James Adam, Commentary on Plato, Republic, ed. James Adam, 7.525E

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[525E] ἐάν τις κτλ. αὐτὸ τὸ ἕν means ‘the unit itself’ i.e. the mathematical number ‘one’ which is ex hypothesi and by definition ἀμέριστον καὶ ἀδιαίρετον (Theo Smyrn. 18). If any one maintains that the mathematical unit is divisible, the mathematicians καταγελῶσί τε καὶ οὐκ ἀποδέχονται. Quâ mathematicians, they never condescend to justify either this or any other mathematical definition ( οὐδένα λόγον οὔτε αὑτοῖς οὔτε ἄλλοις ἔτι ἀξιοῦσι—διδόναι VI 510 C), and think it ridiculous that any one should question the foundations of their science. The moment they begin to render an account of their ὑποθέσεις they cease to be mathematicians and become διαλεκτικοί. See also on VI 510 C and App. III.

ἐὰν σὺ κερματίζῃς κτλ. : ‘if you mince it, they multiply it.’ If you insist on dividing their unit, they insist on multiplying it (viz. by your divisor), and so defeat your purpose and keep the unit one and indivisible as before. ‘I cut that unit up!’ you exclaim. ‘I multiply it!’ is their reply; and you are checkmated. They have just as much right to multiply it as you to divide it; for the mathematical unit is only a ὑπόθεσις when all is said and done. Plato is humorously describing a passage-atarms between mathematicians and some obstinate fellow who will not admit the indivisibility of their unit. The words ‘back again’ in D. and V.'s translation “they multiply it back again” correspond to nothing in the Greek and suggest an erroneous idea; nor can the Greek mean “that division is regarded by them as a process of multiplication, for the fractions of one continue to be units” (as Jowett suggests). Each of these explanations misses the humour of the original. The word μόρια is doubtless genuine, though its rejection (proposed by Herwerden) would improve the antithesis. Cf. μόριόν τε ἔχον ἐν ἑαυτῷ οὐδέν (526 A), for which μόρια here prepares the way.

Commentary on Plato, Republic. James Adam. ed. James Adam. Cambridge. 1926-1929.

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Current edition Perseus

Commentary on Plato, Republic (English) (Plato. The Republic, Vol 1-2. Adam, James, editor. Cambridge: Cambridge University Press, 1902-1903.)

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Πολιτεία Perseus (Platonis Opera Tomus IV: Tetralogia VIII. Burnet, John, editor. Oxford: Clarendon Press, 1905.) — 7.525 focus

[525] εἰ δʼ ἀεί τι αὐτῷ ἅμα ὁρᾶται ἐναντίωμα, ὥστε μηδὲν μᾶλλον ἓν ἢ καὶ τοὐναντίον φαίνεσθαι, τοῦ ἐπικρινοῦντος δὴ δέοι ἂν ἤδη καὶ ἀναγκάζοιτʼ 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 γʼ ἔχει οὐχ ἥκιστα ἡ περὶ αὐτὸ ὄψις· ἅμα γὰρ ταὐτὸν ὡς ἕν τε ὁρῶμεν καὶ ὡς ἄπειρα τὸ πλῆθος.
οὐκοῦν εἴπερ τὸ ἕν, ἦν δʼ ἐγώ, καὶ σύμπας ἀριθμὸς ταὐτὸν πέπονθε τοῦτο;
πῶς δʼ οὔ;
ἀλλὰ μὴν λογιστική τε καὶ ἀριθμητικὴ περὶ ἀριθμὸν πᾶσα.
καὶ μάλα. 525b
ταῦτα δέ γε φαίνεται ἀγωγὰ πρὸς ἀλήθειαν.
ὑπερφυῶς μὲν οὖν.
ὧν ζητοῦμεν ἄρα, ὡς ἔοικε, μαθημάτων ἂν εἴη· πολεμικῷ μὲν γὰρ διὰ τὰς τάξεις ἀναγκαῖον μαθεῖν ταῦτα, φιλοσόφῳ δὲ διὰ τὸ τῆς οὐσίας ἁπτέον εἶναι γενέσεως ἐξαναδύντι, ἢ μηδέποτε λογιστικῷ γενέσθαι.
ἔστι ταῦτʼ, ἔφη.
ὁ δέ γε ἡμέτερος φύλαξ πολεμικός τε καὶ φιλόσοφος τυγχάνει ὤν.
τί μήν;
προσῆκον δὴ τὸ μάθημα ἂν εἴη, ὦ Γλαύκων, νομοθετῆσαι καὶ πείθειν τοὺς μέλλοντας ἐν τῇ πόλει τῶν μεγίστων 525c μεθέξειν ἐπὶ λογιστικὴν ἰέναι καὶ ἀνθάπτεσθαι αὐτῆς μὴ ἰδιωτικῶς, ἀλλʼ ἕως ἂν ἐπὶ θέαν τῆς τῶν ἀριθμῶν φύσεως ἀφίκωνται τῇ νοήσει αὐτῇ, οὐκ ὠνῆς οὐδὲ πράσεως χάριν ὡς ἐμπόρους ἢ καπήλους μελετῶντας, ἀλλʼ ἕνεκα πολέμου τε καὶ αὐτῆς τῆς ψυχῆς ῥᾳστώνης μεταστροφῆς ἀπὸ γενέσεως ἐπʼ ἀλήθειάν τε καὶ οὐσίαν.
κάλλιστʼ, ἔφη, λέγεις.
καὶ μήν, ἦν δʼ ἐγώ, νῦν καὶ ἐννοῶ, ῥηθέντος τοῦ περὶ 525d τοὺς λογισμοὺς μαθήματος, ὡς κομψόν ἐστι καὶ πολλαχῇ χρήσιμον ἡμῖν πρὸς ὃ βουλόμεθα, ἐὰν τοῦ γνωρίζειν ἕνεκά τις αὐτὸ ἐπιτηδεύῃ ἀλλὰ μὴ τοῦ καπηλεύειν.
πῇ δή; ἔφη.
τοῦτό γε, ὃ νυνδὴ ἐλέγομεν, ὡς σφόδρα ἄνω ποι ἄγει τὴν ψυχὴν καὶ περὶ αὐτῶν τῶν ἀριθμῶν ἀναγκάζει διαλέγεσθαι, οὐδαμῇ ἀποδεχόμενον ἐάν τις αὐτῇ ὁρατὰ ἢ ἁπτὰ σώματα ἔχοντας ἀριθμοὺς προτεινόμενος διαλέγηται. οἶσθα γάρ που τοὺς περὶ ταῦτα δεινοὺς αὖ ὡς, ἐάν τις αὐτὸ τὸ 525e ἓν ἐπιχειρῇ τῷ λόγῳ τέμνειν, καταγελῶσί τε καὶ οὐκ ἀποδέχονται, ἀλλʼ ἐὰν σὺ κερματίζῃς αὐτό, ἐκεῖνοι πολλαπλασιοῦσιν, εὐλαβούμενοι μή ποτε φανῇ τὸ ἓν μὴ ἓν ἀλλὰ πολλὰ μόρια.
ἀληθέστατα, ἔφη, λέγεις.

Translations (1)

Republic Perseus (Plato in Twelve Volumes, Vol. 5-6. Shorey, Paul, translator. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1935-37 (printing).) — 7.525 focus

[525] But if some contradiction is always seen coincidentally with it, so that it no more appears to be one than the opposite, there would forthwith be need of something to judge between them, and it would compel the soul to be at a loss and to inquire, by arousing thought in itself, and to ask, 525a whatever then is the one as such, and thus the study of unity will be one of the studies that guide and convert the soul to the contemplation of true being.” “But surely,” he said, “the visual perception of it¹ does especially involve this. For we see the same thing at once as one and as an indefinite plurality.²” “Then if this is true of the one,” I said, “the same holds of all number, does it not?” Of course. “But, further, reckoning and the science of arithmetic³ are wholly concerned with number.” 525b “They are, indeed.” “And the qualities of number appear to lead to the apprehension of truth.” “Beyond anything,” he said. “Then, as it seems, these would be among the studies that we are seeking. For a soldier must learn them in order to marshal his troops, and a philosopher, because he must rise out of the region of generation and lay hold on essence or he can never become a true reckoner.⁴” “It is so,” he said. “And our guardian is soldier and philosopher in one.” Of course. “It is befitting, then, Glaucon, that this branch of learning should be prescribed by our law and that we should induce those who are to share the highest functions of state 525c to enter upon that study of calculation and take hold of it, not as amateurs, but to follow it up until they attain to the contemplation of the nature of number,⁵ by pure thought, not for the purpose of buying and selling,⁶ as if they were preparing to be merchants or hucksters, but for the uses of war and for facilitating the conversion of the soul itself from the world of generation to essence and truth.” “Excellently said,” he replied. “And, further,” I said, “it occurs to me,⁷ now that the study of reckoning has been mentioned, 525d that there is something fine in it, and that it is useful for our purpose in many ways, provided it is pursued for the sake of knowledge⁸ and not for huckstering.” “In what respect?” he said. “Why, in respect of the very point of which we were speaking, that it strongly directs the soul upward and compels it to discourse about pure numbers,⁹ never acquiescing if anyone proffers to it in the discussion numbers attached to visible and tangible bodies. For you are doubtless aware 525e that experts in this study, if anyone attempts to cut up the one in argument, laugh at him and refuse to allow it; but if you mince it up,¹⁰ they multiply, always on guard lest the one should appear to be not one but a multiplicity of parts.¹¹” “Most true,” he replied.

James Adam Commentary on Plato, Republic 7.525E

ed. James Adam

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