Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Paradoxes of the Infinite' and 'On the Infinite'
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13 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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A truly infinite quantity does not need to be a variable [Bolzano]
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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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The idea of an infinite totality is an illusion [Hilbert]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
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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 / 4. Axioms for Number / d. Peano arithmetic
17887
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PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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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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