Incommensurable theories are said to be both incompatible and incomparable. This is paradoxical, because, being incompatible, these theories must have the same subject-matter, yet incomparability implies that their subject-matter is different. This paper's proposed resolution of the paradox makes use of the distinction between internal subject-matter and external subject-matter for languages (frameworks) as outlined by W. Sellars. Incommensurability arises when two languages share the same external subject-matter but differ in internal subject-matter. When they share the same external subject-matter, they can (...) be inconsistent (hence incompatible), and yet incomparable (because they are about distinct internal subject-matter). A substantial part of the paper is devoted to the technical development of the notion of inconsistency as a relationship between languages in contrast to the traditional notion of inconsistency between statements. (shrink)