more on this theme | more from this text
Full Idea
From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth.
Gist of Idea
For intuitionists excluded middle is an outdated historical convention
Source
Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2
Book Ref
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.179
A Reaction
[Brouwer 1952:510-11]
Related Idea
Idea 9195 Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
| 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| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |