Amongst a number of other no doubt fascinating potted insights at this site, Joshua Greene gives us a condensed version of supervenience. The issue of human mind and consciousness was harped on by Marilynne Robinson in her RSA talk, and at one point she ridiculed what she would describe as the reduction of the mind to that glob of grey matter inside the skull. As everyone knows, this has long been a contentious point between materialists, or to use Greene's term, physicalists, and their opponents, be they dualists or some other ists. Greene's supervenience concept - which doubtless has been around for ages - is that mind is supervenient on the brain. We can't have minds without brains, but that doesn't mean they're identical. You can have a brain without a mind, but more importantly, they operate at different levels. Greene gives the example of a computer image made up of pixels. The image was generated using pixels, but the image also exists on another, human, psychological level, imparting emotion or ideas. Altering the number of pixels might change the resolution but it won't generally alter what the image intends to convey - that 'information', if you like, operates on another level. It is supervenient on the process by which the image was generated.
Greene provides this general definition of supervenience:
Supervenience is a relationship between two sets of properties. Call them Set A and Set B. The Set A properties supervene on the Set B properties if and only if no two things can differ in their A properties without also differing in their B properties.He then 'concretises' this piece of abstraction rather well - though you can see just by the definition how it works for the mind/brain conundrum, including the asymmetry of the relationship. Essentially the world can be seen as operating on different levels, but there's a basic level upon which everything else supervenes. This is the 'hard' level that physicists work on, and explains why physics is the most fundamental science. When physicists talk about developing a 'Theory of Everything' [TOE] they don't of course mean this quite literally, though in a sense they do - what they mean is the possibility of developing a theory of that upon which everything supervenes.
As this isn't a new approach, no doubt philosophers have been pulling it apart for some time, though on the face of it, it seems very helpful. My strong sense from people like Robinson is that their emphasis on human brilliance and the specialness of human consciousness is really not so much to urge scientists to get their finger out and start studying this stuff, but to put a god-shaped spanner in the works, to almost sneakily claim that there's something that can't be explained, something that's god's doing. Most religious beliefs are self-aggrandising, or 'human-aggrandising' if you will. Certainly this is true of the Judeo-Christian religion, in which only humans are in the image of the creator-deity, and therefore get to lord it over other creatures and to revel in their own specialness and brilliance. Perhaps if Robinson were to focus a bit more on other species and their minds [bearing in mind my quote at the top of this post], she might start to get a clearer view of consciousness as an evolving property, and she might be more impressed with the differently evolving cognitive qualities of pigs and elephants and cetaceans and other beasties. I'm not sure though that she really wants to do that.