Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'A Completeness Theorem in Modal Logic' and 'Lectures 1930-32 (student notes)'

expand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

18738

We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

18708

Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein]

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]