Unfortunately, statement 1 fails to capture even a necessary condition for physicalism to be true at a world "w". To see this, imagine a world in which there are "only" physical properties—if physicalism is true at any world it is true at this one. But one can conceive physical duplicates of such a world that are "not" also duplicates simpliciter of it: worlds that have the same physical properties as our imagined one, but with some additional property or properties. A world might contain "epiphenomenal ectoplasm", some additional pure experience that does not interact with the physical components of the world and is not necessitated by them (does not supervene on them). To handle the epiphenomenal ectoplasm problem, statement 1 can be modified to include a "that's-all" or "totality" clause or be restricted to "positive" properties. Adopting the former suggestion here, we can reformulate statement 1 as follows: