  Both classical and quantum mechanics assume that physical laws are invariant
under changes in the way that the world is labeled. This Principle of
Decompositional Equivalence is formalized, and shown to forbid finite
experimental demonstrations that given pointer states |p1> and |p2> refer to
the same physical system S. It is then shown that any extra-theoretical
assumption that given pointer states |p1> and |p2> with indistinguishable
coefficients in a Schmidt basis for the universe refer to the same physical
system S is stronger than the assumption of classicality. Standard
interpretations of quantum mechanics make such as assumption in analyzing
measurement; hence they are logically inconsistent.
