more from Luitzen E.J. Brouwer

Single Idea 12454

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

Full Idea

The intuitionist recognises only the existence of denumerable sets.

Gist of Idea

Intuitionists only accept denumerable sets


Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.80

A Reaction

That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days.

Related Idea

Idea 12543 Intuition gives us direct and certain knowledge of what is obvious [Locke]