Full Idea
Dummett claims that a realistic conception of reference can be sustained for concrete objects (possible objects of ostension), but breaks down for (putative) names of (pure) abstract objects.
Gist of Idea
A realistic view of reference is possible for concrete objects, but not for abstract objects
Source
report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II
A Reaction
An extremely hard claim to evaluate, because a case must first be made for abstract objects which are fundamentally different in kind. Realistic reference must certainly deal with these hard cases. Field rejects Dummett's abstract points.