Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Action' and 'The Boundary Stones of Thought'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

18842

Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt]

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 / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals

18834

Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

18846

Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt]

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]