My research is primarily in the philosophy of maths, but frequently goes in to logic, metaphysics, and epistemology.
I’m particularly interested in new axioms for mathematics — what ones there are, why we want them, what counts as evidence for them — and the nature of the mathematical universe — whether it is inherently potential, whether there a single universe or many, whether there are collections other than sets.
Currently, I’m looking at classes in set theory. Typically, a class is a collection of sets too large to be a set itself. I’m trying to get clear on why we might want classes — what work they do for us; what they are exactly, given that they aren’t sets; and what consequences they have for various views about the nature of sets.