχερείας ἣν περὶ τὴν μακρολογίαν τὴν περὶ τὴν ὑφαντικὴν ἀπεδεξάμεθα δυσχερῶς, καὶ τὴν περὶ τὴν τοῦ παντὸς ἀνείλιξιν καὶ τὴν τοῦ σοφιστοῦ πέρι τῆς τοῦ μὴ ὄντος οὐσίας, ἐννοοῦντες ὡς ἔσχε μῆκος πλέον, καὶ ἐπὶ τούτοις δὴ πᾶσιν ἐπεπλήξαμεν ἡμῖν αὐτοῖς, δείσαντες μὴ περίεργα ἅμα καὶ μακρὰ λέγοιμεν. ἵνʼ οὖν εἰς αὖθις μηδὲν πάσχωμεν τοιοῦτον, τούτων ἕνεκα πάντων τὰ πρόσθε νῷν εἰρῆσθαι φάθι.
ΝΕ. ΣΩ. ταῦτʼ ἔσται. λέγε ἑξῆς μόνον.
ΞΕ. λέγω τοίνυν ὅτι χρὴ δὴ μεμνημένους ἐμὲ καὶ σὲ τῶν νῦν εἰρημένων τόν τε ψόγον ἑκάστοτε καὶ ἔπαινον ποιεῖσθαι βραχύτητος ἅμα καὶ μήκους ὧν ἂν ἀεὶ πέρι λέγωμεν, μὴ πρὸς ἄλληλα τὰ μήκη κρίνοντες ἀλλὰ κατὰ τὸ τῆς μετρητικῆς μέρος ὃ τότε ἔφαμεν δεῖν μεμνῆσθαι, πρὸς τὸ πρέπον.
ΝΕ. ΣΩ. ὀρθῶς.
Str. We must therefore endeavor by practice to acquire the power of giving and understanding a rational definition of each one of them; for immaterial things, which are the noblest and greatest, can be exhibited by reason only, and it is for their sake that all we are saying is said. But it is always easier to practise in small matters than in greater ones.
Y. Soc. Excellent.
Str. Let us, then, remember the reason for all that we have said about these matters.
Y. Soc. What is the reason?
Str. The reason is chiefly just that irritating impatience which we exhibited in relation to the long talk about weaving and the revolution of the universe and the sophist’s long talk about the existence of not-being. We felt that they were too long, and we reproached ourselves for all of them, fearing that our talk was not only long, but irrelevant. Consider, therefore, that the reason for what has just been said is my wish to avoid any such impatience in the future.
Y. Soc. Very well. Please go on with what you have to say.
Str. What I have to say, then, is that you and I, remembering what has just been said, must praise or blame the brevity or length of our several discussions, not by comparing their various lengths with one another, but with reference to that part of the science of measurement which we said before must be borne in mind; I mean the standard of fitness.
Y. Soc. Quite right.
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