It's that, and that's it! Exhaustivity and homogeneity presuppositions in clefts (and definites)

Abstract

This paper proposes a way to encode exhaustivity in clefts as a presupposition, something which has been claimed to be adequate, but never successfully implemented. We furthermore show that the facts that prompted the need for such an analysis carry over to identity sentences with definite DPs and propose a way to achieve the same presuppositions for definite DPs.

Contradicting (not-)at-issueness in exclusives and clefts: An empirical study

“…At issue content, that which directly addresses the Question under Discussion (QUD) (Simons, Beaver, Tonhauser & Roberts 2010;Tonhauser, Beaver, Roberts & Simons 2013), is a critical factor that has not been properly controlled for in prior experimental work (see Section 2.2). Crucially, exhaustivity in clefts is considered to be not-at-issue; by contrast, exhaustivity in exclusives is claimed to be at-issue (see, e.g., Horn 1981;Velleman et al 2012;Büring & Križ 2013;Horn 2014;Destruel et al 2015). Perhaps the simplest contrast to illustrate this is found in the examples in (3) (from Büring & Križ 2013: 2; modelled on Horn 1981).…”

“…However, they differ in what the at-issue content is: That is, they take exclusives and clefts to encode the same semantics, but while clefts presuppose exhaustivity (the MAX operator in their analysis) and assert the truth of the answer to the current question (the MIN operator), for exclusives these operators are reversed, i.e., MAX is asserted and MIN is presupposed. Alternatively, there are several proposals in the literature in which clefts are argued to be parallel to definite descriptions in their underlying syntax and semantics (Percus 1997;Hedberg 2000;Büring & Križ 2013). Similar to Velleman et al 2012, Büring & Križ (2013 argue that exhaustivity in clefts is presuppositional; unlike Velleman et al 2012, however, in this analysis cleft exhaustivity is captured indirectly as a homogeneity-not a maximality-presupposition, which they propose for definite descriptions as well.…”

“…Alternatively, there are several proposals in the literature in which clefts are argued to be parallel to definite descriptions in their underlying syntax and semantics (Percus 1997;Hedberg 2000;Büring & Križ 2013). Similar to Velleman et al 2012, Büring & Križ (2013 argue that exhaustivity in clefts is presuppositional; unlike Velleman et al 2012, however, in this analysis cleft exhaustivity is captured indirectly as a homogeneity-not a maximality-presupposition, which they propose for definite descriptions as well. Given homogeneity, clefts and definite descriptions presuppose that the elements in the identity statement are not a proper part of the sum individual which satisfies the backgrounded predicate.…”

“…• Assuming cleft exhaustivity is semantic (e.g., presuppositional following Velleman et al 2012;Percus 1997;Büring & Križ 2013), if its status as not-at-issue is responsible for the higher acceptability rates when violated, then schema (b) across sentence types will show similar patterns.…”

“…2 On the one hand there are the semantic accounts, in which exhaustivity is argued to be conventionally coded in the cleft structure (e.g., Atlas & Levinson 1981;Percus 1997;Velleman et al 2012;Büring & Križ 2013); on the other hand there is the pragmatic account, in which exhaustivity in clefts is claimed to be a conversational implicature (Horn 1981(Horn , 2014.…”