Some philosophers hold to the identity theory of mind, which says that each type of brain state is identical to a type of mental state. For example, pain must be identical to something like C-fiber stimulation if the identity theory is correct.

According to Putnam’s multiple realizability argument, this can’t quite be correct, because the same mental state can be experienced by two beings with different physical constitutions. The Internet Encyclopedia of Philosophy puts the multiple realizability argument like this:

(1) according to the Mind-Brain Type Identity theorist (at least post-Armstrong), for every mental state there is a unique physical-chemical state of the brain such that a life-form can be in that mental state if and only if it is in that physical state. (2) It seems quite plausible to hold, as an empirical hypothesis, that physically possible life-forms can be in the same mental state without having brains in the same unique physical-chemical state. (3) Therefore, it is highly unlikely that the Mind-Brain Type Identity theorist is correct.

There are various ways of handling this objection. For example, one could take the functionalist view that it is the functional role of a brain state within the system of brain states that makes it a specific mental state. You don’t even have to reject the identity theory to handle the multiple realizability argument if you weaken the theory to say that each individual mental state is a specific, individual brain state rather than articulating it in terms of types, as I did above.