Parts of Classes by David K. Lewis

By David K. Lewis

Does the proposal of half and entire have any software to sessions? Lewis argues that it does, and that the smallest elements of any classification are its one-membered "singleton" subclasses. That ends up in a reconception of set concept. The set-theoretical making of 1 out of many is simply the composition of 1 complete out of many components. yet first, one singleton needs to be made from its one member - this is often the distinctively set-theoretical primitive operation. hence set thought is entangled, with mereology: the speculation of components and wholes.

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You could do the same trick with any old relations. Possum is 'maternally identical' to Magpie, if by that you just mean that something that is mother of one is identical to something that is mother of the other. The six numbers 2, 8, 4, 7, 6 and 3 are 'on average' identical to the one number 5, if by that you just mean that the average of the six is identical to the one. So what? But the doubter misses the point. Never mind that mereological relations can be equivalently restated so as to drag in identity.

Maybe the singularist replies that some mystical censor stops us from quantifying over absolutely everything without restriction. Lo, he violates his own stricture in the very act of proclaiming it! We embrace plural quantification over all the things there a~e ~ even those, if any, that we may now be wrongly repudIatmg. How do we differ from the singularist, and from ourselves as he interprets us? We differ about what's true under anyone fixed hypothesis about what there is and what there isn't.

Two adjoining terra_ce houses that share a common wall are not identical, but they are not completely distinct from each other either. They are partially identical, and this partial identity takes the form of having a common part. Australia and New South Wales are not identical, but they are not completely 82 distinct from each other. They are partially identical, and this partial identity takes the form of the whole-part 'relation' .... Partial identity admits of at least rough-and-ready degree.

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