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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.
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