Single Idea 12321

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

Full Idea

The axiom of choice actually amounts to admitting an absolutely indeterminate infinite set whose existence is asserted albeit remaining linguistically indefinable. On the other hand, as a process, it is unconstructible.

Gist of Idea

The axiom of choice must accept an indeterminate, indefinable, unconstructible set

Source

Alain Badiou (Briefings on Existence [1998], 2)

Book Reference

Badiou,Alain: 'Briefings on Existence', ed/tr. Madarsz,Norman [SUNY 2006], p.52


A Reaction

If only constructible sets are admitted (see 'V = L') then there is a contradiction.