[526a]
“Suppose now, Glaucon, someone were to ask them, ‘My good
friends, what numbers1 are these you are talking about, in which
the one is such as you postulate, each unity equal to every other without the
slightest difference and admitting no division into parts?’ What do
you think would be their answer?” “This, I
think—that they are speaking of units which can only be conceived by
thought, and which it is not possible to deal with in any other way.”
“You see, then, my friend,” said I, “that this
branch of study really seems to be
1 This is one of the chief sources of the fancy that numbers are intermediate entities between ideas and things. Cf. Alexander, Space, Time, and Deity, i. p. 219: “Mathematical particulars are therefore not as Plato thought intermediate between sensible figures and universals. Sensible figures are only less simple mathematical ones.” Cf. on 525 D. Plato here and elsewhere simply means that the educator may distinguish two kinds of numbers—five apples, and the number five as an abstract idea. Cf. Theaet. 19 E: We couldn't err about eleven which we only think, i.e. the abstract number eleven. Cf. also Berkeley, Siris, 288.
Plato. Plato in Twelve Volumes, Vols. 5 & 6 translated by Paul Shorey. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1969.
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