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'fragments/reports', 'Modality' and 'On Second-Order Logic'
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8 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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14249
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Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
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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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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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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 / G. Quantification / 2. Domain of Quantification
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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
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5740
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Second-order logic needs second-order variables and quantification into predicate position [Melia]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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5741
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If every model that makes premises true also makes conclusion true, the argument is valid [Melia]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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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
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13841
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Why should compactness be definitive of logic? [Boolos, by Hacking]
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