more from Penelope Maddy

Single Idea 18185

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

Full Idea

The single unified area of set theory provides a court of final appeal for questions of mathematical existence and proof.

Gist of Idea

Unified set theory gives a final court of appeal for mathematics


Penelope Maddy (Naturalism in Mathematics [1997], I.2)

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.26

A Reaction

Maddy's third benefit of set theory. 'Existence' means being modellable in sets, and 'proof' means being derivable from the axioms. The slightly ad hoc character of the axioms makes this a weaker defence.

Related Ideas

Idea 18183 Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]

Idea 18184 Making set theory foundational to mathematics leads to very fruitful axioms [Maddy]