Extensions in Compositional Semantics

The paper scrutinizes the very notion of extension, which is central to many contemporary approaches to natural language semantics. The starting point is a puzzle about the connection between learnability and extensional compositionality, which is frequently made in semantics textbooks: given that extensions are not part of linguistic knowledge, how can their interaction serve as a basis for explaining it? Before the puzzle is resolved by recourse to the set-theoretic nature of intensions, a few clarifying observations on extensions are made, starting from their relation to (and the relation between) reference and truth. Extensions are then characterized as the result of applying a certain heuristic method for deriving contributions to referents and truth-values, which also gives rise to the familiar hierarchy of functional types. Moreover, two differences between extensions and their historic ancestors, Frege's Bedeutungen, are pointed out, both having repercussions on the architecture of compositional semantics: while the index-dependence of extensions invites a weak, unattested form of 'non-uniform' compositionality, Bedeutungen do not; and while the former are semantic values of expressions, the latter pertain to occurrences and, as a result, give rise to a universal principle of extensional compositionality. However, unlike extensions, they are of no help in resolving the initial mystery about learnability.