 A broader reason for Lewis to care about Humean supervenience comes from looking at his overall approach to metaphysics. When faced with something metaphysically problematic, say  free will,  there are three broad approaches. Some philosophers will argue that free will can’t be located in a scientific world-view, so it should be eliminated. Call these ‘the eliminativists’. Some philosophers will agree that free will can’t be located in the scientific world-view, so that’s a reason to expand our metaphysical picture to include free will, perhaps as a new primitive. Call these ‘the expansionists’. And some philosophers will reject the common assumption of an incompatibility. Instead they will argue that we can have free will without believing in anything that isn’t in the scientific picture. Call these ‘the compatibilists’.