Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Remarks on the definition and nature of mathematics' and 'The Mind in Nature'

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5 ideas

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 / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17806

It is untenable that mathematics is general physical truths, because it needs infinity [Curry]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17808

Saying mathematics is logic is merely replacing one undefined term by another [Curry]