Combining Philosophers
Ideas for Aeschylus, Michel Foucault and George Boolos
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14 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249
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Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
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10225
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Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro]
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10830
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Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
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10736
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Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo]
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10780
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Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829
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A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
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5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10697
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Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
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5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832
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'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
13671
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Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro]
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
10267
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We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
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10698
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Plural forms have no more ontological commitment than to first-order objects [Boolos]
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5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
7806
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Boolos invented plural quantification [Boolos, by Benardete,JA]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
10834
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Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
13841
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Why should compactness be definitive of logic? [Boolos, by Hacking]
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