Common Ground and Presupposition

Communication depends on a shared body of assumptions that speakers build up as they talk. The common ground is the set of propositions that both interlocutors accept as true. A presupposition is to assume the truth of a proposition and to assume that the addressee will assume it as well. An assertion, by contrast, is content that a speaker puts forward to be added to the common ground. Information is organized, and presented as either asserted or presupposed, according to what the speaker thinks the addressee will readily accept.

A key mechanism here is accommodation, the addressee's willingness to quietly add a presupposition to the common ground. Krifka (2007) illustrates this with ordering effects. The sequence I have a cat, and I had to bring my cat to the vet sounds fine, but I had to bring my cat to the vet, and I have a cat sounds odd. The reason is that I had to bring my cat to the vet already presupposes that the speaker has a cat: the phrase my cat carries that presupposition even if the addressee did not previously know it. The addressee simply accommodates it, so explicitly adding and I have a cat afterward is redundant and strange.

Accommodation is not automatic, however, and this is what makes presupposition relevant to how discourse is structured. I had to bring my cat to the vet because it was sick poses no problem. But I had to bring my gorilla to the vet because it was sick is jarring, because the presupposition that the speaker owns a gorilla is hard to accommodate. To communicate it, a speaker would likely need to lead with I have a pet gorilla, supply some backstory, and only then report the trip to the vet. Because the cat presupposition is easily accommodated and the gorilla presupposition is not, the two would be organized very differently across a discourse.

A further striking property of presuppositions is that they survive negation, a phenomenon called projection (or presupposition projection). This is clearest with factive verbs such as know, which contrast with non-factive verbs such as believe. Susie knows that her husband is returning today leads the hearer to assume that he is in fact returning; Susie believes that her husband is returning today carries no such assumption. Merely swapping know for believe removes the inference that the complement clause is true.

The remarkable point is what happens under negation. Susie doesn't know that her husband is returning today still conveys that her husband is indeed returning; only her awareness is denied. The presupposition triggered by the factive know projects past the negation, even though negation normally cancels the truth of other elements such as entailments. And again the contrast with believe holds: Susie doesn't believe that her husband is returning today yields no inference that he is returning. The stability of presuppositions under negation, backed by a large technical literature, is one of the defining features that sets them apart from ordinary truth-conditional content.