Most answers to the mind-body problem are claims about the nature of mental properties and substances. But advocates of non-reductive physicalism have generally neglected the topic of the nature of substance, quickly nodding to the view that all substances are physical, while focusing their intellectual energy on understanding how mental properties relate to physical ones. Let us call the view that all substances are physical or are exhaustively composed of physical substances substance physicalism (SP). Herein, I argue that non-reductive physicalism (...) (NRP) cannot uphold substance physicalism and is thereby false. For NRP faces a mind problem: its commitment to property irreducibility prevents that which bears the mental properties—the mind, or on some views, the self or person—from being a physical thing. (shrink)