According to contemporary computational neuroscience the mental is associated with computations implemented in the brain. We analyze in physical terms based on recent results in the foundations of statistical mechanics two well-known (independent) problems that arise for this approach: the problem of multiple-computations and the problem of multiple-realization. We show that within the computational theory of the mind the two problems are insoluble by the physics of the brain. We further show that attempts to solve the problems by the interactions (...) of the systems implementing the computations with an environment (in or outside the brain) must introduce non- physical factors, and therefore fail on physical grounds. We also show that the problems are endemic and pertain to other forms of functional theories of the mind, most notably, causal functionalism. Finally, we propose a physicalist reductive identity theory, which is a generalization of statistical mechanics for all the special sciences, and show that only a theory of this kind can provide physical solutions to the above two problems in computational neuroscience. We conclude that functionalism in the theory of mind must be replaced with a reductive identity theory. This result has far-reaching implications with respect to the research programs in brain science. (shrink)