Intuition in Mathematics

In Barbara Held & Lisa Osbeck (eds.), Rational Intuition. Cambridge University Press (forthcoming)
Abstract
The literature on mathematics suggests that intuition plays a role in it as a ground of belief. This article explores the nature of intuition as it occurs in mathematical thinking. Section 1 suggests that intuitions should be understood by analogy with perceptions. Section 2 explains what fleshing out such an analogy requires. Section 3 discusses Kantian ways of fleshing it out. Section 4 discusses Platonist ways of fleshing it out. Section 5 sketches a proposal for resolving the main problem facing Platonists—the problem of explaining how our experiences make contact with mathematical reality.
Keywords Intuition  Mathematical Knowledge  Platonism
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