Combining Texts

All the ideas for 'fragments/reports', 'On the Question of Absolute Undecidability' and 'There is no a Priori'

expand these ideas     |    start again     |     specify just one area for these texts

---

10 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

17884

Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]

17893

'Reflection principles' say the whole truth about sets can't be captured [Koellner]

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

17894

We have no argument to show a statement is absolutely undecidable [Koellner]

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]

12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities

9354	Why should necessities only be knowable a priori? That Hesperus is Phosporus is known empirically [Devitt]

12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts

9353	We explain away a priori knowledge, not as directly empirical, but as indirectly holistically empirical [Devitt]

12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori

9356	The idea of the a priori is so obscure that it won't explain anything [Devitt]

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]