Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'What are Sets and What are they For?' and 'Sapiens: brief history of humankind'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
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If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
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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 / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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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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Arithmetical undecidability is always settled at the next stage up [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
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