Combining Texts
Ideas for
'Thinking About Mathematics', 'Liberal Individualism and Liberal Neutrality' and 'Investigations in the Foundations of Set Theory I'
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7 ideas
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
8764
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Categories are the best foundation for mathematics [Shapiro]
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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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8762
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Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
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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 / a. Structuralism
8760
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Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
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8761
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A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
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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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