Zeno’s Arrow

I wrote about Zeno’s Achilles paradox – along with the Dichotomy (a.k.a. Racetrack) and the lesser know Plurality – here. You should read that before reading this. In that post, I didn’t mention Zeno’s other very famous paradox: the Arrow. Though a huge majority of philosophers think Zeno’s other paradoxes were cleared up by calculus and set theory, many consider the Arrow still unsolved. I’ll be arguing that the Arrow, though it appears to deal with separate issues, is really the same Achilles paradox in a different form.

Consider an arrow traveling down a trajectory. Take a snapshot at one static instant. In this one duration-less instant, the arrow is at rest. It is not moving, insofar as motion requires movement from one point to another, and this arrow is, in this one instant, in only one spot. So the arrow is at rest in one instant, at rest again in the next, at rest again in the next. If the arrow is at rest at every instant along its journey, how can we say that the arrow is in motion? When exactly does this arrow travel?

One aspect of the Arrow is simple enough to dissolve: being at rest, defined as “not being in motion,” only makes sense over some duration of time. Motion is defined as distance traveled over some period of time, so it makes no sense to even inquire as to whether motion is happening or not happening when we’re limited to a time range of 0.…

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