Combining Philosophers
Ideas for Anaxarchus, Augustin-Louis Cauchy and David Hilbert
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11 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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12461
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We believe all mathematical problems are solvable [Hilbert]
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12456
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I aim to establish certainty for mathematical methods [Hilbert]
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8717
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Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend]
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6. Mathematics / A. Nature of Mathematics / 2. Geometry
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13472
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Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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9633
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No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
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12460
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We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
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12462
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Only the finite can bring certainty to the infinite [Hilbert]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
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12455
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The idea of an infinite totality is an illusion [Hilbert]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
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12457
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There is no continuum in reality to realise the infinitely small [Hilbert]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
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18085
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Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
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18084
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When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
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