Combining Texts

Ideas for 'fragments/reports', 'The Justification of Deduction' and 'Vagueness'

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13 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11066 Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
19058 Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
21611 Formal semantics defines validity as truth preserved in every model [Williamson]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
8078 Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
21606 'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
6023 Every proposition is either true or false [Chrysippus, by Cicero]
21605 Excluded Middle is 'A or not A' in the object language [Williamson]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
21612 Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [Williamson]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
19063 Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett]
19059 In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett]
19062 Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett]
5. Theory of Logic / K. Features of Logics / 4. Completeness
19065 Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
21599 A sorites stops when it collides with an opposite sorites [Williamson]