Full Idea
Frege opts for his famous definition of numbers in terms of extensions of the concept 'equal to the concept F', but he then (in 'Grundgesetze') needs a theory of extensions or classes, which he provided by means of Basic Law V.
Gist of Idea
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions
Source
report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' §1
Book Reference
Hale,B/Wright,C: 'The Reason's Proper Study' [OUP 2003], p.3