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'Thinking About Mathematics', 'Consciousness, Philosophy and Mathematics' and 'Parts of Classes'
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7 ideas
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
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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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Zermelo's model of arithmetic is distinctive because it rests on a primitive of set theory [Lewis]
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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
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Giving up classes means giving up successful mathematics because of dubious philosophy [Lewis]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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To be a structuralist, you quantify over relations [Lewis]
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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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A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
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