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Terminology - Alternatively one might object to(1 on the...

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Terminology R the runner S the starting point (= Z 0 ) G the end point Z 1 the point halfway between S and G Z 2 the point halfway between Z 1 and G Z n the point halfway between Z n -1 and G Z -run a run that takes the runner from one Z -point to the next Z -point Zeno’s Argument formulated 1. In order to get from S to G , R must make infinitely many Z -runs. 2. It is impossible for R to make infinitely many Z -runs. 3. Therefore, it is impossible for R to reach G . Evaluating the argument a. Is it valid ? Yes : the conclusion follows from the premises. b. Is it sound ? I.e., is it a valid argument with true premises ? This is what is at issue. c. One might try to object to the first premise, (1), on the grounds that one can get from S to G by making one run, or two (from S to Z 1 and from Z 1 to G ). But this is not an adequate response. For according to the definitions above, the runner, if he passes from S to G , will have passed through all the Z -points. But to do that is to make all the Z -runs.
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Unformatted text preview: Alternatively, one might object to (1) on the grounds that passing through all the Z-points (even though there are infinitely many of them) does not constitute making an infinite number of Z-runs. The reason might be that after you keep halving and halving the distance, you eventually get to distances that are so small that they are no larger than points. But points have no dimension, so no “run” is needed to “cross” one. But this is a mistake . For every Z-run, no matter how tiny, covers a finite distance (>0). No Z-run is as small as a point. So we have established that the first premise is true . (Note: this does not establish that R can actually get from S to G . It only establishes that if he does, he will make all the Z-runs.) d. The crucial premise is (2). Why can’t R make infinitely many Z-runs? Our difficulty here is that Zeno gives no explicit argument in support of (2)....
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