Single Idea 18139

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

Full Idea

The usual accounts of ZF are not restricted to subsets that we can describe, and that is what justifies the axiom of choice.

Gist of Idea

The Axiom of Choice relies on reference to sets that we are unable to describe

Source

David Bostock (Philosophy of Mathematics [2009], 8.4 n36)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.256


A Reaction

This contrasts interestingly with predicativism, which says we can only discuss things which we can describe or define. Something like verificationism hovers in the background.

Related Idea

Idea 18136 If we can only think of what we can describe, predicativism may be implied [Bostock]