Note for translation: inspired by C. D. C. Reeve’s work, I reworked Socrates’ reported speech into direct conversation between him and Glaucon.

Socrates: Surely we will posit knowledge necessary for a warrior, that is, to be able to calculate and count?

Glaucon: Of all things, at any rate, most of all, if he is able to understand even whatever thing of arranging troops, rather if he is about to be even a man.

Socrates: Do you have in mind then concerning this learning the very thing which I do?

Glaucon: What sort of thing?

Socrates: It runs the risk of being by nature of the things leading, which we seek, toward the understanding, but no one runs the risk of using it correctly, although being fit for drawing altogether toward reality.

Glaucon: How do you mean?

Socrates: I will try to show forth my opinion. For the things which I divide for myself in myself to be leading towards whither we say and not leading, since becoming a fellow-spectator, agree or deny, in order that we may see also this thing more clearly whether it is that sort of thing which I surmise.

Glaucon: Show.

Socrates: I am showing, in fact, if you pay attention, that some things in the perceptions do not summon the understanding into inspection, since being sufficiently judged by the perception; other things exhort in every way to inspect that thing, since the perception making nothing sound.

Glaucon: It is clear that you are talking about the things seeming from afar and the things being painted with the shadows.

Socrates: Not quite did you obtain the thing which I speak.

Glaucon: What sorts of things are you truly saying?

Socrates: The things more summoning, on the one hand, are as many things as do not proceed into opposite perception at the same time; I put the things proceeding, on the other hand, as the things summoning, when the perception makes clear this thing no more than the opposite, whether striking from close at hand or from afar. And you will know the things which I say in this way. These, just as say, would be three fingers, the smallest and the second and the middle.

Glaucon: Certainly.

Socrates: Suppose that, while me talking, they are seen as nearby, accordingly. But consider this thing for me concerning them.

Glaucon: What sort of thing?

Socrates: I suppose, each of them similarly seems to be a finger, on the one hand, and it makes no difference in this way, at any rate, whether it is seen in the middle or at the edge, whether white or black, whether thick or thin and everything whatever is that sort. For in all these things, the soul of the many men is not compelled to ask again the understanding what ever is a finger; for the sight in no way indicated to it at the same time that the finger is the opposite thing than a finger.

Glaucon: For it certainly did not.

Socrates: Accordingly, that sort of thing, at any rate, reasonably would not be stimulating or awaking understanding.

Glaucon: Reasonably. 

Socrates: And what now? Does the sight sufficiently see the largess of them and the smallness, and does it make no difference to it for some one of them to be placed in the middle or at the edge? And does the sense of touch in like manner sufficiently perceive thickness and thinness or softness and hardness? Also, do the other senses not deficiently make clear these sorts of things? Or does each of them do in this way: first, on the one hand, the perception having been arranged on hardness has been compelled also to have been arranged on softness, and it passes on a message to the soul that it perceives hardness and softness as the same thing?

Glaucon: In this way. 

Socrates: Accordingly, I said, it is necessary in these sorts of things, at any rate, in turn for the soul to be at a loss what ever that very perception indicates hardness to be, just if it says that the same thing is also softness, and the perception of lightness and the perception of heaviness, what lightness and heaviness is, if the perception indicts heaviness to be light and lightness to be heavy?

Glaucon: And indeed, these explanations, at any rate, are paradoxical to the soul and being in need of inspection.

Socrates: Reasonably then, in these sorts of things, first, on the one hand, by summoning calculation and understanding, soul tries to examine whether one or two are each of the things being reported. 

Glaucon: Yes.

Socrates: Accordingly, if they appear to be two, each of two appears to be a different thing and one thing?

Glaucon: Yes.

Socrates: If then each is one, and both are two, the soul will think that the two things, at any rate, have been separated; for it would not be considering undivided things, at any rate, as two things, but one thing.

Glaucon: Correctly.

Socrates: Truly, sight was also seeing largeness and smallness, just we say, but not something having been separated but something having been mixed together. Isn’t it?

Glaucon: Yes.

Socrates: And on account of the clearness of this thing, the understanding was compelled to see largeness, in turn, and smallness not as things having been mixed together but having been divided, in the opposite way than sight.

Glaucon: Yes.

Socrates: Accordingly, is it from here whence it first occurs to us to ask what then ever is largeness, in turn, and smallness?

Glaucon: In every way, certainly.

Socrates: And in this way, of course, we called one conceptual, another visible.

Glaucon: Most correctly.

Socrates: I was attempting to say these things, accordingly, also before, namely that, some things are stimulating the thought, others do not; the prior things which, on the one hand, fall upon into the perception together with the things opposite to themselves, since I marking out for myself summoners, and as many things as do not, on the other hand, are not awaking the thought.

Glaucon: I understand now, accordingly, and it seems to me in this way.

Socrates: What then? Of which of two does number and the number one seem to be?

Glaucon: I do not understand.

Socrates: But consider from the things having been said beforehand. For if, on the one hand, the number one is sufficiently seen itself by itself or taken by means of some other perception, it would not be fit for drawing toward the reality, just like we were saying in the case of the finger; if, on the other hand, something opposite is always seen together with it, so as for it to appear to be one no more than also the thing opposite, now it would then require the man deciding, and soul in him would be compelled to be at a loss and to seek, by calling forth the understanding in itself, and to question what ever is the very number one, and in this way, the knowledge concerning the number one would be in this way of the things leading and fit for directing toward the contemplation of being.

Glaucon: But however, the sight concerning it not least holds this thing, at any rate; for at the same time we are seeing the same thing as one and as boundless with respect to its number.

Socrates: Accordingly, if indeed the number one is, also number altogether has experienced this same thing?

Glaucon: Yes.

Socrates: Yet truly, calculation and arithmetic are concerned with number, entirely.

Glaucon: Very much so.

Note: The Greek text below is from:

Plato. Platonis Opera, ed. John Burnet. Oxford University Press. 1903.

Credits to the Perseus Digital Library for digitalizing the work.

[522e] ἄλλο τι οὖν, ἦν δ᾽ ἐγώ, μάθημα ἀναγκαῖον πολεμικῷ ἀνδρὶ θήσομεν λογίζεσθαί τε καὶ ἀριθμεῖν δύνασθαι;

πάντων γ᾽, ἔφη, μάλιστα, εἰ καὶ ὁτιοῦν μέλλει τάξεων ἐπαΐειν, μᾶλλον δ᾽ εἰ καὶ ἄνθρωπος ἔσεσθαι.

ἐννοεῖς οὖν, εἶπον, περὶ τοῦτο τὸ μάθημα ὅπερ ἐγώ;

τὸ ποῖον;

[523a] κινδυνεύει τῶν πρὸς τὴν νόησιν ἀγόντων φύσει εἶναι ὧν ζητοῦμεν, χρῆσθαι δ᾽ οὐδεὶς αὐτῷ ὀρθῶς, ἑλκτικῷ ὄντι παντάπασι πρὸς οὐσίαν.

πῶς, ἔφη, λέγεις;

ἐγὼ πειράσομαι, ἦν δ᾽ ἐγώ, τό γ᾽ ἐμοὶ δοκοῦν δηλῶσαι. ἃ γὰρ διαιροῦμαι παρ᾽ ἐμαυτῷ ἀγωγά τε εἶναι οἷ λέγομεν καὶ μή, συνθεατὴς γενόμενος σύμφαθι ἢ ἄπειπε, ἵνα καὶ τοῦτο σαφέστερον ἴδωμεν εἰ ἔστιν οἷον μαντεύομαι.

δείκνυ᾽, ἔφη.

δείκνυμι δή, εἶπον, εἰ καθορᾷς, τὰ μὲν ἐν ταῖς αἰσθήσεσιν [523b] οὐ παρακαλοῦντα τὴν νόησιν εἰς ἐπίσκεψιν, ὡς ἱκανῶς ὑπὸ τῆς αἰσθήσεως κρινόμενα, τὰ δὲ παντάπασι διακελευόμενα ἐκείνην ἐπισκέψασθαι, ὡς τῆς αἰσθήσεως οὐδὲν ὑγιὲς ποιούσης.

τὰ πόρρωθεν, ἔφη, φαινόμενα δῆλον ὅτι λέγεις καὶ τὰ ἐσκιαγραφημένα.

οὐ πάνυ, ἦν δ᾽ ἐγώ, ἔτυχες οὗ λέγω.

ποῖα μήν, ἔφη, λέγεις;

τὰ μὲν οὐ παρακαλοῦντα, ἦν δ᾽ ἐγώ, ὅσα μὴ ἐκβαίνει [523c] εἰς ἐναντίαν αἴσθησιν ἅμα: τὰ δ᾽ ἐκβαίνοντα ὡς παρακαλοῦντα τίθημι, ἐπειδὰν ἡ αἴσθησις μηδὲν μᾶλλον τοῦτο ἢ τὸ ἐναντίον δηλοῖ, εἴτ᾽ ἐγγύθεν προσπίπτουσα εἴτε πόρρωθεν. ὧδε δὲ ἃ λέγω σαφέστερον εἴσῃ. οὗτοί φαμεν τρεῖς ἂν εἶεν δάκτυλοι, ὅ τε σμικρότατος καὶ ὁ δεύτερος καὶ ὁ μέσος.

πάνυ γ᾽, ἔφη.

ὡς ἐγγύθεν τοίνυν ὁρωμένους λέγοντός μου διανοοῦ. ἀλλά μοι περὶ αὐτῶν τόδε σκόπει.

τὸ ποῖον;

δάκτυλος μέν που αὐτῶν φαίνεται ὁμοίως ἕκαστος, καὶ [523d] ταύτῃ γε οὐδὲν διαφέρει, ἐάντε ἐν μέσῳ ὁρᾶται ἐάντ᾽ ἐπ᾽ ἐσχάτῳ, ἐάντε λευκὸς ἐάντε μέλας, ἐάντε παχὺς ἐάντε λεπτός, καὶ πᾶν ὅτι τοιοῦτον. ἐν πᾶσι γὰρ τούτοις οὐκ ἀναγκάζεται τῶν πολλῶν ἡ ψυχὴ τὴν νόησιν ἐπερέσθαι τί ποτ᾽ ἐστὶ δάκτυλος: οὐδαμοῦ γὰρ ἡ ὄψις αὐτῇ ἅμα ἐσήμηνεν τὸ δάκτυλον τοὐναντίον ἢ δάκτυλον εἶναι.

οὐ γὰρ οὖν, ἔφη.

οὐκοῦν, ἦν δ᾽ ἐγώ, εἰκότως τό γε τοιοῦτον νοήσεως οὐκ [523e] ἂν παρακλητικὸν οὐδ᾽ ἐγερτικὸν εἴη.

εἰκότως.

τί δὲ δή; τὸ μέγεθος αὐτῶν καὶ τὴν σμικρότητα ἡ ὄψις ἆρα ἱκανῶς ὁρᾷ, καὶ οὐδὲν αὐτῇ διαφέρει ἐν μέσῳ τινὰ αὐτῶν κεῖσθαι ἢ ἐπ᾽ ἐσχάτῳ; καὶ ὡσαύτως πάχος καὶ λεπτότητα ἢ μαλακότητα καὶ σκληρότητα ἡ ἁφή; καὶ αἱ ἄλλαι αἰσθήσεις ἆρ᾽ οὐκ ἐνδεῶς τὰ τοιαῦτα δηλοῦσιν; ἢ [524a] ὧδε ποιεῖ ἑκάστη αὐτῶν: πρῶτον μὲν ἡ ἐπὶ τῷ σκληρῷ τεταγμένη αἴσθησις ἠνάγκασται καὶ ἐπὶ τῷ μαλακῷ τετάχθαι, καὶ παραγγέλλει τῇ ψυχῇ ὡς ταὐτὸν σκληρόν τε καὶ μαλακὸν αἰσθανομένη;

οὕτως, ἔφη.

οὐκοῦν, ἦν δ᾽ ἐγώ, ἀναγκαῖον ἔν γε τοῖς τοιούτοις αὖ τὴν ψυχὴν ἀπορεῖν τί ποτε σημαίνει αὕτη ἡ αἴσθησις τὸ σκληρόν, εἴπερ τὸ αὐτὸ καὶ μαλακὸν λέγει, καὶ ἡ τοῦ κούφου καὶ ἡ τοῦ βαρέος, τί τὸ κοῦφον καὶ βαρύ, εἰ τό τε βαρὺ κοῦφον καὶ τὸ κοῦφον βαρὺ σημαίνει;

[524b] καὶ γάρ, ἔφη, αὗταί γε ἄτοποι τῇ ψυχῇ αἱ ἑρμηνεῖαι καὶ ἐπισκέψεως δεόμεναι.

εἰκότως ἄρα, ἦν δ᾽ ἐγώ, ἐν τοῖς τοιούτοις πρῶτον μὲν πειρᾶται λογισμόν τε καὶ νόησιν ψυχὴ παρακαλοῦσα ἐπισκοπεῖν εἴτε ἓν εἴτε δύο ἐστὶν ἕκαστα τῶν εἰσαγγελλομένων.

πῶς δ᾽ οὔ;

οὐκοῦν ἐὰν δύο φαίνηται, ἕτερόν τε καὶ ἓν ἑκάτερον φαίνεται;

ναί.

εἰ ἄρα ἓν ἑκάτερον, ἀμφότερα δὲ δύο, τά γε δύο κεχωρισμένα [524c] νοήσει: οὐ γὰρ ἂν ἀχώριστά γε δύο ἐνόει, ἀλλ᾽ ἕν.

ὀρθῶς.

μέγα μὴν καὶ ὄψις καὶ σμικρὸν ἑώρα, φαμέν, ἀλλ᾽ οὐ κεχωρισμένον ἀλλὰ συγκεχυμένον τι. ἦ γάρ;

ναί.

διὰ δὲ τὴν τούτου σαφήνειαν μέγα αὖ καὶ σμικρὸν ἡ νόησις ἠναγκάσθη ἰδεῖν, οὐ συγκεχυμένα ἀλλὰ διωρισμένα, τοὐναντίον ἢ ‘κείνη.

ἀληθῆ.

οὐκοῦν ἐντεῦθέν ποθεν πρῶτον ἐπέρχεται ἐρέσθαι ἡμῖν τί οὖν ποτ᾽ ἐστὶ τὸ μέγα αὖ καὶ τὸ σμικρόν;

παντάπασι μὲν οὖν.

καὶ οὕτω δὴ τὸ μὲν νοητόν, τὸ δ᾽ ὁρατὸν ἐκαλέσαμεν.

[524d] ὀρθότατ᾽, ἔφη.

ταῦτα τοίνυν καὶ ἄρτι ἐπεχείρουν λέγειν, ὡς τὰ μὲν παρακλητικὰ τῆς διανοίας ἐστί, τὰ δ᾽ οὔ, ἃ μὲν εἰς τὴν αἴσθησιν ἅμα τοῖς ἐναντίοις ἑαυτοῖς ἐμπίπτει, παρακλητικὰ ὁριζόμενος, ὅσα δὲ μή, οὐκ ἐγερτικὰ τῆς νοήσεως.

μανθάνω τοίνυν ἤδη, ἔφη, καὶ δοκεῖ μοι οὕτω.

τί οὖν; ἀριθμός τε καὶ τὸ ἓν ποτέρων δοκεῖ εἶναι;

οὐ συννοῶ, ἔφη.

ἀλλ᾽ ἐκ τῶν προειρημένων, ἔφην, ἀναλογίζου. εἰ μὲν γὰρ ἱκανῶς αὐτὸ καθ᾽ αὑτὸ ὁρᾶται ἢ ἄλλῃ τινὶ αἰσθήσει [524e] λαμβάνεται τὸ ἕν, οὐκ ἂν ὁλκὸν εἴη ἐπὶ τὴν οὐσίαν, ὥσπερ ἐπὶ τοῦ δακτύλου ἐλέγομεν: εἰ δ᾽ ἀεί τι αὐτῷ ἅμα ὁρᾶται ἐναντίωμα, ὥστε μηδὲν μᾶλλον ἓν ἢ καὶ τοὐναντίον φαίνεσθαι, τοῦ ἐπικρινοῦντος δὴ δέοι ἂν ἤδη καὶ ἀναγκάζοιτ᾽ ἂν ἐν αὐτῷ ψυχὴ ἀπορεῖν καὶ ζητεῖν, κινοῦσα ἐν ἑαυτῇ τὴν ἔννοιαν, καὶ ἀνερωτᾶν τί ποτέ ἐστιν αὐτὸ τὸ ἕν, καὶ οὕτω τῶν [525a] ἀγωγῶν ἂν εἴη καὶ μεταστρεπτικῶν ἐπὶ τὴν τοῦ ὄντος θέαν ἡ περὶ τὸ ἓν μάθησις.

ἀλλὰ μέντοι, ἔφη, τοῦτό γ᾽ ἔχει οὐχ ἥκιστα ἡ περὶ αὐτὸ ὄψις: ἅμα γὰρ ταὐτὸν ὡς ἕν τε ὁρῶμεν καὶ ὡς ἄπειρα τὸ πλῆθος.

οὐκοῦν εἴπερ τὸ ἕν, ἦν δ᾽ ἐγώ, καὶ σύμπας ἀριθμὸς ταὐτὸν πέπονθε τοῦτο;

πῶς δ᾽ οὔ;

ἀλλὰ μὴν λογιστική τε καὶ ἀριθμητικὴ περὶ ἀριθμὸν πᾶσα.

καὶ μάλα.