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Ideas for
'On the Question of Absolute Undecidability', 'Minds, Brains and Science' and 'Metaphysics: the logical approach'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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3332
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Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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3330
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Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA]
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3337
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Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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17890
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There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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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
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17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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