Resumen: We say that a sentence A is a permissive consequence of a set of
premises Gamma whenever, if all the premises of Gamma hold up to some standard, then A
holds to some weaker standard. In this paper, we focus on a three-valued version
of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness
toward a unified treatment of the paradoxes of vagueness and self-referential
truth. For vagueness, st-consequence supports the principle of tolerance; for truth,
it supports the requisit of transparency. Permissive consequence is non-transitive,
however, but this feature is argued to be an essential component to the understanding
of paradoxical reasoning in cases involving vagueness or self-reference