 We have seen that Davidson supplements his monism with a claim of supervenience. There are many different conceptions of the supervenience relation (see Kim 1993b), and Davidson ultimately came to identify his version with what is called “weak” supervenience, in contrast to “strong” and “global” supervenience. Briefly, the basic differences between these positions are as follows. Weak supervenience links specific mental and physical properties within but not across possible worlds, while strong supervenience links those properties across worlds. Global supervenience links the class of mental properties as a whole with the class of physical properties as a whole within but not across worlds, but does not constrain relations between specific pairs of mental and physical properties. Weak supervenience comes down to the view that mental properties depend upon those physical properties they are correlated with within a particular possible world, but those very same physical properties may, in another possible world, correlate with very different (or even no) mental properties. Weak supervenience is thus stronger than global supervenience, in that it posits correlations between particular pairs of mental and physical properties, but weaker than strong supervenience in that it recognizes the possibility that these correlations can fail to obtain in other possible worlds. (It should be noted that Davidson never brought his views on supervenience into contact with his later views, noted above, about the broad nature of the physical properties that mental events must instantiate according to Anomalous Monism. It is not at all clear whether or how these views can be combined. In the following discussion of supervenience, this complication will be ignored, and it will be assumed that the physical properties in question are not of this broad nature, since this is how Davidson’s own discussions of supervenience seem to proceed, and certainly what his critics presuppose.)