Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Truth and Predication' and 'Sets and Numbers'
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10 ideas
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 / 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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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17823
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If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
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6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
17829
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Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
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