Tuesday, May 17, 2016

Relative identity and relative shape

Take a classic case of relative-identity. At time 1, we have a lump of clay, Lumpy1, that is formed into a statue of a horse, a statue I will call "Bucephalus". At time 2, the lump continues to exist as Lumpy2, but is reformed into into a statue of a big man, a statue I will call "Goliath". Then Lumpy1 is the same lump as Lumpy2, Lumpy1 is the statue as Bucephalus, Lumpy2 is the same statue as Goliath, but it does not follow that Lumpy1 is the same statue as Lumpy2, since we only have transitivity of relative identity when we keep the kind fixed.

Now suppose a four-dimensionalism that says that ordinary objects are four-dimensional (no further commitments on temporal parts, etc.). Then it seems we have a very odd thing. Lumpy1 the lump has a different shape and size from Bucephalus the statue. For Lumpy1 the lump is extended temporally up to and including at least time 2, while Bucephalus the statue does not extend temporally up to time 2. So shape and size are kind-relative. As a lump, Lumpy1 has one four-dimensional shape and size. As a statue, it's Bucephalus and it has a different four-dimensional shape and size. The causal powers are different, too. Lumpy1 can still be seen at time 2, while Bucephalus can no longer be seen then (except in photographs). So the causal powers of a thing are kind-relative, too. Moreover, this kind of thing happens routinely--it's not a miracle as when Christ is omnipresent qua God but only in Jerusalem qua human. It seems implausible that we would have routine kind-relative variation of size and shape.

This makes relative identity not so plausible given four-dimensionalism. But four-dimensionalism (in the weak sense I'm using) is clearly true. :-)

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