I work in logic and the philosophy of mathematics. I am an associate professor of philosophy and mathematics at the University of Illinois at Urbana-Champaign.
During the 2014-15 academic year I am a EURIAS fellow at the Mediterranean Institute of Advanced Research (IMéRA) in Marseille, France.
I am also an editor of the Review of Symbolic Logic.
My CV may be found here.
Voici mon CV français.
Here are some articles I've written.
- On the depth of Szemerédi's theorem. Forthcoming in Philosophia Mathematica (2015).
- Plane and solid geometry: a note on purity of methods (with Paolo Mancosu). In From Logic to Practice : Italian Studies in the Philosophy of Mathematics, edited by Gabriele Lolli, Marco Panza, and Giorgio Venturi, Springer (2015), pp. 23-31.
- Purity in arithmetic: some formal and informal issues.In Formalism and Beyond. On the Nature of Mathematical Discourse, edited by Godehard Link, De Gruyter (2014), pp. 315-336.
- On the relationship between plane and solid geometry (with Paolo Mancosu). Review of Symbolic Logic 5:2 (2012), 294-353.
- Geometria piana e solida: una nota sulla purezza del metodo (with Paolo Mancosu). Notae Philosophicae Scientiae Formalis 1:1 (2012), 89-102.
- L'infinité des numbers premiers : une étude de cas de la pureté des méthodes. Les études philosophiques 2:97 (2011).
- Purity of methods (with Mic Detlefsen). Philosophers' Imprint 11:2 (2011).
- Descartes and the cylindrical helix (with Paolo Mancosu). Historia Mathematica 37:3 (2010), 403-427.
- Proof theory in philosophy of mathematics. Philosophy Compass 5:4 (2010), 336-347.
- On formally measuring and eliminating extraneous notions in proofs. Philosophia Mathematica 17 (2009).
- Logical and semantic purity. Protosociology vol. 25 (2008), pp. 36-48; reprinted in Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism, Gerhard Preyer and Georg Peter (eds.), Ontos, 2008. (Reviewed here, here, and here)
- Possible m-diagrams of models of arithmetic. In Reverse Mathematics 2001, edited by Stephen Simpson, Lecture Notes in Logic 21, A.K. Peters Publishers / Association for Symbolic Logic, 2005, pp. 27-41.
- Arithmetical independence results using higher recursion theory. The Journal of Symbolic Logic 69:1 (2004) 1-9.
- Solovay's Theorem Cannot Be Simplified. Annals of Pure and Applied Logic 112 (2001). (Reviewed here)
Here are some videos of talks I've given.
Here are some book reviews I've written.
- Review of Jeremy Gray's Plato's Ghost: The Modernist Transformation of Mathematics, Philosophia Mathematica 20:2 (2012).
- Review of Marcus Giaquinto's Visual Thinking In Mathematics, Analysis 69 (2009), pp. 401-403.
- Review of José Ferreiros and Jeremy Gray's The Architecture of Modern Mathematics, Mathematical Intelligencer 30:4 (2008).
- Review of David Corfield's Toward a Philosophy of Real Mathematics, Mathematical Intelligencer 29:2 (2007).
- Review of Solomon Feferman's In The Light of Logic, Mathematical Intelligencer 27:4 (2005).
In recent years I've taught courses in logic, the history of modern philosophy, epistemology, and the philosophy of religion.