Full Idea
Tarski's Theorem on the undefinability of truth says in a language sufficiently rich to talk about itself (which Gödel proved possible, via coding) the liar paradox can be carried out.
Gist of Idea
Tarski proved that any reasonably expressive language suffers from the liar paradox
Source
report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 02.2
Book Reference
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.18
A Reaction
The point is that truth is formally indefinable if it leads inescapably to contradiction, which the liar paradox does. This theorem is the motivation for all modern attempts to give a rigorous account of truth.
Related Idea
Idea 6006 If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]