 The puzzling aspect of Davidson’s doctrine of supervenience arises independently of fine points of the disagreement between the competing conceptions of supervenience sketched above. Whether the dependency is between particular mental and physical properties, or sets of the two, and whether or not the dependency holds only within or also across possible worlds, it appears that it entails that there will exist strict laws on the basis of which mental events can be predicted and explained that were supposed to be ruled out by the anomalism principle. Davidson sometimes claims (Davidson 1995a, 266) that supervenience is actually entailed by Anomalous Monism, in which case it would appear to follow that Anomalous Monism itself is an inconsistent theory—entailing both that there cannot be any strict psychophysical laws (the anomalism principle) and that there must be such laws (supervenience). But generally his position appears to be that Anomalous Monism is simply consistent with supervenience (Davidson 1993, 7). If supervenience and Anomalous Monism are indeed inconsistent, and the former is rejected, the question of the plausibility of a materialist position with no discernible relation between mental and physical properties arises (see the supplement on  Supervenience and the Explanatory Primacy of the Physical).  (The caveat about the relation between Davidson’s later views about physical descriptions and supervenience noted at the end of  5.1.  should be kept in mind here.)