The form of the third man argument

Apeiron 12 (2):6 - 13 (1978)
Our interpretation of the "parmenides" 132a1 - 132b2 has the following features. (i) it stresses that the third man argument is an infinite regress and (ii) notes its epistemological thrust. (iii) a faithful translation of the last line of the argument reads "and no longer will each of the forms be for you one but each is infinite in multitude." parmenides' point is that each form, which socrates believed to be complete (one), turns out to be an unbounded, incompletable series of subforms useless for comprehending the unity of many particulars. (iv) related problems are seen to occupy plato in the "philebus" and in the "sophist"
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