Introducing the Ancient Greeks: From Bronze Age Seafarers to Navigators of the Western Mind

by Edith Hall

Parmenides also used argumentative methods that Socrates later developed at length, such as the identification of contradiction. Parmenides’ argument that motion is illusory was defended by a younger Eleatic, Zeno, in a series of colorful paradoxes. These are fascinating because they show the classroom training that a young philosopher might have experienced in Parmenides’ school. Even today, they are often the first philosophical bones that undergraduates are given to chew on. The term paradox technically means “demonstrations that absurd consequences can follow from seemingly reasonable assumptions.” The most famous is known as “Achilles and the tortoise.” The majority of people assume that because Achilles can run faster than the tortoise, he will overtake it if he chases it. But Zeno said that every time Achilles is just about to catch up with the tortoise, the tortoise has a chance to progress forward very slightly. If taken to infinity, this means that Achilles can never actually get to the place the tortoise is in before the tortoise leaves it. A second notorious paradox argued that a flying arrow is not in motion, even though most people believe it is, because at any single instant it is in a particular place, and therefore still. These and Zeno’s other paradoxes are actually harder to disprove than it might appear.