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'On the Question of Absolute Undecidability', 'Content Preservation' and 'Defending the Axioms'
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6 ideas
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 / 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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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
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The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
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