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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 Ref
'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]
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |