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Full Idea
The standard account of the relationship between numbers and sets is that numbers simply are certain sets. This has the advantage of ontological economy, and allows numbers to be brought within the epistemology of sets.
Gist of Idea
Standardly, numbers are said to be sets, which is neat ontology and epistemology
Source
Penelope Maddy (Sets and Numbers [1981], III)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.347
A Reaction
Maddy votes for numbers being properties of sets, rather than the sets themselves. See Yourgrau's critique.
Related Idea
Idea 17823 If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |