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,
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 it Footnote 1See crit. note and Adam ad loc. does especially involve this. For we see the same thing at once as one and as an indefinite plurality. Footnote 2This is the problem of the one and the many with which Plato often plays, which he exhaustively and consciously illustrates in the Parmenides, and which the introduction to the Philebus treats as a metaphysical nuisance to be disregarded in practical logic. We have not yet got rid of it, but have merely transferred it to psychology. ” “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 arithmetic Footnote 3Cf. Gorg. 450 D, 451 B-C. are wholly concerned with number.” “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. Footnote 4Cf. my review of Jowett, A.J.P. xiii. p. 365. My view there is adopted by Adam ad loc., and Apelt translates in the same way. ” “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 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, Footnote 5It is not true as Adam says that the nature of numbers cannot be fully seen except in their connection with the Good.
Plato never says that and never really meant it, though he might possibly have affirmed it on a challenge. Numbers are typical abstractions and educate the mind for the apprehension of abstractions if studied in their nature, in themselves, and not in the concrete form of five apples. There is no common sense nor natural connection between numbers and the good, except the point made in the Timaeus 53 B, and which is not relevant here, that God used numbers and forms to make a cosmos out of a chaos. by pure thought, not for the purpose of buying and selling, Footnote 6Instead of remarking on Plato’s scorn for the realities of experience we should note that he is marking the distinctive quality of the mind of the Greeks in contrast with the Egyptians and orientals from whom they learned and the Romans whom they taught. Cf. 525 D καπηλεύειν
, and Horace, Ars Poetica 323-332, Cic. Tusc. i. 2. 5. Per contra Xen. Mem. iv. 7, and Libby, Introduction to History of Science, p. 49: In this the writer did not aim at the mental discipline of the students, but sought to confine himself to what is easiest and most useful in calculation,
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, Footnote 7Cf. on 521 D, p. 147, note e. now that the study of reckoning has been mentioned, 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 knowledge Footnote 8Cf. Aristot. Met. 982 a 15 such as men constantly require in cases of inheritance, legacies, partition, law-suits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computation, and other objects of various sorts and kinds are concerned.
τοῦ εἰδέναι χάριν
, and Laws 741 C. Montesquieu apud Arnold, Culture and Anarchy, p. 6: The first motive which ought to impel us to study is the desire to augment the excellence of our nature and to render an intelligent being more intelligent.
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, Footnote 9Lit. numbers (in) themselves,
i.e. ideal numbers or the ideas of numbers. For this and the following as one of the sources of the silly notion that mathematical numbers are intermediate between ideal and concrete numbers, cf. my De Platonis Idearum Doctrina, p. 33, Unity of Plato’s Thought, pp. 83-84, Class. Phil. xxii. () pp. 213-218. never acquiescing if anyone proffers to it in the discussion numbers attached to visible and tangible bodies. For you are doubtless aware 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, Footnote 10Cf. Meno 79 C κατακερματίζῃς
, Aristot. Met. 1041 a 19 ἀδιαίρετον πρὸς αὑτὸ ἕκαστον· τοῦτο δ’ ἦν τὸ ἑνὶ εἶναι
, Met. 1052 b a ff., 15 ff. and 1053 a 1 τὴν γὰρ μονάδα τιθέασι πάντῃ ἀδιαίρετον. κερματίζειν
is also the word used of breaking money into small change. they multiply, always on guard lest the one should appear to be not one but a multiplicity of parts. Footnote 11Numbers are the aptest illustration of the principle of the Philebus and the Parmenides that thought has to postulate unities which sensation (sense perception) and also dialectics are constantly disintegrating into pluralities. Cf. my Ideas of Good in Plato’s Republic, p. 222. Stenzel, Dialektik, p. 32, says this dismisses the problem of the one and the many das ihn (Plato) später so lebhaft beschäftigen sollte.
But that is refuted by Parmen. 159 C οὐδὲ μὴν μόριά γε ἔχειν φαμὲν τὸ ὡς ἀληθῶς ἕν
. The problem
was always in Plato’s mind. He played with it when it suited his purpose and dismissed it when he wished to go on to something else. Cf. on 525 A, Phaedr. 266 B, Meno 12 C, Laws 964 A, Soph. 251. ” “Most true,” he replied.
Book 7