Metaphysical dependence and the subset relation between powers

Abstract What is the relation between the token powers of higher‐level occurrences and the token powers of more basic physical occurrences? In related but somewhat different ways, Sydney Shoemaker and Jessica Wilson argue that the former are a proper subset of the latter, and that this can provide a viable account of higher‐level causation within a nonreductive physicalist metaphysic. Contra Wilson, I argue that various accounts of how higher‐level properties metaphysically depend on physical properties do not support, and do not comport well with, the view that the token powers of the former are a proper subset of the token powers of latter. I address an argument for thinking that lower‐level occurrences have all the token powers of the higher‐level occurrences that depend on them and argue that it is not compelling. Finally, I consider Wilson's distinction between “weak” and “strong” emergence, and how it might be reformulated, given the previous results.