Varieties of class-theoretic potentialism

TL;DR

This paper investigates class-theoretic potentialism, analyzing its motivations, exploring the structure of potentialist systems, and examining the implications of certain failures of modal axioms within this framework.

Contribution

It provides new results on the structure of class-theoretic potentialist systems, including failures of specific modal axioms, and discusses their significance for the philosophy of set theory.

Findings

Failures of the .2 and .3 modal axioms in class-theoretic potentialist systems

Analysis of motivations behind class-theoretic potentialism

Implications for understanding the nature of classes in set theory

Abstract

We explain and explore class-theoretic potentialism -- the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the .2 and .3 axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialist.