Philosophy of Mathematics seminar




Chris Scambler, Oxford
Axiomatic Potentialism
In this talk I will discuss some logical questions regarding the relation between modal axiom systems for settheoretic 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 oldfashioned 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 socalled ‘topological regularity’ axioms. I will also try to say something about what I take the significance of these results to be.

