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6 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
9188
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Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
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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 / 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 / I. Semantics of Logic / 2. Formal Truth
10620
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Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17883
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Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
6407
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The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
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