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'Clitophon', 'Logicism in the 21st Century' and 'Introduction to Mathematical Logic'
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11 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 / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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8784
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Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
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8787
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The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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8788
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Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
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8783
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Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
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