more from Penelope Maddy

Single Idea 17828

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory]

Full Idea

I propose that ...numbers are properties of sets, analogous, for example, to lengths, which are properties of physical objects.

Gist of Idea

Numbers are properties of sets, just as lengths are properties of physical objects


Penelope Maddy (Sets and Numbers [1981], III)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.349

A Reaction

Are lengths properties of physical objects? A hole in the ground can have a length. A gap can have a length. Pure space seems to contain lengths. A set seems much more abstract than its members.