Combining Texts
Ideas for
'Defending the Axioms', 'The Iliad' and 'On the Infinite'
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12 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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 / 5. The Infinite / a. The Infinite
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No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
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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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The idea of an infinite totality is an illusion [Hilbert]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
12457
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There is no continuum in reality to realise the infinitely small [Hilbert]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614
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The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
12459
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The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
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6. Mathematics / C. Sources of Mathematics / 8. Finitism
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Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
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