### 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