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26 - The Race Course Part 2 1 Our look at the plurality...

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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 233a21-24). 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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