Combining Texts
Ideas for
'Why coherence is not enough', 'Investigations in the Foundations of Set Theory I' and 'Essay Conc Human Understanding (2nd Ed)'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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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 / 3. Nature of Numbers / m. One
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12488
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The idea of 'one' is the simplest, most obvious and most widespread idea [Locke]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
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12489
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If there were real infinities, you could add two together, which is ridiculous [Locke]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
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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
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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
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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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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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12556
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Mathematics is just about ideas, so whether circles exist is irrelevant [Locke]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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7782
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Every simple idea we ever have brings the idea of unity along with it [Locke]
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