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Ideas for '', 'The Tarskian Turn' and 'The Confessions'

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10 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
15326 Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
15341 Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
15328 A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
15349 It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
15366 Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
15353 The first incompleteness theorem means that consistency does not entail soundness [Horsten]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
15355 Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten]