Full Idea
Every really adequate theory of truth should also prove the law of non-contradiction. Therefore Tarski's notion of adequacy in Convention T fails to capture the intuitive notion of adequacy he is after.
Gist of Idea
Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction
Source
comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3
Book Reference
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.19
A Reaction
Tarski points out this weakness, in a passage quoted by Halbach. This obviously raises the question of what truth theories should prove, and this is explored by Halbach. If they start to prove arithmetic, we get nervous. Non-contradiction and x-middle?