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Ideas for 'On the Question of Absolute Undecidability', 'fragments/reports' and 'Sets and Numbers'

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7 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

17887

PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

17891

Arithmetical undecidability is always settled at the next stage up [Koellner]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

17825

Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]

17826

Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]

17828

Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory

17827

Sets exist where their elements are, but numbers are more like universals [Maddy]

17830

Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]