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'A Structural Account of Mathematics', 'Vagueness' and 'Constitutional Code I'
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7 ideas
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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
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
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 / E. Structures of Logic / 6. Relations in Logic
9561
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The mathematics of relations is entirely covered by ordered pairs [Chihara]
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
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 / K. Features of Logics / 2. Consistency
9552
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Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
21599
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A sorites stops when it collides with an opposite sorites [Williamson]
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