 To accommodate multiple realizability, Hooker (1981: Part III) supplements his general theory of reduction with an account of “token-to-token” reductions. He notes explicitly that this supplement builds the possibility of handling multiple realizability directly into his revised definition of the reduction relation. Let S be the predicate, “satisfies functional theory F”, T be the class of systems to which the token system in question belongs, S′ be an appropriate predicate in some lower level theory of T-system causal mechanisms, and T* be the class of systems to which S′ applies. Then, according to Hooker, 