Ideas from 'works' by Luitzen E.J. Brouwer [1930], by Theme Structure

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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
For intuitionists excluded middle is an outdated historical convention
                        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.
                        From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2
                        A reaction: [Brouwer 1952:510-11]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Brouwer saw reals as potential, not actual, and produced by a rule, or a choice
                        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.
                        From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6
                        A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer.