Parts Of Classes

Parts of Classes

Does the notion of part and whole have any application to classes? Lewis argues that it does, and that the smallest parts of any class are its one-membered singleton subclasses. That results in a reconception of set theory. The set-theoretical making of one out of many is just the composition of one whole out of many parts. But first, one singleton must be made out of its one member - this is the distinctively set-theoretical primitive operation. Thus set theory is entangled, with mereology: the theory of parts and wholes.