 Does subset realization physicalism entail supervenience physicalism? Well, there is a problem here too having to do with (what is sometimes called) a causal theory of properties, that is, a theory according to which the causal powers or features that a property bestows on the things that have it are exhaustive of the nature of that property. Suppose that a causal theory is false. Then, in principle, one property might subset realize another and yet be quite different from it in nature. And this in turn suggests that subset physicalism does not by itself entail supervenience physicalism. Of course, one might respond by asserting that the causal theory is true. But to do that is controversial; indeed, even those philosophers who hold both a subset model and a causal theory want to separate out these two commitments (e.g. Shoemaker 2007; see also Wilson 2011). Alternatively, one might respond by denying that physicalism entails supervenience in the first place, by saying that “lack of … supervenience is compatible with physicalism” (Wilson 2014, 255, see also Wilson 2011). But this too is controversial; as we saw above, most philosophers assume that supervenience is necessary for physicalism. Hence the status of the subset approach remains controversial. 