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
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Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
9718
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Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9721
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A logical truth or tautology is a logical consequence of the empty set [Enderton]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
9994
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A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10158
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A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
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10162
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Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10160
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Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
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10159
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Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
9719
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A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
9720
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A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton]
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10161
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If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
9995
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Proof in finite subsets is sufficient for proof in an infinite set [Enderton]
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5. Theory of Logic / K. Features of Logics / 7. Decidability
9996
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Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton]
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10156
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'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
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10155
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Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
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5. Theory of Logic / K. Features of Logics / 8. Enumerability
9997
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For a reasonable language, the set of valid wff's can always be enumerated [Enderton]
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