Full Idea
A proper account of Tarski's truth definition explains truth in terms of three other semantic notions: what it is for a name to denote something, and for a predicate to apply to something, and for a function symbol to be fulfilled by a pair of things.
Gist of Idea
Tarski really explained truth in terms of denoting, predicating and satisfied functions
Source
Hartry Field (Tarski's Theory of Truth [1972])
Book Reference
'The Nature of Truth', ed/tr. Lynch, Michael P. [MIT 2001], p.368
A Reaction
This is Field's 'T1' version, which is meant to spell out what was really going on in Tarski's account.