more from Luitzen E.J. Brouwer

Single Idea 8728

[catalogued under 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism]

Full Idea

Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths.

Gist of Idea

Intuitionist mathematics deduces by introspective construction, and rejects unknown truths


Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.8

A Reaction

Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time!