Single Idea 12420

[catalogued under 6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics]

Full Idea

If mathematical statements are don't merely report features of transient and private mental entities, it is unclear how pure intuition generates mathematical knowledge. But if they are, they express different propositions for different people and times.

Gist of Idea

If mathematics comes through intuition, that is either inexplicable, or too subjective

Source

Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.1)

Book Reference

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.50


A Reaction

This seems to be the key dilemma which makes Kitcher reject intuition as an a priori route to mathematics. We do, though, just seem to 'see' truths sometimes, and are unable to explain how we do it.