Combining Philosophers
Ideas for Anaxarchus, Michal Walicki and Michael Potter
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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 / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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10712
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If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
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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 / d. Peano arithmetic
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17882
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It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
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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 / 7. Formalism
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22310
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The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter]
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6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
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22298
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Why is fictional arithmetic applicable to the real world? [Potter]
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