Speaker: Omri Doron, Danny Fox, and Jad Wehbe (MIT)
Title: Assertion, Presupposition and Local Accommodation
Time: Thursday, February 27th, 12:30pm - 2pm
Location: 32-D461
Abstract: Sudo (2012) provides important evidence that trivalent (or partial) semantics is not rich enough to account for certain presupposition projection phenomena. Specifically, he observes that presuppositions triggered by different lexical items project differently in the same environment. These differences could not follow from any recipe for presupposition projection, if the input for projection is the trivalent semantic value of the relevant constituents. In fact, the differences cannot even be described. Sudo shows, however, that the facts can be described in 2-dimensional semantics by a rule that considers both the assertion and the presupposition of the relevant expressions. This argument was strengthened in later literature, with the observation that certain sentences, but not others, can be affirmed when their presupposition is known to be false (beginning with Cummins et al. 2013). It has been pointed out that the observed patterns can further support Sudo’s conclusion, as they suggest that it is sensible to ask whether the assertive component of an expression entails its presupposition – a question that is meaningful under 2d-semantics but not under Trivalence. Moreover, it has been pointed out that the assertions needed in the two domains (projection and affirmation) are the same.
We find the arguments compelling and the correlation between the two diagnostics very informative. There are, however, three important questions that we want to investigate. First, to describe the projection facts, Sudo needs to depart from predictive theories of presupposition projection (Strong Kleene, Local Context, Transparency) in favor of what seem to us to be ad hoc statements. The question is whether there is a way to modify Sudo’s proposal so that it is compatible with predictive theories of projection (Q1). The Second question, Q2, is whether the lexical stipulations that are commonly invoked to yield 2d-semantics can be eliminated in favor of a general algorithm that would allow us to keep to the more impoverished (and more predictive) trivalent semantics. And finally, there is a second correlation hinted at in the literature (Zehr and Schwarz, 2018), which we think is highly informative, namely that a presupposition can be cancelled (by Local Accommodation) only when it is entailed by the assertion (that hard triggers yield assertions and presuppositions that are logically independent, and that presuppositions are entailed by assertions in the case of soft triggers). So our third question, Q3, is whether there is a way to account for this new correlation. We, of course, hope that there could be affirmative answers to all three questions. To address Q3 affirmatively, we propose that there is no process of presupposition cancellation of the sort suggested by Heim. (Local Accommodation does not exist nor does the A operator invoked in Trivalent Semantics.) Instead there is a process of presupposition weakening, PW, that weakens the presupposition of a sentence S<p,A> (a sentence S with presupposition p and Assertion A): PW(S<p,A>) = S<a>.
It is an automatic consequence that PW leads to surface cancelation iff the assertion entails the presupposition. (Only in such a case is A → p a tautology.) We propose, moreover, to derive PW from the general theory of presupposition, on the assumption that the assertion can be parsed as a separate conjunct and evaluated “before” the presupposition (drawing on the representation in Schlenker 2008 and on the flexible view on incrementality argued for in Chemla and Schlenker 2012). This affirmative answer to Q3 turns out to provide an affirmative answer to Q1 as well. To answer Q2 we develop the algorithm proposed and rejected by Zehr and Schwarz (2018) based on a third correlation, namely that hard triggers are precisely those that can be deleted while maintaining (Strawson) equivalence. (We argue that apparent exceptions that worried Zehr and Schwarz can be accommodated with reasonable auxiliary assumptions.) Finally, if time allows for this, we will argue that the emerging perspective can make sense of otherwise puzzling conditional presuppositions, such as those identified by Schlenker for co-speech gestures.