Full Idea
Frege's argument for abstract objects is: 1) singular terms in true expressions must denote objects, 2) numerals function as singular terms, 3) there must exist numbers denoted by those expressions.
Gist of Idea
Frege says singular terms denote objects, numerals are singular terms, so numbers exist
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Bob Hale - Abstract Objects Ch.1
Book Reference
Hale,Bob: 'Abstract Objects' [Blackwell 1987], p.11
A Reaction
[compressed] Given that most of the singular term usages can be rephrased adjectively, this strikes me as a weak argument, though Hale pins his whole book on it.