Combining Philosophers
Ideas for Richard Cumberland, Prodicus and Herbert B. Enderton
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9 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
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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 / K. Features of Logics / 3. Soundness
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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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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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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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