Ideas from 'Sets and Numbers' by Penelope Maddy [1981], by Theme Structure

[found in 'Philosophy of Mathematics: anthology' (ed/tr Jacquette,Dale) [Blackwell 2002,0-631-21870-x]].

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4. Formal Logic / F. Set Theory ST / 7. Natural Sets

17824

The master science is physical objects divided into sets

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

17825

Set theory (unlike the Peano postulates) can explain why multiplication is commutative

17826

Standardly, numbers are said to be sets, which is neat ontology and epistemology

17828

Numbers are properties of sets, just as lengths are properties of physical objects

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

17827

Sets exist where their elements are, but numbers are more like universals

17830

Number theory doesn't 'reduce' to set theory, because sets have number properties

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17823

If mathematical objects exist, how can we know them, and which objects are they?

6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival

17829

Number words are unusual as adjectives; we don't say 'is five', and numbers always come first