Philosophy 100 Essential Thinkers

by Philip Stokes

Suppose Achilles decides to see how fast he can run the track in a stadium. Before he can reach the end he must first get to the half way point, but before he does so he must get to the halfway point of that, and the half way point of that, and so on indefinitely. If space is made up of an infinite series of points one can never move any distance at all; to complete a journey one would have to pass every point, and one cannot pass an infinite series of points in a finite amount of time. Similarly, in the famous Achilles and the Tortoise paradox, Zeno asks us to imagine Achilles giving the tortoise a head start. But before he can get to where the tortoise is, it will have moved a little farther on, and before he can get to that spot the it will have moved a little farther on again, and so on indefinitely. Achilles can never catch the tortoise no matter how fast he runs, for every time he moves the tortoise moves too. Therefore motion through time (i.e. change) is impossible.