more from Penelope Maddy

### Single Idea 13025

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX]

Full Idea

Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule.

Gist of Idea

Modern views say the Choice set exists, even if it can't be constructed

Source

Penelope Maddy (Believing the Axioms I [1988], §1.7)

Book Reference

-: 'Journal of Symbolic Logic' [-], p.488

A Reaction

This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence?