Combining Texts

Ideas for 'works', 'Continuity and Irrational Numbers' and 'Understanding the Infinite'

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5 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

15926

Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine]

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

15934

Mathematical proof by contradiction needs the law of excluded middle [Lavine]

5. Theory of Logic / K. Features of Logics / 8. Enumerability

10082

There are infinite sets that are not enumerable [Cantor, by Smith,P]

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox

13483

Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD]

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox

8710	The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend]