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'Thinking About Mathematics', 'Frege philosophy of mathematics' and 'The Upanishads'
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6 ideas
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
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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
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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 / 7. Mathematical Structuralism / a. Structuralism
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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
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9829
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The identity of a number may be fixed by something outside structure - by counting [Dummett]
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9828
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Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
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