This post is part of my series on physicalism.
I like the computer program example so much I want to expand on it beyond what Melnyk says.
Take two computers, one a PC and one a Mac, that are both running some program (say, Windows 7). The two have different processors that must be programmed with different machine languages, so the actual physical events that occur in each computer will be quite different. Yet, if the programming and compiling has been done correctly, the two will be functionally equivalent. The two screens will look the same, and the same changes will occur when I click on the same icon on each.
Even if we were unaware of the details of the program the two computers were running, a careful investigation would reveal the existence of certain groups of physical processes that correspond to particular subroutines of the program in both computers. Thus, the physical-level description could be used to explain why the two computers were behaving in the same way.
But the existence of a physical-level explanation doesn't invalidate an explanation at the level of the program itself. The same phenomena can be described in terms of IF-THEN statements and FOR loops. Realization physicalism says both types of explanation are valid.
This makes a terrific analogy for understanding the physical realization of mental phenomena like thoughts, emotions, or qualia. There is no way that the physical events occurring in my brain when I look at a red wall are the same as the events occurring in your brain when you look at the same wall. But I see no reason to doubt that there might be a functional equivalence of some sort between the events in the two brains, in a similar manner as between the two computers. It might even be possible, at some point in the future, to analyze the patterns of neural activity and identify groups of processes that correspond to particular aspects of the visual experience. These patterns could then be used to explain why the two people were having a similar experience.
Here, too, the existence of a physical-level explanation doesn't invalidate the explanation of mental phenomena at the level of mental events. ("The baby reached for the pacifier because it wanted something to suck on.") Physicalists don't deny the truth of mental causation any more than they deny that the billiard ball moved because it was struck by the cue ball. The existence of another description of both balls at the level of neutrons, protons, and electrons doesn't invalidate the causal efficacy of the cue ball. Rather, it explains it. And in the same way, the (postulated) physical realization of mental events explains (rather than denies) mental causation.
This is not to claim, of course, that science is at a point where it can prove the physical realization of mental phenomena. But the idea doesn't seem ridiculous on its face. The burden of proof, rather, lies with anyone who would claim that it is impossible for such mental phenomena to be physically realized.