Combining Philosophers

Ideas for Anaxarchus, Anon (Tor) and Luitzen E.J. Brouwer

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4 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
18119 Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
     Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language.
     From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1
     A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking!
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18247 Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
     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.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
12451 Scientific laws largely rest on the results of counting and measuring [Brouwer]
     Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring.
     From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77)
     A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'.
18118 Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
     Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals.
     From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1
     A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses.