24 - Zeno: Argument against Plurality 1. I nt roduction The...

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Unformatted text preview: Zeno: Argument against Plurality 1. I nt roduction The argument is contained in 4=B1 and 3=B2 (from Simplicius’ commentary on A r istotle’s Physics). But there is a problem with the text, and some of the argument is garbled or lost. Fortunately, we can reconstruct i t. Zeno attempts to show that the assumption that t here are many things leads to a contradiction: viz., that each t hing is both i nfini tely small and infinitely large. T here are two limbs to the argument. The pluralist’s assumption, “There are many t hings,” leads to these two conclusions: A . Each thing is “so small as not to have size.” B. Each thing is “so large as to be unlimited.” Simplicius’s text does not preserve (A) completely. I t starts with (A), and then is garbled and switches over to (B). But we can reconstruct the argument for (B). 2. The Argument Simplicius (in 4=B1) preserves one key principle (“if i t exists, each thing must have some size and thickness”). I t is a premise that Zeno thinks his materialist/pluralist opponents must accept. 3=B2 contains an argument in support of this principle ( “Suppose that x has no size. Then when x is added to a thing i t does not increase the size of that thing, and when x is subtracted from a thing, that thing does not decrease in size. Clearly, x i s nothing, i.e., does not exist.”). So the argument begins w ith this premise: A . What exists has size (magnitude). Zeno also seems to be making the following two assumtions: B. What has size can be divided into (proper) p ar ts t hat exist. C. The part of relation is t ransitive , i r reflexive , and asymmetical . P roper parts: x is a proper part of y i ff x i s a part of y and y is not a part of x T r ansitive : if x i s a part of y and y is a part of z, then x is a part of z. I r reflexive : x i s not a part of x. Asymmetical : if x is a part of y, then y is not a part of x. D. The rest of his argument is preserved in 4=B1. Roughly paraphrased, i t runs: ...
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This note was uploaded on 01/31/2011 for the course PHILOSOPHY 101 taught by Professor Markelwin during the Summer '09 term at UC Davis.

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24 - Zeno: Argument against Plurality 1. I nt roduction The...

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