Its core idea is that mental states can be accounted for without taking into consideration the underlying physical medium (the neurons), but instead attending to higher-level functions such as beliefs, desires, and emotions.
For (an avowedly simplistic) example, a functionalist theory might characterize pain as a state that tends to be caused by bodily injury, to produce the belief that something is wrong with the body and the desire to be out of that state, to produce anxiety, and, in the absence of any stronger, conflicting desires, to cause wincing or moaning. According to this theory, all and only creatures with internal states that meet these conditions, or play these roles, are capable of being in pain. Suppose that, in humans, there is some distinctive kind of neural activity (C-fiber stimulation, for example) that meets these conditions. If so, then according to this functionalist theory, humans can be in pain simply by undergoing C-fiber stimulation. But the theory permits creatures with very different physical constitutions to have mental states as well: if there are silicon-based states of hypothetical Martians or inorganic states of hypothetical androids that also meet these conditions, then these creatures, too, can be in pain. ...
satisfy the descriptions - then it's also logically possible for non-physical states to play the relevant roles, and thus realize mental states, in some systems as well. So functionalism is compatible with the sort of dualism that takes mental states to cause, and be caused by, physical states.
Still, though functionalism is officially neutral between materialism and dualism, it has been particularly attractive to materialists, since many materialists believe (Lewis, 1966) that it is overwhelmingly likely that any states capable of playing the roles in question will be physical states. If so, then functionalism can stand as a materialistic alternative to the Psycho-Physical Identity Thesis, the thesis that each type of mental state is identical with a particular type of neural state. This thesis, once considered the dominant materialistic theory of the mind, entails that no creatures with brains unlike ours can share our sensations, beliefs, and desires, no matter how similar their behavior and internal organization may be to our own. This is a consequence that many regard as implausible. Thus functionalism, with its claim that mental states can be multiply realized, is widely regarded as providing a more inclusive, less "(species-) chauvinistic" (Block, 1980) - and thus more plausible - theory that is (at least arguably) compatible with materialism.
Within this broad characterization of functionalism, however, a number of distinctions can be made. Functionalism has three distinct sources. First, Putnam and Fodor saw mental states in terms of an empirical computational theory of the mind. Second, Smart's "topic neutral" analyses led Armstrong and Lewis to a functionalist analysis of mental concepts. Third, Wittgenstein's idea of meaning as use led to a version of