 The grounding problem is sometimes characterized in terms of supervenience failure. Lumpl and Goliath differ in their persistence conditions without differing in their physical or categorical properties (see Yablo 1987 for a discussion of categoricity). And it is true that many forms of supervenience fail: weak and strong individual supervenience and strong global supervenience all fail. But there are forms of supervenience that can hold. Both weak and intermediate global supervenience hold, as does (as the name suggests) coincidence-friendly supervenience, and possibly other versions of multiple-domain supervenience (c.f. Zimmerman 1995, Rea 1997b, Sider 1999, Baker 2000). All of these forms hold on the plausible assumption that any two regions physically/categorically just like this one will contain an object with Goliath’s persistence conditions, and an object with Lumpl’s persistence conditions.