Does the supervenience argument generalize?

We evaluate the scope of Jaegwon Kim's “supervenience argument” for reduction. Does its conclusion apply only to psychology, or does it generalize to all the special sciences? The claim that the supervenience argument generalizes to all the special sciences if it goes through for psychology is often raised as an objection to the supervenience argument. We argue that this objection is ambiguous. We distinguish three readings of it and suggest that some of them make it a plausible claim, whereas other readings make it implausible. We suggest that this ambiguity is the result of picturing the world as being hierarchically organized in levels, with the domain of physics at the bottom and the domains of the social sciences at the top. The plausibility of the objection depends on how we think of this picture. This popular picture, we suggest, involves three different dimensions along which reduction may occur.