Full Idea
A standard objection to minimalist truth is the 'incompleteness objection'. Since there are propositions inexpressible in present English the concept of truth isn't captured by all the instances of the Tarski biconditional.
Clarification
The Tarksi biconditional is "'P' is true iff P"
Gist of Idea
Instances of minimal truth miss out propositions inexpressible in current English
Source
Thomas Hofweber (Inexpressible Properties and Propositions [2006], 5.3)
Book Reference
'Oxford Studies in Metaphysics vol.2', ed/tr. Zimmerman,Dean W. [OUP 2006], p.195
A Reaction
Sounds like a good objection.