Combining Philosophers
Ideas for Sebastian Gardner, Timothy Williamson and Robert S. Wolf
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19 ideas
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
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6858
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Formal logic struck me as exactly the language I wanted to think in [Williamson]
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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 / B. Logical Consequence / 4. Semantic Consequence |=
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21611
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Formal semantics defines validity as truth preserved in every model [Williamson]
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5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
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21606
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'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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21605
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Excluded Middle is 'A or not A' in the object language [Williamson]
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5. Theory of Logic / G. Quantification / 1. Quantification
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18492
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Not all quantification is either objectual or substitutional [Williamson]
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5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
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15136
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Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson]
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5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
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15138
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Not all quantification is objectual or substitutional [Williamson]
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
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21612
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Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [Williamson]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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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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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 / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
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21599
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A sorites stops when it collides with an opposite sorites [Williamson]
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