Page:Early Greek philosophy by John Burnet, 3rd edition, 1920.djvu/332

 318 everything must be "in" something, or must have something beyond it, had been used against the Parmenidean theory of a finite sphere with nothing outside it.

163. Zeno's arguments on the subject of motion have been preserved by Aristotle himself. The system of Parmenides made all motion impossible, and his successors had been driven to abandon the monistic hypothesis in order to avoid this very consequence. Zeno does not bring any fresh proofs of the impossibility of motion; all he does is to show that a pluralist theory, such as the Pythagorean, is just as unable to explain it as was that of Parmenides. Looked at in this way, Zeno's arguments are no mere quibbles, but mark a great advance in the conception of quantity. They are as follows

The "hypothesis" of the second argument is the same as that of the first, namely, that the line is a series of points; but the reasoning is complicated by the introduction of another moving object. The difference, accordingly, is not a half every time, but diminishes in. a constant ratio. Again, the first argument shows that, on this hypothesis, no moving object can ever traverse any distance at all, however fast it