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'On the Question of Absolute Undecidability', 'Mathematical logic and theory of types' and 'Understanding the Infinite'
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4 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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Mathematical proof by contradiction needs the law of excluded middle [Lavine]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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We have no argument to show a statement is absolutely undecidable [Koellner]
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
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The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
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