Colloquium with Danny Fox with Omri Doron and Jad Wehbe, Massachusetts Institute of Technology

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 --> p,A>}. It is an automatic consequence that PW leads to surface

cancellation 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.