Thanks, Faldage; I read the link. I'd like to comment on several parts of it, but I'd either have to take it on faith that everybody's read it, or post nearly the whole thing so people could see what I was referring to, but that would be just too unwieldy. I'll stick with his def.:
supervenience - A set of properties or facts M supervenes on a set of properties or facts P if and only if there can be no changes or differences in M without there being changes or differences in P.
I really wish he hadn't called the non-physical properties mental properties. He uses objects in space in his example; now, to me, objects in space do not have mental properties. They just don't.

By the way, Bingley, you blew me away (yet again) with your explanations of reductionism and emergentism.