A version of the identity thesis goes like this: each type/token of mental state is identical with a particular type/token of neural state. There is an important distinction between the type/token versions. Non-reductive materialists accept the token/token identity, and turn it into a contingent fact by rejecting type identity. Though this world is such that the tokens of mental states are identical with tokens of neural states, it is not necessarily so. I now think there is an interesting argument against this thesis, even in its token-token version. Of course, reductive physicalism (the thesis that all mental states are reducible to neural states) would go too.
Baltes has famously argued for a highly general account of cognitive development. His view deals with two basic causal determinants of cognitive development: biological endowment (e.g., the brain) and culture or society (e.g., family and school). His claim is that these two causal determinants follow exactly opposite directions. On the one hand, the cognitive benefits (e.g., neural capacities) we get from our biological endowment decrease through life span (e.g., human beings age). On the other hand, the cognitive benefits (e.g., knowledge, information) we get from our cultural surroundings increase (e.g., we get more and more, better and better education). It is a further claim of Baltes that the efficacy of culture in cognitive development decreases. Once humans reach the fourth age (80-85 years and beyond) there is, to put it bluntly, nothing that society (or its institutions) can do to stop decrepitude (therefore, human ontogeny is incomplete).
This decrepitude, however, is not a general one. It is mainly a biological one. Think of it this way: The peak of brain-power (i.e., memory size, processing speed, etc.) is mainly distributed between infancy and adolescence. For instance, the biggest amount of neural connections appears between 3 and 7 years of age, when the human infant is acquiring her native language. The point is, once you are 25, neural connections are not going to increase. And once you are 35, they will start shutting down. However, our cultural cognitive capacities, clearly, do not decrease. It would be just ridiculous to suggest that a 22-year-old graduate student is more capable (cognitively speaking) than a 50-year-old faculty member.
If this is so, then there is a very important property of neural states that is not a property of mental states: decrepitude. Baltes conceives of the mind in a rather Aristotelian way: it’s got a mechanics and a pragmatics. The former collapses through life span, the latter does not, in fact, it increases and thrives (of course, provided certain mechanical and social conditions). “Our reading and writing skills, educational qualifications and professional skills (…) can extend further into the life course than the mechanics.” p 373
Now, let’s go back to the identity thesis. If it is true that every token of a mental state is identical with a particular token of a neural state, then it must be the case that every property of a neural state is a property of a mental state, and vice-versa. But neural states reduce their capacities and collapse earlier in the life span than (at least) some mental states. Thus, there are some mental states that do not share all the properties of ANY neural states, namely, those that constitute our intellectual capacities. It is false that any token of a mental state is identical with a particular token of a neural state. And so is any claim to the point that the mind just is the brain, either contingently or necessarily. Eliminativism (the thesis that there are no genuinely mental states, but merely neural ones) is not even worth considering.
Baltes, Paul. “1996 Award Address: On the Incomplete Architecture of Human Ontogeny” in American Psychologist, April 1997, Vol. 52, No.4, pp.366-380