The Tweedledum and Tweedledee of Supervenience

Summary

A growing number of philosophers have turned to supervenience in hopes of finding a nonreductive form of determination. The search, however, is complicated by the fact that there is an entire family of supervenience relations, not all of which have the same reductive and determinative capacities. Among these various relations, two have come to receive a considerable amount of attention and interest, namely, strong supervenience and global supervenience.

Strong supervenience is a relation that holds between sets of properties and the individual objects that exemplify these properties. In particular, for two sets of properties A and B:

(SS)A strongly supervenes on B just in case, necessarily, for each object x and each property F in A, if x has F, then there is a property G in B such that x has G, and necessarily if any object y has G, it has F.

In contrast to strong supervenience, global supervenience is a holistic relation that applies to entire worlds rather than individual objects:

(GS)A globally supervenes on B just in case worlds that are indiscernible with regard to B are also indiscernible with regard to A.

Some philosophers prefer global supervenience over strong, arguing that although strong supervenience might be strong enough to function as a relation of determination, it is not weak enough to be nonreductive. Others prefer strong supervenience over global, arguing that although global supervenience might be weak enough to be nonreductive, it is not strong enough to serve as a relation of determination.