Full Idea
Objections to Frege's argument for abstract objects: that the objects would not have the right sort of independence; that we could have no knowledge of them; that the singular term statements can't be had; that thoughts of abstracta can't be identified.
Gist of Idea
Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated
Source
Bob Hale (Abstract Objects [1987], Ch.1)
Book Reference
Hale,Bob: 'Abstract Objects' [Blackwell 1987], p.13
A Reaction
[compressed] [See Idea 10309 for the original argument] It is helpful to have this list, even if Hale rejects them all. They are also created but then indestructible, and exist in unlimited profusion, and seem relative to a language. Etc!
Related Idea
Idea 10309 Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Frege, by Hale]