My main research interests are in the philosophies of mathematics and logic, in mathematical logic and in the philosophy of science. A common theme in my philosophical and mathematical research is the comparison and evaluation of a variety of approaches (philosophical and/or formal) to the concept of set, with a particular focus on concepts of set which are computational or operational. My current work is especially on predicative and constructive approaches to mathematics. A long-term project is to clarify the differences between distinct proposals that have emerged in this context. My approach to these questions gives central role to the mathematical practice and to philosophical questions that arise directly from it.
I am presently Marie Skłodowska Curie Individual Fellow, with a project founded by the European Union Horizon 2020 programme. The project's title is: Infinity in Mathematics: A Philosophical analysis of Critical Views of Infinity.
This project’s research goal is a systematic philosophical and mathematical analysis of critical views of infinity: views which have questioned one or more aspects of standard Cantorian approaches to infinity in mathematics. Criticism of infinity originates in fundamental debates at the turn of the 20th century, partly motivated by the discovery of the set-theoretic paradoxes. It re-emerges in contemporary mathematics under the stimulus of computer applications, as it underpins constructive and computational approaches to type theory (Martin-Löf type theory). The project’s first aim is to develop a novel rigorous examination of what is objected to infinity and why. The next goal is a philosophical and mathematical analysis of this criticism and of strategies proposed to overcome the perceived problematic nature of the infinite.
I received my first PhD from the School of Mathematics, University of Leeds (2000), with a thesis on the proof theory of constructive set theory. I subsequently held Postdoctoral positions at the Mathematics Institute LMU Munich, the Philosophy Department University of Florence and the School of Mathematics, University of Leeds. In 2017, I completed a second PhD at the School of Philosophy, Religion and History of Science, University of Leeds, with a thesis on the philosophy of Constructive and Predicative mathematics. In the academic years 2017-18 and 2018-19 I was Teaching Fellow at the Department of Philosophy, University of Birmingham.