Combining Philosophers

Ideas for Luitzen E.J. Brouwer, Stephen Read and Thomas Grundmann

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11 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
18119 Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
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]
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]
18118 Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
11025 Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10979 Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read]
10980 Second-order arithmetic covers all properties, ensuring categoricity [Read]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
10997 Von Neumann numbers are helpful, but don't correctly describe numbers [Read]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
12454 Intuitionists only accept denumerable sets [Brouwer]
12453 Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
8728 Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]