Combining Philosophers

Ideas for Eubulides, Rahulabhadra and Kurt Gdel

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

display all the ideas for this combination of philosophers

---

7 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

17886

The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner]

5. Theory of Logic / K. Features of Logics / 2. Consistency

10071

Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P]

5. Theory of Logic / K. Features of Logics / 3. Soundness

19123

If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh]

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

17883

Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]

10621

Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel]

17888

The undecidable sentence can be decided at a 'higher' level in the system [Gödel]

5. Theory of Logic / K. Features of Logics / 8. Enumerability

10038

A logical system needs a syntactical survey of all possible expressions [Gödel]