Combining Texts
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'Parmenides', 'A Tour through Mathematical Logic' and 'Metaphysics: the logical approach'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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3332
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Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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3330
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Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA]
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3337
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Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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13530
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An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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13518
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Modern mathematics has unified all of its objects within set theory [Wolf,RS]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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16150
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One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
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