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'fragments/reports', 'The Runabout Inference Ticket' and 'On Second-Order Logic'
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12 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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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 / B. Logical Consequence / 5. Modus Ponens
8078
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Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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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 / 2. Excluded Middle
6023
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Every proposition is either true or false [Chrysippus, by Cicero]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
17896
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We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap]
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17898
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Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN]
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11021
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Prior rejected accounts of logical connectives by inference pattern, with 'tonk' his absurd example [Prior,AN, by Read]
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13836
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Maybe introducing or defining logical connectives by rules of inference leads to absurdity [Prior,AN, by Hacking]
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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 / 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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