Thomas Nagel on the Insufficiency of Supervenience"Conceiving the Impossible and the Mind-Body Problem" in Philosophy 73:285 (1998), pp. 337-52.
I believe that the explanatory gap in its present form cannot be closed — that so long as we work with our present mental and physical concepts no transparently necessary connection will ever be revealed, between physically described brain processes and sensory experience, of the logical type familiar from the explanation of other natural processes by analysis into their physico-chemical constituents. We have good grounds for believing that the mental supervenes on the physical — i.e. that there is no mental difference without a physical difference. But pure, unexplained supervenience is not a solution but a sign that there is something fundamental we don’t know. We cannot regard pure supervenience as the end of the story because that would require the physical to necessitate the mental without there being any answer to the question how it does so. But there must be a "how," and our task is to understand it. An obviously systematic connection that remains unintelligible to us calls out for a theory.