Full Idea
An adequate definition of truth can only be given for the fragment of our language that does not contain the truth predicate. A model can never encompass the whole of the domain of discourse of our language. The axiomatic approach avoids these problems.
Gist of Idea
Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models
Source
Leon Horsten (The Tarskian Turn [2011], 10.1)
Book Reference
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.141