Combining Texts
Ideas for
'What is Logic?st1=Ian Hacking', 'The Discourses' and 'Philosophical Logic: Intro to Advanced Topics'
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11 ideas
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845
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The various logics are abstractions made from terms like 'if...then' in English [Hacking]
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13850
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In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward]
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5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840
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First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
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13844
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A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
13849
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Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13842
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Second-order completeness seems to need intensional entities and possible worlds [Hacking]
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5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
13851
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Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13837
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With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839
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Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843
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If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
13852
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Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward]
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