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'', 'A Mathematical Introduction to Logic (2nd)' and 'Pyrrhonian Arguments (frags)'
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12 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton]
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If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
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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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
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The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
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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
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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
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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
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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
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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
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For a reasonable language, the set of valid wff's can always be enumerated [Enderton]
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