Combining Philosophers

Ideas for Luitzen E.J. Brouwer, Paul Ricoeur and Baruch de Spinoza

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10 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
17185 Mathematics deals with the essences and properties of forms [Spinoza]
18119 Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
17222 The sum of its angles follows from a triangle's nature [Spinoza]
17197 The idea of a triangle involves truths about it, so those are part of its essence [Spinoza]
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 / 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]