 One problem with Davidson’s response here is its reversal of the dependency relationship between mental and physical properties typically claimed in supervenience relationships. A central rationale for positing supervenience is to mark a kind of explanatory primacy to the subvenient properties (see the supplement on  Supervenience and the Explanatory Primacy of the Physical).  And this is reflected in the first part of Davidson’s formulation above—surely a difference in psychological properties entails (requires) a difference in physical properties because the difference in physical properties is needed in order to explain the difference in psychological properties. So the sense in which psychological properties ‘matter’ to physical properties is that changing the former amounts to a change in the latter because a change in the latter explains a change in the former. This does not appear to be helpful in establishing the explanatory relevance of mental properties. Another problem, discussed above  (5.3),  is that it is difficult to see how a supervenience relation of sufficient power to make mental properties explanatory of an event’s physical properties in the way Davidson seems to suggest does not issue in strict laws. So it is unclear how supervenience is consistent with the anomalism principle, and thus how it can help block epiphenomenalist concerns, although we did previously note one potentially worthwhile but unexplored possibility—a ceteris paribus supervenience relation—which Davidson endorses.