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Full Idea
A set of things is located where the aggregate of those things is located, ...but a number is simultaneously located at many different places (10 in my hand, and a baseball team) ...so numbers seem more like universals than particulars.
Gist of Idea
Sets exist where their elements are, but numbers are more like universals
Source
Penelope Maddy (Sets and Numbers [1981], III)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.349
A Reaction
My gut feeling is that Maddy's master idea (of naturalising sets by building them from ur-elements of natural objects) won't work. Sets can work fine in total abstraction from nature.
Related Idea
Idea 17824 The master science is physical objects divided into sets [Maddy]
| 16896 | If numbers can be derived from logic, then set theory is superfluous [Frege, by Burge] |
| 18161 | The theory of classes is superfluous in mathematics [Wittgenstein] |
| 8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
| 8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
| 9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
| 17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |
| 17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
| 10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
| 10222 | Mathematical foundations may not be sets; categories are a popular rival [Shapiro] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |