more from Penelope Maddy

Single Idea 17826

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

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


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

Book Reference

'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]