It is widely held that a successful theory of the mind will be neuroscientific. In this paper we ask, first, what this claim means, and, secondly, whether it is true. In answer to the first question, we argue that the claim is ambiguous between two views--one plausible but unsubstantive, and one substantive but highly controversial. In answer to the second question, we argue that neither the evidence from neuroscience itself nor from other scientific and philosophical considerations supports the controversial view.