  However, suitably formulated theses concerning the supervenience of the moral on the natural are plausible enough that some philosophers have held them to be analytic. Global supervenience theses are perhaps the most plausible ones, claiming merely that two entire possible worlds cannot differ only in their moral properties without also differing in some of their natural properties. To deny this thesis would be to allow that it could have been the case that the world was exactly like the actual world in all of its naturalistic features but in that world what Hitler did was not wrong. Since all the natural facts are the same in this possible world it will still be true that Hitler killed the same people, had the same intentions, etc. Such bare moral differences seem inconceivable. Very plausibly, the moral facts are in some way entirely fixed by the natural facts. The problem for the non-naturalist is that non-naturalism seems unable to explain this supervenience. For if moral properties and natural properties really are, in Hume’s terms, “distinct existences” then it is hard to see why it should be impossible for the former to differ with no difference in the latter and since the natural properties are non-moral ones (given non-naturalism) this makes supervenience seem problematic. Non-naturalism’s apparent inability to explain such a basic platitude as global supervenience poses a serious problem (see Mackie 1977, Blackburn 1984, and Blackburn 1988).