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Philosophia Mathematica Advance Access originally published online on March 23, 2007
Philosophia Mathematica 2007 15(2):227-237; doi:10.1093/philmat/nkm014
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Copyright © The Author 2007. Published by Oxford University Press.

Kitcher, Mathematical Intuition, and Experience{dagger}

Mark McEvoy*

*Department of Philosophy, Hofstra University, Hempstead, New York 11549-1000, U.S.A.

Correspondence: phimvm{at}hofstra.edu

Mathematical apriorists sometimes hold that our non-derived mathematical beliefs are warranted by mathematical intuition. Against this, Philip Kitcher has argued that if we had the experience of encountering mathematical experts who insisted that an intuition-produced belief was mistaken, this would undermine that belief. Since this would be a case of experience undermining the warrant provided by intuition, such warrant cannot be a priori.

I argue that this leaves untouched a conception of intuition as merely an aspect of our ordinary ability to reason. Thus the apriorist may still hold that some mathematical beliefs are warranted by intuition.

{dagger} I would like to thank an anonymous referee for Philosophia Mathematica and an audience at the Spring 2006 Long Island Philosophy Society/New Jersey Regional Philosophical Association conference for helpful comments.


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