Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Modern Philosophy:introduction and survey' and 'Identity and Reference'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

3907	Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton]

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 / 10. Constructivism / b. Intuitionism

3908	If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton]