Combining Texts
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'On the Question of Absolute Undecidability', 'Truth and Predication' and 'Sets and Numbers'
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7 ideas
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 / 6. Mathematics as Set Theory / a. Mathematics is set theory
17825
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Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
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17826
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Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
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17828
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Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
17827
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Sets exist where their elements are, but numbers are more like universals [Maddy]
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17830
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Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
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