Related Terms • paradox

Biography:
Zeno of Elea (c. 490 BCE) was a pre-Socratic Greek philosopher and a pupil of Parmenides whose work has not survived directly, but we do know of it from the reports of others.

Zeno is most famous for his paradoxes involving time and motion, using reductio ad absurdum to show that neither can be infinitely divisible.

Stadium Paradox: Zeno argues that it is impossible to ever reach the finish line when running around a stadium. In order to reach the finish line, you must first reach the halfway point. But before you reach the halfway point, you must reach the halfway point to that - and so on, and so on to infinity. Thus, if space is infinitely divisible then any finite distance must consist of an infinite number of points. It is impossible to reach the end of an infinite series in a finite amount of time.

Achilles Paradox: If Achilles races a tortoise and gives the tortoise a head start, then Achilles will never be able to overtake the tortoise. When Achilles reaches the point where the torotise started, the tortoise will have moved on. When Achilles reaches that point, the tortoise will have moved on farther - and so on indefinitely.

Arrow Paradox: Whenever an object is sitting at rest, it occupies a space which is equal to its dimensions. Any arrow in flight must, at any one moment, occupy a space equal to its dimensions. Therefore, an arrow in flight is, at any given moment, really at rest.

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Related Resources:

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