Single Idea 10252

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

Full Idea

If the Axiom of Choice says we can choose one member from each of a set of non-empty sets and put the chosen elements together in a set, this licenses the constructor to do an infinite amount of choosing.

Gist of Idea

The Axiom of Choice seems to license an infinite amount of choosing

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 6.3)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.188


A Reaction

This is one reason why the Axiom was originally controversial, and still is for many philosophers.