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English it-clefts are thought to be exhaustive (e.g. Chomsky 1977, Atlas & Levinson 1981, Percus 1997, É. Kiss 1998, Krifka 2008, Szabolcsi 1981, Zimmermann & Onea 2011), such that in a sentence like It was John who left, John is the only one who left. However, we report three experiments whose results indicate that it-clefts do not have to be exhaustive, but rather, the impression of exhaustivity may be a scalar conversational implicature (following Horn 1981): in a cleft such as It was John who left, listeners assume the speaker named everyone who left if they are relevant. Experiments 1a and 1b were judgment experiments, where participants rated the naturalness of nonexhaustive it-clefts as compared to fully canonical, exhaustive it-clefts (our baseline measurement for acceptable) and noncontrastive it-clefts (our baseline measurement for unacceptable). We used noncontrastive it-clefts because contrastiveness is widely agreed to involve presuppositional failure, and in case exhaustivity is a presupposition of the it-cleft as is sometimes proposed, we wanted to compare the result of violating it to the result of violating a different presupposition: contrastiveness. We found that participants rated the nonexhaustive it-clefts as more natural than the noncontrastive it-clefts, but there was no significant difference between the nonexhaustive it-clefts and the canonical, grammatical it-clefts. Participants did not reject nonexhaustive it-clefts. This is the first experimental evidence for English showing that the pre-verbal focus position is not necessarily exhaustive. In Experiment 2, we further support this result by repeating the study with insitu contrastive foci which are almost always considered to be structurally nonexhaustive (ex: Rooth 1985, Krifka 2001). We found the same pattern of results: participants did not reject the nonexhaustive foci. Exhaustivity appears to be a conversational implicature of the it-cleft.

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