Combining Philosophers

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

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16 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
9722 Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
9718 Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9721 A logical truth or tautology is a logical consequence of the empty set [Enderton]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
9994 A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10158 A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
10162 Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10160 Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
10159 Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
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]