I offer support for the view that physicalist theories of cognition don't reduce to neurophysiological theories. On my view, the mind-brain relationship is to be explained in terms of evolutionary forces, some of which tug in the direction of a reductionistic mind-brain relationship, and some of which which tug in the opposite direction. This theory of forces makes possible an anti-reductionist account of the cognitive mind-brain relationship which avoids psychophysical anomalism. This theory thus also responds to the complaint which arguably lies behind the Churchlands' strongest criticisms of anti-reductionism — namely the complaint that anti-reductionists fail to supply principled explanations for the character of the mind-brain relationship. While lending support to anti-reductionism, the view defended here also insures a permanent place for mind-brain reduction as an explanatory ideal analogous to Newtonian inertial motion or Aristotelian natural motion.