Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Philosophy of Mind (Encylopedia III)' and 'Ontology and Mathematical Truth'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
9965
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There couldn't just be one number, such as 17 [Jubien]
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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
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 / 7. Mathematical Structuralism / a. Structuralism
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The subject-matter of (pure) mathematics is abstract structure [Jubien]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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If we all intuited mathematical objects, platonism would be agreed [Jubien]
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9962
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How can pure abstract entities give models to serve as interpretations? [Jubien]
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9964
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Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
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