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'fragments/reports', 'Metaphysics of Morals I: Doctrine of Right' and 'Philosophical Logic'
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20 ideas
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
15404
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Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess]
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
15405
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Classical logic neglects the non-mathematical, such as temporality or modality [Burgess]
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15427
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The Cut Rule expresses the classical idea that entailment is transitive [Burgess]
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15421
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Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess]
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5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
15403
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Philosophical logic is a branch of logic, and is now centred in computer science [Burgess]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
8078
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Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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Every proposition is either true or false [Chrysippus, by Cicero]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
15407
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Formalising arguments favours lots of connectives; proving things favours having very few [Burgess]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
15424
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Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
15409
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All occurrences of variables in atomic formulas are free [Burgess]
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
15414
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The denotation of a definite description is flexible, rather than rigid [Burgess]
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5. Theory of Logic / H. Proof Systems / 1. Proof Systems
15406
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'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess]
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5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
15426
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We can build one expanding sequence, instead of a chain of deductions [Burgess]
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15425
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The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
15408
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'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
15418
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Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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We only need to study mathematical models, since all other models are isomorphic to these [Burgess]
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15412
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Models leave out meaning, and just focus on truth values [Burgess]
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15416
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We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess]
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