Zeno of Elea

Zeno was Parmenides' student and defender. When critics mocked the idea that change is impossible, Zeno answered not with theories but with puzzles. If Achilles gives a tortoise a head start, he can never catch it, because he must first reach where the tortoise was, by which time it has moved on. An arrow in flight is at rest at every instant, so it never moves. These paradoxes were not riddles. They were arguments designed to show that the critics' own assumptions about space, time, and motion led to absurdity.