Zeno
Paradoxes

Space.

If there is such a thing as space, it will be in something, for all being is in something, and that which is in something is in some space. So this space will be in a space, and so on ad infinitum. Accordingly, there is no such thing as space.

Motion.

The Arrow in Flight

If, Zeno says, everything is at rest when it is in a space equal to itself, and the moving body is always in the present moment in a space equal to itself, then the moving arrow is still. Therefore the arrow in flight is stationary.

The Race Course

Motion does not exist because the moving body must go half the distance before it goes the whole distance.

Achilles and the Tortoise

The slow runner will never be overtaken by the swiftest, for it is necessary that the pursuer should first reach the point from which the pursued started, so that necessarily the slower is always somewhat in advance. This argument is the same as the preceding, the only difference being that the distance is not divided each time into halves.

The Stadium

With reference to equal bodies moving in opposite directions past equal bodies in the stadium with equal speed, some form the end of the stadium, others from the middle, Zeno thinks half the time equal to twice the time.