<p>Motivated by a generalization of Hempel’s dilemma, I introduce a novel notion of empirical structure, as well as theory supervenience as a new reductive relationship between theories. One theory supervenes on another theory if the empirical structure of the latter theory refines the empirical structure of the former theory. I then argue that (1) empirical structure physicalism, the thesis that the current special sciences supervene both on current and on future physics, avoids both horns of Hempel’s dilemma; (2) in particular, mental theories remain empirically dispensable in the future; (3) empirical structure realism, the thesis that earlier theories of physics supervene on later theories of physics, is supported by an optimistic meta-induction; (4) this optimistic meta-induction can coexist with the well-known pessimistic meta-induction; (5) empirical structure physicalism is appropriately labeled as a type of physicalism; and (6) empirical structure physicalism is compatible with multiple realization. To illustrate the plausibility of empirical structure physicalism, I also briefly address the so-called knowledge argument.</p>