Evaluation of the argumentEverything is fine up to step (9). But (9) does not entail (10). Zeno seems to be implicitly assuming (what I’ll call) the Infinite Sum Principle: viz., that the sum of an infinite number of terms is infinitely large. (9), together with the Infinite Sum Principle, entails (10). And from (10) it follows (by Universal Generalization) that everymagnitude is infinitely large, which is the conclusion of the second limb. The Infinite Sum Principle appears to be correct. But is it? What makes it seemcorrect is the observation that you can make something as large (a finite size) as you want out of parts as small as you want, and it takes only a finite number of them to do this! To see that this is so, consider the following: pick any magnitude, y, as large as you like; and pick any small magnitude, z, as small as you like (but z> 0). It is obvious that you can obtain a magnitude at least as large as y by adding zto itself a finitenumber of times. That is: 2200y2200z5x(x· zy) For every yand for every z
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