Functionalist theories of consciousness: unfolding, substitution and the indeterminacy of function by the physics of the brain.

We consider two recent arguments concerning the question of empirical falsifiability of consciousness theories: the Unfolding Argument (UA) against causal structure theories and the Substitution Argument (SA) according to which if prediction of experience and inference from behaviour are independent, any non-behavioural theory of consciousness is a priori falsified. We argue that the UA is unsound, because the universal approximation theorems don't support it. We then examine whether the SA can be circumvented by "looking inside the brain", i.e., by direct measurements of brain observables. We show that this option is not open to any functionalist theory of consciousness, i.e., any theory that identifies conscious states with some "functional role" (e.g., input-output function, computational role, causal profile) implemented by brain processes. Also, we show that this deeper problem pertains only to functionalist theories. The reason is that functionalism by construction allows for multiple realization of the mental by the physical, and therefore the function identified with consciousness must be defined by some abstract formal structure. But we argue that a theorem first proved by Putnam and recently generalized by Hemmo and Shenker implies that the physics of the brain in its entirety cannot determine uniquely any formal structure: any (complex enough) physical system (e.g., the neural system) implements at once infinitely many formal structures (this is the indeterminacy of function by physics). Finally, we argue that the only way to counter the indeterminacy problem while avoiding behaviourism is to adopt a reductive mind-brain identity theory like Flat Physicalism.