Full Idea
No nice theory can define truth for its own language.
Clarification
[an extensive discussion of 'nice' precedes this theorem]
Gist of Idea
No nice theory can define truth for its own language
Source
Peter Smith (Intro to Gödel's Theorems [2007], 21.5)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.180
A Reaction
This leads on to Tarski's account of truth.