display all the ideas for this combination of philosophers
5 ideas
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! |
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. |
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. |
7555 | Zeno achieved the statement of the problems of infinitesimals, infinity and continuity [Russell on Zeno of Citium] |
Full Idea: Zeno was concerned with three increasingly abstract problems of motion: the infinitesimal, the infinite, and continuity; to state the problems is perhaps the hardest part of the philosophical task, and this was done by Zeno. | |
From: comment on Zeno (Citium) (fragments/reports [c.294 BCE]) by Bertrand Russell - Mathematics and the Metaphysicians p.81 | |
A reaction: A very nice tribute, and a beautiful clarification of what Zeno was concerned with. |