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ἐπιθυμιῶν: a defining genitive. For εἶδος see III 402 C note

ἆρ᾽ οὖν κτλ. This discussion (down to 438 E) is apparently regarded by Susemihl (Gen. Entw. II pp. 163 f.) as unnecessary for the immediate purposes of the argument, but it is not so. Plato's object is to remove a difficulty which might be felt in holding that desire is restrained, and that by the λογιστικόν. Why should thirst be restrained? an objector might ask. You yourself, Socrates, hold that (1) desire is always of the good; consequently (2) thirst is always the desire of good drink, and (3) is therefore always good. See 438 A, where the gist of the objection is contained. Socrates would reply: The fallacy lurks in (2), for ‘good’ drink is ambiguous. If ‘good’ drink means drink which desire thinks good, then (2) is true; if it means drink which is in reality good, (2) is not true. Desire cannot know what is good. We must therefore amend (2) by omitting ‘good,’ for in reality it is sometimes good and sometimes bad to drink. To what then is the final appeal? To the λογιστικόν. It is this which decides on each occasion whether it is really good or bad to drink, and gives or refuses its assent accordingly (439 C). Bosanquet takes a somewhat similar view (Companion p. 154). See also notes on 438 A.

οἷον δίψα -- ψυχροῦ. ‘Thus thirst is thirst—of hot drink, is it, or of cold?’ For the genitive with δίψα (which Richards doubts) cf. 439 A. The repetition of δίψα is like that of ἐπιστήμη in 438 C, and makes the statement formal and precise.

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