In an earlier paper, “Concepts of Supervenience,” I characterized two distinct concepts of supervenience, “strong” and “weak,” and compared them with each other and with a third concept, “global supervenience.” In this paper I wish to correct an error in the earlier paper and present further material on supervenience, including a new characterization of strong supervenience, which I believe is particularly perspicuous, and a discussion of the adequacy of global supervenience as a determination relation. I shall also present a strengthened relation of global supervenience based on similarity rather than indiscernibility between worlds, which may well be a more useful concept than the currently popular conception of global supervenience.

A NEW CHARACTERIZATION OF “STRONG SUPERVENIENCE”

Let A and B be two sets of properties (closed under complementation, conjunction, disjunction, and perhaps other property-forming operations). A is said to weakly supervene on B just in case:

1. (I) Necessarily, for any x and y, if x and y share all properties in B, then x and y share all properties in A - that is, indiscernibility in B entails indiscernibility in A.

This corresponds in a straightforward way to the informal characterization of supervenience commonly found in the literature. As was shown in the earlier paper, weak supervenience can be equivalently explained as follows:

1. (II) Necessarily, for any object x and any property F in A, if x has F, then there exists a property G in B such that x has G, and if any y has G, it has F.