Global Supervenience without Reducibility

Abstract

Does the global supervenience of one class on another entail reductionism, in the sense that any property in the former class is definable from properties in the latter class? This question appears to be at the same time formally tractable and philosophically significant. It seems formally tractable because the concepts involved are susceptible to rigorous definition. It is philosophically significant because in a number of debates about inter-level relationships, there are prima facie plausible positions that presuppose that there is no such entailment: standard versions of non-reductive physicalism and of normative non-naturalism accept global supervenience while rejecting reductionism. I identify a gap in an influential argument for the entailment, due to Frank Jackson and Robert Stalnaker, and draw on the model theory of infinitary languages to argue that some globally supervening properties are not reducible.