We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field.

In a recent paper, Philip Kremer proposes a formal and theory-relative desideratum for theories of truth that is spelled out in terms of the notion of ‘no vicious reference’. Kremer’s Modified Gupta-Belnap Desideratum (MGBD) reads as follows: if theory of truth T dictates that there is no vicious reference in ground model M, then T should dictate that truth behaves like a classical concept in M. In this paper, we suggest an alternative desideratum (AD): if theory of truth T dictates (...) that there is no vicious reference in ground model M, then T should dictate that all T-biconditionals are (strongly) assertible in M. We illustrate that MGBD and AD are not equivalent by means of a Generalized Strong Kleene theory of truth and we argue that AD is preferable over MGBD as a desideratum for theories of truth. (shrink)