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'works', 'What Required for Foundation for Maths?' and 'The Problem of Empty Names'
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13 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
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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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Only second-order logic can capture mathematical structure up to isomorphism [Mayberry]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
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'I' is the perfect name, because it denotes without description [Derrida]
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Names have a subjective aspect, especially the role of our own name [Derrida]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
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Even Kripke can't explain names; the word is the thing, and the thing is the word [Derrida]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
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Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
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5. Theory of Logic / G. Quantification / 2. Domain of Quantification
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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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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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'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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'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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No logic which can axiomatise arithmetic can be compact or complete [Mayberry]
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