Change, motion, and explanation › Continuity and the infinite

The discussion of motion leads Aristotle to the infinite. He rejects an actually infinite bodily magnitude while allowing an infinity of further division. A finite length can always be divided again; we need not suppose that an infinite collection of bodily parts has been completed as a separate object. The relevant infinity concerns the inexhaustibility of the procedure (Physics III.6–7).

In Book VI, he connects the divisibility of distance, motion, and time. A continuous line is not assembled out of indivisible points as if points were tiny lengths. Points mark boundaries, while a segment can be divided into further segments. Correspondingly, the divisibility of a journey does not alone show that the journey needs an unlimited duration (Physics VI.1–2).

This bears on the argument attributed to Zeno that a traveller must first traverse half the route, then another division, and so on. Aristotle distinguishes an infinity in respect of divisibility from an infinite extent. A finite time is also divisible, so infinitely many possible divisions of a route do not by themselves preclude its traversal in a finite time (Physics VI.2, VI.9). This is his response within a theory of continuity, not a presentation of modern calculus.