Intro:

A set of properties A supervenes upon another set B just in case no two things can differ with respect to A-properties without also differing with respect to their B-properties. In slogan form, “there cannot be an A-difference without a B-difference”.

So, in physicalist philosophy of mind we should like to say something like: "you cannot have variance in a subject's mental state (A) without some change in their physical constituents (B)." Two subjects that are physically identical must have the same mental properties/experiences. However, crucially this is not a one-to-one relationship. Subjects might have different physical properties and yet have the same experiences (as measured over some given duration). Mental states are multiply realizable in terms of physical states.

One of the things that has become re supervenience is that the above definition is wholly inadequate to do the job supervenience is brought in to do. This leads to the introduction of two new concepts: P-Regions and B-Minimal Properties. What I will try to show here is why these both end up with significant difficulties.

What is the job we'd like superveniance to do? We'd like to show how the mental is in some way dependant on the physical, whereas the physical is not dependant on the mental in this same way.

Local and Global Supervenience

Global supervenience can be defined in two ways. First, we could say that two worlds cannot differ in their mental properties without differing in their physical properties. Agents in a world cannot experience different mental events, but have the same physical properties.

This ends up being an inadequate definition. Consider this example. World A is identical to World B except for the fact that in World B there is an extra molecule of dust on Mars. Given our definition, it is now possible for every entity in World A to have experiences that differ from those in World B. There is a B difference, so we can have all the A differences we like.

Local Superveniance tries to get around this issue with the formulation along the lines of "two entities' experiences cannot differ without some difference in their physical constituents. If Sue and Jane are physically identical, they cannot have different mental properties. Does this fix the problem?

Consider the case where Sue and Jane are physically identical, except for the fact that Sue has an extra red blood cell floating around in her blood steam. It now seems like Sue can have entirely different mental properties without violating a local superveniance defined solely by "no change in A without a change in B." There is a variance in B, so now it seems any changes in A are up for grabs.

Introducing P-Regions and B-Minimal Properties

To avoid this problem, and problems related to relational/extrinsic properties, we can invoke the concept of P-regions, regions of space-time defined as "incorporating all the relevant physical 'stuff' needed to explain the physical side of the mental phenomena we are analyzing." Alternatively, we can go with Kim's "B-minimal" properties, where what is "B-minimal," is just those physical properties that are needed to explain the mental phenomena.

So, for example, we might allow that the body of a runner could change in very many ways without it affecting their gait, and so while "the running depends on the body," we only need define superveniance in terms of the relevant B-minimal properties of the body that relate to the running (or only the P region that incorporates all those properties).

The Problems

I am skeptical of these approaches because it seems that, to properly explain a person's mental life throughout the day, we must continually adjust what constitutes our P-Region or B-minimal properties. And just how are these two going to be defined? In relation to the very mental properties, we are examining. So, consider the case when we cut an hour of some person's experience up into 10 second durations. As they perform different mental activities, the relevant P-Region swings around wildly and frenetically, as do the B-Minimal properties.

If we allow for a "global workspace," model of self-conscious, recursive awareness, then the P-Region involved in explaining that awareness would have to look akin to a candle flame, changing moment to moment, constantly involving different physical constituents.

Consider the P-Region corresponding to our "zoning out" in deep thought, unaware of what we are hearing except perhaps in some disinterested, half unconscious way (T1). Then suppose that over the next interval (T2) we begin "listening intently," after we hear our neighbors screaming at one another.

Our awareness of the sounds of screaming has caused us to shift our focus, and as a result what is B Minimal or P relevant has to shift in order to describe this next interval. Physical properties that could be ignored in terms of the first interval have now become essential to self-conscious awareness in the second. The presence or absence of some of these physical properties was indiscernible to the agent during the first interval, but not in the second. Whole regions of our auditory cortex suddenly become P relevant, whereas before we could probably ignore more neurons in that specific regions (or more properties of that region).

Then suppose we realize that the noise is actually coming from a TV, nothing to worry about. We stop listening intently. Again, the relevant spatio-temporal region / physical properties must radically change so as to match what is necessary to produce the corresponding conscious awareness.

This seems very much like the cart is driving the horse. We are saying that A cannot vary without a variance in B, but then B has to constantly be redefined in terms of what A is. That A cannot change without a change in B is tautological because B is defined in terms of A such that something is only said to be B in virtue of its being essential to A. If A changes, we are forced to redefine (change) B. But if the definition of B is malleable in this way, then it seems A can change all it likes, and B will necessarily change with it because B is defined by A, the opposite of the relationship we wanted to have.

"But doesn't B at least determine any changes in A?"

No, which seems to make the problem more acute.

Consider two intervals T1 and T2, with corresponding B-minimal physical properties P1 and P2, and corresponding mental properties M1 and M2. It is the case that the P-Region or B-Minimal properties corresponding to T1 do not give us all the information we need to determine the mental contents of M2. P1 has been defined so as to only contain what is absolutely necessary for M1, and so it is possible for it to leave out physical properties that are required to show how P1 evolves into P2. To be sure, we could define a new P-Region or set of B-Minimal properties for T1 + T2. However, this doesn't get around the problem that P1 does not uniquely determine P2, and thus cannot uniquely determine M2.

So now we have a case where P cannot vary without variance in M, where P is P only in virtue of its relation to M, and where P does not specify future states of M (or future states of P). This does not seem like supervenience accomplishing the job envisioned for it. That is, we'd like to show how the mental is in some way dependant on the physical, whereas the physical is not dependant on the mental in this same way — but here it seems like the two are mutually dependent such that changes in M entail changes in P AND neither current states of M nor P determine future states of M or P.

Aside from this, there is also the problem of P-regions ballooning in size quite rapidly if we take into account what is causally necessary to produce any instance of mental life that lasts for a meaningful duration. For example, one cannot spend an hour reading a book outside using the sun's light without the sun itself being a causal factor in that instance of mental experience. Granted, the whole Sun isn't necessary for the experience, we might remove some hydrogen atoms from it and have the experience remain unchanged, but we also can't do without something instantiating the same B-Minimal properties.