more from Penelope Maddy

### Single Idea 17827

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory]

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 Reference

'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]**