  Non-naturalism has trouble explaining the necessary dependence of the moral facts on the natural facts. So long as our characterization of natural properties is broad enough to include both all of the mental properties and all of the properties that would figure in the best physical theory, it is very plausible to suppose that the moral supervenes on the natural in the following sense: there can be no moral difference between two situations or entire possible worlds without some natural difference but not vice-versa (there can be non-moral differences without moral differences). On some ways of understanding the natural properties, of course, it is unclear whether mental properties are natural ones and this is an important point. Perhaps mental properties elude scientific investigation but are real nonetheless. If we characterize the non-natural properties as ones that elude scientific investigation then mental properties will be non-natural ones. This is very important since it is not nearly so plausible that the moral supervenes on a set of facts that does not include the mental facts—as if the wrongness of an action could float independently of facts about pain, intentions and beliefs. For purposes of the present discussion I shall simply assume that the natural properties include the mental properties.