Supervenience and counterfactuals

On typical functionalist views of mind, what mental states a physical system has depends on counterfactual connections between physical properties in that system. But we can have two worlds that are exactly the same physically—have exactly the same tapestry of physical objects, properties and relations—but differ in what counterfactual connections hold between the physical properties. To see that, just imagine that one of the two worlds is purely physical, and in that world, w₁, striking a certain match causes a fire, and:

1. Were that match not struck, there would have been no fire.

But now imagine another world, w₂, which is physically exactly the same, but there is a nonphysical spirit who wants the fire to happen, and who will miraculously cause the fire if the match is not struck. But since the match is struck, the spirit does nothing. In w₂, the counterfactual (1) is false. (This is of course just a Frankfurt case.)

Thus physicalist theories where counterfactual connections are essential are incompatible with supervenience of the mental upon the physical.

I suppose one could insist that the supervenience base has to include counterfactual facts, and not just physical facts. But this is problematic. Even in purely physical worlds, counterfactual facts are not grounded in physical facts, but in physical facts combined with the absence of spirits, ghosts, etc. And in worlds that are only partly physical, counterfactual connections between physical facts may be grounded in the dispositions of non-physical entities.