First, let’s return to the Dichotomy paradox. Here it is again, without the tennis-court: whenever you move from A to B, you have to move to C, the point halfway between A and B; to do that, you have to move to D which is halfway between A and C; and so on. There will be an infinite number of such points, meaning that to move from A to B you have to perform an infinite number of tasks, which is impossible. Or, to put it as Aristotle does when he relates the paradox (§320), you have to come into contact with infinitely many things (namely the halfway points). But why is this impossible? It’s
...more
