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'Metaphysics', 'A Structural Account of Mathematics' and 'The Analects (Lunyu)'
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6 ideas
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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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 / b. Greek arithmetic
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Each many is just ones, and is measured by the one [Aristotle]
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Number is plurality measured by unity [Aristotle]
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The idea of 'one' is the foundation of number [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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Mathematics studies abstracted relations, commensurability and proportion [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
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We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
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