Combining Philosophers

Ideas for Herbert B. Enderton, Clive Bell and Feferman / Feferman

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

display all the ideas for this combination of philosophers

---

8 ideas

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

9719	A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton]

5. Theory of Logic / K. Features of Logics / 4. Completeness

9720	A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton]

10161

If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]

5. Theory of Logic / K. Features of Logics / 6. Compactness

9995	Proof in finite subsets is sufficient for proof in an infinite set [Enderton]

5. Theory of Logic / K. Features of Logics / 7. Decidability

9996	Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton]

10156

'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]

10155

Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]

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

9997	For a reasonable language, the set of valid wff's can always be enumerated [Enderton]