If you look at the literature on mathematics – the prefaces to math textbooks, discussion pieces by mathematicians, mathematical popularizations and biographies, philosophical works about the nature of mathematics, psychological studies of mathematical cognition, educational material on the teaching of mathematics – you will regularly find talk about intuition. This suggests that there is some role intuition plays in mathematics, specifically as a ground of belief about mathematical matters. The aim of the present chapter is to stake out some ideas about how best to understand intuition as it occurs in mathematics, in other words, about the nature of mathematical intuition.A closer look at the textbooks, discussion pieces, popularizations and biographies, philosophical works, psychological studies, and educational material reveals, however, that there are a number of distinct notions that correspond to talk about mathematical intuition. The first order of business will be to draw some distinctions between these notions and pick an appropriate focus for our present inquiry. That is the aim of Section 1. The notion I will focus on is one according to which mathematical intuition is a kind of experience that is like sensory perception in giving its subjects non-inferential access to a world of facts, but different from sensory perception in that the facts are about abstract mathematical objects rather than concrete material objects. Let us call this the perceptualist view of intuition. It has been the dominant conception of mathematical intuition in the Western philosophical tradition since Plato, and the alternatives one finds all more or less derive from it, as I will indicate.
|Original language||English (US)|
|Title of host publication||Rational Intuition|
|Subtitle of host publication||Philosophical Roots, Scientific Investigations|
|Publisher||Cambridge University Press|
|Number of pages||18|
|State||Published - Jan 1 2014|
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