 The primary challenge to Humean supervenience comes from those who hold that providing a subvenient basis for all the truths of this world requires more than intrinsic properties of point-sized objects and spatiotemporal relations. Some of these challenges come from theorists who think best physics will need non-spatiotemporal relations in order to explain  Bell’s Theorem.  But more commonly it comes from those who think that grounding the modal, the nomic or the mental requires adding properties and relations to any Humean mosaic constructed from properties found in fundamental physics. (I’m using ‘mental’ here to cover all the properties that Lewis considered mental, broadly construed. This includes contents, since Lewis thought content was grounded in mental content, and value, since he thought values were grounded in idealised desires. So it’s a fairly broad category, and there is a lot that isn’t obviously reducible to fundamental physics. As we’ll see, Lewis attempts to reduce it all step-by-step.)