The liar and kindred paradoxes make it difficult to construct a consistent and plausible formal theory of truth. One approach is to tackle them not by restricting the principles about truth that pre-theoretically seem correct, but by deviating from classical logic. I outline a nonclassical propositional logic I have constructed within that approach, as well as a theory of truth embedded in the framework of the logic. (Preliminary presentation of some of the material that eventually became the paper 'A propositional theory of truth'.)