Single Idea 13461

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

Full Idea

When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice.

Gist of Idea

We can choose from finite and evident sets, but not from infinite opaque ones

Source

William D. Hart (The Evolution of Logic [2010], 1)

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.27


A Reaction

The socks example in from Russell 1919:126.