Combining Texts

Ideas for 'A Short History of Ethics', 'Identity and Existence in Logic' and 'Knowledge and the Philosophy of Number'

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3 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity

23626

Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory

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Numbers are properties, not sets (because numbers are magnitudes) [Hossack]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

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We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]