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Ideas for 'Metaphysics: the logical approach', 'Knowledge and the Philosophy of Number' and 'Introduction: Truth and Truth-Making'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

3332	Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

3330	Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA]

3337	Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA]

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

23621

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

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

23622

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