(8) Physicalism is true at a possible world _w_ iff every fundamental property instantiated at _w_ is a physical property.Suppose we call physicalism so defined _fundamentality physicalism_ ; what is the relation between it and supervenience physicalism? Supervenience physicalism does not entail fundamentality physicalism, since the fact that a property _F_ supervenes on a property _G_ does not entail that either property is fundamental. Nevertheless, it is reasonable to think that fundamentality physicalism entails supervenience physicalism, especially in the light of Lewis’s comment about supervenience just quoted.How plausible is (8) as an account of physicalism? One objection concerns the notion of a fundamental property quite generally. For at least some philosophers, Lewis’s ideas about fundamentality are, as he himself puts it, a throwback to medieval metaphysics (Lewis 1983). Another objection is that physicalism on this view seems empirically speculative, since it seems to entail that there is a fundamental level in the world; if so, definitions in terms of grounding may do better (Schaffer 2003). Whatever is the truth about these objections, it is an interesting historical fact that Lewis defines physicalism twice-over. He defines it as supervenience physicalism (as we saw above) and also as fundamentality physicalism. There is no suggestion in his work that these are in any sense in tension (for further discussion, see Stoljar 2015). This underscores the point made earlier, namely, that in practice all versions of physicalism, and hence any answer to the completeness question, will include modal and non-modal elements. ## 3. Varieties of PhysicalismWe have been considering various answers to the completeness question, namely, what it means to say that everything is physical. At this point, it is worth considering two issues associated with completeness that have not so far been brought to the surface, and which suggest different varieties of physicalism. The first is whether physicalism involves a kind of reductionism; the second is whether physicalism involves what philosophers call a priori entailment or deducibility. ### 3.1 Reductive and Non-reductive PhysicalismThe main problem in assessing whether a physicalist must be a reductionist is that there are various non-equivalent versions of reductionism.One idea is tied to the notion of conceptual or reductive analysis. When philosophers attempt to provide an analysis of some concept or notion, they often try to provide a reductive analysis of the notion in question, i.e. to analyze it in other terms. Applied to the philosophy of mind, this notion might be thought of entailing the idea that every mental concept or predicate is analyzed in terms of a physical concept or predicate. A formulation of this idea is (9): (9)