16 May 2022: gabriel uzquiano

Singletons of classes

Abstract: We will explore the prospects of a mereological account of proper classes. That is, we will take set theory for granted and consider the hypothesis that proper classes are mereological sums of their parts. Unlike the plural account of classes, for example, the hypothesis construes proper classes as bona fide objects, which are nonetheless significantly different from sets. On the other hand, a mereological account raises questions of its own: if proper classes are bona fide objects, they should be allowed to be members and they should each come with a singleton. But since singletons are arguably mereological atoms, the account will turn out to be incompatible with classical mereology. The question is whether a weaker mereological framework may support a sufficiently rich domain of classes.