My doctoral research was supervised by Keith Hossack and Øystein Linnebo.
The PhD thesis looked at plural interpretations of second-order logic. In particular, I cast doubt on the commonplace claim that the modal behaviour of plurals renders them unsuitable to interpret predicates. My work on this has been engaged with by leading philosophers. At the formal end of things: I showed that widely assumed principles about the modal behaviour of plurals are independent of the most obvious pluralisations of normal quantified modal logic.
My thesis also developed a system permitting quantification over the semantic values of ordered lists, which can be used to interpret polyadic second-order logic, and discussed the relationship of plural logic to set-theory.
Ex falso nihil
My major research interest is now in philosophical and formal aspects of the less explored variants of paraconsistent logics which validate ex falso nihil (from a contradiction, no proposition whatsoever may be inferred). Quite apart from being a relatively uncharted part of logic, these are of historical interest (since EFN enjoyed wide assent in ancient and medieval logic), have potential applications in computer science and mathematics, and raise philosophical questions about reasoning under inconsistent suppositions. You can read about my research in this area here.
Philosophy of Religion
In general, I'm interested in philosophy of religion in a Wittgensteinian vein (including 'grammatical thomism') and in the interactions between philosophy of religion and the philosophies of logic and language (particularly around realism/ anti-realism debates). I'm keen to encourage philosophical interest in the Dominican thinker Herbert McCabe, particularly with respect to his thought on the interaction between religion and politics. I'm currently co-editing a special issue of the International Journal of Philosophy and Theology on the philosophy of living religion with Tasia Scrutton.