Combining Philosophers
Ideas for David Hilbert, Isaac Beeckman and Euclid
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13 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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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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12456
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I aim to establish certainty for mathematical methods [Hilbert]
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12461
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We believe all mathematical problems are solvable [Hilbert]
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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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6297
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Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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9603
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An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
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9894
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A unit is that according to which each existing thing is said to be one [Euclid]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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8738
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Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
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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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