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) numbers seem more like universals than particulars.

Gist of Idea

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


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]