I believe that there is a necessary connection in both directions between the physical and the mental, but that it cannot be discovered a priori. Opinion is strongly divided on the credibility of some kind of functionalist reductionism, and I won't go through my reasons for being on the antireductionist side of that debate. Despite significant attempts by a number of philosophers to describe the functional manifestations of conscious mental states, I continue to believe that no purely functionalist characterization of a system entails simply in virtue of our mental concepts that the system is conscious.
"Conceiving the Impossible and the Mind-Body Problem," Royal Institute of Philosophy annual lecture, given in London on February 18, 1998, published in Philosophy vol. 73 no. 285, July 1998, pp 337-352, Cambridge University Press, p. 337.
Eventually, I believe, current attempts to understand the mind by analogy with man-made computers that can perform superbly some of the same external tasks as conscious beings will be recognized as a gigantic waste of time.Thomas Nagel
Everyone is entitled to commit murder in the imagination once in a while, not to mention lesser infractions.Thomas Nagel
If sub specie aeternitatis [from eternity's point of view] there is no reason to believe that anything matters, then that does not matter either, and we can approach our absurd lives with irony instead of heroism or despair.Thomas Nagel