Full Idea
On Frege's approach (of accepting abstract objects if they fall under a concept) the existence of the number 0, from which the series of numbers starts, is of course guaranteed by the citation of a concept under which nothing falls.
Gist of Idea
If objects exist because they fall under a concept, 0 is the object under which no objects fall
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
Book Reference
Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.504
A Reaction
Frege cites the set of all non-self-identical objects, but he could have cited the set of circular squares. Given his Russell Paradox problems, this whole claim is thrown in doubt. Actually doesn't Frege's view make 0 impossible? Am I missing something?