Friday, August 04, 2006

every whole is smaller than its parts

Either there's an infinite hierarchy of composition for concrete objects, or there isn't. If there are basic parts of concrete objects, themselves without parts, then the basic parts have real magnitude, for if they didn’t, then neither would composite concrete objects.

Now, suppose A is a composite concrete object. A has at least three parts: its proper parts and at least one improper part (A itself). But the improper part is identical to A and hence has the same magnitude as A. However, all the proper parts have real magnitude and are each distinct from the other, as well as the whole and the improper part. Hence, for any composite object built out of basic parts, the sum of the magnitude of its parts is always greater than the magnitude of the object. So, either there is no end to composition, or every composite object has a magnitude smaller than the the combined magnitude of its parts.

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