§7.526τί οὖν οἴει, ὦ Γλαύκων, εἴ τις ἔροιτο αὐτούς· ὦ θαυμάσιοι, περὶ ποίων ἀριθμῶν διαλέγεσθε, ἐν οἷς τὸ ἓν οἷον ὑμεῖς ἀξιοῦτέ ἐστιν, ἴσον τε ἕκαστον πᾶν παντὶ καὶ οὐδὲ σμικρὸν διαφέρον, μόριόν τε ἔχον ἐν ἑαυτῷ οὐδέν; τί ἂν οἴει αὐτοὺς ἀποκρίνασθαι; τοῦτο ἔγωγε, ὅτι περὶ τούτων λέγουσιν ὧν διανοηθῆναι μόνον ἐγχωρεῖ, ἄλλως δʼ οὐδαμῶς μεταχειρίζεσθαι δυνατόν. ὁρᾷς οὖν, ἦν δʼ ἐγώ, ὦ φίλε, ὅτι τῷ ὄντι ἀναγκαῖον ἡμῖν κινδυνεύει εἶναι τὸ μάθημα, ἐπειδὴ φαίνεταί γε προσαναγκάζον αὐτῇ τῇ νοήσει χρῆσθαι τὴν ψυχὴν ἐπʼ αὐτὴν τὴν ἀλήθειαν;
"What then, Glaucon, do you think if someone should ask them: 'O wonderful men, about what kind of numbers are you discussing, in which the "one" is such as you claim, each one being entirely equal to every other and not differing even a little, and having no part within itself?' What do you think they would answer?" "I, for my part, think they would answer this: that they are speaking of those numbers which it is possible only to grasp by thought, and which cannot be dealt with in any other way." "Do you see then, my friend," I said, "that this study really risks being necessary for us, since it appears to compel the soul to use intellection itself for the sake of truth itself?" "And indeed," he said, "it does that very strongly." "And what about this?
καὶ μὲν δή, ἔφη, σφόδρα γε ποιεῖ αὐτό. τί δέ; τόδε ἤδη ἐπεσκέψω, ὡς οἵ τε φύσει λογιστικοὶ εἰς πάντα τὰ μαθήματα ὡς ἔπος εἰπεῖν ὀξεῖς φύονται, οἵ τε βραδεῖς, ἂν ἐν τούτῳ παιδευθῶσιν καὶ γυμνάσωνται, κἂν μηδὲν ἄλλο ὠφεληθῶσιν, ὅμως εἴς γε τὸ ὀξύτεροι αὐτοὶ αὑτῶν γίγνεσθαι πάντες ἐπιδιδόασιν;
Have you already observed that those who are naturally quick at calculation turn out to be sharp, so to speak, in all studies, while those who are slow, if they are educated and exercised in this, even if they receive no other benefit, nevertheless all improve at least in becoming sharper than they were before?" "It is so," he said.
ἔστιν, ἔφη, οὕτω. καὶ μήν, ὡς ἐγᾦμαι, ἅ γε μείζω πόνον παρέχει μανθάνοντι καὶ μελετῶντι, οὐκ ἂν ῥᾳδίως οὐδὲ πολλὰ ἂν εὕροις ὡς τοῦτο. οὐ γὰρ οὖν. πάντων δὴ ἕνεκα τούτων οὐκ ἀφετέον τὸ μάθημα, ἀλλʼ οἱ ἄριστοι τὰς φύσεις παιδευτέοι ἐν αὐτῷ.
"And indeed, as I think, you would not easily find many things that present greater labor to the learner and practitioner than this." "No indeed." "For all these reasons, then, this study must not be neglected, but those with the best natures must be educated in it." "I agree," he said.
σύμφημι, ἦ δʼ ὅς. τοῦτο μὲν τοίνυν, εἶπον, ἓν ἡμῖν κείσθω· δεύτερον δὲ τὸ ἐχόμενον τούτου σκεψώμεθα ἆρά τι προσήκει ἡμῖν.
"Let this, then," I said, "be established as our first point; and let us examine the second one which follows it, to see if it is at all fitting for us." "Of what sort?
τὸ ποῖον; ἢ γεωμετρίαν, ἔφη, λέγεις;
Do you mean geometry?" he said.
αὐτὸ τοῦτο, ἦν δʼ ἐγώ.
"Exactly so," I said.
ὅσον μέν, ἔφη, πρὸς τὰ πολεμικὰ αὐτοῦ τείνει, δῆλον ὅτι προσήκει· πρὸς γὰρ τὰς στρατοπεδεύσεις καὶ καταλήψεις χωρίων καὶ συναγωγὰς καὶ ἐκτάσεις στρατιᾶς καὶ ὅσα δὴ ἄλλα σχηματίζουσι τὰ στρατόπεδα ἐν αὐταῖς τε ταῖς μάχαις καὶ πορείαις διαφέροι ἂν αὐτὸς αὑτοῦ γεωμετρικός τε καὶ μὴ ὤν. ἀλλʼ οὖν δή, εἶπον, πρὸς μὲν τὰ τοιαῦτα καὶ βραχύ τι ἂν ἐξαρκοῖ γεωμετρίας τε καὶ λογισμῶν μόριον·
"As for that part of it," he said, "which relates to military matters, it is clear that it is fitting; for in pitching camps, occupying positions, concentrating and deploying an army, and all the other maneuvers that they perform with armies both in actual battles and on marches, a geometrician would differ vastly from one who is not." "But indeed," I said, "for such things a small portion of geometry and calculation would suffice; but we must examine whether the greater part of it and that which advances further tends at all toward that other end —to make it easier to discern the idea of the good.
τὸ δὲ πολὺ αὐτῆς καὶ πορρωτέρω προϊὸν σκοπεῖσθαι δεῖ εἴ τι πρὸς ἐκεῖνο τείνει, πρὸς τὸ ποιεῖν κατιδεῖν ῥᾷον τὴν τοῦ ἀγαθοῦ ἰδέαν. τείνει δέ, φαμέν, πάντα αὐτόσε, ὅσα ἀναγκάζει ψυχὴν εἰς ἐκεῖνον τὸν τόπον μεταστρέφεσθαι ἐν ᾧ ἐστι τὸ εὐδαιμονέστατον τοῦ ὄντος, ὃ δεῖ αὐτὴν παντὶ τρόπῳ ἰδεῖν. ὀρθῶς, ἔφη, λέγεις.
And we say that everything tends in that direction which compels the soul to turn itself toward that region where is the happiest part of reality, which the soul must by all means behold." "You speak rightly," he said.
οὐκοῦν εἰ μὲν οὐσίαν ἀναγκάζει θεάσασθαι, προσήκει, εἰ δὲ γένεσιν, οὐ προσήκει. φαμέν γε δή. §7.527οὐ τοίνυν τοῦτό γε, ἦν δʼ ἐγώ, ἀμφισβητήσουσιν ἡμῖν ὅσοι καὶ σμικρὰ γεωμετρίας ἔμπειροι, ὅτι αὕτη ἡ ἐπιστήμη πᾶν τοὐναντίον ἔχει τοῖς ἐν αὐτῇ λόγοις λεγομένοις ὑπὸ τῶν μεταχειριζομένων. πῶς;
"Therefore, if it compels the soul to contemplate reality, it is fitting; but if it compels it to contemplate generation, it is not fitting." "Yes, we certainly say so." "Then, indeed," I said, "those who are even slightly experienced in geometry will not dispute this with us: that this science is entirely contrary to the language spoken in it by those who practice it." "How?" he said.
ἔφη. λέγουσι μέν που μάλα γελοίως τε καὶ ἀναγκαίως· ὡς γὰρ πράττοντές τε καὶ πράξεως ἕνεκα πάντας τοὺς λόγους ποιούμενοι λέγουσιν τετραγωνίζειν τε καὶ παρατείνειν καὶ προστιθέναι καὶ πάντα οὕτω φθεγγόμενοι, τὸ δʼ ἔστι που πᾶν τὸ μάθημα γνώσεως ἕνεκα ἐπιτηδευόμενον. παντάπασι μὲν οὖν, ἔφη.
"They speak, I suppose, in a very ridiculous and yet necessary way; for they speak as if they were doing something and making all their words for the sake of action, saying 'to square,' 'to apply,' 'to add,' and uttering all their words in this way, whereas the entire study is pursued for the sake of knowledge." "By all means," he said.
οὐκοῦν τοῦτο ἔτι διομολογητέον; τὸ ποῖον; ὡς τοῦ ἀεὶ ὄντος γνώσεως, ἀλλὰ οὐ τοῦ ποτέ τι γιγνομένου καὶ ἀπολλυμένου. εὐομολόγητον, ἔφη· τοῦ γὰρ ἀεὶ ὄντος ἡ γεωμετρικὴ γνῶσίς ἐστιν. ὁλκὸν ἄρα, ὦ γενναῖε, ψυχῆς πρὸς ἀλήθειαν εἴη ἂν καὶ ἀπεργαστικὸν φιλοσόφου διανοίας πρὸς τὸ ἄνω σχεῖν ἃ νῦν κάτω οὐ δέον ἔχομεν. ὡς οἷόν τε μάλιστα, ἔφη.
"Then must we agree further on this?" "On what?" "That it is for the sake of knowledge of that which always is, and not of that which at some time comes to be and perishes." "That is easy to agree," he said, "for geometrical knowledge is of that which always is." "Then, my noble friend, it would be a drawer of the soul toward truth, and productive of a philosophical mind for holding upward those things which we now, as we ought not, hold downward." "As much as possible," he said.
ὡς οἷόν τʼ ἄρα, ἦν δʼ ἐγώ, μάλιστα προστακτέον ὅπως οἱ ἐν τῇ καλλιπόλει σοι μηδενὶ τρόπῳ γεωμετρίας ἀφέξονται.
"Then, as much as possible," I said, "it must be commanded that the citizens in your beautiful city should in no way abstain from geometry.
καὶ γὰρ τὰ πάρεργα αὐτοῦ οὐ σμικρά. ποῖα; ἦ δʼ ὅς.
For indeed, its by-products are not small." "Of what kind?" he said.
ἅ τε δὴ σὺ εἶπες, ἦν δʼ ἐγώ, τὰ περὶ τὸν πόλεμον, καὶ δὴ καὶ πρὸς πάσας μαθήσεις, ὥστε κάλλιον ἀποδέχεσθαι, ἴσμεν που ὅτι τῷ ὅλῳ καὶ παντὶ διοίσει ἡμμένος τε γεωμετρίας καὶ μή. τῷ παντὶ μέντοι νὴ Δίʼ, ἔφη.
"Those which you mentioned," I said, "concerning war, and indeed also for all studies, so as to receive them more beautifully, we surely know that one who has touched geometry and one who has not will differ entirely and completely." "Completely indeed, by Zeus," he said.
δεύτερον δὴ τοῦτο τιθῶμεν μάθημα τοῖς νέοις; τιθῶμεν, ἔφη.
"Then shall we place this as the second study for the young?" "Let us do so," he said.
τί δέ;
"And what?
τρίτον θῶμεν ἀστρονομίαν;
Shall we place astronomy as the third?
ἢ οὐ δοκεῖ; ἐμοὶ γοῦν, ἔφη· τὸ γὰρ περὶ ὥρας εὐαισθητοτέρως ἔχειν καὶ μηνῶν καὶ ἐνιαυτῶν οὐ μόνον γεωργίᾳ οὐδὲ ναυτιλίᾳ προσήκει, ἀλλὰ καὶ στρατηγίᾳ οὐχ ἧττον. ἡδὺς εἶ, ἦν δʼ ἐγώ, ὅτι ἔοικας δεδιότι τοὺς πολλούς, μὴ δοκῇς ἄχρηστα μαθήματα προστάττειν.
Or does it not seem so?" "To me at least," he said; "for to be more sensitive to seasons, months, and years is fitting not only for agriculture and navigation, but no less so for military command." "You are amusing," I said, "because you seem to be afraid of the multitude, lest you should seem to command useless studies.
τὸ δʼ ἔστιν οὐ πάνυ φαῦλον ἀλλὰ χαλεπὸν πιστεῦσαι ὅτι ἐν τούτοις τοῖς μαθήμασιν ἑκάστου ὄργανόν τι ψυχῆς ἐκκαθαίρεταί τε καὶ ἀναζωπυρεῖται ἀπολλύμενον καὶ τυφλούμενον ὑπὸ τῶν ἄλλων ἐπιτηδευμάτων, κρεῖττον ὂν σωθῆναι μυρίων ὀμμάτων· μόνῳ γὰρ αὐτῷ ἀλήθεια ὁρᾶται.
But this is not at all trivial, though it is difficult to believe that in these studies an instrument of the soul in each person is purified and rekindled, which had been destroyed and blinded by other pursuits—an instrument more worth saving than ten thousand eyes, for by it alone is truth beheld.
οἷς μὲν οὖν ταῦτα συνδοκεῖ ἀμηχάνως ὡς εὖ δόξεις λέγειν, ὅσοι δὲ τούτου μηδαμῇ ᾐσθημένοι εἰσὶν εἰκότως ἡγήσονταί σε λέγειν οὐδέν· ἄλλην γὰρ ἀπʼ αὐτῶν οὐχ ὁρῶσιν ἀξίαν λόγου ὠφελίαν.
To those, therefore, who agree on these things, you will seem to speak incredibly well; but those who have in no way perceived this will naturally think you are saying nothing, for they see no other benefit from them worthy of mention."