Full Idea
It is valuable to know that a theory is complete, because then we know it cannot be strengthened without passing to a more powerful language.
Gist of Idea
If a theory is complete, only a more powerful language can strengthen it
Source
Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.5)
Book Reference
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.191