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Ideas for 'What is Logic?st1=Ian Hacking', 'Identity, Essence and Indiscernibility' and 'The Tarskian Turn'

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14 ideas

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845 The various logics are abstractions made from terms like 'if...then' in English [Hacking]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840 First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
13844 A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
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 / A. Overview of Logic / 7. Second-Order Logic
13842 Second-order completeness seems to need intensional entities and possible worlds [Hacking]
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
13837 With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839 Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
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 / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
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]