David Lewis, answered from the texts and cited to the page.
Mental states are physical states — specifically, in human beings, neural states. But "type-type identity" is relativized to an appropriate population. Pain in human beings is the type of neural state that occupies the pain role for our population (the role specified by folk psychology's network of causal connections to typical causes, typical effects, and other mental states).123
Pain in Martians is whatever (perhaps quite different) physical state occupies the pain role for their population; pain in a madman is the human pain state, even though it does not do its typical work in him, because he is a member of a population where it usually does.45 The analytic functionalist apparatus — the Ramsey-Carnap-Lewis method of defining theoretical terms by their roles in implicit theory — delivers folk psychology as an implicit theory of the mental whose Ramsey sentence specifies the roles; type- type identity is the result of the empirical discovery that neural state N occupies the role role-T specifies.
I am a realizer functionalist rather than a role functionalist: pain is the neural state that plays the role, not the higher-order property of being in some state or other that plays it. On Jackson's Mary case: Mary, leaving the black-and-white room, does not learn a new propositional fact she could not have learned from her complete physical theory.
She gains new abilities — to recognize red things by sight, to imagine seeing red, to remember the experience of red. The ability hypothesis (developed in parallel by Nemirow and me) is a materialist account of what that gain is, and what experience teaches is the abilities, not a body of non-physical knowledge.
Or, better, since Martians may come here and we may go to Mars, it may designate one state for Earthlings and another for Martians. We may say that some state occupies a causal role for a population, We may say this whether the population is situated entirely at our actual world, or partly at our actual world and partly at other worlds, or entirely at other worlds.Part 2: Philosophy of Mind, pp. 126–127
Human pain might be one thing, Martian pain might be something else. 21 As with contingency, which is variation across worlds, so likewise with variation in a single world: the variability in no way infects the identity relation, but rather con¬ cerns the reference of the mental name. The threat of variation has led many to retreat from 'type—type' to 'token—token' identity.Papers in Metaphysics and Epistemology, p. 316
It might be a non¬ physical or a physical state, and if it is physical it might be a state of neural activity in the brain, or a pattern of currents and charges on a silicon chip, or the jangling of an enormous assemblage of beer cans. What state occupies the M-role and thereby deserves the name M is an a posteriori matter.Papers in Metaphysics and Epistemology, pp. 313–314
Myself, I don't see how the physical or non-physical nature of the actual occupant of the role has anything to do with whether the two situations can be distin¬ guished. Talk of'phenomenal character' and the like doesn't help. Ei¬ ther it is loaded with question-begging philosophical doctrine, or else it just reiterates the undisputed fact that pain is a kind of experience.Papers in Metaphysics and Epistemology, pp. 315–316
I don't object to the strategy of claiming ambiguity. As you'll see, I shall defend a version of it. But it's not plausible to cook up an ambiguity ad hoc to account for the compossibility of mad pain and Martian pain. It would be better to find a widespread sort of ambiguity, a sort we would believe in no matter what we thought about pain, and show that it will solve our problem. That is my plan.Part 2: Philosophy of Mind, pp. 124–125
Lewis's identity theory is the standard analytic- functionalist version of materialism about mind for the late twentieth century. The principal opponents are the anti-materialists: Jackson's knowledge argument (the Mary case), Chalmers's modal argument from the conceivability of zombies, Nagel's "What Is It Like to Be a Bat?", the property-dualist tradition. The principal rivals within materialism are the role-functionalists (the higher-order view that pain is the role-property), the eliminativists (the Churchlands), and the dispositionalists about mental content. Frank Jackson himself later abandoned the knowledge argument and adopted an a-priori-physicalist position closer to mine. The Lewis-Nemirow ability hypothesis has been the standard materialist response to Mary for two decades, against which most contemporary anti-materialist arguments are positioned. Daniel Stoljar's ignorance hypothesis is the closely related response that we lack relevant physical knowledge rather than that there is non-physical knowledge to be had.