We learn from Frankfurt counterexamples to the Principle of Alternate Possibility that we should not use counterfactuals and nomic modality to characterize intrinsic features of things. What Frankfurt cases show is that it is frequently possible to modify counterfactual and nomic modal properties of a thing, event or process without actually causally affecting the thing, event or process in itself.
This is a useful lesson. Here is one interesting application: standard functionalist theories of mind cannot be right. I will give the roughest sketch of the argument. Start with two observations:
- Functional characterizations of a system depend crucially on the system's counterfactual properties. (An and-gate is a system of which it is true that it would produce a 0 given two 0's or one 0 and one 1, and would produce a 1 given two 1's, even if in the course of the system's functioning it is actually only fed one of these options.)
- That a system exemplifies a functioning mind is an intrinsic property of the system.
Now, what we learn from Frankfurt cases is that we can radically alter the counterfactual properties of a system in just about any way we wish without actually causally interacting with the system, and hence without altering its intrinsic properties. It follows from this observation and (1) and (2) that whether a system exemplifies a functioning mind cannot be a matter of the system's functional characterization. (We can, for instance, make sure that a given logic gate could never have produced a different output from what it actually produced, because someone watching the system would have intervened and forced it to produce the output it actually produced, had this watcher seen the inputs being different. But if this were done, then this would not be an and-gate, as it would not have the counterfactual properties of the relevant kind of logic gate.)
I should say that there is a way out of this argument, and it is to embrace an Aristotelian functionalism that instead of characterizing functions counterfactually, characterizes them teleologically. But that is not what "functionalism" means in the context of the theory of mind. (One might also try to do the Aristotelian move and define the functionalism evolutionarily. But not hard to see that this fails [e.g., see this, or this, or just extend the argument here].)
Or maybe we could try to get out of the argument by supposing that we can cut a system away from its environmental context and characterize the functioning of the system by looking at how the system would function apart from its environment, thereby isolating the system from the kind of purely counterfactual interference that a Frankfurt-style watcher would impose on it. But that simply doesn't work. How does the human body work absent its environmental context? It simply dies, pretty quickly, when not supplied with air, food and water.
Of course one might try to define a notion of an appropriate environment and then calculate the counterfactuals relative to that. But if we are allowed to be completely free in choosing what environment counts as appropriate, then just about everything is up for grabs. And if there is an objectively appropriate environment for the system, then again we get some version of Aristotelian teleology, which is not what functionalism wants.