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'fragments/reports', 'The Tarskian Turn' and 'On the General Idea of Proof Theory'
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11 ideas
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
15326
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Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten]
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13827
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Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
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Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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15341
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Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
6023
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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 / 8. Theories in Logic
15328
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A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
15349
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It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
15366
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Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13826
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Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
15353
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The first incompleteness theorem means that consistency does not entail soundness [Horsten]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten]
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