Jaegwon Kim’s causal inheritance principle says that the causal powers of a mental property instance are identical with the causal powers of its particular physical realizer. Sydney Shoemaker’s subset account of realization is at odds with Kim’s principle: it says that a mental property instance has fewer causal powers than Kim’s principle entails. In this paper, I argue that the subset account should be rejected because it has intolerable consequences for mental causation, consequences that are avoided by accepting causal inheritance. (...) I develop my argument in part by drawing on one of the central debates that has arisen regarding the extended mind hypothesis defended by Andy Clark and David Chalmers. (shrink)