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 All: Your definition of Supervenience doesn't get off on the right foot. Supervenience does not deal with "higher" and "lower" level properties at all; that is a matter for reductionism and anti-reductionism. Here is an observation: All physicalists must hold that mental states supervene on physical states, but this does not imply that physicalists must have a particular view on the reductionism of higher-level properties to lower-level ones. I will attempt to clean this up, but you should read http://plato.stanford.edu/entries/supervenience/ for a discussion. There is a systematic misunderstanding on Wikipedia about what supervenience is (the main article is not very focussed, occasionally conflating reductionism with supervenience; it also introduces exotic views rarely associated with supervenience) so this will likely take a while.