Single Idea 10542

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

Full Idea

We may suppose that with each set is associated an object as its cardinal number, but we have no systematic way, without appeal to the Axiom of Choice, of selecting a representative set of each cardinality.

Gist of Idea

To associate a cardinal with each set, we need the Axiom of Choice to find a representative

Source

Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)

Book Reference

Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.484