Full Idea
The set theory axioms developed in producing foundations for mathematics also have strong consequences for existing fields, and produce a theory that is immensely fruitful in its own right.
Gist of Idea
Making set theory foundational to mathematics leads to very fruitful axioms
Source
Penelope Maddy (Naturalism in Mathematics [1997], I.2)
Book Reference
Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.26
A Reaction
[compressed] Second of Maddy's three benefits of set theory. This benefit is more questionable than the first, because the axioms may be invented because of their nice fruit, instead of their accurate account of foundations.
Related Ideas
Idea 18183 Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]
Idea 18185 Unified set theory gives a final court of appeal for mathematics [Maddy]
Idea 18189 ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]