I am working on a nominalistic philosophy of mathematics. That is, I try to show that mathematics can get by without a need to assume the existence of abstract objects. I believe that a mathematical ontology consisting of possible sentences plus human beings’ ability to commit to conventional truth conditions for those sentences will suffice. However, I do not think it suffices for classical (i.e. mainstream) mathematics, just that it suffices for a mathematics that again suffices for the empirical sciences. An important part of my project is to develop this non-classical mathematics in detail. Thus, in order to do philosophy of mathematics, I do a lot of mathematics.

My philosophy of mathematics is closely connected to a conventionalist solution to the semantic paradoxes that I have developed (see my personal website for a draft paper). I can also sometimes be caught working on projects concerned with supertasks, decision theory, and principles of probability.