Back to the course home page. If anything moves from one place to another, then it performs infinitely many tasks. Nothing can perform infinitely many tasks. To complete an infinite number of tasks would require an infinite amount of time. Nothing can do anything which requires an infinite amount of time.
Nothing can perform infinitely many tasks.
Aristotle rejects this argument in terms of the distinction between infinite divisibility and infinite extension. But, Aristotle's argument is not quite right, since the infinite divisibility of the motion is reduced to the infinite divisibility of the temporal interval of the motion. If this interval is infinitely divisible then it has an infinite number of parts and to get from one moment to the next requires an infinite series of steps. Aristotle introduces a new distinction between potential and actual infinities. Infinitely divisible intervals are only potentially infinite.