Combining Texts
Ideas for
'Parmenides', 'Function and Concept' and 'A Mathematical Introduction to Logic (2nd)'
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13 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 / E. Structures of Logic / 5. Functions in Logic
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First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
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5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
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Relations are functions with two arguments [Frege]
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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 / 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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5. Theory of Logic / L. Paradox / 3. Antinomies
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Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle]
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Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
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