Jon Ander Mendia Colloquium

Structuring ignorance

Certain constructions in natural language are tied to an inference that the speaker cannot be more informative; they give rise to what is often referred to as ‘ignorance inferences’. For instance, the sentences in (1) convey that the speaker doesn’t know who/how many people came to the party.

1) a. Liz or Sue came to the party.
b. At least five people came to the party.

It is generally agreed that such ignorance inferences are a form of Gricean conversational implicature, arising as the product of listeners reasoning about a set of relevant alternatives that the speaker chose not to utter. In this talk, I focus on the modifier ‘at least’ as a case study and show that the precise nature of ignorance inferences depends directly on the structural relations among the alternatives themselves, i.e. whether they are totally or partially ordered. In fact, I show that the ordering among alternatives is the only factor that the implicature calculation procedure is sensitive to. The implications are broad: if this reliance on structure can be generalized to other forms of conversational implicature, then issues surrounding the role of logical vs. contextual entailment in implicature calculation no longer arise (cf. Hirschberg 1985, Magri 2011).