This paper is driven by the idea that the contextualism-relativism debate regarding the semantics of value-attributions turns upon certain extra-semantic assumptions that are unwarranted. One is the assumption that the many-place predicate of truth, deployed by compositional semantics, cannot be directly appealed to in theorizing about people's assessments of truth value, but must be supplemented (if not replaced) by a different truth-predicate, obtained through certain "postsemantic" principles. Another is the assumption that semantics assigns to sentences not only truth values (as (...) a function of various parameters, such as contexts, worlds and times), but also semantic contents, and that what context-sensitive expressions contribute to content are certain contextually determined elements. My first aim in this paper will be to show how the two assumptions have shaped two ways of understanding the debate between contextualism and relativism, as regards value-attributions. My second aim will be to show that both assumptions belong outside semantics, and are moreover questionable. (shrink)