## 1 Characterizing Presupposition


### 1.1 Introduction



Speakers take a lot for granted. That is, they *presuppose*
information. As we wrote this, we presupposed that readers would
understand English. We also presupposed as we wrote the last sentence,
repeated in (1), that there was a time when we wrote it, for otherwise
the fronted phrase "as we wrote this" would not have
identified a time interval.



(1)
As we wrote this, we presupposed that readers would understand
English.


Further, we presupposed that the sentence was jointly authored, for
otherwise "we" would not have referred. And we presupposed
that readers would be able to identify the reference of
"this", i.e., the article itself. And we presupposed that
there would be at least two readers, for otherwise the bare plural
"readers" would have been inappropriate. And so on.



Note that some of these presuppositions arise by default from specific
words that we used. The existence of a time when we wrote the article
is a requirement associated with our use of "as". It is a
requirement built into the meaning of the temporal preposition
"as", which has a similar meaning to temporal "while",
that in a phrase "as *X*", the
"*X*" has to hold at some time. We say that
"as" is a *presupposition trigger*. Similarly,
"this" is a presupposition trigger requiring something
salient to refer to, the bare plural is a presupposition trigger
requiring existence of multiple individuals, and "would"
is a presupposition trigger requiring a salient future or hypothetical
circumstance.



In contrast, some of the presuppositions above have nothing to do with
the meanings of any of those words. For example, we can say that the
presupposition that the addressee speaks English, like the
presupposition that the addressee is interested in what the speaker
(or writer) has to say, is a *conversational presupposition*
or, following Stalnaker (1972; 1974), *speaker presupposition*
or *pragmatic presupposition*. The presuppositions associated
with specific triggers are said to be *conventional* or
*semantic*. The terminological distinction between semantic and
pragmatic presupposition is of theoretical import: as we will see
later, some theorists regard it as an open question whether there are
any purely conventional presuppositions. A halfway house, suggested
for example by Karttunen (1973) and Soames (1982), is to define a
notion of *utterance presupposition*, thus involving a specific
form that is uttered, but allowing that what is actually presupposed
may depend also on the attitudes of the speaker who utters it.



It is important to note that to call presuppositional expressions
"conventional" or "semantic" is not
necessarily to imply that the presuppositions they trigger don't
depend on the context in any way. For example, although
"this" may be viewed as a conventional presupposition
trigger, the interpretation very much depends on the context, and the
presupposition, although typically regarded as conventional, is
normally seen precisely as a constraint on the utterance context.



What makes presuppositions special? That is, to the extent that
presuppositions are just a part of the conventional meaning of some
expressions, what makes them sufficiently distinctive that they merit
their own entries in handbooks and encyclopedias, as well as many
hundreds of other articles and book chapters elsewhere? First,
presuppositions are ubiquitous. And second, there are various respects
in which the behavior of presuppositions differs sharply from other
aspects of meaning.



As regards the ubiquity of presuppositions, at least the following
lexical classes and constructions are widely agreed to be
presupposition triggers:


* *factives* (Kiparsky and Kiparsky, 1970)
  

Berlusconi knows that he is signing the end of Berlusconism.
  

- Berlusconi is signing the end of Berlusconism.
* *aspectual verbs* ("stop, continue") (Simons,
2001; Abusch, 2002; Lorenz, 1992)
  

China has stopped stockpiling metals.
  

- China used to stockpile metals.
* *temporal clauses headed by "before",
"after", "since", etc.* (Beaver and
Condoravdi, 2003; Heinamaki, 1974)
  

The dude released this video before he went on a killing spree.
  

- The dude went on a killing spree.
* *manner adverbs* (Abbott, 2000)
  

Jamie ducked quickly behind the wall.
  

- Jamie ducked behind the wall.
* *sortally restricted predicates of various categories (e.g.,
"bachelor")* (Thomason, 1972)
  

Julius is a bachelor.
  

- Julius is an adult male.
* *cleft sentences* (Delin, 1995; Prince, 1986)
  

It was Jesus who set me free.
  

- Somebody set me free.
* *quantifiers* (Roberts, 1995; Gawron, 1995; Abusch and
Rooth, 2000; Cooper, 1983)
  

I have written to every headmaster in Rochdale.
  

- There are headmasters in Rochdale.
* *definite descriptions* (Strawson, 1950)
  

The Prime Minister of Trinidad and Tobago stood up and wagged his
finger.
  

- Trinidad and Tobago have a (unique) prime minister.
* *names* (van der Sandt, 1992)
  

The author is Julius Seidensticker.
  

- Julius Seidensticker exists.
* *intonation (e.g., focus, contrast)* (Jackendoff, 1972;
Geurts and van der Sandt, 2004; Roberts, 1998)
  

HE set me
 free.[1]
  

- Somebody set me free.



And this is only a small sample of the words and syntactic
constructions that have been classified as presupposition triggers, so
even if in some cases there may be doubts about this diagnosis, it can
hardly be doubted that presupposition triggers abound in everyday
language. In the following sections we will discuss the behaviors
which mark out presuppositions from ordinary entailments, and then
introduce some of the theories that have been developed to account for
those behaviors.


### 1.2 Projection



The hallmark of presuppositions, as well as the most thoroughly
studied presuppositional phenomenon, is *projection*
(Langendoen and Savin, 1971). Consider (2). This has all the
presuppositions in (3). These presuppositions all follow from
utterances of the base sentence in (2), as do the regular entailments
in (4): someone who sincerely uttered (2) would certainly be expected
to accept the truth of (3) and (4), as well:



(2)
It's the knave that stole the tarts.
(3a)
There is a (salient and identifiable) knave.
(3b)
There were (salient and identifiable) tarts.
(3c)
Somebody stole the tarts.
(4a)
The knave did something illegal.
(4b)
The knave took possession of the tarts.


Now consider the sentences in (5):



(5a)
It isn't the knave that stole the tarts. (*negation*)
(5b)
If it's the knave that stole the tarts, he will be punished.
(*antecedent of a conditional*)
(5c)
Is it the knave that stole the tarts? (*question*)
(5d)
Maybe/It is possible that it's the knave that stole the tarts.
(*possibility modal*)
(5e)
Presumably/probably it's the knave that stole the tarts.
(*evidential modal, probability adverb*)
(5f)
The king thinks it's the knave that stole the tarts. (*belief
operator*)


In all these examples, sentence (2) is embedded under various
operators. What is notable is that whereas the statements in (4) do
not follow from any of these embeddings (and would not be expected to
follow according to classical logics), the presuppositions do follow.
We say that the presuppositions are *projected*. Certainly, the
inference is more robust in some cases than in others: while it is
hard to imagine sincerely uttering (5a) without believing some tarts
to be salient, it is easier to imagine a circumstance in which (5f)
could be uttered when in fact the tarts were not stolen, but hidden.
But in the absence of special factors, to which we will turn shortly,
someone who sincerely uttered any of the sentences in (5) might be
expected to believe all of the presuppositions in (3a)-(3b).



Projection from embeddings, especially negation, is standardly used as
a diagnostic for presupposition (hence the term "negation
test"). However it is important to try several types of
embedding when testing for presupposition for a few different reasons.
First of all, it is not always clear how to apply a given embedding
diagnostic. For example, although it is widely agreed that the
additive particle "too" is a presupposition-inducing
expression, the negation test is awkward to apply because it is not
immediately clear whether the negation outscopes the additive or
*vice versa* in (6b), and it's not obvious how the negation
interacts with focus:



(6a)
Fred kissed BETTY, too.
(6b)
Fred didn't kiss BETTY, too.


We leave it as an exercise for the reader to show that embedding (6a)
under a different operator e.g., under a modal or in the antecedent of
a conditional, provides evidence that this sentence presupposes that
someone other than Betty was kissed by Fred.



Additionally, some inferences seem to project from negation but not
other embeddings. For example, both (7a) and (7b) seem to presuppose
that the speaker has sensory experience with the pie, and this type of
data has led some to conjecture that uses of predicates of personal
taste are associated with a presupposition that the judgment of taste
resulted from direct
 experience.[2]
 However, we don't get any projection of this inference from the
conditional in (7c), and example (7d) seems to imply that the speaker
has not tasted the pie themselves. This data suggests that any account
claiming a presupposition of direct experience for predicates of
personal taste needs to be highly nuanced.



(7a)
The pie is tasty.
(7b)
The pie isn't tasty.
(7c)
If the pie is tasty, it will go quickly.
(7d)
Is the pie tasty?


More generally, such examples demonstrate why it's important to look
at a wide range of embeddings when identifying presuppositions on the
basis of their projection behavior.


### 1.3 Cancellability



What makes the "projection problem" problematic? If some
part of the meaning of an expression a was never affected by the
linguistic context in which a was embedded, that would be
philosophically interesting, and would demand a theoretical
explanation, but it would at least be trivial to completely describe
the data: all presuppositional inferences would survive any embedding,
end of story. But that isn't what happens. Presuppositions typically
project, but often do not, and most of the empirical and theoretical
work on presupposition since the 1970s has been taken up with the task
of describing and explaining when presuppositions project, and when
they don't.



When a presupposition does not project, it is sometimes said to be
"cancelled". The classic cases of cancellation occur when
the presupposition is directly denied, as in the following variants of
some of the sentences in (5):



(8a)
In this court, it isn't the knave that steals the tarts: the king
employs no knaves precisely because he suspects they are responsible
for large-scale tart-loss across his kingdom.
(8b)
If it's the knave that stole the tarts, then I'm a Dutchman: there
is no knave here.
(8c)
Is it the knave that stole the tarts? Certainly not: there is no
knave here.
(8d)
The king thinks it's the knave that stole the tarts, but he's
obviously gone mad, since there is no knave here.


Presuppositional inferences are typically subject to cancellation by
direct denial only when the presupposition trigger is embedded under
some other operator. When the presupposition is not embedded, such
cancellation (by the same speaker) is usually infelicitous, just as is
cancellation of entailed content which is not embedded. Thus the
denial of a presupposition in (9) and the denial of an ordinary
entailment in (10) both lead to pragmatically infelicitous utterances
(marked by a "#").



(9)
#It's the knave that stole the tarts, but there is no knave.


(10)
#It's the knave that stole the tarts, but he didn't do anything
illegal.


The fact that presuppositions associated with unembedded triggers are
not cancellable, except in an outright retraction of what the speaker
has previously claimed, is one of the features that distinguishes most
presuppositions from Gricean conversational implicatures (Grice,
1989). For example, an utterance of (11a) might ordinarily lead to the
so-called scalar implicature in (11b). But while this implicature is
cancellable, as in (11c), the presupposition that there is a knave,
once again, is not cancellable, as shown by the oddity of (11d).



(11a)
The knave stole most of the tarts.
(11b)
The knave did not steal all of the tarts.
(11c)
The knave stole most of the tarts--in fact, he stole them
all.
(11d)
#The knave stole most of the tarts, but there was no knave.


We can summarize the typical behavior of entailments, presuppositions,
and conversational implicatures as follows:




|  |  |  |  |
| --- | --- | --- | --- |
|  | Entailments | Presuppositions | Implicatures |
| Project from embeddings | no | yes | no |
| Cancellable when embedded | -- | yes | -- |
| Cancellable when unembedded | no | no | yes |



Because presuppositions are typically only cancellable when embedded,
Gazdar (1979a, 1979b) argues that presuppositions are usually entailed
when the trigger is not embedded.



The literature is choc-a-bloc with examples of presuppositional
inferences apparently disappearing. Whether such examples are
appropriately described as involving *cancellation* is partly a
theoretical decision, and, as we will see, many scholars avoid using
the term "cancellation" for some or all such cases. One
reason for this is that the term "cancellation" appears to
suggest that an inference has been made, and then removed. But in many
cases there are theoretical reasons not to regard it as an apt
characterization, and in considering early views on presupposition in
the next section, we will come across one class of such cases
(specifically, cases involving hypothetical reasoning in
conditionals).


## 2. The Frege-Strawson tradition



The early literature on presupposition almost exclusively revolved
around definite descriptions, which are said to presuppose the
existence of a unique referent. A problem arises when a definite
description, like *the King of France*, fails to refer. Russell
(1905) claimed that sentences like "The King of France is bald" are
false because the logical form of definite descriptions contains a
false existential claim. However, Strawson (1950) famously argued
against Russell's theory by proposing that when a definite description
fails to refer, the result can be a sentence which lacks a truth
value. Thus presuppositions are understood as definedness conditions,
necessary requirements for an expression to have a meaning.



Strawson's intuition, which can be traced back to Frege (1892), leads
to the following
 definition:[3]



**Definition 1** **(Strawsonian presupposition)**
  

One sentence presupposes another *iff* whenever the first is true
or false, the second is true.



Another definition that is often used is this:



**Definition 2** **(Presupposition via negation)**
  

One sentence presupposes another *iff* whenever the first
sentence is true, the second is true, and whenever the negation of the
first sentence is true, the second sentence is
 true.[4]



hese two definitions are equivalent if negation maps true onto false,
false onto true, and is undefined when its argument is undefined.
However, the second definition is notable in the context of the above
discussion of projection, because it seems to directly encode the
projection properties of at least one operator: negation.
Specifically, it says that presuppositions are inferences that survive
embedding under
 negation.[5]



It is clear that if the above assumptions about presupposition are
made, then the presuppositions of a sentence will be the same as the
presuppositions of the negation of the sentence. But what about
projection from embeddings other than negation? A very simple account
of projection is based on the *cumulative hypothesis*, first
discussed by Morgan (1969) and Langendoen and Savin (1971). This is
the idea that presuppositions always project from embedding, as if
there were no effects like cancellation. A trivalent semantics that
yields this behavior is obtained by using the *Weak Kleene*
connectives (Kleene, 1952). Assume (for all the partial/multivalent
semantics given in this article) that for classically valued
arguments, the connectives behave classically. Then Weak Kleene
connectives (also known as the Bochvar Internal connectives) are
defined as follows:



**Definition 3** **(Weak Kleene)**
  

If any argument of a sentence with a Weak Kleene connective lacks a
classical truth value, then the sentence as a whole lacks a truth
value.




Weak Kleene fails as a theory of presupposition because it entails
that presuppositions project uniformly, whereas in fact they do not.
Another system of Kleene's, the Strong Kleene connectives, does not
have this property:



**Definition 4** **(Strong Kleene)**
  

If the classically-valued arguments of a sentence with a Strong Kleene
connective would suffice to determine a truth value in standard logic,
then the sentence as a whole has that value; otherwise it doesn't have
a classical value.




For example, in classical logic a conjunction is bound to be false if
one of its conjuncts is false, and therefore the same holds for Strong
Kleene "and". Similarly, since in classical logic a
disjunction must be true if one of its disjuncts is true, the same
holds for Strong Kleene "or". We obtain the following
truth tables for the main binary connectives:




|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Conjunction



|  |  |  |  |
| --- | --- | --- | --- |
| ph [?] ps | t | f |  |
| t | t | f |  |
| f | f | f | f |
|  |  | f |  |

 | Disjunction



|  |  |  |  |
| --- | --- | --- | --- |
| ph [?] ps | t | f |  |
| t | t | t | t |
| f | t | f |  |
|  | t |  |  |

 | Implication



|  |  |  |  |
| --- | --- | --- | --- |
| ph - ps | t | f |  |
| t | t | f |  |
| f | t | t | t |
|  | t |  |  |

 |



Now consider the following example:



(12)
If there is a knave, then the knave stole the tarts.


Let's ignore all presupposition triggers in (12) save "the
knave", and show that Strong Kleene predicts that the sentence
as a whole does not presuppose that there is a knave. Using Definition
1, it suffices to find at least one model where (12) has a classical
truth value, but in which there is no knave. This is easy: in such a
model, the antecedent is false, and inspection of the above Strong
Kleene table shows that when the antecedent of a conditional is false,
the conditional is true, as would be the case classically. In fact,
Strong Kleene predicts no presupposition for (12). This is in
contradistinction to Weak Kleene, which would fail to give (12) a
classical value in knave-less models, and hence predict that (12)
presupposes the existence of a knave.



There are other cases where Strong Kleene does predict a
presupposition, and the presupposition predicted is not what we might
have expected. Thus Strong Kleene gives (13a) a classical truth value
in all models where there is a knave, and in all models where there
was trouble. So while we might have expected the presupposition in
(13b), Strong Kleene predicts the presupposition in
 (13c).[6]
 We will return to this issue shortly.



(13a)
If the knave stole the tarts, then there was trouble.
(13b)
There is a knave.
(13c)
If there was no trouble, then there is a knave.


Much of the discussion of partial and multivalent approaches to
presupposition over the last three decades has centered on the
treatment of
 negation.[7]
 Specifically, the issue has been the treatment of cancellation
examples like (14).



(14)
The tarts were not stolen by the knave: there is no knave.


A standard approach is to propose that negation is ambiguous between a
presupposition-preserving negation and a presupposition-denying
negation; see e.g., the discussion by Horn (1985, 1989). The
presupposition-preserving negation (aka *choice* negation) we
have already seen, and it is found in both the Weak and Strong Kleene
systems. The presupposition-denying (or *exclusion*) negation
is typically taken to map true to false and false to true, as usual,
but also to map an argument lacking a classical value to true. Thus if
(14) is interpreted in a model where there is no knave, but
"not" is understood as a presupposition-denying negation,
then "the tarts were stolen by the knave" would lack a
classical value, but "The tarts were not stolen by the
knave", and (14) as a whole, would be true.


## 3. Pragmatic presupposition



Probably the most significant philosophical counterpoint to the
Frege-Strawson approach to presupposition, other than the original
non-presuppositional work of Russell, is due to Stalnaker (1972, 1973,
1974), and later clarified in Stalnaker
 (1998).[8]
 Stalnaker suggests that a pragmatic notion of presupposition is
needed, so that the proper object of philosophical study is not what
words or sentences presuppose, but what people presuppose when they
are speaking. A pragmatic presupposition associated with a sentence is
a condition that a speaker would normally expect to hold in the common
ground between discourse participants when that sentence is
 uttered.[9]



One consequence of Stalnaker's view is that, *contra* semantic
accounts of presupposition, presupposition failure need not produce a
semantic catastrophe. There are, however, two weaker types of failure
that can occur: (*i*) a speaker uttering some sentence
*S* can fail to assume that some proposition *P* is in
the common ground, even though most utterances of *S* would be
accompanied by the presupposition that *P*; and (*ii*) a
speaker can presuppose something that is not in the common ground. We
see these two types of failure respectively in (15a), where there is
no presupposition that Mullah Omar is alive, and (15b) where it is
presupposed that Luke was alive.



(15a)
I don't know that Mullah Omar is alive. I don't know if he's dead
either. (General Dan McNeill, Reuters, 19 May 2008)
(15b)
Vader didn't know that Luke was alive, so he had no intentions of
converting Luke to the Sith. (Web example)


These examples involve a subclass of factive verbs called
"semifactives," which Karttunen (1971b) concluded only trigger a
presupposition in some person and tense forms. As Karttunen himself
realized, such a stipulation is unmotivated. For Stalnaker's pragmatic
account of presupposition, these examples are not problematic; the
verb "know" need not presuppose that its complement is true. When an
addressee hears the first sentence of (15a), he will realize that if
it were in the common ground that Mullah Omar was alive, then the
speaker would know this, and so the speaker's claim would be false.
Therefore the hearer can reason that the speaker is not presupposing
the complement of "know" to be true. On the other hand,
when a hearer is confronted by (15b), it is consistent to assume that
Luke was alive. Since speakers using "know" typically
presuppose the truth of the complement, we can assume that this is the
case here.



Stalnaker's work was part of an avalanche of pragmatic attacks on the
semantic conception of presupposition. Working in the immediate
aftermath of Grice's 1967 William James 
 lectures[10],
 accounts like Atlas (1976; 1977; 1979), Atlas and Levinson (1981),
Kempson (1975), Wilson (1975), and Boer and Lycan (1976) all
present detailed arguments that presuppositions should be understood
as something akin to conversational implicatures. Generally speaking,
these approaches justify presuppositional inferences by using the
maxims of relevance and quantity. Thus, for example, Atlas (1976)
suggests that an embedding of a definite under a negation will tend to
produce a meaning that is ruled out as insufficiently strong to
satisfy the maxim of quantity, unless it is strengthened by treating
the definite as if it had wide scope and could act referentially.
Contemporary descendants of this pragmatic tradition include Abbott
(2000; 2006; 2008), Simons (2001; 2003; 2004; 2006; 2007), and
Schlenker (2007; 2008). Both Abbott and Simons are at pains to
distinguish between different presupposition triggers, rather than
lumping them all together. Thus Simons, for example, makes a case for
deriving presuppositional inferences associated with factives and
aspectual adverbs using a combination of Stalnakerian and Gricean
reasoning, allowing that typically anaphoric triggers like the
additive "too" might function conventionally. On the other
hand, Schlenker's pragmatic derivation of projection properties, using
both standard maxims and at least one rule specific to
 presuppositions[11],
 does not make fine-grained distinctions between presupposition
triggers.



There is a contrast among pragmatic approaches to presupposition as
regards whether the source of presuppositions is discussed. The
approaches mentioned in the preceding paragraph, which attempt to
derive presuppositional inferences from general conversational
principles, aim to explain both the source of presuppositions, and the
phenomenon of projection. But Stalnaker made no attempt whatsoever to
explain where presuppositions came from, beyond indicating that they
are inferential tendencies that might or might not be associated with
semantic presuppositions. This emphasis on the projection of
presuppositions rather than their source, which holds also of the
contemporaneous work by Karttunen (1974; 1973), to which we shall turn
shortly, lived on in much of the work influenced by these theories. It
is particularly obvious in what we can collectively term
*cancellation*-based theories of presupposition, led by Gazdar
(1979a; 1979b), and including Soames (1979; 1982), Mercer (1987;
1992), Gunji (1981), Marcu (1994), Horton (1987), Horton and Hirst
(1988), Bridge (1991), and van der Sandt (1982; 1988).



Cancellation accounts can be traced back in spirit to Stalnaker's
account of semifactives, discussed above, in which presuppositions are
defeated by competing conversational inferences: the general idea is
simply to make presuppositions into defaults, and wipe them out
whenever they would cause pragmatic embarrassment. Gazdar provided a
remarkably straightforward formalization of this account, as well as
extending to many other projection phenomena, based on a general
principle he characterizes as "All the news that fits". In
Gazdar's model, the strategy for a hearer is first to identify sets of
entailments, conversational implicatures, and presuppositions, and
then to try adding them to the speaker's set of commitments.



**Definition 5** **(Gazdar: cancellation)**
  

Implicatures and entailments defeat presuppositions, so a hearer adds
to his or her commitments only those presuppositions that are
compatible with both implicatures and entailments. All remaining
presuppositions are cancelled.




Consider (16a), and assume there are no relevant pre-existing
commitments:



(16a)
If the king is angry, then the knave stole the tarts.
(16b)
If there is a knave, then the knave stole the tarts.


According to Gazdar, (16a) entails that if there is an angry king then
there is a knave and he stole some set of tarts. (This much all
theories agree on; some theories may predict stronger entailments.)
The set of implicatures would include the clausal implicature that the
speaker doesn't know whether a king is angry, and doesn't know whether
a knave stole tarts. The presuppositions (or "potential
presuppositions", in Gazdar's terms) are that there is a unique
king, a unique knave, and a unique set of tarts. The hearer proceeds
by adding the entailments to (their representation of) the speaker's
commitment set, then adding whatever implicatures fit in, and then
adding the presuppositions that fit after that. In this case, all the
entailments, implicatures, and presuppositions are consistent, and all
can be added without any being cancelled.



But now consider (16b), repeated from (12). Here there is an
implicature that the speaker doesn't know whether there is a knave.
The hearer accepts this and other implicatures, and then considers the
presuppositions that there is a knave and that there are some tarts.
The presupposition that there are tarts is unproblematic, and is
added, but the hearer cannot consistently add the presupposition that
there is a knave. So this presupposition is canceled, and (16b) does
not presuppose that there is a knave. Hence, according to Gazdar,
presuppositions are sometimes blocked by conversational
implicatures.



Within the space of cancellation-based accounts of presupposition, it
is hard to beat Gazdar's for its conceptual and technical simplicity,
and its empirical coverage. Some conceptual questions remain, however,
such as why it should be that *presuppositions* are the last
things to be added in the process of updating commitments. Van der
Sandt's (1982, 1988) reformulation of the cancellation model gives us
an alternative way to think about this, by modeling projection in
terms of whether presuppositions could have come first.



**Definition 6** **(Van der Sandt: cancellation)**
  

Project only those presuppositions that could be conjoined to the
beginning of the sentence while leaving the utterance consistent with
(neo-Gricean) conversational
 principles.[12]




The intuitive idea underlying van der Sandt's proposal is that
presuppositions are *given* information, and in this sense
"precede" their carrier sentences, if not *de
facto* then at least *de jure*, in the sense that the
context would have legitimated their presence. In the case of (16),
fronting the presupposition that there are some tarts yields the
sentences in (17).



(17a)
There are some tarts and if the king is angry then the knave stole
the tarts.
(17b)
There are some tarts and if there is a knave, then the knave stole
the tarts.


The fronting of the presupposition does not lead to a clash with any
Gricean principles, so the presuppositions are predicted to project in
(16a) and (16b). Similarly, fronting the presupposition that there is
a knave to (16a), as in (18a), produces no clash, so (16a) presupposes
that there is a knave. But adding the presupposition that there is a
knave to (16b), as in (18b), does result in a clash: since (18b) is
truth-conditionally equivalent to the simple conjunction "there
is a knave and the knave stole the tarts", it is redundant,
conflicting with the requirement of brevity in Grice's Maxim of
Manner. On van der Sandt's analysis, if fronting a presupposition
would produce a redundant result, then that presupposition cannot
project. So (16b) is correctly predicted not to presuppose that there
is a knave.



(18a)
There is a knave and if the king is angry then the knave stole the
tarts.
(18b)
There is a knave and if there is a knave, then the knave stole the
tarts.


It should be noted, however, that even if (18b) is redundant, it is
arguably a felicitous discourse, and therefore some subtlety is needed
in applying van der Sandt's cancellation principle in the simplified
form above. The issue is not simply whether a discourse is felicitous,
but whether there is any clash with the maxims. And this will of
course depend on how exactly the maxims are formulated. But for the
purposes of understanding the intention of van der Sandt's analysis,
we can take it that though an utterance of (18b) could be felicitous,
it would be a case of *flouting* (in Grice's sense), a case
where a maxim is disobeyed in order to preserve some greater
conversational goal.



A more recent pragmatic approach situates presuppositions in a wider
taxonomy of projective content based on the property of
at-issueness. Once we've identified the QUD, we can identify
content that is meant to be relevant towards answering it. In other
words, content that is at-issue. Simons et al (2010) propose that
this pragmatic property is relevant to projection such that only
not-at-issue content projects.



**Definition 7** **(Cancellation via at-issueness)**
  

Project only those presuppositions that are not-at-issue.



Consider examples (19) and (20) from Beaver (2010). These examples
involve the factive verb "discover", and hence are expected to trigger
a presupposition that its complement is true, i.e. that the
addressee's work is plagiarized. In (19), where "discover" is
stressed, this presupposition seems to project, with the implication
that, absent the T.A. finding out what's going on, the speaker is
prepared to overlook the plagiarism. In this case, we might say that
what is at-issue is the question of whether the T.A. finds out about
the plagiarism. However, in (20), where stress in on "plagiarized", it
is far less clear whether the speaker believes the addressee's work is
plagiarized. This can be explained if stress on "plagiarized" is
marking the proposition that the work is plagiarized as at-issue. So,
the generalization in Definition 7 predicts that this proposition does
not project.



(19)
If the T.A. disCOVers that your work is plagiarized, I will be
forced to notify the Dean.
(20)
If the T.A. discovers that your work is PLAgiarized, I will be
forced to notify the Dean.


Pragmatic approaches to presupposition take the burden of projection
off conventional triggering and allow for discourse structure to
influence projection when triggers are placed in different contexts.
One consequence of this view is that it can be applied
cross-lingustically (e.g. Tonhauser et al 2013) without running into
the issue of language-specific conventionalized triggers. Additionally
it allows us to account for the projection of expressions that don't
display other properties that we associate with presupposition, for
example appositives, expressives and honorifics (Potts 2005). In other
words, there's a reason why some things that aren't presuppositions
still behave like them.



A new trend of psycholinguistic research potentially offers some
promising new evidence about the degree to which presuppositions are
processed like pragmatic inferences or semantic entailments. The
methods in these studies typically rely on identifying at what point
during the processing of an utterance presuppositions become available
to the listener. The line of reasoning goes like this: if
presuppositions are conventionally encoded in their triggers and are
conditions for contexts to update, they should arise immediately when
a trigger is used. However, if presuppositions are the result of
pragmatic reasoning, there should be a delay in their processing.
While the results of these studies have been somewhat inconsistent,
they largely suggest that presuppositions are processed immediately.
For example, one of the experiments in Tiemann et al. (2011) finds
that presupposition triggers themselves carry a processing cost
relative to other non-presuppositional expressions. In an eye-tracking
study, Kim (2008) finds that there are shifts in eye movements quite
rapidly after the utterance of the trigger *only*. These
studies and the methodologies used in them are still relatively
new. However, empirical work on the processing of presuppositions
remains a promising strand of research in determining the extent to
which we can consider presuppositions to be conventional


## 4. Local contexts and the dynamic turn



In static theories of meaning, such as the trivalent accounts of
presupposition discussed above, when a sentence is interpreted in a
given context, every expression in that sentence is interpreted
relative to that same context. In dynamic theories of meaning, the
context is allowed to change as a sentence is interpreted. The
earliest and perhaps still clearest motivation for this dynamism is
what might be termed the *anaphoric asymmetry*. The anaphoric
asymmetry consists in pronouns across languages being usually resolved
to expressions that have already occurred, and only being resolved
cataphorically to expressions that occur later in the sentence in
quite special configurations. The dynamic explanation for this is that
pronouns are resolved to referents via the context, and that the
context is updated during processing so that it typically only
contains information about things that have already been mentioned.
The question might then be asked: how does the processing of anaphora
relate to the processing of presuppositions? It turns out that there
are remarkably strong parallels between phenomena involving anaphora
and presupposition, and this in turn provides a motivation for
considering not only anaphora but also presupposition to be an
intrinsically dynamic phenomenon. In this section, we will first study
the parallels between presupposition and anaphora, seen as a possible
motivation for considering context change in analyzing presupposition,
and then describe in largely historical terms the sequence of
developments that led to contemporary dynamic theories.


### 4.1 Presupposition and anaphora



While a number of authors have noted that presuppositions behave in
some respects like anaphors (e.g., Kripke 2009 and Soames 1989), it
was van der Sandt (1989; 1992) who brought out the connection the most
forcefully. He noted that for every configuration of anaphors and
antecedents where a pronoun is interpreted anaphorically but is not
interpretable as a bound variable, a similar configuration is possible
with
 presuppositions.[13]
 In each of the following quadruples, we illustrate some configuration
in the (a) and (b) examples, while the (c) and (d) cases show that a
slight divergence from the original configurations (i.e. those in (a)
and (b)), produces infelicity. Note that the (a) and (c) examples
include an anaphoric pronoun ("it"), and the (b) and (d)
examples include the factive verb "knows", which triggers
a presupposition that its propositional complement is true (i.e., that
Fred left). So, anaphora is felicitous in configurations in which
presuppositions are felicitous, and anaphora is infelicitous in
configurations in which presuppositions are infelicitous. It is clear
that connections between anaphoric pronouns and their antecedents on
the one hand, and presupposition triggers and their antecedents on the
other, are sensitive to very similar configurational requirements.


**Inter-sentential (discourse) anaphora**



(21a)
 There was a storm. It was fierce.
(21b)
Fred left. Mary knows that Fred left.
(21c)
#It was fierce. There was a storm.
(21d)
#Mary knows that Fred left. Fred left.

**Donkey anaphora**



(22a)
If a farmer owns a donkey then he beats it.
(22b)
If Fred left then Mary knows that Fred left.
(22c)
#If a farmer doesn't own a donkey, then he beats it.
(22d)
#If Fred didn't leave left then Mary knows that Fred left.

**Modal subordination**



(23a)
A wolf might come to the door. It would eat you.
(23b)
Fred might have left. Mary would know that Fred has left.
(23c)
#A wolf might come to the door. It's brown.
(23d)
#Fred might have left. Mary knows that Fred has left.

**Bathroom anaphora**



(24a)
Either there's no bathroom in this house, or else it's in a
funny place.
(24b)
Either Fred didn't leave, or else Mary knows that he left.
(24c)
#Either there is a bathroom, or else it's in a funny place.
(24d)
#Either Fred left, or else Mary knows that he left.

### 4.2 Satisfaction in local contexts



As previously noted, early work on presupposition was primarily
focused on definite descriptions, and definite descriptions have
continued to be the paradigmatic example of a presupposition trigger
in philosophical literature over the last fifty years. However, by the
early 1970s, more linguistically oriented work had expanded the
empirical domain of presupposition theory from definite descriptions
to other trigger types, including factives (Kiparsky and Kiparsky,
1970), implicatives (Karttunen, 1971a), focus particles (Horn, 1969),
verbs of judging (Fillmore, 1971) and sortal constraints (Thomason,
1972). Stalnaker's discussion of Karttunen's semifactives provides an
early example of how this linguistic expansion of the empirical domain
has impacted philosophical work. Also by the early 1970s, linguists
had expanded the empirical domain in another direction. The
philosophical literature was largely oriented towards unembedded
presupposition triggers and triggers under negation, but as we have
already mentioned, Morgan (1969) and Langendoen and Savin (1971)
generalized the issue by considering arbitrary embeddings. However, it
was not until Karttunen (1973) that the full complexity of the
projection problem became apparent. By methodically considering
projection behavior construction by construction, Karttunen showed
that there was more variation in projection behavior than had been
previously described, making it quite clear that none of the extant
Frege-Strawson derived systems could hope to cover every case, and
this ultimately led to the application of dynamic models of meaning to
the problem of presupposition projection.



Karttunen (1973) presented a taxonomy of embedding constructions that
divided them into three classes: *plugs*, *holes* and
*filters*. Plugs comprise a class of predicates and operators
which Karttunen claimed block the projection of presuppositions, while
holes are a class of predicates and operators which allow
presuppositions to project freely. So, for example, since "told
that" is a plug, according to
 Karttunen,[14]
 (25) is predicted not to presuppose that there is a King of France.
On the other hand, since "perhaps" is a hole, (26) is
predicted to presuppose that there is a King of France.



(25)
Mary told Jim that the King of France was bald.


(26)
Perhaps the King of France is bald.


Karttunen's filters include the binary logical connectives "if
then", "and", and "or". The intuition
behind the filter metaphor is that these constructions allow only some
presuppositions to project, others being caught in the filter, and we
have already seen examples of this phenomenon. Thus example (12)
showed that sometimes a presupposition in the consequent of a
conditional does not project: here the presupposition that there was a
knave is filtered out. But the same example includes an occurrence of
the definite "the tarts" in the consequent, and the
presupposition that there are (or at least were) some tarts projects
from the conditional. Karttunen concluded that the consequent of a
conditional acts as a hole to some presuppositions, but filters out
all those presuppositions which are entailed by the antecedent, or,
more generally, by a combination of the antecedent and contextually
supplied background information.



Karttunen's key example showing the role of context bears
repetition:



(27)
Either Geraldine is not a mormon or she has given up wearing her
holy underwear.


The second half of (27) contains (at least) two presupposition
triggers: the definite description "her holy underwear"
and the aspectual verb "give up", which trigger the
presuppositions that Geraldine used to have and wear holy underwear,
respectively. Karttunen's filtering condition for disjunctions removes
from the right disjunct any presuppositions that are entailed by a
combination of the context and the negation of the left disjunct. Now
consider a context supporting the proposition that all mormons have
holy underwear which they wear regularly. It follows from this
proposition and the negation of the left disjunct, i.e., the
proposition that Geraldine is a mormon, that Geraldine has holy
underwear and has worn it regularly. But these are exactly the
presuppositions triggered in the right disjunct, so they are filtered
out. It follows that (27) has no presuppositions.



Karttunen's (1973) account is of interest not only for its triptych of
plugs, holes and filters, but also because it sets the background for
a crucial shift of perspective in Karttunen (1974), and thence to the
dynamic approaches to presupposition that have been dominant in recent
years. What remained unclear in the 1973 paper was the motivation for
filtering, i.e. why presuppositions should be filtered out when
entailed by other material. Karttunen (1974) suggests an alternative
conception based on the idea of *local contexts* of evaluation.
The idea is that the parts of a sentence are not necessarily evaluated
with respect to the same context as that in which the sentence as a
whole is evaluated: a *local context* may contain more
information than the *global context*. For example, when
evaluating a conjunction, the second conjunct is evaluated in a local
context which contains not only the information in the global context,
but also whatever information was given by the first conjunct.
Karttunen (1974) defines local contexts of evaluation for a range of
constructions, and suggests the following requirement: presuppositions
always need to be entailed (or "satisfied", as he put it)
in the local context in which the trigger is evaluated. Given this
requirement, the overall presuppositions of a sentence will just be
whatever propositions must be in a context of an utterance in order to
guarantee that the requirements associated with presupposition
triggers are satisfied in their local contexts of interpretation.



Karttunen spelled out how local satisfaction should be calculated
separately for each connective and operator he considered. However,
recent developments in Schlenker (2008) provide a general way of
calculating what the local context should be. In the following
reformulation of Karttunen's model we incorporate Schlenker's insights
along the lines proposed by Beaver (2008).



Let us say that some clause in a complex sentence is
*redundant* relative to some context of utterance if you can
replace that clause by a tautology without affecting the amount of
factual information conveyed by the sentence in that context. For
example, in (28), the first conjunct is redundant in any context of
utterance. Here, the same factual information would be conveyed by
"Mary is Mary and Mary owns a sheep", where the first
conjunct is replaced by the tautology "Mary is Mary".



(28)
Mary owns an animal and Mary owns a sheep.


Now let us say that a clause is *left-redundant* if it is
possible to tell by looking at the material in the sentence to the
left of the clause that the clause is redundant. So "Mary owns
an animal" is not left-redundant in (28) (except if the context
of utterance already entails that Mary owns an animal), because there
is no material before that clause, implying that it is impossible to
tell by looking at material to the left of the clause that the clause
is redundant. On the other hand, the same sentential fragment,
"Mary owns an animal", is left-redundant in (29) and also
in (20):



(29)
Mary owns a sheep and Mary owns an animal. (*Truth-conditionally
equivalent to:* Mary owns a sheep and Mary is Mary)


(30)
If Mary owns a sheep then Mary owns an animal.
(*Truth-conditionally equivalent to:* If Mary owns a sheep then
Mary is Mary)


Now we use this idea of left redundancy, which echoes the above van
der Sandt analysis of the effect of fronting presuppositions, to
define the crucial notion in Karttunen's (1974) account.



**Definition 8 (Karttunen/Schlenker: Presupposition via
satisfaction)**
  

A presupposition *P* is *satisfied* at point *X*
in *S* iff *P* would be left-redundant if added at point
*X*. A sentence presupposes whatever propositions must hold in
global contexts of utterance such that each locally triggered
presupposition is satisfied where its trigger occurs.




As an example, let us consider the presuppositions predicted for (27),
repeated below:



(27)
Either Geraldine is not a mormon or she has given up wearing her
holy underwear.


Note first that for all sentences of the form "*A* or
*B*", the negation of *A* is satisfied within the
right disjunct. So "Geraldine is a mormon" is satisfied in
the right disjunct of (27). And more generally, anything entailed by a
combination of propositions in the context and the negation of the
left disjunct will be satisfied in the right disjunct. Now, let us
consider the clause "she has given up wearing her holy
underwear": we take this to trigger the presupposition that
Geraldine has had holy underwear that she wore. This presupposition
will be satisfied provided the global context of utterance, combined
with the negation of the left disjunct, entails that she has had holy
underwear that she wore. And classically this will be the case if and
only if the context supports the conditional "if Geraldine is a
mormon, then she has had holy underwear that she wore" (which
would also be the case if the context supported something stronger).
Hence, this conditional is the presupposition Karttunen (1974)
predicts for (27).



One notable property of Karttunen's 1974 treatment of examples like
(27), a property not found in his 1973 model, is that the
presupposition predicted is conditionalized. That is, (27) is not
predicted to presuppose that Geraldine has had holy underwear that she
wore, but that if she is a mormon then she has had such underwear. We
already encountered such conditionalized presuppositions in our
discussion of Strong Kleene; in fact, Strong Kleene predicts exactly
the same conditionalized presupposition in this case. Karttunen's 1974
model also predicts conditionalized presuppositions when the
presupposition trigger is in the right conjunct of a conjunction, or
in the consequent of a
 conditional.[15]
 Thus in (16a), repeated below, the presuppositions predicted are that
there is a king (since presuppositions triggered in the antecedent are
not conditionalized), and that if the king is angry, then there is a
knave. In (16b), the conditional presupposition (that if there is a
knave, then there is a knave) is trivial, so in effect there is no net
 presupposition.[16]



(16a)
If the king is angry then the knave stole the tarts.
(16b)
If there is a knave, then the knave stole the tarts.


Although Karttunen's (1974) model is distinct conceptually from any of
its predecessors, we have already noted that it shares at least some
predictions with Strong Kleene. An observation made by Peters (1979)
showed that the 1974 model is surprisingly closely related to the
semantic accounts of presupposition discussed above. In particular,
Peters showed that Karttunen's way of calculating presuppositions for
the truth conditional connectives is equivalent to what would be
obtained within a three-valued logic, but with special non-symmetric
connectives. Here is a general way of defining the Peters Connectives,
inspired both by Schlenker (2009; 2008) and George (2008):



**Definition 9** **(Middle Kleene/Peters connectives)**
  

Go from left to right through the sentence. For each argument
*X* that takes a non-classical value, check whether on the
basis of material on its left, assigning an arbitrary classical value
to *X* could conceivably have an effect on the overall value.
If so, the sentence as a whole lacks a classical truth value. If not,
just assign *X* an arbitrary value, and carry on. If this
procedure allows all non-classical values to be filled in classically,
then the sentence can be assigned a classical value.




For example, this procedure makes a conjunction classical if both its
arguments are classical, false if the left conjunct is false, and
undefined otherwise. Thus undefinedness of the left conjunct forces
undefinedness of the entire conjunction, whereas undefinedness of the
right conjunct only sometimes yields undefinedness of the entire
conjunct, as seen in the following comparison of truth tables in
various systems. The net effect is that presuppositions of the left
conjunct project in the Middle Kleene system, just as in the Weak
Kleene system, but presuppositions of the right conjunct are
conditionalized, just as in the Strong Kleene system. This behavior
precisely mirrors that of the Karttunen (1974) model.



**Definition 10** **(Trivalent truth tables for
conjunction)**




|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Weak Kleene



|  |  |  |  |
| --- | --- | --- | --- |
| ph [?] ps | t | f |  |
| t | t | f |  |
| f | f | f |  |
|  |  |  |  |

 | Middle Kleene/Peters



|  |  |  |  |
| --- | --- | --- | --- |
| ph [?] ps | t | f |  |
| t | t | f |  |
| f | f | f | f |
|  |  |  |  |

 | Strong Kleene



|  |  |  |  |
| --- | --- | --- | --- |
| ph [?] ps | t | f |  |
| t | t | f |  |
| f | f | f | f |
|  |  | f |  |

 |



The equivalence between Peters' connectives and Karttunen's model
paved the way for a more complete reformulation of the Karttunen model
in Karttunen and Peters (1977; 1979), where certain types of
presupposition (which Karttunen and Peters regard as conventional
implicatures rather than presuppositions) are treated in a
compositional grammar fragment. This fragment uses two dimensions of
meaning, one for presupposition and one for assertion, and is
effectively an implementation of the Peters connectives in a
four-valued logic; see Krahmer (1994); Krahmer (1998), Beaver (2001),
and Beaver and Krahmer (2001) for discussion, and the latter for a
fragment that mirrors that of Karttunen and Peters, but allows for
richer interactions between presuppositions and
 quantifiers.[17]


### 4.3 Satisfaction theories



Although Karttunen's (1974) model turned out to be equivalent to a
system which, from a purely technical point of view, is in the
Frege-Strawson tradition, Karttunen (1974) was one of the seminal
papers of the dynamic zeitgeist that swept through semantics and
pragmatics in the last decades of the twentieth century. Also relevant
here are Hamblin (1970), Stalnaker (1972; 1974) , Gazdar (1979) and
Lewis (1979), all of whom advanced dynamic models of pragmatics in
which the (joint) commitments of speakers and hearers evolve as new
assertions are made and their content becomes part of the linguistic
context available for future utterances. It is against this background
that Heim (1982; 1983) offered the first dynamic semantic account of
presupposition. Heim's model utilizes Stalnaker's notion of a context
as a set of all possible worlds compatible with what has been
established at that point in a conversation, but involves a crucial
twist adapted from Karttunen. In Stalnaker's model, a single
*global* context is updated each time new information is
asserted, but in Heim's model the context is updated *locally*
in the process of computing the meanings of subparts of a complex
 expression.[18]
 We can define a simplified version of Heim's system as follows:



**Definition 11** **(Dynamic Semantics)**
  

Assuming that the *context set* *C* is a set of possible
worlds and *S* and *S*' are sentences:

1. *C* + *S* = the subset of worlds in *C* that
are compatible with *S*, but this is defined  *iff*
*S*'s presuppositions (if any) are true in all worlds in
*C*.
2. *C* + !*S* = *C* [?] (*C* +
*S*)
3. *C* + *S* [?] *S*' = (*C* +
*S*) + *S*'
4. *C* + *S* * *S*', where *
is some truth functional operator, is given by the simplest classical
definition of * in terms of ! and [?] that preserves the
order of the two sub-clauses.
5. *S* is *satisfied* in a context *C* iff
*C* + *S* = *C* (i.e., updating *C* with
*S* has no effect).
6. *S* *presupposes* *S*' iff
*S*' is satisfied in all contexts where update with
*S* is defined.




Clause (*iv*) entails that update with a conditional is defined
via the equivalence *A* - *B* [?] !
(*A* [?] ! *B*) (provided that the subordinate
clause precedes the main clause). To see how this will work, let's
consider the following example:



(31)
If the king is angry, then the knave stole the tarts. ( =
(16a))

In order to update a context with (31), we must do the
equivalent of updating with (32a). Now clause (*ii*) says that
to update a context with (32a), we must first try updating with (32b),
and subtract the result from the original context (so as to leave
behind whichever worlds are *not* compatible with (32a)). But
(32b) is a conjunction, so we must first update with the left conjunct
(32c), and then with the right (32d). Updating with (32c) is only
defined if the presupposition that there is a king is satisfied in all
worlds in the context set. We immediately see that (31) and (32a),
(32b), and (32c) all have this requirement, i.e., they presuppose that
there is a king. Provided this presupposition is satisfied, updating
with (32c) produces a subset of worlds where the king is angry. We use
this reduced context set for update with (32d). But update with (32d)
again uses the negation clause (*ii*) of the above definition.
So we started off with a set of worlds where there is a king, we
reduced it to a set of worlds where the king is angry, and now we must
update that context with (32e), an update which will only be defined
if there is a knave.



(32a)
It's not the case that [the king is angry and the knave didn't
steal the tarts].
(32b)
The king is angry and the knave didn't steal the tarts.
(32c)
The king is angry.
(32d)
The knave didn't steal the tarts.
(32e)
The knave stole the tarts.


The upshot of the above argumentation is that update of a context with
(31) is only defined for contexts in which (a) there is a king, and
(b) all the worlds where the king is angry are worlds where there is a
knave. Following the definitions through, it turns out that, once
again, the original sentence carries both a non-conditionalized
presupposition, that there is a king, and the conditionalized
presupposition that if the king is angry, then there is a knave.



The satisfaction based model has seen considerable further
development--see e.g., Beaver (1992; 2001), Chierchia (1995),
Heim (1992), Zeevat (1992), and, for a rather different formalization
of a dynamic semantic approach, van Eijck (1993; 1994;
 1995).[19]


## 5. Accommodation



The most important feature of the satisfaction model not covered in
the description above is accommodation. Accommodation was first
discussed by Karttunen (1974) and Stalnaker (1974), though only named
as such by Lewis (1979). Karttunen introduces the concept as
follows:



> 
> Ordinary conversation does not always proceed in the ideal orderly
> fashion described earlier. People do make leaps and shortcuts by using
> sentences whose presuppositions are not satisfied in the
> conversational context. This is the rule rather than the exception
> [...] I think we can maintain that a sentence is always taken to
> be an increment to a context that satisfies its presuppositions. If
> the current conversational context does not suffice, the listener is
> entitled and expected to extend it as required. (Karttunen 1974: 191)
> 



If this looks reasonably straightforward, the reader should be warned
that accommodation is among the more contentious topics in
presupposition theory.
 [20]



To begin with, there are various notions of accommodation, some of
which are stricter than others. To explain, consider the following
example by Heim (1982):



(33)
John read a book about Schubert and wrote to the author.


In order to determine the intended meaning of "the
author", the hearer has to infer (*i*) that there is an
author and (*ii*) that the said author wrote the book read by
John. Whereas on a broad understanding of accommodation, all of this
is accommodated, on a strict construal only (*i*) is, and
(*ii*) is a bridging inference. This is not just a matter of
terminology. If we choose to be strict, we can argue that there is
something like an "accommodation module", which as such
has nothing to do with world knowledge; whereas if the notion is
construed more broadly, accommodation is of a piece with bridging. To
facilitate the following discussion, we will adopt a strict notion of
accommodation, and take the naive view that what is accommodated is
the presupposition as triggered by, e.g., a definite NP or factive
verb.


### 5.1 Global and Local Accommodation



With these preliminaries out of the way, we turn to the first major
question: *Where* are presuppositions accommodated? Though it
may seem odd at first, this question is inescapable if we assume, as
is standard in dynamic semantics, that an expression may occur in
several contexts at the same time (cf. Section 4.3). For Heim (1982),
following Lewis (1979), accommodation is a process whereby contexts
are adjusted so as to make update possible when presuppositions are
not satisfied. In terms of her treatment of accommodation, Heim's
major innovation over Lewis was to allow this process to take place
not only in the global context of utterance, but also on local
contexts found midway through an update. To illustrate, consider the
following:



(34a)
(*c*0) Maybe (*c*1) Betty is
trying to give up drinking.
(34b)
(*c*0) Maybe (*c*1) Wilma
thinks that (*c*2) her husband is having an
affair.


Here *c*0 refers to the global context in which a
given sentence is uttered, and *c*1and
*c*2 are auxiliary, or local, contexts. In (34a),
the modal "maybe" creates an auxiliary context of possible
states of affairs in which Betty is trying to give up drinking; the
same, mutatis mutandis, for (34b). The presupposition triggered in
(34a), that Betty used to drink, can be accommodated
*globally*, i.e., in *c*0, or
*locally*, in *c*1. In the former case, the
utterance is construed as meaning that Betty used to drink and may be
trying to kick the habit; in the latter, it conveys that, possibly,
Betty used to drink and is trying to give up drinking. Likewise, in
(34b), the presupposition that Wilma is married may be accommodated
globally, or locally in the most deeply embedded context. But here
there is a third option, as well: if the presupposition is
accommodated in *c*1, the sentence is read as
"Maybe Wilma is married and she thinks that her husband is
having an affair", and we speak of *intermediate*
accommodation.



It is widely agreed that the following empirical generalization, made
explicit by Heim (1983), is correct:



**PGA:** Global accommodation is preferred to non-global
accommodation.




While the PGA was initially based solely on intuitions, quantitative
studies on the speed of processing local and global interpretations
have since provided empirical support for it (e.g. Chemla and Bott
2013 and Romoli and Schwartz 2014).



In the examples in (34) the PGA (preference for global accommodation)
clearly holds: non-global interpretations may be possible, but they
require special contexts. One such context may be that the
presupposition contains a variable which is bound by a quantifier:



(35)
Most Germans wash their cars on Saturday.


In (35), with the possessive presupposition trigger "their
cars", there is a global context (outside of the scope of
"most"), a local context corresponding to the scope of the
quantifier (occupied by the VP "wash their cars on
Saturday"), and also an intermediate context in the restrictor
of the quantifier (occupied by "Germans"). The most
natural interpretation of this sentence surely is that most Germans
who own a car wash it on Saturday. So in this case intermediate
accommodation seems to be the preferred option, and this might be
explained, following van der Sandt (1992), by supposing that the
possessive pronoun contains a variable bound by the quantifier.



There are other cases where intermediate accommodation is virtually
impossible:



(36)
(*c*0) If (*c*1) Fred is
coming to the reception, (*c*2) he may
(*c*3) bring his wife.


It is quite unlikely that this may be construed, with intermediate
accommodation in *c*1, which is the antecedent of
the conditional, as "If Fred is married and is coming to the
reception, he may bring his wife." More generally, we don't know
of any clear-cut cases (i.e., cases in which accommodation is not
forced by independent contextual factors) in which a presupposition
triggered in the consequent of a conditional is accommodated in the
antecedent.



The picture is rather confusing. While in some cases, e.g., (34b) or
(35), intermediate accommodation seems possible and sometimes even
preferred, in other cases it doesn't seem possible at all. And things
get even more confused than this. Thus far, we have taken our examples
at face value, but some authors have argued that we shouldn't because,
as a matter of fact, intermediate accommodation doesn't exist. For
instance, according to Beaver (2001), the presupposition in (35) is
taken as evidence that the topic of conversation is car-owning
Germans, and it is this topic that restricts the domain of the
quantifier, making intermediate accommodation redundant. See also von
Fintel (1995) and Geurts and van der Sandt (1999) for discussion.



Returning to the uncontested PGA, let us ask how it can be explained.
Heim (1982) was not explicit about exactly how accommodation should
work and what should be accommodated. And oddly enough, although
virtually all theories of presupposition projection accept that the
PGA holds, there haven't been that many attempts at explanation. One
candidate is what Beaver (2001) calls the "Atlas
Principle", after Atlas (1976):



**AP:** One accommodation alternative is preferred to
another if the former yields a stronger meaning than the latter (i.e.,
if the first meaning unilaterally entails the second).



Advocates of the Atlas Principle include, besides its eponym, Yeom
(1998), Zeevat (1999), and Blutner (2000). One thing to note about the
Atlas Principle is that it does not necessarily vindicate the PGA
across the board: while the predictions made by the Atlas Principle
will tend to comply with the PGA, they don't have to. However, it is
surprisingly difficult to say where exactly the Atlas Principle
deviates from the PGA, because this depends on various extraneous
factors; see Geurts (2000) for discussion.



A major worry about the Atlas Principle is that it is *ad hoc*.
Despite its soothing resemblance to Grice's second Quantity Maxim, it
is questionable whether hearers generally prefer stronger
interpretations to weaker ones. This suggests that the Atlas Principle
may not be justified as an instance of a more general constraint, and
is therefore stipulative. The sad and somewhat embarrassing truth
seems to be that, thus far, we don't really know why the PGA should
hold.



One last issue we would like to mention is that accommodation isn't
always equally easy (or hard). For example:



(37a)
Fred is looking for the person.
(37b)
Wilma is pregnant, too.


In (37a) the presupposition triggered by "the person"
clearly requires a salient discourse referent to hook on to; the
sentence would be infelicitous when uttered out of the blue. The same
goes for the presupposition triggered by "too" in (37b),
viz. that some salient person different from Wilma is pregnant. This
sentence would be very peculiar when uttered out of the blue, or in
any context where no salient person was under discussion who could be
pregnant. Put otherwise: unlike the presuppositions we have seen thus
far, it is very hard to deal with the presuppositions of "the
person" or "too" by accommodation
 alone.[21]
 Why should this be so?



Van der Sandt (1992) proposes that presuppositions whose descriptive
content is relatively poor are hard to accommodate. This
generalization is borne out by pronouns, names, and semantically
attenuate definite NPs like "the person". However, it is
not very clear what "relatively poor" means. Definite NPs
like "the water molecule" or "the lonely
carpenter" don't strike us as particularly poor, but may be hard
to interpret by way of accommodation. Similarly, the presuppositions
associated with "too" may be quite rich, and nevertheless
they are generally hard to accommodate. Geurts and van der Sandt
(2004) propose to account for the latter by adopting Heim's (1992)
idea that the presupposition triggered by "too" contains a
pronominal element, which blocks accommodation, but this proposal has
been criticised by Beaver and Zeevat (2007). Be this as it may, it
seems clear that van der Sandt's generalization cannot be read as
biconditional: even if poor presuppositions are difficult to
accommodate, the reverse doesn't always hold.



Another problem with van der Sandt's generalization is that it is not
clear how it can be justified. Even if it somehow makes sense that
lack of descriptive content should make accommodation hard, we would
like to know more precisely why this should be so. A possible answer
to this question may be found in the work on definites by Hawkins
(1978), Clark and Marshall (1981), Heim (1982), and others. As Heim
observes, "accommodation in response to definites is not
normally a matter of adding just the minimal amount of information
that would restore felicity." (Heim 1982, p. 372) It seems
plausible that this holds for accommodation generally, and it arguably
follows from the nature of accommodation. If a presupposition is to be
interpreted by way of accommodation, new information is presented
*as if* it were given, and it has often been observed that this
will only work if the information is not contentious or otherwise
remarkable. That is to say, it should always be possible to
*integrate* the new information into the common ground: it has
to be linked to what is already given. This will be hard with
semantically attenuate NPs like "the thing" or pronouns
like "he", but also with richer definites whose content
cannot readily be linked to anything in the common ground.
Nevertheless, it will generally be easy with richer presuppositions,
not *because* they have more content, but simply because they
are more likely to contain anchors into the common ground.


### 5.2 Accommodating Presuppositions in Satisfaction Framework



Local satisfaction is at the heart of dynamic theories of
presupposition, but we've already seen that it faces some empirical
challenges in accounting for conditionalized presuppositions.
Specifically, sometimes satisfaction theories generate weaker
conditional presuppositions when intuitively the speaker is
presupposing a stronger, unconditionalized presupposition. Geurts
(1996,1999a) deems this "The Proviso Problem," and the data
surrounding this problem has left quite a mess for proponents of
satisfaction theories to clean
 up.[22]



According to satisfaction theories, only weak conditional
presuppositions should follow from embedding presuppositions in
certain constructions, notably conditionals themselves. For example,
imagine that you are about to go surfing for the first time in the
cold waters of Northern California, and you and your interlocutor
suspect that a common acquaintance, Theo, is a scuba diver, and that
he may be able to help. In this context, the use of *his* in
(38a) intuitively leads to the conditional inference in (38c):



(38a)
If Theo is a scuba diver, then he will bring his wet suit.
(38b)
Theo has a wet suit.
(38c)
If Theo is a scuba diver, then he has a wet suit.


Contrast this with (39a), which strongly suggests that the speaker
believes that Theo has a wet suit (39b), and not the weaker
conditional in (39c):



(39a)
If Theo is in a generous mood, then he will bring his wet suit.
(39b)
Theo has a wet suit
(39c)
If Theo is in a generous mood, then he has a wet suit.


Whatever mechanism is used to determine what is accommodated, it must
ensure that sometimes conditional presuppositions are strengthened (to
become unconditionalized), and sometimes they aren't. What examples
like (38) and (39) suggest is that this might be explained in terms of
plausibility: it could be that the conditional in (39c) is
strengthened because it seems implausible that a speaker would be
assuming that Theo's generosity was linked to his ownership of aquatic
paraphernalia, whereas it seems more plausible that a speaker would
simply be assuming that Theo owned such equipment.



Several proposals (e.g. Beaver 2001, Singh 2007, 2009; Schlenker 2011)
try to motivate this kind of strengthening mechanism to explain
when exactly a conditionalized presupposition should be
strengthened. For example, Beaver's model of accommodation, first
published in Beaver (1992) treats accommodation as a type of filtering
operation. Beaver suggests that due to uncertainty about what the
speaker takes the common ground to be, the hearer has to entertain
multiple alternative context sets, with some ranking of which is the
most plausible. All these alternative contexts are updated
simultaneously. Accommodation is then what happens when the update is
not defined on what was previously considered to be the most plausible
context, in which case the hearer drops that context from contention.
What remains is a new set of contexts in which the most plausible one
is a context that has been successfully updated.



Unfortunately for this style of explanation of presupposition
strengthening, plausibility appears to have its limits. Consider the
two examples in (40a,b). If we assume that a cleft "it is *X*
that *Y*-ed" presupposes an existential, roughly
"someone/something *Y*-ed" then in a dynamic theory of
presupposition (40b) will generate the same conditionalized
presupposition as results from (40a), which involves the factive
"knows", namely the conditional in (40c). However, there is a clear
difference in the inferences we would tend to draw from utterances of
(40a) and (40b). Whereas (40a) licenses an inference only to the
conditional presupposition in (40c), example (40b) leads to the
stronger, unconditionalized presupposition in (40d). Under the
assumptions we have made, namely that (40a) and (40b) generate exactly
the same underlying conditionalized presupposition, the plausibility
approach used in Beaver's framework fails to predict a difference in
what is accommodated in these cases.



(40a)
Peter knows that if the problem was easy, someone solved it.
(40b)
If the problem was easy then it was Kristie who solved it.
(40c)
If the problem was easy, someone solved it.  

 [*Conditional presupposition for (40a,b), accommodated for (40a)*]
(40d)
Someone solved the problem.  

 [*Unconditionalized presupposition, accommodated for (40b) but not
 (40a)*]


One relevant factor here that might influence accomodation is
information structure. In (40b), the cleft structure might be said to
reflect the presence of a *Question Under Discussion* (QUD), in
the sense of Roberts (2012), concerning who solved the problem. To the
extent that such a question is under discussion, the interlocutors
will presumably know that this is so. And if "Who solved the problem?"
is indeed the question the interlocutors are trying to answer, then
they are likely to mutually accept that someone solved the problem,
thus explaining projection. Crucially, this line of reasoning depends
on the cleft in (40b) having a particular information structural
function, and a similar argument could not be made in a case like
(39a), where there is no constructional marking of information
structure, and in particular no indicator that "Who solved the
problem?" is the QUD.



(41a)
If the problem was easy then Peter knows that someone solved it.
(41b)
If the problem was easy then Peter KNOWS that someone solved it.
(41c)
If the problem was easy then even PETER knows that someone solved it.


We may have reasonable motivations for when we might expect a
conditional presupposition to be strengthened. But even with such
mechanisms, satisfaction theories still fall short when confronting
certain data. For example, consider (42) below.



(42)
If when Sam gets back from vacation he finds moldy fruit in the
kitchen, he'll be annoyed that he had food in the house.


Here, the consequent presupposes that Sam had food in the house, which
is also entailed by the antecedent. Since satisfaction theories assume
that presuppositions in a complex sentence will be satisfied locally,
we're left with a tautology. So, the local satisfaction constraint
generates presuppositions which are redundant.



The proviso problem is still a relevant hurdle for proponents of
modern satisfaction theories. Mandelkern (2016) presents a version of
satisfaction theory designed to avoid the proviso problem entirely.
Romoli et al (2011) explore this issue experimentally by asking which
presupposition -the conditional or unconditional option- is more
basic. But, ultimately the proviso problem is less problematic for
other accounts of presupposition, which don't rely on local context
updates.


### 5.3 Resolving and Accommodating Presuppositions in DRT



In order to account for both presupposition projection facts and the
parallels between presupposition and anaphora, van der Sandt proposed
an accommodation-based model as an extension of Discourse
Representation Theory (see the SEP entry on
 discourse representation theory
 for an introduction). Presupposed information is information that is
presented as given, and in van der Sandt's theory this means that
presuppositions want to have discourse referents to bind to. However,
whereas anaphoric pronouns are rarely interpretable in the absence of
a suitable antecedent, the same does not hold for all
presupposition-inducing expressions. For instance, a speaker may
felicitously assert that he met "Fred's sister" even if he
knows full well that his audience isn't aware that Fred has a sister.
In such cases, presuppositions are generally accommodated, which is to
say that the hearer accepts the information as given, and revises his
representation of the context accordingly. Accommodation, thus
understood, is a form of exploitation in Grice's sense: the purpose of
presuppositional expressions is to signal that this or that
information is given, and if some information is new but not
particularly interesting or controversial (like the fact that somebody
has a sister) the speaker may choose to "get it out of the
way" by presuppositional means.



Van der Sandt's theory incorporates the notion of accommodation as
follows. Presuppositions, according van der Sandt, introduce
information that prefers to be linked to discourse referents that are
already available in the hearer's representation of the discourse, and
in this respect they are like pronouns. Van der Sandt in fact uses the
term "binding" to refer to configurations in which presuppositions
have antecedents in the Discourse Representation Structure (DRS), thus
generalizing the standard notion of a bound pronoun to cases involving
multiple discourse referents. However, if a suitable discourse
antecedent is not available, a new one will be accommodated, and the
presupposition is linked to that. Generally speaking, accommodation is
not an option in the interpretation of pronouns, and one reason that
has been suggested for this is that a pronoun's descriptive content is
relatively poor (see Section 5.1 for discussion). Being told that
"she" is wonderful is not particularly helpful if it isn't
clear who the pronoun is meant to refer to. By contrast, if the
speaker refers to "Pedro's sister" there is more to go on,
and accommodation becomes feasible. Hence, van der Sandt hypothesizes
that pronouns are a special class of presuppositional expressions:
while all presupposition triggers prefer to be linked to antecedents,
pronouns almost always must be linked to antecedents because they are
descriptively attenuated, and therefore cannot be construed by way of
accommodation.



To get a better idea how this is supposed to work, let us consider an
example with several presupposition triggers:



(43)
If Fred is protesting, then his son is protesting, too.


This sentence contains the definite NP "his son", which in
its turn contains the pronoun "his", and the focus
particle "too". Assuming the pronoun's antecedent is
"Fred", the definite NP triggers the presupposition that
Fred has a son, while the focus particle triggers the presupposition
that someone other than Fred's son is protesting. Note that in this
example the presupposition triggered by the definite NP is
"inherited" by the sentence as a whole, while the one
triggered by "too" is not: normally speaking, an utterance
of (43) would license the inference that (according to the speaker)
Fred has a son, but not that someone else besides Fred's son is
protesting.



Van der Sandt's theory accounts for these observations as follows. We
suppose that the grammar assigns (43) the intermediate semantic
representation in (44a). Here [ u1,..., u*m*:
ph1,...,ph*n*] is a simple
Discourse Representation Structure in linear form, with u1,...,
u*m* a list of discourse markers, and
ph1,...,ph*n* a list of
conditions on those markers; connectives like = are used to build
up complex conditions. We assume for convenience that most
interpretative problems have been cleared out of the way already, and
that the only thing that remains to be done is resolve the
presuppositions triggered by "his", "his son"
and "too", which are flagged by Beaver's (1992) trigger
symbol, [?].



(44a)
[x: Fred(x), [: protesting(x)] = [: [?][z: [?][y:], z
is y's son], protesting (z), [?][u: u [?] z, protesting(u)]]]
  

...binding y to x...
(44b)
[x: Fred(x), [: protesting(x)] = [: [?][z: z is x's
son], protesting(z), [?][u: u [?] z, protesting(u)]]]
  

...accommodating x...
(44c)
[x, z: Fred(x), z is x's son, [: protesting(x)] = [:
protesting(z), [?][u: u [?] z, protesting(u)]]]
  

...binding u to x...
(44d)
[x, z: Fred(x), z is x's son, [: protesting(x)] = [:
protesting(z), x [?] z]]


(44a) is the initial semantic representation associated with (43), in
which three presuppositions remain to be resolved. The first of these,
triggered by the pronoun "his", is bound to the discourse
referent representing Fred, which results in (44b). The second
presupposition, that Fred has a son, cannot be bound, and therefore
must be interpreted by way of accommodation. Van der Sandt's theory,
like Heim's (Heim, 1983), stipulates that accommodation at the global
level, as shown in (44c), is preferred to accommodation at other
sites. Finally, the presupposition triggered by the focus particle can
be bound in the antecedent of the conditional; after simplification,
this results in (44d), which represents the most natural way of
interpreting (43).


## 6. Born to fail, or unborn?



What happens when a presupposition is false? The textbook
proto-history of answers to this question goes as follows. According
to Frege (1892), if an expression *A* suffers from
presupposition failure, then any sentence containing *A* will
lack a truth value; Russell (1905) famously denied this, holding that
such a sentence will always be true or false; and then Strawson (1950)
reaffirmed Frege's position, more or less. What is less well known, at
least insofar as it usually doesn't make it into introductory classes
on philosophy of language, is that in subsequent work, Strawson partly
recanted his initial view and came to doubt that presupposition
failure invariably entails lack of truth value.



Taking a closer look at how speakers actually assess a sentence,
Strawson's (1964) paper argues that presupposition failure may but
need not cause a sentence to be infelicitous. Two of his examples are
the following:



(45a)
Jones spent the morning at the local swimming pool.
(45b)
The exhibition was visited yesterday by the king of France.


If there is no swimming pool locally, it is "natural
enough", according to Strawson, to say that (45a) is false, and
since the king of France doesn't exist, the same applies to (45b). And
if these sentences are false, their negations must be true. So, if
these subtle judgments are accepted, there are cases in which
presupposition failure does not prevent us from saying that a sentence
is true or false. But Strawson hasn't changed his mind about Russell's
example:



> 
> Confronted with the classical example, "The king of France is
> bald", we may well feel it natural to say, straight off, that
> the question whether the statement is true or false doesn't arise
> because there is no king of France. (Strawson 1964: 90)
> 



Strawson goes on to observe, however, that speakers who subscribe to
this judgment may want to reconsider their verdict if the context is
set up the right way. For instance, if Russell's sentence is used to
answer the question, "What examples, if any, are there of famous
contemporary figures who are bald?", we may be more inclined to
say that the answer is simply false.



Strawson's explanation for these facts is given in terms of
topicality. The most likely purpose of a sentence like (45a) is to
describe what Jones has been doing in the morning, rather than, say,
who the local swimming pool was visited by. That is, in the absence of
further information about the context in which this sentence is
uttered, its topic will be Jones's exploits. Similarly, a sentence
like (45b) will normally be used to convey information about the
exhibition. If so, although the sentence purports to refer to the king
of France, it is not about him; the king of France is not the topic of
discourse, nor part of the topic. In other words, the existence of the
king of France is not *at-issue*. Strawson's suggestion is that
this circumstance influences the way presupposition failure is dealt
with. On this view, presupposition failure results in infelicity only
if it affects the topic of a sentence; otherwise the sentence will be
judged true or false, as appropriate.



One of the appealing features of this analysis is that it takes into
account the context-dependence of speakers' intuitions. As Strawson
notes, Russell's sentence (46) will by default be construed as being
about the king of France, whence a strong tendency to judge the
sentence infelicitous.



(46)
The king of France is bald.


If, however, the discourse is about royal baldness in general, for
instance, the grammatical subject of (46) is used to say something
about that topic, and Strawson's account predicts that the sentence is
more likely to be judged false, which seems correct. Another
observation that neatly falls into place is that word order may have
an effect on speakers' intuitions about presupposition failure. As
Strawson observes, if we compare (45b) with (47), where the defective
description is in subject position, we would be "a shade more
squeamish" to say that the sentence is simply false (p. 91).
This is precisely what one should expect if speakers' intuitions were
topic-dependent.



(47)
The king of France visited the exhibition yesterday.


Assuming that Strawson's observations are correct, should we say (a)
that non-topical definites are non-presuppositional, or (b) that they
do have presuppositions, whose failure happens not to affect speakers'
truth-value judgments? Some authors argue for the former (e.g.,
Reinhart 1982, Horn 1989); this is Strawson's view, as well. Von
Fintel (2004) argues for the latter: topical or non-topical,
"the king of France" always triggers the presupposition
that there is a king of France; it's just our truth-value judgments
that fluctuate.



Von Fintel's position is in line with what has been a working
hypothesis for many years in theories of projection. According to
these theories, presuppositions are never really cancelled: if a
presupposition seems to disappear, it is because it projects to a
non-global context. It bears emphasizing that this view is not
irrevocably linked to these theories. It's just that there is no need
to assume that there are part-time presupposition triggers (in a sense
we expand upon in Section 8 below), because non-global projection can
be relied upon to explain why presuppositions sometimes seem to
disappear. However, this working hypothesis may have to be reassessed
if we want to account for Strawson's observations, which might be
taken to show that presuppositions are cancellable not only in complex
sentences but in simple sentences, as well.



So far we've only talked about definite descriptions. Some other
triggers show similar variability, but not all of them do. On the one
hand, the domain presuppositions associated with strong quantifiers
like "all" and "most" behave very much like
definite presuppositions (de Jong and Verkuyl 1985, Lappin and
Reinhart 1988, Geurts 2007). For example, when uttered out of the
blue, (48) will sound odd, but when proffered in response to
Strawson's question, "What examples, if any, are there of famous
contemporary figures who are bald?", it seems more likely to be
judged false:



(48)
All South-American monarchs are bald.


On the other hand, consider the following:



(49a)
#BENEDICT XVI is the incumbent pope, too.
(49b)
#Carnap managed to be born on May 18, 1891.


Given that there is only one incumbent pope and that it can't have
taken Carnap any effort to be born on May 18, 1891, both (49a) and
(49b) suffer from presupposition failure. But if someone who knew that
there was only one incumbent pope uttered (49a), it would not seem
entirely natural to say that they had lied. One might even say that
these sentences are *true*, and this intuition does not seem to
be topic dependent. The reason for this may be that the
presuppositions in question are *incidental* to the primary
content of these sentences.


## 7. Presuppositions and attitudes



For nearly four decades, the Holy Grail of presupposition research has
been to explain the behavior of presuppositional expressions occurring
in embedded positions. A particularly challenging mode of embedding
arises with attitude verbs. If we embed a presupposition trigger
under, e.g., "believe", we observe two types of inference.
This is seen in the following examples, where "-"
indicates that there is an inference, but of unspecified type:



(50)
Barney believes that *his sister* is drunk.
  

- Barney has a sister.
  

- Barney believes he has a sister.
(51)
Wilma believes that Barney *knows* that his sister is
drunk.
  

- Barney's sister is drunk.
  

- Wilma believes that Barney's sister is drunk.


Both inferences are fairly robust, and both seem to exhibit projection
behavior, as we illustrate here by applying various embedding tests to
(50):



(52a)
Barney doesn't believe that his sister is drunk.
(52b)
Perhaps Barney believes that his sister is drunk.


(52c)
If Barney has a sister, then he believes that his sister is
drunk.
(52d)
If Barney believes that he has a sister, then he also believes
that his sister is drunk.


It is natural to infer from both (52a) and (52b) that Barney has a
sister and that he believes that he has a sister, and these inferences
can be blocked in sentences such as those in (52c) and (52d) , where
"his sister" occurs in the consequent of a conditional
whose antecedent makes one or the other inference explicit. It may
seem odd at first that (52c) should block the inference that Barney
believes that he has a sister, while (52d) blocks the inference that
Barney has a sister. Note however that, generally speaking, Barney has
a sister *iff* he believes that he has a sister. We'll return
to this theme below.



Interestingly, literally the same pattern of observations holds for
other attitude verbs, like "want" for example:



(53)
Barney wants to phone his sister.
  

- Barney has a sister.
  

- Barney believes he has a sister.


The puzzling thing is that (53) does not license the inference that
Barney *wants* to have a sister, but rather that he believes
that he has one.



So, in many cases at least, a presupposition ph triggered within
the scope of "*x*
*V**A*...", where
*V**A* is an attitude verb, gives rise to two
inferences with a candidature for presuppositional status: (a) that
ph and (b) that *x* believes ph. Hence, we have three
possible ways of proceeding, all of which have been defended in the
literature:


1. Both inferences are presuppositions (Zeevat 1992, at least for
certain triggers).
2. Only ph is a presupposition (Gazdar 1979a; van der Sandt 1988;
Geurts 1998).
3. Only "*x* believes that ph" is a
presupposition (Karttunen 1974; Heim 1992).



The first strategy seems to require a stipulation that certain
presuppositions have to be accommodated twice, once inside a belief
context, and once outside, and such a strategy is difficult to
motivate. On the other hand, for (*ii*) and (*iii*),
there is the obvious problem that if we adopt either one of them, we
only account for half of the observed inferences. How to explain the
other half? Three possible answers to this question have been
discussed in the literature, mainly by Heim (1992):


1. *De re construal* (Heim 1992) What at first looks like a
presupposition projecting to the global context may in fact be due to
a *de re* construal of the presupposition trigger. This
solution has several serious drawbacks. In particular, it's hard to
see how this proposal can give us both inferences at the same time,
rather than one (*de re*) or the other (presupposition). For
this and other reasons (see Geurts 1998), we will not consider it any
further.
2. *Exportation* (Karttunen 1974, Heim 1992, Kay 1992) If
Barney believes that he has a sister, then it may plausibly be
inferred that he has a sister. Therefore, if it is presupposed that
Barney believes that he has a sister, then it may plausibly be
inferred that he has a sister.
3. *Importation* (Heim 1992, Geurts 1998) If Barney has a
sister, then it may plausibly be inferred that he believes that he has
a sister. Therefore, if it is presupposed that Barney has a sister,
then it may plausibly be inferred that he believes that he has a
sister.



If our presupposition theory predicts that the inferences projected
from "*x* *V**A*" are of
the form "*x* believes that ph", then we can
appeal to exportation to explain why ph is inferable, as well.
*Vice versa*, a theory which predicts that ph is presupposed
can use importation for deriving "*x* believes that
ph". So we have two options:




|  |  |  |
| --- | --- | --- |
|  | *x* believes that ph | ph |
| Option A | importation | presupposition |
| Option B | presupposition | exportation |



Which is it going to be? That's a hard question, which raises various
issues, only some of which we can mention here. First, it should be
noted that, whereas for theories of the satisfaction family it is hard
to *avoid* making the prediction that presuppositions projected
from attitude contexts are of the form "*x* believes that
ph", DRT-style theories are more flexible, and can predict
either this or that the presupposition is simply ph. In other
words, satisfaction theories are more constrained (which is good), but
therefore practically forced to resort to Option B.



One of the issues that need to be addressed is that of the true nature
of importation and exportation inferences. It seems reasonable to
assume that, generally speaking, people's beliefs are consistent with
the facts, and that we tend to assume by default that this is the
case. But even if this much is true, it is most unlikely that, by
default, people will infer ph from "*x* believes
ph" (for arbitrary *x* and ph), or vice versa.
Whatever importation and exportation are, they aren't general
heuristics; rather, these inferences are almost certainly dependent on
the context to some degree.


## 8. Presupposition variability



Much contemporary work on presupposition has been devoted to case
studies of particular triggers or families of triggers. More often
than not, these studies end up granting some sort of special
consideration to the trigger(s) in question. We have already seen
instances of trigger differentiation above; for example,
anaphoric accounts identify a class of triggers whose content is
"descriptively poor" to explain why their presuppositions are more
difficult to accommodate than those of other triggers (see Sections
5.1 & 5.3). Researchers have noted more and more ways in which the
presuppositions of triggers differ, mostly focused around questions of
how robustly the presupposition projects and in what sorts of contexts
the presupposition disappears.



For some, the blurry boundaries between the sorts of inferences that
are covered by presupposition theories have opened up the door for new
triggers and presupposition-like things that might not be covered by
traditional labels. For example, Schlenker (2015, 2018) applies a
presuppositional framework to iconic co-speech gestures, to identify
what he calls "cosuppositions." There are also inferences that seem to
challenge traditional diagnostics like projection. For instance,
non-restrictive relative clauses ("Fred, who I like, ...") produce
projection like presuppositions, but typically introduce new
information to the discourse (Chierchia & McConnell-Ginet
1990).



Finally, the way that some theories model presuppositions can give
rise to new types of related inferences. For example, Chemla (2008)
notes that the sentence in (54a) strongly suggests that the speaker
does not have a sister. According to Heim (1991), this inference
arises from the fact that the speaker did not utter the alternative in
(54b), which strongly presupposes that the speaker does have a sister.
This prediction follows from Heim's Maximize Presupposition!
principle, that a speaker will use the felicitous sentence with the
strongest presupposition among a set of alternatives. These types of
inferences have been referred to in the literature as
'anti-presuppositions,' a term originating with Percus (2006).



(54a) John believes I have a sister.
  

(54b) John knows I have a sister.



One observed difference between some triggers is that they don't seem
to reliably generate presuppositions in certain contexts. As we
mentioned in Section 6, theories of presupposition projection tend to
adopt the working hypothesis that presuppositions are associated with
expression types: if an expression a triggers a presupposition
ph, then ph will always be triggered by a. This is just a
matter of economy: since a projection theory already provides a
mechanism for explaining how presuppositions, once triggered, can seem
to disappear, there is no need for supposing that there are part-time
presupposition triggers. Indeed, it would be a bit of a nuisance if it
turned out that that some expressions or constructions trigger their
presuppositions on a part-time basis, because then we would have two
ways of explaining why a given presupposition fails to appear: echoing
our discussion in section 6, either it has been canceled (say through
being resolved in an embedded context) or it wasn't triggered in the
first place.



Are there compelling reasons for believing that there are part-time
triggers? Not as far as we know. There are suggestive facts, though.
In the following example from Fauconnier (1985), *A* and
*B* are sitting in a bar observing a stranger who doesn't seem
to be too happy:



(55)
*A*: I wonder why that guy is looking so glum.
  

*B*: Maybe his girlfriend jilted him.


The most natural interpretation of *B*'s answer, in this
context, is that it is possible that the stranger has a girlfriend who
has jilted him; this construal will require local accommodation of the
girlfriend if we assume that "his girlfriend" always
triggers the presupposition that the pronoun's referent has a
 girlfriend.[23]
 The problem is that if this is local accommodation, then it's too
*easy*. Local accommodation is supposed to be dispreferred. If
we allow that in this case the presupposition is locally accommodated,
why can't all embedded presuppositions just be locally accommodated
away and not project? Allowing local accommodation to occur without
constraint would potentially destroy any claim to have explained the
observation that has defined the phenomenon of presupposition since
its inception, the observation that presuppositions tend to
project.



If we could *explain why* this or that expression triggers such
and such a presupposition, one of the corollaries might be that the
expression in question is a part-time trigger. To see how such an
argument might run in outline, consider the presuppositions associated
with aspectual verbs like "start" or
"stop":



(56a)
Jill has started smoking pot.
  

- Jill didn't use to smoke pot.
(56b)
Jill has stopped smoking pot.
  

- Jill used to smoke pot.


Aspectual verbs describe a transition from one state to another, and
it is always the first state that is presupposed, as standard
projection tests confirm. An explanation might be sought in the idea
that interlocutors are more interested in where the story is going
than where it came from, and therefore tend to take the past as given.
A purely pragmatic analysis might involve the hearer reasoning that
since the speaker is likely to intend to provide the information that
is of greatest interest, they are probably assuming a context in which
the pre-state associated with a telic sentence is already in the
common ground, i.e. presupposed. It might further be argued that such
reasoning only applies when the hearer has reason to think that the
speaker has expertise on the situation being described. A part-time
trigger analysis might be based on the idea that the regularity with
which pre-states of telic sentences are in the common ground has led
to this pragmatic reasoning being conventionalized. A part-time
trigger analysis might involve a special triggering condition, e.g.
involving the speaker's expertise. So the part-time trigger analysis
might amount to the claim that when the context determines that the
speaker has expertise about an event, the pre-state is presupposed,
but when the context determines that the speaker lacks expertise,
there is no such presupposition.



The disappearance of a pre-state presupposition in example (57) could
be explained in this way. On a more standard view, the aspectual verb
triggers a quantified presupposition, roughly that *x* used to
smoke. This has to be accommodated locally, perhaps because as
suggested by van der Sandt (1992), bound presuppositions can never be
accommodated outside of the scope of the binder, what he calls
*trapping*. But it is also conceivable that there is no
presupposition to be trapped. The idea would be that the speaker lacks
expertise on the habits of the arbitrary individuals quantified over
by the quantifier "anyone", and that this is just the situation in
which a presupposition is not triggered. The ease with which the
existence presupposition of the possessive in example (55) disappears
could be explained along the same lines.



(57)
If anyone stops smoking before July 1, they are eligible for a
payment from the Tobacco Indemnity Fund. (*Example adapted from
Abusch 2002*.)


A different perspective has emerged in recent years to explain the why
certain triggers seem to only result in a presupposition part of the
time. Rather than proposing that there is variation in triggering,
some linguists interpret this behavior as the result of variation in
the inherent cancellability among triggers. Abusch (2002, 2010)
distinguishes between 'soft' triggers which are weak and
context-dependent and 'hard' triggers, which are resistent to
cancellation. For example, she classifies the achievement verb
*win*, in (58a), as a soft trigger, since the presupposition
that John participated in the race is contextually defeasible, whereas
the cleft construction in (58b) is considered a hard trigger because
it cannot be cancelled by the speaker by explicitly expressing
ignorance.



(58a)
 I have no idea whether John ended up participating in the Road
Race yesterday. But if he won it, then he has more victories than
anyone else in history.
(58b)
 ??I have no idea whether anyone read that letter. But if it is
John who read it, let's ask him to be discreet about the content.


Abusch's soft/hard distinction suggests that degrees of cancellability
are intrinsic properties of the triggers themselves, and those that
buy into this theory must motivate *why* that is. For Abusch,
hard presuppositions are strictly semantic, whereas soft
presuppositions arise from alternative sets generated in the context.
Romoli (2011, 2014) takes this a step further by arguing that
presuppositions from soft triggers aren't presuppositions at all, but
rather entailments or scalar implicatures. In contrast, Abrusan
(2011a, 2011b, 2016) argues that the difference between soft and hard
triggers emerges from how both types interact with the context, for
example with regard to their focus sensitivity.



Despite the arguments made for a distinction between soft and hard
triggers, empirical studies have challenged the view that triggers
differ in their conventional properties. Jayez et al (2014)
find that projection differences between different triggers
depend more on context than on the classification of the trigger
itself. Schwarz (2014) compares processing times between hard and soft
triggers and finds that there is no difference between the two.



With the rise of arguments for more fine-grained variability among
presuppositions, inferences that we may have confidently called
'presuppositions' have become harder to think of as forming a natural
class. For some, the inconsistency in trigger behavior has fed into
something of a presupposition identity crisis, a crisis dating at
least as far back as Boer and Lycan's (1976) description of
semantic presupposition as a "myth". Karttunen (2016) reflects on the
state of the field with an air of regret, saying that the "veritable
zoo" of triggers that were lumped into the same presuppositional cage
should never have been considered the same species in the first place.
Ultimately, in order to either salvage a unified notion of
presupposition, or else argue in a grand tradition (following e.g.
Boer and Lycan 1976 or Karttunen and Peters 1977) for rejecting
the possibility of a unified notion of presupposition, it has become
pressing for linguists to understand how triggers and their inferences
vary and why, fueling a trend in recent years towards systematic
empirical work, looking for evidence of cross-linguistic variation,
and developing methods for experimentally testing the predictions of
different theories.