Weak and Global Supervenience Are Strong

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. Weak and Global Supervenience Are Useless To say that A properties supervene on B properties is merely to say that A properties are a function of B properties, or, more perspicuously, that which A properties a thing has is a function of which B properties it has. It is not to say that A properties depend on B properties, for A properties can be a function of B properties also in virtue of A being identical to B, in virtue of B depending on A, or in virtue of A and B both depending on C.1 Nonetheless, even though supervenience is merely a functional relation and not a newly discovered type of dependency, as many once thought, a dependency relation of some kind, or, in the limiting case, an identity relation, will underlie any supervenience relation.2 A supervenience relation holds because of the underlying dependency. Kim, however, 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. In sections I and II 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. In section III, I 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. 1 B depending on A: A = {being male}, B = {being a bachelor, being a husband}. A and B both depending on C: A = {being a husband}, B = {being a bachelor, being a bachelorette, being a wife}, C = {being male}. 2 I will consider identity to be a degenerate or limiting case of dependency just as identity is considered a degenerate case of (improper) parthood. Thus, I will henceforth drop the ‘or identity’ qualification.