Full Idea
The intuitionist recognises only the existence of denumerable sets.
Gist of Idea
Intuitionists only accept denumerable sets
Source
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]