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'fragments/reports', 'The Justification of Deduction' and 'Gentzen's Analysis of First-Order Proofs'
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9 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11066
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Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna]
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13831
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Logic is based on transitions between sentences [Prawitz]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
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Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13823
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In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
19063
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Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett]
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19059
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In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett]
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19062
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Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
19065
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Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett]
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