This is a talk in the University of Konstanz Philosophy of Mathematics Seminar, on 2020 December 18.
As far back as Cantor it was realized that some collections, call them (proper) classes, are too large to be sets. A question then for the philosopher of set theory is to explain what classes are, how they differ from sets, and what properties they should satisfy. In this talk I will discuss class theoretic potentialism, a framework for studying some of the possible answers to this question. This builds on work in set theoretic potentialism, where the same tools have been applied to elucidate different ideas of what sets are. This talk is about joint work with Carolin Antos and Neil Barton.