Kitcher, Mathematical Intuition, and Experience

Philosophia Mathematica 15 (2):227-237 (2007)
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Abstract

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

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Mark McEvoy
Hofstra University