Functionalist Interrelations Amongst Human Psychological States Inter Se, ditto for Martians

One job for theories of mental representation is to distinguish between different kinds of mental representation: beliefs, desires, intentions, perceptual states, etc. What makes a mental state a belief that p rather than a desire that p or a visual representation that p? Functionalism is a leading approach for doing so: for individuating mental states.
Functionalism is designed to allow that psychological states can be multiply realized. Mark Sprevak has argued that, for a functionalist account of psychological states to apply to creatures that are organised in a very different way to humans (call them Martians), the way a psychological state is functionally individuated has to be relatively coarse-grained (Sprevak 2009). Psychological research might show that human beliefs are directly available to consciousness, that they are formed as the result of deliberate judgement, and so on, but theorists would be precluded from including these roles in their account of belief, if Sprevak is right.
The argument for coarse-grained individuation fails if we distinguish functionalism about what it takes to be a psychological state in general from functionalism about a particular state type such as belief. Functionalism individuates a psychological state like believing that p partly by reference to its relations to other psychological states: desiring that p, perceiving that p, intending that p, etc. Functionalist motivations do indeed suggest that Martians with a functional organisation and physical substrate quite unlike humans could have psychological states, but not that they should have states with the interrelated collection of functional roles to count as beliefs, desires, intentions, etc. Thus, theorists are not precluded from including functional relations to consciousness or deliberate judgement in their account of (human) belief, consistent with allowing that Martians would have their own collection of functionally interrelated psychological states.
Sprevak’s coarse-grained functionalism implies an implausibly liberal form of extended cognition. The point about functional interrelations allows us to avoid that conclusion without jettisoning functionalism (as Sprevak suggests we should): records in a human notebook may not enter into the right interrelations with other human psychological states to count as beliefs; nor do they enter into any interrelations with Martian psychological states. Functionalism can therefore allow that Martians have psychological states while holding that few if any of the beliefs we humans have are, as a matter of fact, extended.