* offered this term (fall, 2009)
# U—undergraduate course, G—graduate course, B—open to both


Research:
Currently, I am working on a ‘truly’ naturalistic philosophy of mathematics. See the article [12] below for an introduction, and see the articles [3], [4] [8], [9], [10], [11] and the book draft (1) for more details. This research includes efforts to naturalize some related notions, in particular, content (or semantics, intentionality, truth, etc, see the articles [5], [6] and [7]) and modality (see the article [13]), which should belong to the philosophy of mind and the philosophy of language.

Book Draft:

(1) Strict Finitism and the Logic of Mathematical Applications.


Papers:

[15] 'Naturalized Truth and Plantinga's Argument Against Naturalism' (for June, 2009 Conference on Science, Philosophy and Belief at Peking University) 

[14] 'A strictly finitistic system for applied mathematics'

[13] 'A naturalistic interpretation of the Kripkean modality', Frontiers of Philosophy in China, Vol. 4 (2009), No. 3, 454-470.  http://www.springerlink.com/content/16m327v306316615

[12] ‘Introduction to a Naturalistic Philosophy of Mathematics’.

[11] ‘The Applicability of Mathematics as a Scientific and a Logical Problem’, forthcoming on Philosophia Mathematica. Online version: http://philmat.oxfordjournals.org/cgi/content/abstract/nkp014

[10] ‘Naturalism and the Apriority of Logic and Arithmetic’.

[9] ‘Naturalism and Objectivity in Mathematics’

[8] ‘On What Really Exist in Mathematics’

[7] ‘Truth and Serving the Biological Purpose’

[6] ‘On Some Puzzles about Concepts’

[5] ‘A Structural Theory of Content Naturalization’

[4] ‘Naturalism and Abstract Entities’

[3] ‘What Anti-realism in Philosophy of Mathematics Must Offer’, to appear on Synthese, special issue on analytic philosophy in China, online version: http://www.springerlink.com/content/w025726317224651/

[2] ‘Toward a constructive theory of unbounded linear operators on Hilbert spaces’, Journal of Symbolic Logic, 65(2000), no. 1.

[1] Strict Constructivism and the Philosophy of Mathematics, PhD dissertation, Princeton University, 2000.


Presentations/Reviews:

[ii] 'A strictly finitistic system for applied mathematics'

[i] ‘Review of Second Philosophy by P. Maddy’. International Studies in the Philosophy of Science, vol. 22(2008), no. 2, pp. 227-230.