Combining Philosophers
Ideas for Einstein,A/Infeld,L, Keith Hossack and Galen Strawson
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8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10680
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The theory of the transfinite needs the ordinal numbers [Hossack]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10684
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I take the real numbers to be just lengths [Hossack]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
23626
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Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10674
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A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10681
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In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
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10685
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Set theory is the science of infinity [Hossack]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
23621
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Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
23622
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We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
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