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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 sense he also has an infinite amount of time to do it in. (If a finite distance is infinitely divisible, then why isn’t 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. 1. On this reading, Zeno’s argument attempts to show that it is logically impossible for R to reach G . That is, Zeno’s puzzle is not that the runner has to run too far , or that the runner has to run for too long a time , but that the claim that the runner has completed all the Z - runs leads to a contradiction . 2. Following James Thomson [“Tasks and Super-Tasks,” on reserve], let us define a super- task as an infinite sequence of tasks. Can one perform a super-task? Bertrand Russell thought that one could, as Thomson explains [“Tasks and Super-Tasks,” p. 93]: “Russell suggested that a man’s skill in performing operations of some kind might increase so fast that he was able to perform each of an infinite sequence of operations after the first in half the time he had required for its predecessor. Then the time required for all of the infinite sequence of tasks would be only twice that required for the first. On the strength of this Russell said that the performance of all of an infinite sequence of tasks was only medically impossible.” But Thomson argues that to assume that a super-task has been performed in accordance with Russell’s “recipe” leads to a logical contradiction. a.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online