In this talk I will discuss some logical questions regarding the relation between modal axiom systems for set-theoretic potentialism and more familiar axiom systems in purely quantificational languages. I’ll start by sketching extant results relating axiomatic systems for ‘height’ potentialism to good old-fashioned ZFC. I’ll then turn to some new, analogous results I have attained that relate combined systems for ‘height and width’ potentialism to second order arithmetic extended by so-called ‘topological regularity’ axioms. I will also try to say something about what I take the significance of these results to be.
Meeting will be in person. Those who wish to attend online via Zoom, please write to Daniel Isaacson.
Philosophy of Mathematics Seminar Convenors: Daniel Isaacson and James Studd