Parts of Classes

Aimed at philosophers of logic, set theory and mathematics, this philosophical treatise argues that the notion of part and whole - the theory of mereology - has application to classes because of one-membered "singleton" subclasses, thus resulting in a reconception of set theory.

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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.