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