My aim in this article is to analyze and to discuss what I think are the two most important approaches to a theory of truth from a non-realist standpoint: the proposal of Crispin Wright and the proposal enounced by Putnam in Reason, Truth and History. Wright argues for a minimalist theory of truth according to which truth has to be a metaphysically neutral notion and admits several possible models. One of these possible models is Putnam's notion of "rational acceptability under (...) ideal epistemic circumstances"; the other one is Wright's own proposal of truth as "superassertibility". Both authors are seeking for a notion of truth that is both absolute and stable (in contrast with warranted assertibility). I will claim that neither of the proposals satisfies these requirements as long as we understand them as generalizations from the mathematical (proof-based) model. (shrink)