Combining Texts
Ideas for
'The Evolution of Logic', 'Philosophical Logic: Intro to Advanced Topics' and 'Machine Man'
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13 ideas
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
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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 / 6. Classical Logic
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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 / D. Assumptions for Logic / 4. Identity in Logic
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Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]
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5. Theory of Logic / G. Quantification / 3. Objectual Quantification
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The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD]
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Model theory studies how set theory can model sets of sentences [Hart,WD]
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Model theory is mostly confined to first-order theories [Hart,WD]
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Models are ways the world might be from a first-order point of view [Hart,WD]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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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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5. Theory of Logic / K. Features of Logics / 6. Compactness
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First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD]
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5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
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Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD]
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
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The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD]
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