Combining Texts
Ideas for
'The Correspondence Theory of Truth', 'A Tour through Mathematical Logic' and 'Intro to 'Philosophy of Logic''
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14 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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9457
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The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette]
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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3746
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Logic seems to work for unasserted sentences [O'Connor]
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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 / I. Semantics of Logic / 5. Extensionalism
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9458
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Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette]
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5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
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9461
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Intensionalists say meaning is determined by the possession of properties [Jacquette]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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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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13519
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Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS]
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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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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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