Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Minds, Brains and Science' and 'What is Cantor's Continuum Problem?'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

10868

The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]

13517

If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]

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 / a. Mathematical empiricism

10271

Basic mathematics is related to abstract elements of our empirical ideas [Gödel]