Combining Texts
Ideas for
'Mahaprajnaparamitashastra', 'What Required for Foundation for Maths?' and 'Principia Mathematica'
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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
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 / 7. Strict Implication
8204
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Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
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9359
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Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
21707
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Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
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5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
10036
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In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
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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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