My doctoral research was supervised by Keith Hossack and Øystein Linnebo. My thesis explored issues around plural interpretations of second-order logic and their usefulness (or otherwise) in the philosophy of mathematics. It was examined by Bob Hale and Mark Textor.
These days I can be persuaded to be interested in pretty much any part of philosophy. Here I some things I am thinking about presently:
Ex falso nihil
I work on 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.
Existence and Quantification in Mathematics
I'm interested in accounts of existence according to which it isn't fully or adequately analysed quantificationally in the standard Frege-Russell fashion. If there is something to be said for these accounts, might this allow us to deflate worries about the ontological commitments of mathematics and to navigate a more attractive path between platonism and constructivism?
Philosophy of Religion/ Analytic theology
At the moment I'm working on apophatic theology, a form of theology which claims there are radical limits to what can be appropriately said of God. In spite of its historical place in many major religious traditions, this kind of theology has been either ignored or denigrated by philosophical thinkers within the analytic tradition. 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 recently co-editing a special issue of the International Journal of Philosophy and Theology on the philosophy of living religion with Tasia Scrutton. I'm writing a dialogue on apophaticism in the thomist and Maimonidean traditions with Sam Lebens.