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'fragments/reports', 'Categories' and 'Introduction to the Philosophy of Mathematics'
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11 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
11044
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One is prior to two, because its existence is implied by two [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17928
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Ordinal numbers represent order relations [Colyvan]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
11042
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Parts of a line join at a point, so it is continuous [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17923
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Intuitionists only accept a few safe infinities [Colyvan]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
17941
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Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17922
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Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17936
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Transfinite induction moves from all cases, up to the limit ordinal [Colyvan]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
11041
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Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17940
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Most mathematical proofs are using set theory, but without saying so [Colyvan]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
17931
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Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
17932
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If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan]
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