Combining Texts
Ideas for
'Saundaranandakavya', 'Knowledge and the Philosophy of Number' and 'Letters to Russell'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
18253
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I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
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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 / 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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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18166
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The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
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