The Race Course - one by one in a finite time ( Physics...

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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
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Unformatted text preview: 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 sense he also has an infinite amount of time to do it in. (If a finite distance is infinitely divisible, then why isnt a finite time also infinitely divisible?) 4. So Zeno cannot establish (2) for either of the first two reasons we considered: to make all the Z-runs, R does not have to run infinitely far. Nor does R have to keep running forever....
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