research

I work in the philosophy of maths, metaphysics, and logic.

I’m particularly interested in questions concerning notions of collection (like sets, pluralities, properties, and Fregean concepts), infinity, and possibility, and the connections between them. At the moment I’m working on two larger projects. 

In the first, I’m developing what I call the iterative conception of properties, building on work of Øystein Linnebo and Kit Fine. It is based on a radically new approach to paradox and does for properties what the iterative conception of sets does for sets. The basic idea is that instead of building an ontology stage by stage—as we do with sets according to the iterative conception of sets—we build an ideology stage by stage—in particular, we build the relation of application for properties. With the right assumptions, it is surprisingly powerful, with interesting applications in semantics, set theory, and higher-order metaphysics. 

In the second, 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. In particular, I think it has important consequences for potentialism—the view that the universe of sets is inherent potential.