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'fragments/reports', 'What Required for Foundation for Maths?' and 'Mathematical logic and theory of types'
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12 ideas
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
17786
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The mainstream of modern logic sees it as a branch of mathematics [Mayberry]
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5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
17788
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First-order logic only has its main theorems because it is so weak [Mayberry]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
17791
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Only second-order logic can capture mathematical structure up to isomorphism [Mayberry]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
8078
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Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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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 / G. Quantification / 2. Domain of Quantification
17787
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Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17790
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No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17779
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'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry]
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17778
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Axiomatiation relies on isomorphic structures being essentially the same [Mayberry]
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17780
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'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
17789
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No logic which can axiomatise arithmetic can be compact or complete [Mayberry]
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
6407
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The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
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