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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
Source
Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2
Book Ref
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!
| 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| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |