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Ideas for 'Thinking About Mathematics', 'Economy and Society' and 'The Scope and Language of Science'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

8764	Categories are the best foundation for mathematics [Shapiro]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers

8762	Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

8463	Maths can be reduced to logic and set theory [Quine]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

8760	Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]

8761	A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]