more from Luitzen E.J. Brouwer

Single Idea 18247

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy]

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


report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6

Book Reference

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.