more from Penelope Maddy

### Single Idea 13026

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

Full Idea

Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic.

Gist of Idea

A large array of theorems depend on the Axiom of Choice

Source

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

Book Reference

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

A Reaction

The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking.