In the recent literature on presuppositions, Schlenker (2008a, 2009), building on previous observations by Soames (1989) and Heim (1990), has questioned the explanatory power of traditional dynamic approaches to presupposition projection (Karttunen 1974, Heim 1983, Beaver 2001 among others). Schlenker poses an explanatory challenge for theories of presupposition projection, as follows:Explanatory Challenge for Presupposition Projection:Find an algorithm that predicts how any operator transmits presuppositions once its syntax and its classical semantics have been specified. (Schlenker 2009)This challenge has sparked a debate which has led to a variety of new theories, both static (Schlenker 2009, Fox 2008, 2012, Chemla 2010, George 2008) and dynamic (Chierchia 2009, Rothschild 2008, 2011).One aspect of this debate is whether the algorithm for predicting presupposition projec- tion should be based on parsing, a process which takes as input a string of linguistic items; or on the compositional calculation of meanings, a process which takes as input a syntactic structure. This debate is important because, in turn, it relates to the more general question as to whether presupposition calculation should be thought of as a pragmatic post-compositional phenomenon, in the sense of Chierchia et al. (2012), or as part of compositional semantics, as in the more traditional dynamic approaches.In this paper, we will discuss sentences in which presuppositions are triggered in the antecedent of an antecedent-final conditional. We will argue that these cases present a challenge to parsing-based accounts of presupposition projection, as well as to theories of triviality that build on those accounts. We will focus in particular on the predictions of Schlenker (2009), who uses a parsing-based approach to reconstruct the notion of a local context. This allows us to illustrate the challenge to parsing-based accounts of both presupposition and triviality in a simple way. However, as we will show, the problems extend to other parsing-based accounts, including those which make use of a trivalent valuation instead of local contexts (e.g. Fox 2008, 2012) as well as pragmatic parsing-based theories (Schlenker 2008a).
- presupposition projection
- local context