Combining Philosophers
Ideas for Archimedes, Ernst Zermelo and John L. Pollock
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6 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
13487
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In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity
15897
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Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007
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Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
18178
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For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13027
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Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9627
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Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
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