Combining Texts
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'An Ontology of Art', 'Outlines of Pyrrhonism' and 'A Tour through Mathematical Logic'
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12 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
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13534
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In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS]
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13535
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First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS]
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5. Theory of Logic / B. Logical Consequence / 8. Material Implication
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12196
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A valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood' [Sext.Empiricus]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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13531
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Model theory reveals the structures of mathematics [Wolf,RS]
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13532
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Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS]
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13519
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Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS]
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13533
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First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
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13537
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An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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13539
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The LST Theorem is a serious limitation of first-order logic [Wolf,RS]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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13538
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If a theory is complete, only a more powerful language can strengthen it [Wolf,RS]
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5. Theory of Logic / K. Features of Logics / 10. Monotonicity
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13525
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Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS]
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5. Theory of Logic / L. Paradox / 7. Paradoxes of Time
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1902
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Since Socrates either died when he was alive (a contradiction) or died when he was dead (meaningless), he didn't die [Sext.Empiricus]
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