more on this theme | more from this thinker
Full Idea
In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities.
Gist of Idea
Brouwer saw reals as potential, not actual, and produced by a rule, or a choice
Source
report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6
Book Ref
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.200
A Reaction
This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer.
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |