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Ideas for 'On the Question of Absolute Undecidability', 'works' and 'Replies on 'Limits of Abstraction''

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8 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

10573

Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts

10575

Why should a Dedekind cut correspond to a number? [Fine,K]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero

10574

Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890

There are at least eleven types of large cardinal, of increasing logical strength [Koellner]

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 / b. Mathematics is not set theory

10560

Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

10568

Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]