My work began from methodological questions in the foundations of set theory, especially how new axioms can be properly criticized or defended. This focused inquiry led to more general questions in the metaphysics and epistemology of mathematics and logic, and the relations of these subjects to natural science. Progress on all this seemed to me to require some attention to the methodology of philosophy itself; I’ve been especially interested in naturalism, but also logical positivism, ordinary language philosophy and its descendents, various ‘therapeutic’ approaches, etc. -- and in radical skepticism as a diagnostic tool for comparing and contrasting these schools of meta-philosophical thought. This is coupled with an amateur’s historical interest in such figures as Descartes, Hume, Reid, Kant, Frege, Wittgenstein, Moore, Austin, Carnap and Quine.
Here's the syllabus for the current seminar:
A few recent seminars:
- Conceptual Analysis -- Fall 2012/Winter 2013
- Philosophy of Perception -- Fall 2011/Winter 2012
- Philosophy of Logic -- Fall 2010/Winter 2011
- Philosophies of common sense -- Fall 2009/Winter 2010
- Defending the Axioms -- Winter 2009
- Skepticism, naturalism and therapy -- Fall 2007/Winter 2008
- Philosophy of Mathematics -- Fall 2006/Winter 2007
- Philosophy of Logic -- Fall 2005/Winter 2006
- Word - World Connections -- Fall 2004/Winter 2005
- Naturalism -- Fall 2003/Winter 2004
- Philosophy of logic -- Fall 2002/Winter 2003
- Indeterminacy -- Winter 2002
- The role of mathematics in applications -- Fall 2001
- Fictionalism -- Spring 2001
- 'The philosophy of logic', ASL retiring presidential address, Bulletin of Symbolic Logic, 2012.
- 'Naturalism and common sense', Analytic Philosophy, Volume 52, issue 1, March 2011, pp. 2-34.
- 'Naturalism, transcendentalism and therapy', in J. Smith and P. Sullivan, eds., Transcendental Philosophy and Naturalism, Oxford University Press, 2011.
- 'How applied mathematics became pure', The Review of Sybolic Logic, 2008.
- Second Philosophy, Oxford 2007.
- 'Mathematical existence', Bulletin of Symbolic Logic, September 2005.
- 'Second philosophy', Lakatos Award Lecture, published in Journal of Indian Council of Philosophical Research, July-September 2003
- 'Three forms of naturalism', in S. Shapiro, ed., Oxford Handbook of Philosophy of Logic and Mathematics.
- 'A naturalistic look at logic', Proceedings of the APA, November 2002.
- 'Some naturalistic reflections on set theoretic method', Topoi, 2001.
- 'Naturalism: friends and foes', in J. Tomberlin, ed., Philosophical Perspectives 15, Metaphysics 2001, Blackwell 2001.
- 'Naturalism and the a priori', in P. Boghossian and C. Peacocke, eds., New Essays on the A Priori, Oxford, 2000.
- 'Logic and the discursive intellect', Notre Dame Journal of Formal Logic, 1999.
- Naturalism in Mathematics, Oxford 1997.
- 'Wittgenstein's anti-philosophy of mathematics', in J. Czermak and K. Paul, eds., Wittgenstein's Philosophy of Mathematics, 1993.
- Realism in Mathematics, Oxford 1990.
- 'Believing the axioms, Part I' , and 'Believing the axioms, Part II' , Journal of Symbolic Logic, 1988. (For a copy with corrections, click here)