Two main conceptual developments were required for the Greeks to achieve a scientific understanding of motion. First, they needed a coherent conception of nonbeing: if something moves then it is not somewhere at one time where it $is$ at another time; and Parmenides showed that this causes problems if you think of it in the wrong way. Second, they had to conceive an appropriate relation between space and time, such that space and time could be combined in an understanding of speed. Before Aristotle, Greek thinkers could not with full generality think of one motion as faster or slower than another; they could only make this comparison in special cases (such as when two runners run the same course and one finishes first).

So runs the organizing thesis of Barbara Sattler’s valuable and wide-ranging book. The book traces the problem of nonbeing with a focus on Parmenides, the...