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'Thinking About Mathematics', 'A Structural Account of Mathematics' and 'fragments/reports'
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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 / 3. Axioms for Geometry
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9553
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Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
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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 / c. Nominalist structuralism
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10192
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We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
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