12 - Classes

Summary

CLASSES AND AGGREGATES

If we want to bring classes down to earth, down to spacetime, out of the clutches of those who call them abstract (meaning apparently by this that classes stand above and beyond particulars, even when their members are all ordinary particulars!), nothing is more helpful than to attend to the close relations between a class and its corresponding aggregate. The aggregate is what David Lewis calls the fusion of the members of the class, and an excellent account of the class/fusion distinction can be found in Lewis' 1991, 1.1. Peter Simons (1987) calls aggregates ‘sums’. I retain the word aggregate because it is the term I have used in earlier writings.

It will be assumed here, as Lewis also assumes but Simons denies, that to every class there corresponds its aggregate. Indeed, still in agreement with Lewis, it will be assumed that wherever there are some things, there is an aggregate of them, whether or not there is a class of these things. This is the principle of Unrestricted Mereological Composition. As has been emphasized a number of times already, this ‘permissive mereology’ is an ontologically uncostly assumption because the aggregate supervenes on the sum of its parts, a supervenience that seems an excellent candidate for an ontological free lunch.

Considering the more restricted principle, that for every class there exists the aggregate of their members, it is interesting to ask whether something near to its converse is true.