Combining Texts
Ideas for
'Through the Looking Glass', 'Introduction to the Philosophy of Mathematics' and 'Review of Husserl's 'Phil of Arithmetic''
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14 ideas
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 / 4. Using Numbers / e. Counting by correlation
17446
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Counting rests on one-one correspondence, of numerals to objects [Frege]
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9582
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Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege]
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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 / c. Fregean numbers
9586
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In a number-statement, something is predicated of a concept [Frege]
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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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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
9580
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Our concepts recognise existing relations, they don't change them [Frege]
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9589
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Numbers are not real like the sea, but (crucially) they are still objective [Frege]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
9577
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The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege]
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