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'German Philosophy: a very short introduction', 'Introduction to Mathematical Logic' and 'works'
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9 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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17758
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Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
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17755
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Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
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17756
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The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
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17760
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Two infinite ordinals can represent a single infinite cardinal [Walicki]
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17757
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Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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17762
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In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
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17754
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Inductive proof depends on the choice of the ordering [Walicki]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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8466
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For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein]
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8467
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Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein]
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