There is no way of expressing the notion of truth in sufficiently powerful Formal systems, such as TNT.

If there was a way, one could represent Epiminede's paradox, with a formula with G number T. If the Tarski formula T actually existed, then it would be a statement about natural numbers that is both true and false at once (or neither)! If we believe this is a ridiculous state of affairs, then we have to undo our assumption that the formula TRUE{a} exists . Thus, there is no way of expressing the notion of truth inside TNT. Notice that this makes truth a far more elusive property than theoremhood, for the latter is expressible.

So this assumes, a priori facts about how truth works, I guess as axioms of Logic

See Godel, Escher, Bach, page 581