The Monist

Volume 83, Issue 2, April 2000

Applying Mathematics

Are There Really Instantaneous Velocities?

Zeno argued that since at any instant an arrow does not change its location, the arrow does not move at any time, and hence motion is impossible. I discuss the following three views that one could take in view of Zeno's argument: (i) the "at-at" theory, according to which there is no such thing as instantaneous velocity, while motion in the sense of the occupation of different locations at different times is possible, (ii) the "impetus" theory, according to which instantaneous velocities do exist but these are only contingently and causally related to the temporal developments of positions, (iii) the "no instants" theory, according to which instants in time do not exist, and hence instantaneous velocities do not exist, while motion, in the sense of different areas occupied during different time intervals, is possible. I argue that, despite the fact that there have been interesting and relevant developments in mathematics and physics since the time of Zeno, each of these views still has serious drawbacks.