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The Race Course: Part 2
1.
Our look at the plurality argument suggests that Zeno may have thought that to run all the
Z
runs would be to run a distance that is
infinitely long
. If this is what he thought, he was
mistaken.
The reason the sum of all the
Z
intervals is not an infinitely large distance is that there is
no smallest
Z
interval. And Zeno does not establish that there is some smallest
Z
run. (If
there were a smallest
Z
run, he wouldn’t have been able to show that R had to make
infinitely many
Z
runs.)
2.
What about Aristotle’s understanding of Zeno? Here is what he says [RAGP
8
]:
“
Zeno’s argument makes a false assumption when it asserts that it is impossible
to traverse an infinite number of positions or to make an infinite number of
contacts one by one
in a finite time
” (
Physics
233a2124).
3.
Aristotle points out that there are two ways in which a quantity can be said to be infinite:
in
extension
or in
divisibility
. The race course is infinite in divisibility. But, Aristotle
goes on, “the time is also infinite in this respect.”
Hence, there is a sense in which
R
has an infinite number of distances to cross. But in that
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This note was uploaded on 01/31/2011 for the course PHILOSOPHY 101 taught by Professor Markelwin during the Summer '09 term at UC Davis.
 Summer '09
 MarkElwin

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