I have a question about functionalism that may have been covered fully by e.g. Block or others but not as far as I have discovered. Is it impossible by definition? I would value opinions.
Functionalism is, at least in some places, defined as the view that 'mental states are constituted solely by their functional role'. Functional role appears to imply an input-output relation in the context of the rest of the world. This role appears to be something definable in computational, logical or other abstract relational terms and thus 'multiply realisable' in physical causal chains. 


If I take the example of the mental state of being in pain Mp it is not entirely clear to me what the functional role is in input-output terms but let us say that it is Fp, which might include the input of stepping on a tack and the output 'Ow, that hurts'. Functionalism suggests that Mp and Fp are associated with a physical causal chain Pp(b(x)) which is an instance of a set of possible chains Pp(a,b,c,...(x,yz...)) where a,b,c are classes of realising systems and x,y,z instances thereof. Given what we know of brains it seems reasonable to assume that for a brain (b(x)) pain is the mental state only in the context of the specific physical causal chain Pp(b(x)) and not Pq,r,s...(b(x)). 


If Fp is an input-output relation in the context of the rest of the world it includes the last event in Pp(b(x)), say Pp(b(x))O, which, crucially, is an output interaction with the world which may depend on the state of the world at that time (the receptivity of the world to the output aspect of Fp). The nature of this event is not accessible to the brain b(x) (except through feedback from yet later events which may reflect it, but in an unreliable way suffering from verification constraints). Thus functionalism states that Mp is determined in part by Pp(b(x))O. That is to say that if Pp(b(x))O were to be instantaneously altered by some unexpected change in circumstances Mp would be different. Yet, in physical causal terms Pp(b(x))O must follow the chain Pp(b(x)), which can only be the sort of Pp(b(x)) that goes with Mp. Thus it appears that Pp(b(x))O must determine Pp(b(x)) (because Fp determines Mp), but Pp(b(x)) is what leads to Pp(b(x))O. This appears to be nonsense.


I can imagine arguments in defense relating to precisely what is meant by determine, but my non-verbal mind tells me that the paradox is genuine. Functionalism is incompatible with causality and therefore impossible. 


In simple terms: since nothing can be reliably informed of its output, nothing can be informed of, and thereby experience, its function.