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15941 | For intuitionists excluded middle is an outdated historical convention |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] |
18247 | 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. |