Abstract

Attempts to characterise time seem to throw up paradox at every turn. Some of the most famous of the paradoxes are also the oldest—those due to Aristotle (384–322 BC) and Zeno (b. c. 488 BC), as described in Aristotle’s Physics. For example, Zeno argued that in order to traverse any distance, one must always first traverse half that distance; but since this half is itself a distance to be traversed, one must in turn first traverse half of the half, and so on ad infinitum. Since it is impossible to traverse an infinite number of distances in a finite time, all motion must be impossible—indeed, incoherent. A similar argument can be used to show that a line cannot be composed of a set of points, a problem which was only satisfactorily resolved with the development of the modern mathematics of infinity. A central question for the philosophy of time, then, becomes whether (and how) the mathematics of infinity applies to time.