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# 23 - Terminology R S G Z1 Z2 Zn the runner the starting...

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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 . ø 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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23 - Terminology R S G Z1 Z2 Zn the runner the starting...

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