Combining Philosophers
Ideas for Luitzen E.J. Brouwer, Michael Potter and Johann Winckelmann
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11 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
18119
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Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18247
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Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712
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If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
12451
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Scientific laws largely rest on the results of counting and measuring [Brouwer]
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18118
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Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17882
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It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
22310
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The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter]
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6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
22298
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Why is fictional arithmetic applicable to the real world? [Potter]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
12454
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Intuitionists only accept denumerable sets [Brouwer]
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12453
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Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
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8728
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Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
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