4. The necessary beings problem
(Cf. Jackson 1998) Imagine a necessary being -- that is, a being which exists in all possible worlds -- which is essentially nonphysical. If such a non-physical being exists, it is natural to suppose that physicalism is false. But if physicalism is defined according to (2), the existence of such a being is compatible with physicalism. For consider: if the actual world is wholly physical, apart from the necessary non-physical being, any minimal physical duplicate of the actual world is a duplicate simpliciter. Since the non-physical being exists in all possible worlds, it exists at all worlds which are minimal physical duplicates of the actual world. So we seem to face a problem: the existence of the non-physical necessary being entails that physicalism is false, but the definition of physicalism permits it to be true in this case.