Volume 57, Issue 1, March 1997
Getting in Touch with Numbers
Intuition and Mathematical Platonism
Mathematics is about numbers, sets, functions, etc. and, according to one prominent view, these are abstract entities lacking causal powers and spatio-temporal location. If this is so, then it is a puzzle how we come to have knowledge of such remote entities. One suggestion is intuition. But ‘intuition’ covers a range of notions. This paper identifies and examines those varieties of intuition which are most likely to playa role in the acquisition of our mathematical knowledge, and argues that none of them, singly or in combination, can plausibly account for knowledge of abstract entities.