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'fragments/reports', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'On the Question of Absolute Undecidability'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
18252
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Real numbers are ratios of quantities, such as lengths or masses [Frege]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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 / 1. Foundations for Mathematics
18271
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We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
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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 / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10623
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Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
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9975
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Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18165
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My Basic Law V is a law of pure logic [Frege]
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