In common usage, the word “paradox” often refers to statements that may be both true and false i.e. ironic or unexpected. Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One well-known example is Zeno’s arrow paradox, where it appears to show that motion is impossible. Zeno of Elea  (c. 490 – c. 430 BC) was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides. His paradox works by taking a snapshot of an arrow at a point (either in space or in time) in its flight. At that point, and at every other, the arrow is motionless. If there is no point, spatially or temporally, at which the arrow is moving, though, then the arrow is motionless. Contrary to appearances, an arrow in flight cannot move.

If we had a film of the arrow in flight, and broke it down to its individual frames, we would see that in each frame the arrow is simply hovering in the air. It is only when you put all the frames together that the arrow appears to move. In each frame, i.e. at each point, the arrow is motionless.

This is true irrespective of whether we think in terms of time or space.

Motion occurs through space, not at a single point in space. To move, something must get from one point to another, and so at each point considered individually, the arrow is still.

Similarly, motion takes time, it doesn’t occur instantaneously. At any specific point in time, therefore, the arrow cannot be moving.

If at every point and at every moment in its flight the arrow is still, though, then how is it possible for it to move from the bow to its target? If the arrow is made of wood at every point in its flight, then it must be wooden; it can’t be metal. If it is sharp at every point in its flight, then it must be sharp, not blunt. Similarly, if the arrow is motionless at every point in its flight, then it must be still, not moving.

Contrary to appearances, then, arrows cannot move towards targets. In fact, similar reasoning applies to any other alleged case of motion, so it seems that movement in general is impossible.