s: B-properties supervene naturally on A-properties if any time two situations which could naturally arise in our world share the same A-properties, they also share the same B-properties. Whether some property naturally supervenes on another property depends upon our world and the natural laws (i.e., the laws of physics) in our world. Natural supervenience has to do with empirical possibilitysituations which are causally necessitated in our world (though not in all possible worlds). The example of the ideal gas laws is an example of a naturally necessary phenomena which is not logically necessary (it's conceivable, at least, that it could be different). If B-properties naturally supervene on A-properties, then while it is conceivable that the same B-properties could be instantiated without the same A-properties, it could never happen in our world because it would break the laws of physics. Finally, the notion of metaphysical supervenience is based upon rather subtle distinctions between a priori and a posteriori identities of substances. Metaphysical supervenience stems from the notion of metaphysical identity, which Saul Kripke is credited with discovering. In his book Naming and Necessity, Kripke distinguishes between two subtly different notions of identity. Logical identity is just the same as has been explained earliertwo things are said to be logically identical if, because of the meanings of the terms, it is impossible that they could be distinct things. Metaphysical identity, on the other hand, depends upon how our world turns out. The classic example of metaphysical identity is the identity of water and H2O. Kripke argues that although it is imaginable that the stuff we find in lakes and oceans, which is good to drink, and which we call 'water', might not have had the chemical composition H2O, once we discover that it does have this chemical composition in our world, H2O will be 'water' in all possible worlds (even those which ...
