Strengthening, exhaustification, and rational inference

The literature in semantics and pragmatics provides extensive evidence for the strengthening of linguistic expressions, both in matrix positions and when embedded under various operators. We study the properties of such strengthening using a very simple setting. Specifically, we look at when the expression “crate with a banana” can be understood as a unique crate even though two different crates have a banana in them. By varying the scenarios in which an expression such as “Pick the crate with a banana” is evaluated, we show that the strengthening of “crate with a banana” within the scope of the definite article parallels the entailments of “crate with only a banana” (with an overt exhaustivity operator, ‘only’). We use this observation to argue that strengthening in embedded positions follows the logic of an exhaustivity operator rather than that of rational inference. We then note that a similar pattern obtains in matrix positions.