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The Arrow
Zeno of Elea · c. 5th century BCE
The puzzle
At any given instant, a flying arrow occupies a region of space exactly its own size. It is therefore at rest at that instant. Time is a sequence of instants. So the arrow never moves.
Note
The standard reply — that motion is the rate of change of position with respect to time, and rates are defined over intervals — is technically correct and philosophically dissatisfying. It says motion is real but only in some derivative sense. If you take the instant as primary, the arrow doesn’t move; if you take the interval as primary, you have conceded that the instant has no real existence on its own. Two thousand years of physics has not entirely settled which side of that to pick. Zeno’s other arguments — Achilles, the Stadium, the Dichotomy — all probe the same gap from different sides, which is part of why he is still read.