have a substance with a different chemical composition in the lakes and oceans). Therefore, even though it is imaginable that water is not H2O, one can discover the identity of water and H2O a posteriori, and this identity is as valid an identity as those which can be known a priori. So, water is metaphysically identical to H2O. The fact that the metaphysical identity of water and H2O is a posteriori explains the apparent contingency of the statement "water is H2O" because, had the world been different, that statement might have been false. Getting back to supervenience, the formal definition of metaphysical supervenience is: B-properties supervene metaphysically on A-properties if it is metaphysically impossible for two situations/objects to have exactly the same B-properties without having the same A-properties. For example, properties of physical objects in our universe metaphysically supervene on properties of atoms (or whatever the true fundamental particles are) because it is metaphysically impossible for two physical objects to have the same properties without the same properties of their respective atoms being instantiated. This is different from logical supervenience because it is imaginable that physical objects might not have been made up of atoms, in which case the properties of atoms would make no difference to the properties of physical objects. However, because we have empirically discovered that objects in our world are made up of atoms, then in all possible worlds the properties of those things which classify as physical objects will depend on the properties of atoms. Having established that framework, we can now move on to discuss Chalmers' arguments. In the recent debate over the problem of consciousness, materialists often appeal to some form of metaphysical identity or metaphysical supervenience as a way of holding on to materialism while still admitting that the problems Chalmers points out are real. Chalmers disag...
