What are Zeno’s Paradoxes? Greek Pre-Socratics Read more from Chapter Ancient Philosophy

Zeno’s paradoxes continue to occupy mathematicians and philosophers, today. His paradox of motion applies to any distance. The paradox states that, before you can walk across a room, you have to travel half of the distance (1/2), but before that, you must traverse half of that half-distance (1/4), and before that, half of that distance (1/8), and so on. Because there are an infinite number of divisions of any given distance traveled, it is impossible to go anywhere from anywhere else.

Zeno’s paradox of Achilles and the tortoise applies a slightly different principle to a race. Suppose that Achilles, in a race with a tortoise, gives the tortoise a head start. Before Achilles can pass the tortoise, he must get to the place where the tortoise has been. But because the tortoise will always have moved on from that place, Achilles will never be able to pass the tortoise!