Abstract

There are a variety of puzzling features about this argument. One of them—questions of validity apart—is its apparent redundancy. Parmenides’ initial division provided him with an infinite plurality of parts. He might therefore have given an existence proof of infinitely many numbers, conceived as pluralities of units, by means of this division. Instead, he introduces a new principle of division for the purpose. Again, he derives the conclusion that Unity has infinitely many parts from the infinity of number; but he has already shown that Unity is infinitely divisible into parts consisting of being and unity. In short, the new principle of division introduced for number seems unnecessary, and Parmenides has twice shown that Unity has infinitely many parts.