Full Idea
The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.
Clarification
'Predicative' definitions introduce a new predicate
Gist of Idea
Hume's Principle is either adequate for number but fails to define properly, or vice versa
Source
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
Book Reference
-: 'Philosophical Studies' [-], p.312
A Reaction
I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.