Full Idea
Frege's root confusion (over abstraction by identity, and other things) was to believe that he could simultaneously fix the truth-conditions of such statements and the domain over which the individual variables were to range.
Gist of Idea
You can't simultaneously fix the truth-conditions of a sentence and the domain of its variables
Source
comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64-68) by Michael Dummett - Frege philosophy of mathematics Ch.18
Book Reference
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.232
A Reaction
This strikes me as a wonderfully penetrating criticism, but it also seems to me to threaten Dummett's whole programme of doing ontology through language. If a quantified sentences needs a domain, how do you first decide your domain?