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The Paradox
Zeno argues that it is impossible for a runner to traverse a race course. His reason is that
“motion is impossible, because an object in motion must reach the halfway point before it gets
to the end” (Aristotle,
Physics
239b1113).
Why is this a problem? Because the same argument can be made about
half
of the race course: it
can be divided in half in the same way that the entire race course can be divided in half. And so
can the half of the half of the half, and so on,
ad infinitum
.
So a crucial assumption that Zeno makes is that of
infinite divisibility
: the distance from the
starting point (
S
) to the goal (
G
) can be divided into an infinite number of parts.
Progressive vs. Regressive versions
How did Zeno mean to divide the race course? That is,
which half
of the race course Zeno mean
to be dividing in half? Was he saying (a) that before you reach
G
, you must reach the point
halfway from the halfway point to
G
? This is the
progressive
version of the argument: the
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This note was uploaded on 11/14/2011 for the course PHI PHI2010 taught by Professor Jorgerigol during the Fall '09 term at Broward College.
 Fall '09
 JorgeRigol

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