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'fragments/reports', 'Problems of Philosophy' and 'What Required for Foundation for Maths?'
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12 ideas
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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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
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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
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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
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5395
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Demonstration always relies on the rule that anything implied by a truth is true [Russell]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
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5386
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Proper names are really descriptions, and can be replaced by a description in a person's mind [Russell]
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
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5385
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The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description [Russell]
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5. Theory of Logic / G. Quantification / 2. Domain of Quantification
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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
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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
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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
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17789
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No logic which can axiomatise arithmetic can be compact or complete [Mayberry]
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