– The basic idea for supervenience is that there is no change in the mental (M) unless there is a change in the physical (P). Put differently, no mental activity without physical activity – the mental supervenes on the physical.
– What supervenience attempts to secure, generally speaking, is a non-reductive physicalist account of the mind – ie, this isn’t a simple identity theory (mind = brain) or an eliminative theory. In other words, it’s a theory of the mind that aims at an account of the mind that, while not reducing the mental to the physical, shows the mental to not be independent of the physical.
– There are various accounts of supervenience, but generally it’s accepted that it must be of the strong kind to be a really physicalist theory of the mind. This means, roughly, that in no nomologically possible world (this move is made so as to preclude the metaphysical possibility of, say, dualism) :
‘Necessarily, for each property M in M, if anything x has M, then there is a property P in P such that x has P, and necessarily if anything has P it has M.’ (‘A Companion to the Philosophy of Mind’, p. 579)
– As Jaegwon Kim notes, its difficult to see exactly how this isn’t a reductive theory – if for M it’s necessary for P, there it certainly seems like M entails P. Kim goes so far as to declare that supervenience won’t give up a nonreductive theory of mind, in fact.
– A further difficulty (and the above is a very crude sketch of one objection) comes when the issue of causation comes into play – Kim appropriately dubs his theory of causation ‘supervenient causation’ – M causes P because M supervenes on P. Kim holds to a theory of ‘causal explanatory exclusion’, or the doctrine that there is at most one full, complete causal explanation for a given event, and this, coupled with his principle of ‘causal closure’ – any physical event that has a cause at time t has a physical cause at t – seems to really nix any idea of mental causation in the bud, which is precisely what Kim is trying to hold on to (the spectre of epiphenomenalism is always hovering nearby). If M causes P, and M supervenes on P, and M really is distinct from P, then it would appear that we have two causes of P – M and P. But given Kim’s commitment to the causal priority of P, what causal role is there really for M? It seems that epiphenomenalism has been invited in here.
Theologians, Inc. 
I have appreciated that ideas of ‘supervenience’ (of different stripes) take into account the intuitions: A) people are really embodied, and this means something B) my mind is distinct from my body, in some way.
I don’t know how any serious contention of epiphenomenalism can escape psycho-somatic disorders.
LikeLike
Kim’s causal exclusion argument is pretty strong I think, and is going to force anyone who claims that mental properties supervene on physical properties to either embrace epiphenomenalism or go with some kind of identity theory. (So I think property dualists, for example, who tend to want supervenience but no identity, are going to have to be epiphenomenalists.)
That said, the criteria for strong supervenience you quoted does seem very strong, and I’m pretty sure it excludes some versions of the identity theory (and surely they qualify as physicalisms?) Davidson’s anomalous monism, for example (what we would now call a kind of “token physicalism”), would agree that whenever x has M there exists some physical property P such that x has P—but I do not think it would agree that whenever something has P it has M., let alone necessarily In other words, while each mental property instance identifies with a physical property instance, there may be no correlates between mental properties and physical properties—a particular pain may on one occasion be an instance of c-fibres firing, but on other occasions a pain may be physically realised in a completely different way; and an instance of c-fibre firing may on one occasion be a pain, but not on another.
So I think there are versions of (non-reductive) physicalism that don’t have to sign up to this sort of strong supervenience.
Sam
LikeLike