THE NOTION OF SUPERVENIENCE

In the preceding four chapters the theory may be said to have been on the defensive. I have been trying to show that the theory can meet, or has reasonable prospects of meeting, certain difficulties. At this point, however, we can relax and draw certain more or less interesting consequences from the theory.

We have a theory of possible worlds intended to be compatible with Naturalism. We can go on to use the possible worlds to define the notion of supervenience, and then use the latter notion to draw metaphysical conclusions of great importance.

I propose to work with the following simple definition of supervenience: If there exist possible worlds which contain an entity or entities R, and if in each such world there exists an entity or entities S, then and only then S supervenes on R. For instance, if there exist worlds in which two or more individuals have the property F, then, in each world containing such states of affairs, these same individuals stand in the relation of resemblance (at least in some degree). These resemblances are therefore supervenient on the individuals in question having property F.

This definition allows there to be cases where not only is S supervenient on R, but R is at the same time supervenient on S. This does not hold in the case just considered. Consider the individuals which are all F, and which therefore all resemble one another.