The philosophy of mathematics was the subject of my Ph.D. thesis and remains a major research interest of mine. In particular, I have defended nominalist accounts of mathematics: those which do not posit mathematical objects such as numbers or sets. Other ontological debates also interest me, particularly those concerning possible worlds, composite objects, and propositions. I have tended to explore theories which posit less rather than more, which has led me to think about paraphrase, pretence, fictionalism, and error theory. At present I am trying to bring some of these ideas into discussions of truth.
Philosophical method is a related interest. In particular, I am interested in how, if at all, our philosophical theories should be moulded by our pre-theoretical beliefs and by our best theories in mathematics, natural science, and linguistics. I am working on these questions in collaboration with my colleague Chris Daly.
I am also interested in grounding. Investigating grounding will help us to work out whether there are mathematical objects or analytic truths – at least, I hope it will.
Other research interests concern metaontology and metaethics.