Kim argues that weak and global supervenience are too weak to guarantee any sort of dependency. Of the three original forms of supervenience, strong, weak, and global, each commonly wielded across all branches of philosophy, two are thus cast aside as uninteresting or useless. His arguments, however, fail to appreciate the strength of weak and global supervenience. I investigate what weak and global supervenience relations are functionally and how they relate to strong supervenience. For a large class of properties, weak and global supervenience are equivalent to strong supervenience. I then offer a series of arguments showing that it is precisely because of their strength, not their weakness, that both weak and global supervenience are useless in characterizing any dependencies of interest to philosophers.
Moyer, Mark, "Weak and Global Supervenience Are Strong" (2008). College of Arts and Sciences Faculty Publications. 2.