Property dualism and relativity theory

On property dualism, we are wholly made of matter but there are irreducible mental properties.

What material object fundamentally has the irreducible mental properties? There are two plausible candidates: the body and the brain. Both of them are extended objects. For concreteness, let’s say that the object is the brain (the issue I will raise will apply in either case) Because the properties are irreducible and are fundamentally had by the brain, they are are not derivative from more localized properties. Rather, the whole brain has these properties. We can think (to borrow a word from Dean Zimmerman) that the brain is suffused with these fundamental properties.

Suppose now that I have an irreducible mental property A. Then the brain as a whole is suffused with A. Suppose that at a later time, I cease to have A. Then the brain is no longer suffused with A. Moreover, because it is the brain as a whole that is a subject of mental properties, it seems to follow that the brain must instantly move from being suffused as a whole with A to having no A in it at all. Now, consider two spatially separated neurons, n₁ and n₂. Then at one time they are both participate in the A-suffusion and at a later time neither participates in the A-suffusion. There is no time at which n₁ (say) participates in A-suffusion but n₂ does not. For if that were to happen, then A would be had by a proper part of the brain then rather than by the brain as a whole, and we’ve said that mental properties are had by the brain as a whole.

But this violates Relativity Theory. For if in one reference frame, the A-suffusion leaves n₁ and n₂ simultaneously, then in another reference frame it will leave n₁ first and only later it will leave n₂.

I think the property dualist has two moves available. First, they can say that mental properties can be had by a proper part of a brain rather than the brain as a whole. But the argument can be repeated for the proper part in place of the brain. The only stopping point here would be for the property dualist to say that mental properties can be had by a single point particle, and indeed that when mental properties leave us, at some point in time in some reference frames they are only had by very small, functionally irrelevant bits of the brain, such as a single particle. This does not seem to do justice to the brain dependence intuitions that drive dualists to property dualism over substance dualism.

The second move is to say that the brain as a whole has the irreducible mental property, but to have it as a whole is not the same as to have its parts suffused with the property. Rather, the having of the property is not something that happens to the brain qua extended, spatial or composed of physical parts. Since physical time is indivisible from space, mental time will then presumably be different from physical time, much as I think is the case on substance dualism. The result is a view on which the brain becomes a more mysterious object, an object equipped with its own timeline independent of physics. And if what led people to property dualism over substance dualism was the mysteriousness of the soul, well here the mystery has returned.