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Republic

§7.521-7.522

Number and Calculation as the First Education of Rulers

Socrates explains that to nurture suitable rulers, an education is needed that turns the soul from becoming to being, and proposes "number and calculation" as the first such study.

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§7.521

οὕτω γὰρ ἔχει, ἦν δʼ ἐγώ, ὦ ἑταῖρε· εἰ μὲν βίον ἐξευρήσεις ἀμείνω τοῦ ἄρχειν τοῖς μέλλουσιν ἄρξειν, ἔστι σοι δυνατὴ γενέσθαι πόλις εὖ οἰκουμένη· ἐν μόνῃ γὰρ αὐτῇ ἄρξουσιν οἱ τῷ ὄντι πλούσιοι, οὐ χρυσίου ἀλλʼ οὗ δεῖ τὸν εὐδαίμονα πλουτεῖν, ζωῆς ἀγαθῆς τε καὶ ἔμφρονος.1 εἰ δὲ πτωχοὶ καὶ πεινῶντες ἀγαθῶν ἰδίων ἐπὶ τὰ δημόσια ἴασιν, ἐντεῦθεν οἰόμενοι τἀγαθὸν δεῖν ἁρπάζειν, οὐκ ἔστι· περιμάχητον γὰρ τὸ ἄρχειν γιγνόμενον, οἰκεῖος ὢν καὶ ἔνδον ὁ τοιοῦτος πόλεμος αὐτούς τε ἀπόλλυσι καὶ τὴν ἄλλην πόλιν. ἀληθέστατα, ἔφη. ἔχεις οὖν, ἦν δʼ ἐγώ, βίον ἄλλον τινὰ πολιτικῶν ἀρχῶν καταφρονοῦντα ἢ τὸν τῆς ἀληθινῆς φιλοσοφίας; οὐ μὰ τὸν Δία, ἦ δʼ ὅς. ἀλλὰ μέντοι δεῖ γε μὴ ἐραστὰς τοῦ ἄρχειν ἰέναι ἐπʼ αὐτό· εἰ δὲ μή, οἵ γε ἀντερασταὶ μαχοῦνται. πῶς δʼ οὔ; τίνας οὖν ἄλλους ἀναγκάσεις ἰέναι ἐπὶ φυλακὴν τῆς πόλεως ἢ οἳ περὶ τούτων τε φρονιμώτατοι διʼ ὧν ἄριστα πόλις οἰκεῖται, ἔχουσί τε τιμὰς ἄλλας καὶ βίον ἀμείνω τοῦ πολιτικοῦ; οὐδένας ἄλλους, ἔφη. βούλει οὖν τοῦτʼ ἤδη σκοπῶμεν, τίνα τρόπον οἱ τοιοῦτοι ἐγγενήσονται, καὶ πῶς τις ἀνάξει αὐτοὺς εἰς φῶς, ὥσπερ ἐξ Ἅιδου λέγονται δή τινες εἰς θεοὺς ἀνελθεῖν; πῶς γὰρ οὐ βούλομαι; ἔφη. τοῦτο δή, ὡς ἔοικεν, οὐκ ὀστράκου ἂν εἴη περιστροφή, ἀλλὰ ψυχῆς περιαγωγὴ2 ἐκ νυκτερινῆς τινος ἡμέρας εἰς ἀληθινήν, τοῦ ὄντος οὖσαν ἐπάνοδον, ἣν δὴ φιλοσοφίαν ἀληθῆ φήσομεν εἶναι. πάνυ μὲν οὖν. οὐκοῦν δεῖ σκοπεῖσθαι τί τῶν μαθημάτων ἔχει τοιαύτην δύναμιν; πῶς γὰρ οὔ; τί ἂν οὖν εἴη, ὦ Γλαύκων, μάθημα ψυχῆς ὁλκὸν ἀπὸ τοῦ γιγνομένου ἐπὶ τὸ ὄν; τόδε δʼ ἐννοῶ λέγων ἅμα· οὐκ ἀθλητὰς μέντοι πολέμου ἔφαμεν τούτους ἀναγκαῖον εἶναι νέους ὄντας; ἔφαμεν γάρ. δεῖ ἄρα καὶ τοῦτο προσέχειν τὸ μάθημα ὃ ζητοῦμεν πρὸς ἐκείνῳ. τὸ ποῖον; μὴ ἄχρηστον πολεμικοῖς ἀνδράσιν εἶναι. δεῖ μέντοι, ἔφη, εἴπερ οἷόν τε. γυμναστικῇ μὴν καὶ μουσικῇ ἔν γε τῷ πρόσθεν ἐπαιδεύοντο ἡμῖν. ἦν ταῦτα, ἔφη. καὶ γυμναστικὴ μέν που περὶ γιγνόμενον καὶ ἀπολλύμενον τετεύτακεν· σώματος γὰρ αὔξης καὶ φθίσεως ἐπιστατεῖ. φαίνεται. τοῦτο μὲν δὴ οὐκ ἂν εἴη ὃ ζητοῦμεν μάθημα.

”For that is how it is, my friend,” I said. “If you discover a life better than ruling for those who are going to rule, it is possible for you to have a well-governed city. For in it alone will those rule who are truly rich, not in gold but in what a happy person must be rich in, a good and prudent life. But if those who are poor and starving for private goods go to public affairs, thinking that they must snatch the good from there, it is not possible. For when ruling becomes a thing fought over, such a war, being domestic and internal, destroys both them and the rest of the city.” “Most true,” he said. ”Do you have, then,” I said, “any other life that despises political offices than that of true philosophy?” “No, by Zeus,” he said. “But indeed, those who are not lovers of ruling must go to it; otherwise, their rivals will fight.” “How could it be otherwise?” “Whom else, then, will you compel to go to the guard of the city than those who are most prudent about those things through which a city is best governed, and who have other honors and a life better than the political one?” “No others,” he said. ”Would you like us now to consider this: in what way such people will arise, and how one will lead them up into the light, just as some are said to have gone up from Hades to the gods?” “How indeed could I not wish it?” he said. “This, as it seems, would not be the turning of a shell, but the turning around of a soul from a kind of night-like day to a true day, being an ascent to what is, which we shall say is true philosophy.” “Most certainly.” “Must we not, then, consider which of the studies has such a power?” “How could we not?” “What study, then, Glaucon, would be a drawer of the soul from that which becomes to that which is? And I think of this as I speak: did we not say that these people must necessarily be athletes of war when they are young?” “For we did say so.” “Then this study we are seeking must also have this additional quality besides that one.” “What sort of quality?” “Not to be useless to warlike men.” “It must indeed,” he said, “if it is possible.” “Now, they were educated previously by us in gymnastics and music.” ”They were,” he said. “And gymnastics, I suppose, is concerned with what becomes and perishes, for it presides over the growth and decay of the body.” “So it appears.” “This, then, would not be the study we are seeking.”

§7.522

οὐ γάρ. ἀλλʼ ἆρα μουσικὴ ὅσην τὸ πρότερον διήλθομεν; ἀλλʼ ἦν ἐκείνη γʼ, ἔφη, ἀντίστροφος τῆς γυμναστικῆς, εἰ μέμνησαι, ἔθεσι παιδεύουσα τοὺς φύλακας, κατά τε ἁρμονίαν εὐαρμοστίαν τινά, οὐκ ἐπιστήμην, παραδιδοῦσα,3 καὶ κατὰ ῥυθμὸν εὐρυθμίαν, ἔν τε τοῖς λόγοις ἕτερα τούτων ἀδελφὰ ἔθη ἄττα ἔχουσα, καὶ ὅσοι μυθώδεις τῶν λόγων καὶ ὅσοι ἀληθινώτεροι ἦσαν· μάθημα δὲ πρὸς τοιοῦτόν τι ἄγον, οἷον σὺ νῦν ζητεῖς, οὐδὲν ἦν ἐν αὐτῇ. ἀκριβέστατα, ἦν δʼ ἐγώ, ἀναμιμνῄσκεις με· τῷ γὰρ ὄντι τοιοῦτον οὐδὲν εἶχεν. ἀλλʼ, ὦ δαιμόνιε Γλαύκων, τί ἂν εἴη τοιοῦτον; αἵ τε γὰρ τέχναι βάναυσοί που ἅπασαι ἔδοξαν εἶναι— πῶς δʼ οὔ; καὶ μὴν τί ἔτʼ ἄλλο λείπεται μάθημα, μουσικῆς καὶ γυμναστικῆς καὶ τῶν τεχνῶν κεχωρισμένον; φέρε, ἦν δʼ ἐγώ, εἰ μηδὲν ἔτι ἐκτὸς τούτων ἔχομεν λαβεῖν, τῶν ἐπὶ πάντα τεινόντων τι λάβωμεν. τὸ ποῖον; οἷον τοῦτο τὸ κοινόν, ᾧ πᾶσαι προσχρῶνται τέχναι τε καὶ διάνοιαι καὶ ἐπιστῆμαι—ὃ καὶ παντὶ ἐν πρώτοις ἀνάγκη μανθάνειν. τὸ ποῖον; ἔφη. τὸ φαῦλον τοῦτο, ἦν δʼ ἐγώ, τὸ ἕν τε καὶ τὰ δύο καὶ τὰ τρία διαγιγνώσκειν· λέγω δὲ αὐτὸ ἐν κεφαλαίῳ ἀριθμόν τε καὶ λογισμόν. ἢ οὐχ οὕτω περὶ τούτων ἔχει, ὡς πᾶσα τέχνη τε καὶ ἐπιστήμη ἀναγκάζεται αὐτῶν μέτοχος γίγνεσθαι; καὶ μάλα, ἔφη. οὐκοῦν, ἦν δʼ ἐγώ, καὶ ἡ πολεμική; πολλή, ἔφη, ἀνάγκη. παγγέλοιον γοῦν, ἔφην, στρατηγὸν Ἀγαμέμνονα ἐν ταῖς τραγῳδίαις Παλαμήδης ἑκάστοτε ἀποφαίνει. ἢ οὐκ ἐννενόηκας ὅτι φησὶν ἀριθμὸν εὑρὼν τάς τε τάξεις τῷ στρατοπέδῳ καταστῆσαι ἐν Ἰλίῳ καὶ ἐξαριθμῆσαι ναῦς τε καὶ τἆλλα πάντα, ὡς πρὸ τοῦ ἀναριθμήτων ὄντων4 καὶ τοῦ Ἀγαμέμνονος, ὡς ἔοικεν, οὐδʼ ὅσους πόδας εἶχεν εἰδότος, εἴπερ ἀριθμεῖν μὴ ἠπίστατο; καίτοι ποῖόν τινʼ αὐτὸν οἴει στρατηγὸν εἶναι; ἄτοπόν τινʼ, ἔφη, ἔγωγε, εἰ ἦν τοῦτʼ ἀληθές. ἄλλο τι οὖν, ἦν δʼ ἐγώ, μάθημα ἀναγκαῖον πολεμικῷ ἀνδρὶ θήσομεν λογίζεσθαί τε καὶ ἀριθμεῖν δύνασθαι; πάντων γʼ, ἔφη, μάλιστα, εἰ καὶ ὁτιοῦν μέλλει τάξεων ἐπαΐειν, μᾶλλον δʼ εἰ καὶ ἄνθρωπος ἔσεσθαι. ἐννοεῖς οὖν, εἶπον, περὶ τοῦτο τὸ μάθημα ὅπερ ἐγώ; τὸ ποῖον;

”No indeed.” “But is it music, as much of it as we went through before?” “But that,” he said, “was, if you remember, the counterpart of gymnastics, educating the guardians by habits, transmitting by harmony a certain well-harmonized state, not knowledge, and by rhythm a well-rhythmed state, and having in its discussions other habits akin to these, both in the stories that were mythical and those that were truer. But a study leading to something of the sort which you are now seeking was not in it at all.” “Most precisely,” I said, “you remind me. For in truth it had nothing of the kind. But, my wonderful Glaucon, what could be of this kind? For all the arts seemed to be vulgar.” “How indeed could they not? But what other study is left, separated from music, gymnastics, and the arts?” “Come,” I said, “if we have nothing else left to take outside of these, let us take something of those that extend to everything.” “What sort of thing?” ”For example, this common thing which all arts, understandings, and sciences make use of—which indeed everyone must learn among the very first things.” “What sort of thing?” he said. “This ordinary thing,” I said, “to distinguish the one, the two, and the three. I mean this, in short, as number and calculation. Or is it not so about these, that every art and science is forced to become a sharer in them?” “Very much so,” he said. “Therefore,” I said, “warfare too?” “Of great necessity,” he said. ”At any rate, Palamedes in the tragedies always represents Agamemnon as a completely ridiculous general,” I said. “Or have you not noticed that he says, having found number, he set up the ranks for the army at Ilium and numbered the ships and all other things, as if before this they were unnumbered, and Agamemnon, as it seems, did not even know how many feet he had, if indeed he did not know how to count? Yet what sort of general do you think he was?” “An absurd one, indeed,” he said, “in my opinion, if this was true.” ”Shall we, then,” I said, “set down as a necessary study for a warlike man the ability to calculate and count?” “Most of all,” he said, “if he is to understand anything at all of military arrangements, or rather, if he is to be even a human being.” “Do you notice, then,” I said, “about this study what I do?” “What sort of thing?”

Syntax notes4 items
  1. 521aοὐ χρυσίου ἀλλʼ οὗ δεῖ τὸν εὐδαίμονα πλουτεῖν, ζωῆς ἀγαθῆς τε καὶ ἔμφρονος

    οὗ is a relative pronoun with an omitted antecedent, governed by the infinitive πλουτεῖν (to be rich). ζωῆς ἀγαθῆς τε καὶ ἔμφρονος stands in apposition to οὗ, concretely explaining what the true "wealth" is that a happy person must possess.

  2. 521cτοῦτο δή, ὡς ἔοικεν, οὐκ ὀστράκου ἂν εἴη περιστροφή, ἀλλὰ ψυχῆς περιαγωγὴ

    ὀστράκου περιστροφή (the turning of a shell) is an idiomatic expression originating from an ancient Greek children's game (ostrakinda), signifying a sudden reversal based on chance or luck. It stands in contrast with ψυχῆς περιαγωγὴ (the turning around of a soul), which implies a gradual and fundamental reorientation.

  3. 522aἔθεσι παιδεύουσα τοὺς φύλακας, κατά τε ἁρμονίαν εὐαρμοστίαν τινά, οὐκ ἐπιστήμην, παραδιδοῦσα

    Both παιδεύουσα and παραδιδοῦσα are participles modifying the subject ἐκείνη (music). This structure highlights that musical education is limited to the formation of character through habits (ἔθη) and a well-harmonized state (εὐαρμοστία), rather than transmitting knowledge (ἐπιστήμη).

  4. 522dὡς πρὸ τοῦ ἀναριθμήτων ὄντων

    ἀναριθμήτων ὄντων is a genitive absolute construction. The inclusion of the particle ὡς indicates that this is the assertion or subjective premise presented by the tragic poet Palamedes.

Translated by Gemini 3.5 Flash (published 2026-05-23) · Revision history (1, latest 2026-09-22)
  • 2026-09-22 AI review — source 1
urn:cts:greekLit:tlg0059.tlg030.humanitext-grc2:7.521-7.522