## 1. Situations in direct perception reports



Situations entered natural language semantics with Jon Barwise's
paper *Scenes and Other Situations* (Barwise 1981), followed by
Barwise and Perry's *Situations and Attitudes* (Barwise
& Perry 1983). *Scenes and Other Situations* is about the
meaning of direct (or epistemically neutral) perception reports, a
construction illustrated in (1):



(1)
Beryl saw Meryl feed the animals.


Direct perception reports contrast with indirect (or epistemically
positive) perception reports, which typically have finite embedded
clauses, as in (2):



(2)
Beryl saw that Meryl fed the animals.


Both (1) and (2) presuppose that Meryl fed the animals. But (1) and
(2) still differ with respect to the interpretation of their embedded
complements: the embedded complement in (1) can only be interpreted as
transparent, and this is not so for the embedded complement in (2).
The transparency of the embedded complement in (1) is shown by the
validity of inferences like that in (3), for example:



(3)



|  |
| --- |
| Beryl saw Meryl sprinkle the white powder on Cheryl's
dinner. |
| The white powder was the most deadly poison. |
| Beryl saw Meryl sprinkle the most deadly poison on
Cheryl's dinner. |




In contrast to (3), the first sentence in (4) has an interpretation
that renders the inference in (4) invalid.



(4)



|  |
| --- |
| Beryl saw that Meryl sprinkled the white powder on
Cheryl's dinner. |
| The white powder was the most deadly poison. |
| Beryl saw that Meryl sprinkled the most deadly poison on
Cheryl's dinner. |




A semantic analysis of direct perception reports has to explain what
it is that forces their complements to be transparent. Barwise 1981
proposes to analyze direct perception reports like (1) along the lines
of (5):



(5)
There is an actual past situation *s* that Beryl saw, and
*s* supports the truth of *Meryl feed the animals*.


The virtues of Barwise's analysis can be appreciated even
without seeing the exact details of how situations might support the
truth of sentences. In (5) the verb *see* semantically selects
situations rather than propositions as its first argument, and this
has the desirable effect that the truth value of those sentences does
not change when the description of the perceived situation is replaced
by an extensionally equivalent one. If Meryl fed the animals just once
in the actual world, and she fed them hay, then the set of actual
situations that support the truth of *Meryl feed the animals*
is expected to be the same as the set of actual situations that
support the truth of *Meryl feed the animals hay*. But then (5)
and (6) must have the same actual truth-value, and Barwise's
analysis predicts correctly that (1) and (7) must, too.



(6)
There is an actual past situation *s* that Beryl saw, and
*s* supports the truth of *Meryl feed the animals
hay*.
(7)
Beryl saw Meryl feed the animals hay.


The publication of Barwise 1981 in the *Journal of Philosophy*
was followed by two papers providing commentary: Higginbotham 1983 in
the same journal, and Vlach 1983 in *Synthese*. The peer
verdict on situations was that they were not needed for the semantics
of direct perception reports: the facts could just as well be
explained by Davidsonian event semantics. (Davidson 1967a, 1980. See
the entries
 Donald Davidson
 and
 events.)
 In fact, Barwise's argument showing that direct perception
*see* selects a situation is very much like Davidson's
argument showing that the verb *cause* expresses a relation
between events (Davidson 1967b, 1980). Comparison with Davidsonian
event semantics has been an issue for situation semantics throughout
its history. The relation between situation semantics and Davidsonian
event semantics will be taken up in section 9.


## 2. States of affairs, infons, and information content



Later developments in situation semantics emphasized its role as a
general theory of information content. The key concept is the notion
of a state-of-affair or "infon" (see the entry
 states of affairs).
 State-of-affairs are non-linguistic formal objects that come in
various stages of complexity (see Gawron & Peters 1990 for a brief
overview, Devlin 1991, 2006 for a more detailed exposition, and
Ginzburg & Sag 2000 for a system based on a richer ontology). The
simplest kinds of state-of-affairs consist of a relation, individuals
related by the relation, and a polarity, and might be represented as
in (8):



(8)


a.
<< bothering, Nina, Stella; no >>
b.
<< helping, Stella, Nina; yes >>
 


Arguments of a relation may be parameterized, as in (9):



(9)
<< bothering, *x*, Stella; no >>


Parameterized roles can be anchored to individuals. In (9), the
parameterized botherer role may be anchored to Nina, for example, and
in that case, the result is the unparameterized state-of-affairs in
8(a). Parameterized states-of-affairs can be restricted by other
parameterized state-of-affairs, as in (10), where the subject role for
the property of taking a shower is restricted to individuals who are
singing:



(10)
<< showering, *x* << singing, *x*;
yes >>; no >>


Properties and relations can be produced from parameterized
states-of-affairs by absorbing parameters:



(11)
[ *x* | << bothering, *x*, Stella; no
>>]


Parameter absorption is the situation theory analogue of
l-abstraction. (11) corresponds to the property of not
bothering Stella. There are additional operations that build complex
states-of-affairs from simpler ones, including analogues of
conjunction, disjunction, and existential and universal quantification
(see Devlin 1991, 2006, and Ginzburg & Sag 2000). The ultimate
goal is to provide the necessary tools for a theory of information
content (see the entry
 semantic conceptions of information).
 Barwise 1988 mentions a wide range of applications, including
"a theory of information to account for the role information
pickup plays in the life of the frog, how the information it detects
is related to the actions it takes, actions like flicking its tongue
and hopping about" (Barwise 1988, 257). Other applications
mentioned are theories of vision, databases, robot design,
mathematical proofs, information exchange between speakers of
particular language, and cognitive science as a whole. Finally, the
theory should be able "to be turned on itself, and provide an
account of its own information content, or rather, of the statements
made by the theorist using the theory" (Barwise 1988, 258).



When Barwise and Perry started their joint work, a new, more
fine-grained, notion of information content seemed to be urgently
needed in natural language semantics, because of a known challenge
facing possible worlds semantics, which, under the influence of Lewis
1972 and Montague 1974, was the framework of choice for most formal
semanticists at the time (see the entry on
 possible worlds).
 In possible worlds semantics, propositions are identified with the
set of possible worlds where they are true (see the entry
 propositions).
 Consequently, propositions that are true in the same possible worlds
are identical, and we seem to predict wrongly that a person who
believes a proposition *p* should also believe any proposition
that is true in the same worlds as *p* (see the entry
 propositional attitude reports).
 To distinguish logically equivalent propositions, we seem to need a
more fine-grained notion of what the information content of a sentence
is, and the state-of-affairs or infons of situation semantics were
marketed to provide just that.



The solution that situation semantics offered for the puzzle of
logically equivalents in attitude ascriptions encountered competition
from the very start: state-of-affairs and infons looked suspiciously
like structured propositions (see the entry
 structured propositions).
 Intensional versions of structured propositions had already been
offered as remedies for the attitude ascription problem by Carnap
1947, Lewis 1972, Cresswell & von Stechow 1982, and were also
appealed to for the analysis of information structure and intonational
meaning. The structured meanings of Carnap, Lewis, and Cresswell &
von Stechow are tree structures whose end nodes are intensions, rather
than lexical items. They are thus objects that are independent of the
vocabularies of particular languages, but are nevertheless
hierarchically structured in the way sentences are. Differences
between structured propositions in various frameworks and the
state-of-affairs or infons of situation theory seem to largely boil
down to foundational matters regarding the status of possibilia (see
the entries on
 possible objects
 and possible worlds) and
the nature of properties and relations (see
 properties).



There is currently no consensus about the semantics of attitude
ascriptions, and it is not clear whether situation semantics has a
privileged place in the family of accounts that have been proposed.
Perhaps more importantly, for most empirical generalizations in
linguistic semantics, propositions construed as sets of possible
worlds or situations provide the right level of abstraction. There
seems to be no need to posit unwieldy information contents in areas
where simpler notions provide more elegant accounts. Since this
article is not about theories of information, the concern to provide a
general theory of information content will now have to be set aside,
even though it is central to some areas in situation semantics and
situation theory (Devlin 1991, 2006; Ginzburg and Sag 2000; see also
Barwise & Seligman 1997). The remainder of this article will
review situation-based accounts of selected topics that are currently
under active investigation in linguistics and philosophy: Austinian
topic situations, domain restrictions, donkey sentences, exhaustive
interpretations, and Davidsonian event predication. None of those
phenomena requires a more fine-grained notion of information content.
The discussion will thus be cast within a possibilistic framework
(Kratzer 1989, 2002, 2012; Elbourne 2005, 2013). Possibilistic
versions of situation semantics are conservative extensions of
possible worlds semantics that construe propositions as sets of world
parts, rather than complete possible worlds (see Barwise 1988, chapter
11, for an overview of the major branch points in situation
semantics). There are many areas that situation semantics has
contributed to that could not be reviewed here for reasons of space,
including knowledge ascriptions, questions, discourse relations,
counterfactuals, viewpoint aspect, gerunds, and implicit arguments.
Stojanovich 2012 and Zucchi 2015 are recent general overviews of
situation semantics. Additional references to work on various
phenomena within a situation-based semantics are given below under the
heading *references not mentioned in the text*.


## 3. Austinian topic situations



A core feature of many actual analyses of natural language phenomena
within situation semantics is the idea attributed to John L. Austin
1950 that utterances are about particular situations, with the actual
world being the limiting case (see the entry on
 John Langshaw Austin.)
 Barwise & Etchemendy 1987 illustrate the idea with an imagined
utterance of sentence (12):



(12)
Claire has the three of clubs.


Whether an utterance of (12) is true or false depends, among other
things, on what situation the utterance is about.



> 
> We might imagine, for example, that there are two card games going on,
> one across town from the other: Max is playing cards with Emily and
> Sophie, and Claire is playing cards with Dana. Suppose someone
> watching the former game mistakes Emily for Claire, and claims that
> Claire has the three of clubs. She would be wrong on the Austinian
> account, even if Claire had the three of clubs across town. (Barwise
> and Etchemendy 1987, p. 122)
> 



If assertions are about particular situations, reports of assertions
might not be accurate unless they take into account the situations the
assertions were about. And there are more repercussions of Austinian
reasoning: if assertions are about particular situations, beliefs
should be, too, and this means that our belief ascriptions might not
be accurate unless they take into account the situations the beliefs
are about. That those situations do indeed matter for belief
ascriptions is illustrated by the story of the Butler and the Judge
from Kratzer 1998 (see Ogihara 1996, Kratzer 1990 (Other Internet
Resources), 2002, 2012; Portner 1992, Recanati 2000, for
relevant work on the role of topic situations in attitude ascriptions
and other embedded constructions):



The judge was in financial trouble. He told his butler that he had
been ready to commit suicide, when a wealthy man, who chose to remain
anonymous, offered to pay off his debts. The butler suspected that
Milford was the man who saved his master's life by protecting
him from financial ruin and suicide. While the butler was away on a
short vacation, the judge fell into a ditch, drunk. Unconscious and
close to death, he was pulled out by a stranger and taken to the local
hospital, where he recovered. When the butler returned to the village,
he ran into a group of women who were speculating about the identity
of the stranger who saved the judge's life by taking him to the
hospital. One of the women said she thought that Milford saved the
judge's life. The butler, who hadn't yet heard about the
accident and thought the women were talking about the judge's
financial traumas, reacted with (13):



(13)
I agree. I, too, suspect that Milford saved the judge's
life.


The next day, when discussion of the judge's accident continued,
somebody said:



(14)
The butler suspects that Milford saved the judge's
life.


Given that the butler's suspicion is not about the accident,
there is a sense in which this belief attribution is not true. It
seems infelicitous, if not outright false. This suggests that our
imagined assertion of (14) makes a claim about a particular situation
that the suspicion is about. In the context of the story, that
situation is the one everyone was talking about, and where the judge
was rescued from the ditch. Since the butler has no suspicion about
such a situation, the person who uttered (14) said something
infelicitous or false. If (14) simply said that the butler suspected
that there was a situation where Milford saved the judge's life,
the assertion would be true. There is support for the Austinian
perspective on assertions and attitude ascriptions, then.



Austinian topic situations (also referred to as "focus
situations", "described situations", or
"reference situations" in the literature) are often
non-overt, but the tense of a sentence might give them away. A close
look at tenses tells us that topic situations do not always coincide
with the situations described by the main predication of a sentence.
Klein (1994, 4) imagines a witness who is asked by a judge what she
noticed when she looked into the room. The witness answered with
(15):



(15)
There was a book on the table. It was in Russian.


It is surprising that there is a past tense in the second sentence,
even though the book must have still been in Russian when the witness
was called for testimony. Even more surprising is the fact that the
witness could not have said (16) instead of (15).



(16)
# There was a book on the table. It is in Russian.


Translated into a situation semantics (Klein himself talks about topic
times, rather than topic situations), Klein's explanation is
that tense relates utterance situations to topic situations, which do
not necessarily coincide with the situations described by the main
predication of a sentence. In Klein's scenario, the topic
situation for the second part of the witness's answer was the
past situation that she saw when she looked into the room. Since the
topic situation was past, tense marking in the second sentence of (16)
has to be past, too. Via their temporal locations, topic situations
play an important role in the semantics of both tense and aspect (see
the entry on
 tense and aspect;
 also Smith 1991, Kamp & Reyle 1993, and Cipria & Roberts
2000).



If Austinian topic situations play a role in the grammars of natural
languages, there should be grammatical devices in at least some
languages that track them. Recent work by Andrew McKenzie (McKenzie
2012, 2015) has suggested that certain Switch Reference systems in a
number of genetically unrelated languages seem to track Austinian
topic situations. For example, the North American language Kiowa
(Tanoan, spoken in Oklahoma) uses different forms for certain
sentential connectives (including conjunction), depending on whether
the topic situations of the conjoined conjuncts changes or stays the
same.


## 4. Situation semantics and implicit domain restrictions



Among the most innovative ideas in Barwise & Perry 1983 is the
proposal to exploit the Austinian perspective on utterances to account
for implicit quantifier restrictions and so-called
"incomplete" definite descriptions (see the entry
 descriptions):



> 
> Suppose that I am in a room full of people, some of whom are sleeping,
> some of whom are wide awake. If I say, "no one is
> sleeping," have I told the truth or not? Again, it depends on
> which situation I am referring to. If I am referring to the whole
> situation including all the people in the room, then what I have said
> is false. However, one can well imagine situations where I am clearly
> referring only to a part of that situation. Imagine, for example, that
> I am conducting an experiment which requires an assistant to monitor
> sleeping people, and I look around the sleep lab to see if all of my
> assistants are awake and ready to go. Surely, then I may truly and
> informatively say, "No one is asleep. Let's begin."
> .... The crucial insight needed goes back to Austin ... As
> Austin put it, a statement is true when the actual situation to which
> it refers is of the type described by the statement. (Barwise &
> Perry 1983, 160)
> 



A similar example discusses incomplete definite descriptions:



> 
> Suppose my wife and I collaborate on cooking for a party. And suppose
> that at a certain point in the party I say, "I am the
> cook," referring to *l*. Is what I said true or not?
> 



The answer is, "It depends on which situation I am
describing." First, suppose someone comes up to me and says,
"The food at this party is delicious! Who is the cook?" If
I say "I am the cook," I have clearly not described things
accurately. I have claimed to be *the* person who did the
cooking for the party. But suppose instead someone comes up to me
eating a piece of my famous cheesecake pastry and says, "Who
made this?" Then I may truly say that I am the cook. (Barwise
& Perry 1983, 159)



On the Austinian perspective, at least certain kinds of implicit
restrictions for quantification domains are a direct consequence of
the fact that assertions are about particular actual situations, and
that those situations can be smaller or bigger parts of the actual
world.



The Austinian answer to implicit domain restrictions was endorsed and
developed in Recanati (1986/87, 1996, 2004a) and Cooper 1996.
An influential attack on the situation semantics approach to
"incomplete" definite descriptions came from Soames 1986,
who concluded that "the analysis of definite descriptions is not
facilitated by the kind of partiality that situation semantics
provides" (Soames 1986, 368). Soames' reservations against
the Austinian approach to domain restrictions come from two major
potential counterarguments, both of which are directed against
particular implementations of the approach. One of the potential
problems discussed by Soames concerns attributive readings of definite
descriptions. However, as Soames is careful to note (Soames 1986,
359), this problem does not necessarily affect possibilistic versions
of situation semantics. Since Soames' qualification is not
elaborated in his article, it might be useful to look at a concrete
example illustrating his point. Suppose the two of us observe a bear
crossing the road one night in Glacier National Park. Since it is
dark, we can't see the bear very well, and I say to you:



(17)
The bear might be a grizzly.


I am aware that the bear we see is not the only bear in the world, so
my assertion relies on an implicit domain restriction. On the
Austinian view, my assertion is about a particular situation located
somewhere in Glacier National Park at a particular time in August
2006. Call that situation "Bear Sighting". Bear Sighting
has a particular bear in it, the bear we see. Call that bear
"Bruno". On the intended attributive reading, what I want
to get across to you is not that Bruno may be a grizzly, but that our
evidence about Bear Sighting is compatible with the assumption that
the bear there--whoever he is--is a grizzly. There is a
legitimate question whether we can get that reading on the Austinian
approach to domain restrictions. If Bear Sighting has to give us the
restriction for *bear*, it seems that all it can do is restrict
the bears we are talking about to Bruno. But that wouldn't
produce the attributive reading we are after. For that reading, so it
might seem, domain restrictions must be properties.



The above conclusion might look inevitable, but it is not. It is true
that on the Austinian view, my utterance of (17) is interpreted as a
claim about Bear Sighting. To see that we can nevertheless get the
desired interpretation, we need to look at technical details. 18(a)
gives a plausible interpretation of the possibility modal in (17)
within a possibilistic situation semantics. 18(b) is the
interpretation of the whole sentence (17) before the Austinian
component comes into play:



(18)



|  |  |  |
| --- | --- | --- |
| a.  | [[*might*]]*c* | l*p*l*s*
[?]*s*'[Acc*c*(*s*)(*s*')
& *p*(*s*')] |
| b. | [[(17)]]*c* | l*s* [?]*s*'
[Acc*c*(*s*)(*s*') &
grizzly(i*x*
bear(*x*)(*s*'))(*s*')] |




(18) assumes an intensional semantics that is based on possible
situations. In possible situation semantics, propositions are sets of
possible situations, or characteristic functions of such sets, and all
predicates are evaluated with respect to a possible situation. 18(b)
is the proposition expressed by (17) in context *c*. That
proposition is a property that is true of a situation *s* iff
there is a situation *s*' that is accessible from
*s* and the unique bear in *s*' is a grizzly in
*s*'. The modal *might* introduces existential
quantification over possible situations that are accessible from the
evaluation situation *s* (see the entry
 modal logic).
 The kind of accessibility relation is determined by the lexical
meaning of the modal in interaction with properties of the utterance
context *c* (see the entry
 indexicals).
 In our example, the modality is a particular kind of epistemic
modality that relates two situations *s* and *s*'
in a context *c* just in case *s* and *s*'
are equivalent with respect to the information available in
*c*, that is, whatever evidence about *s* is available
in *c* isn't specific enough to distinguish between
*s* and *s*' (*epistemic contextualism*).
Evidence that counts as available for epistemic modals might include
the distributed knowledge of the discourse participants (see von
Fintel & Gillies 2011), other available sources of information
like ship's logs or computer printouts (Hacking 1967, von Fintel
& Gillies 2011), but, interestingly, not necessarily information
that happens to be hidden from sight like test results in sealed
envelopes (de Rose 1991), babies in wombs (Teller 1972), weather
conditions behind drawn curtains (Gillies 2001), or details of animals
obscured by darkness. Suppose the actual bear in Bear Sighting is in
fact a black bear, and not a grizzly. Since it is night and we
can't see the bear very well, the evidence we have about Bear
Sighting when I utter (17) cannot distinguish the real situation from
many merely possible ones, including some where the bear is a grizzly
and not a black bear. This is what makes my utterance of (17)
true.



When I uttered (17), I claimed that the proposition in 18(b) was true
of Bear Sighting. Applying 18(b) to Bear Sighting yields the desired
attributive interpretation. Bear Sighting is exploited to provide
implicit domain restrictions, but it doesn't do so directly. We
are considering epistemic alternatives of Bear Sighting. The epistemic
alternatives are alternatives of Bear Sighting, hence are partial,
just as Bear Sighting itself is. They have no more than a single bear
in them. This suggests that the analysis of definite descriptions
*is* facilitated by the kind of partiality that situation
semantics provides. Austinian topic situations can give us domain
restrictions for attributive definite descriptions.



Soames' second major objection against the Austinian approach to
domain restrictions relates to the fact that there are instances of
domain restrictions that can't seem to come from Austinian topic
situations (see also Westerstahl 1985). One of Soames'
examples is (19) below (Soames 1986, 357), which is a variation of
Barwise and Perry's sleep lab example quoted above.



(19)
Everyone is asleep and is being monitored by a research
assistant.


If all quantifier domains were provided by Austinian topic situations,
(19) would seem to make contradictory demands on such a situation.
Assuming that there is just a single topic situation for utterances of
(19), we seem to predict that those utterances imply that the research
assistants are among those who are asleep. But there is no such
implication. Soames is aware that proponents of the Austinian approach
are not committed to the assumption that *all* domain
restrictions are directly provided by Austinian topic situations
(Soames 1986, footnote 17, 371), and he therefore emphasizes that he
is only commenting on the particular account of domain restrictions
offered in Barwise and Perry (1983, 1985). Soames' objection
does not apply to Cooper 1996, for example, who allows quantifier
domains to be determined by different resource situations, which he
distinguishes from the Austinian topic situation (his "described
situation"). The objection also does not apply to possibilistic
versions of situation semantics, where every predicate is necessarily
evaluated with respect to an actual or possible situation. Different
predicates in one and the same sentence can then be evaluated with
respect to different situations (Heim 1990, Percus 2000, Elbourne
2002, 2005, 2013). A possible interpretation for (19) might be
(20):



(20)
l*s* [?]*x* [
[person(*x*)(*s*') & *s*'
[?]*p* *s*] -
[asleep(*x*)(*s*) & [?]*y*
[research-assistant(*y*)(*s*) &
monitoring(*x*)(*y*)(*s*)] ] ]


When the doctor of the sleep lab utters (19), she claims that the
proposition in (20) is true of a particular situation, call it
"Sleep Lab". Sleep Lab is the Austinian topic situation,
but it is not the situation that picks out the sleepers. The sleepers
might be recruited from a contextually salient (possibly scattered)
situation *s*' that is related to Sleep Lab via the part
relation [?]*p* and functions as a resource
situation for the evaluation of the predicate *person*
introduced by the quantifier phrase *everyone*. This situation
could be the sum of the patients in the lab, for example.



Neither topic nor resource situations have to be posited for the
exclusive need of domain restriction. In a possibilistic situation
semantics resource situations are the kind of entities that the
evaluation of any predicate routinely depends on. Topic situations,
too, are independently needed: they are the situations that assertions
and beliefs are about, and they are key players in the semantics of
tense and aspect. This means that the contribution of topic and
resource situations to domain restriction comes entirely for free.
Many instances of domain restrictions can thus be explained without
positing any special devices. Some of the remaining cases might also
be accounted for by independently attested mechanisms including
syntactic ellipsis, presupposition projection and conversational
implicatures. But there is also exaggeration, taboo related omissions,
and some such. The implicit domain restriction in the following
sentence, which appeared on a note posted in a bathroom in York
(England), might very well fall in the last-mentioned category:



(21)
Please do not dispose of anything down the toilet, except toilet
paper.


It is hard to see how any theory would want to literally prevent any
kind of pragmatic enrichment processes (Recanati 1993, 2002,
2004) from contributing to implicit quantifier restrictions, given
that humans are able to "interpret utterances replete with
irony, metaphor, elision, anacoluthon, aposiopesis, and on top of all
of this ...identify what a speaker is *implying* as well
as saying" (Neale 2004, 123). Implicit domain restrictions are
likely to be the byproducts of a number of independently attested
mechanisms, then.


## 5. Situation variables or unarticulated constituents?



An important question in situation semantics is how exactly situations
enter the semantic interpretation process. Are they articulated via
syntactically represented variables, or are they "unarticulated
constituents" (Perry 1986, Recanati 2002), possibly mere
indices of evaluation? The issue is well explored for times and
possible worlds (see the entry on
 ontological commitment).
 Kripke's semantics for modal logic allows quantification over
possible worlds only in the metalanguage (see the entry
 modal logic),
 for example. Likewise, in Prior's tense logic (see the entry
 Arthur Prior),
 quantification over times is confined to the metalanguage (see the
entry
 time).



(22)


a.
[[*must* a]]*w* = 1 iff
[[a]]*w*' = 1 for all *w*'
that are accessible from *w*.
b.
[[*past* a]]*t* = 1 iff
[[a]]*t*' = 1 for some *t*'
that precedes *t*.
 


Montague's language of intensional logic (Montague 1974) was
developed in the tradition of Kripke and Prior, and does not have
variables ranging over times or worlds: tense and modal operators
shift evaluation indices, as illustrated in (22), but do not bind
variables in the object language. Quantification over worlds and times
is treated differently from quantification over individuals, then. The
distinction was made deliberately because it predicts differences that
were thought correct at the time. Once an evaluation index is shifted,
it is gone for good, and can no longer be used for the evaluation of
other expressions. This constrains temporal and modal anaphora. Until
the early seventies anaphoric reference to times and worlds in natural
languages was believed to be constrained in precisely the way
predicted by the evaluation index approach. The belief was challenged
by work on temporal anaphora (Kamp 1971, Partee 1973, Vlach 1973, van
Benthem 1977), however. Cresswell 1990 presented parallel arguments
for modal anaphora, and showed more generally that natural languages
have the full expressive power of object language quantification over
worlds and times. Quantification over worlds or times is thus no
different from quantification over individuals, and should be
accounted for in the same way.



Exact analogues of Cresswell's examples can be constructed to
show that natural languages have the full expressive power of object
language quantification over situations. Here is a first taste of the
kind of example we have to look at.



(23)
If, whenever it snowed, it had snowed much more than it actually
did, the town plow would have removed the snow for us.


Suppose (23) is uttered to make a claim about the town of Amherst
during the last 20 years. We are looking at the snowfalls during the
relevant period. For each of those actual snowfalls *s*, we are
considering counterfactual situations *r* where it snowed much
more than it did in *s*. The claim is that each of those
counterfactual situations is part of a situation where the town plow
removed the snow for us. To formalize what was said, we have to be
able to consider for each actual snowfall *s* a set of
counterfactual alternatives and compare the amount of snow in each of
them to the actual amount of snow in *s*. This means that we
have to be able to "go back" to the actual snowfall
situations after considering corresponding counterfactual situations.
To do so we have to keep track of the original situations. The
available bookkeeping tools are either evaluation indices, or else
situation variables and binding relations in the object language. If
we want to avoid possibly unpronounced situation variables, we need
two shiftable evaluation indices for (23). In the long run, even two
indices wouldn't be enough, though. Here is an example that
requires three:



(24)
Whenever it snowed, some local person dreamed that it snowed more
than it actually did, and that the local weather channel erroneously
reported that it had snowed less, but still more than it snowed in
reality.


It is not hard to see that we can complicate such examples
indefinitely, and that there would be no end to the number of
evaluation indices needed. But that suggests that natural languages
have the full power of object language quantification over situations.
Quantification over situations is no different from quantification
over individuals, then, as far as expressive power is concerned. Since
natural languages have syntactically represented individual variables
and it would be surprising if they used two different equally powerful
quantification mechanisms, it seems to be at least a good bet that
there are syntactically represented situation variables in natural
languages (but see Cresswell 1990 and Jacobson 1999 for dissenting
opinions). But then the situations quantified over or referred to in
(23), (24) and their kin do not necessarily correspond to
"unarticulated constituents". They are syntactically
represented, even though they might happen to be unpronounced. The
syntactic representation of situation variables is investigated in
Percus 2000, Keshet (2008, 2010), and F. Schwarz (2008, 2012).


## 6. Situations, minimality, and donkey sentences



One of the most frequent uses of situation-based frameworks is in the
analysis of "donkey" pronouns, that is, anaphoric pronouns
that are interpreted as definite descriptions (see *descriptive
theories of anaphora* under the entry
 descriptions
 and the entry
 anaphora).



(25)


a.
Whenever a donkey appeared, it was greeted enthusiastically.
b.
Whenever a donkey appeared, the donkey was greeted
enthusiastically.
 


The pronoun *it* in 25(a) is an instance of a descriptive
pronoun that is interpreted like the corresponding definite
description in 25(b). Suppose I use 25(a) or (b) to talk about a
particular situation, call it "Donkey Parade". The
situations that *whenever* quantifies over are then all part of
Donkey Parade. They are precisely those subsituations of Donkey Parade
that are minimal situations in which a donkey appeared. Those must
then be situations with a single donkey in them. The claim is that all
those situations are part of situations where the donkey was greeted
enthusiastically. More formally, my claim about Donkey Parade is
(26):



(26)
l*s* [?]*s*' [ [*s*'
[?]*p* *s* & *s*' [?]
Min(l*s* [?]*x*
[donkey(*x*)(*s*) &
appeared(*x*)(*s*)])] - [?]*s*''[
*s*' [?]*p* *s*'' &
greeted-enthusiastically (i*x*
donkey(*x*)(*s*'))(*s*'')] ]


(26) reflects the standard analysis of adverbs of quantification and
descriptive pronouns in a possibilistic situation semantics (Berman
1987; Heim 1990; Portner 1992; von Fintel 1994, 2004b; Elbourne 2002,
2005, 2013, 2016). All resource situations that are introduced in (26)
are directly or indirectly related to the topic situation via the part
relation [?]*p*. The topic situation is the
ultimate anchor for all resource situations. It indirectly restricts
the donkeys being talked about to those that are present in Donkey
Parade. The antecedent of the conditional introduces a further
restriction: we are considering only those subsituations of Donkey
Parade that are minimal situations in which a donkey appeared. Those
situations have just one donkey in them, and they can thus be used as
resource situations for the definite description *the donkey*
or a corresponding descriptive pronoun.



The crucial feature of any analysis of donkey sentences within a
situation semantics is that quantification is over minimal situations
satisfying conditions imposed by the antecedent of the conditional.
The minimality condition is crucial for the analysis of descriptive
pronouns. Without it, we wouldn't be able to analyze those
pronouns as definite descriptions:



(27)
Whenever a man saw a donkey, the man greeted the donkey.


We have to make sure that the situations or events quantified over
have just one man and just one donkey in them, because definite
descriptions have to be unique with respect to their resource
situations. The minimality condition is a source of potential trouble,
however (Reinhart 1986, Dekker 2004; von Fintel 2004a,b). When the
antecedent of a conditional contains a mass noun, negative
quantifiers, or certain kinds of modified quantifier phrases,
quantification over minimal situations or events seems to yield
unwelcome results or isn't possible at all:



(28)


a.
When snow falls around here, it takes ten volunteers to remove
it.
b.
When a cat eats more than one can of Super Supper in a day, it
gets sick.
c.
Whenever there are between 20 and 2000 guests at a wedding, a
single waiter can serve them.
d.
Whenever nobody showed up, we canceled the class.
 


28(a) raises the question whether there ever are minimal situations or
events in which snow falls. But even if there are, we do not quantify
over them in this case. We also do not seem to rely on discrete scales
for measuring portions of Super Supper. But even if we did, this would
not help with 28(b). This sentence does not necessarily quantify over
situations in which a cat eats just a little more than a can of Super
Supper. Minimality also doesn't seem to play a role for 28(c).
If 28(c) quantified over minimal situations that have between 20 and
2000 wedding guests, it would quantify over situations or events with
exactly 20 wedding guests, and might very well be true. 28(d) is even
more dramatic. What would a minimal situation or event look like in
which nobody showed up? If any event- or situation-based analysis of
donkey sentences is to succeed, then, it must keep the events or
situations that are quantified over small enough to contain just one
man and one donkey in cases like (27), but it has to accomplish this
without minimizing the amount of snow, Super Supper, or wedding guests
in cases like 28(a) to (c). And it should not mess with negative
constructions at all. When we are quantifying over situations in
donkey sentences, then, we need to relate possibly very complex
sentences to exemplifying situations in a way that is responsive to
the different behavior of different kinds of antecedents illustrated
by (27) and 28(a) to (d).



There are several proposals in the literature that elucidate the
relation between a sentence and the situations or events that
exemplify it by positing a special recursive mechanism that relates
sentences to the set of exemplifying events or situations (see Schein
1993, chapters 9 and 10 for discussion of this issue). Possibilistic
versions of situation semantics typically start out with a recursive
truth definition that relates utterances of sentences to the sets of
possible situations in which the utterances are true, the propositions
expressed. The situations or events that exemplify a proposition can
then be defined as the "minimal" situations in which the
proposition is true (see the entries on
 events,
 facts,
 states of affairs,
 and truthmakers). The
challenge presented by sentences (27) and 28(a) to (d) is that they
suggest that a naive notion of minimality won't do. A more
flexible notion of minimality seems to be needed. The following
section will document in some detail how the desired notion of
minimality might emerge from a simple definition of exemplification in
interaction with independently justified sentence denotations. The
issue is under active investigation, however, and cannot be considered
settled before a wide range of different constructions has been looked
at. Whatever the ultimate outcome may be, the following discussion
will provide the opportunity to illustrate how the shift from possible
worlds to situations affects the denotations we might want to posit
for an expression. In a situation semantics, there are often several
ways of assigning denotations to an expression that are hard to
distinguish on truth-conditional grounds. Looking at the situations
that exemplify a sentence as well as its truth-conditions helps with
the choice.


## 7. Minimality and exemplification



In possibilistic versions of situation semantics, possible situations
are parts of possible worlds. Some authors also assume that the parts
of a possible world *w* form a join semi-lattice with maximal
element *w* (Bach 1986; Lasersohn 1988, 1990; Portner 1992; see
also the entry
 mereology).
 The part relation [?]*p* and the sum operation +
are then related as usual: *s* [?]*p*
*s*' iff *s* + *s*' =
*s*'. Propositions are sets of possible situations or
their characteristic functions (see the entry
 propositions).
 The notion of a situation that exemplifies a proposition might be
defined as in (29), which is a variation of a definition that appears
in Kratzer 1990 (Other Internet Resources), 1998, 2002:



(29)
**Exemplification**
  

A situation *s* exemplifies a proposition *p* if
whenever there is a part of *s* in which *p* is not
true, then *s* is a minimal situation in which *p* is
true.


Intuitively, a situation that exemplifies a proposition *p* is
one that does not contain anything that does not contribute to the
truth of *p*. The first part of (29) allows two possibilities
for a situation *s* to exemplify *p*. Either *p*
is true in all subsituations of *s* or *s* is a minimal
situation in which *p* is true. The notion of minimality
appealed to in (29) is the standard one: A situation is a minimal
situation in which a proposition *p* is true iff it has no
proper parts in which *p* is true. The situation Mud (Case One
below) gives a first illustration of what (29) does.



**Case One: Mud**




|  |  |
| --- | --- |
| mud (solid circle) | Mud is a situation that consists of mud and only mud. |



Assuming that Mud and all of its parts are mud, Mud and all of its
parts exemplify the proposition in 30(b), since there are no parts of
Mud where there is no mud.



(30)


a.
There is mud.
b.
l*s* [?]*x*
mud(*x*)(*s*)



30(b) is not exemplified by Mud & Moss (Case Two below),
however:



**Case Two: Mud & Moss**




|  |  |
| --- | --- |
| mud and moss (mixed circle) | Mud & Moss is a situation that consists of some mud and some
moss and nothing else. |



Mud & Moss has parts where 30(b) is not true: the parts where
there is only moss. But Mud & Moss is not a minimal situation in
which 30(b) is true.



Next, consider (31):



(31)


a.
There are three teapots.
b.
l*s* [?]*x* [*x*
[?]*p* *s* & |{*y*: *y*
[?]*p* *x* &
teapot(*y*)(*w**s*)}| = 3]
 


31(b) describes situations *s* that have at least three teapots
(individuals that are teapots in the world of *s*) in them. The
proposition in 31(b) seems to be exemplified by the situation Teapots
(Case Three below).



**Case Three: Teapots**




|  |  |
| --- | --- |
| teapots | Teapots has three teapots and nothing else in it. |



There is no proper subsituation of Teapots in which 31(b) is true.
Since Teapots has nothing but three teapots in it, any proper
subsituation of Teapots would have to be one where a part of at least
one of the three teapots is missing. But 31(b) is true in Teapots
itself, and Teapots is thus a minimal situation in which 31(b) is
true.



There is a potential glitch in the above piece of reasoning. It
assumes that when an individual is a teapot in a world, no proper part
of that individual is also a teapot in that world. This assumption can
be questioned, however. Following Geach 1980 (p. 215; see entries
 identity,
 problem of many), we might reason as follows: My teapot would remain a
teapot if we chipped off a tiny piece. Chipping off pieces from
teapots doesn't create new teapots, so there must have been
smaller teapots all along. We might feel that there is just a single
teapot sitting on the table, but upon reflection we might have to
acknowledge that there are in fact many overlapping entities that all
have legitimate claims to teapothood. The unexpected multitude of
teapots is a source of headaches when it comes to counting. A
fundamental principle of counting says that a domain for counting
cannot contain non-identical overlapping individuals (Casati &
Varzi 1999, 112):



(32)
**Counting Principle**
  

A counting domain cannot contain non-identical overlapping
individuals.


(32) implies that just one of the many overlapping teapots on the
table over there can be counted, and the question is which one. If we
are that liberal with teapothood, we need a counting criterion that
tells us which of the many teapots in our overpopulated inventory of
teapots we are allowed to count.



With spatiotemporal objects like teapots, humans seem to rely on
counting criteria that privilege maximal self-connected entities
(Spelke 1990, Casati & Varzi 1999). A self-connected teapot is one
that cannot be split into two parts that are not connected. In
contrast to parthood, which is a mereological concept, connectedness
is a topological notion (see Casati and Varzi 1999 for discussion of
various postulates for a "mereotopology", a theory that
combines mereology and topology). The maximality requirement prevents
counting teapots that are proper parts of other teapots, and the
self-connectedness requirement disqualifies sums of parts from
different teapots. Casati and Varzi point out that not all kinds of
entities, not even all kinds of spatiotemporal entities, come with
counting criteria that involve topological self-connectedness. Obvious
counterexamples include bikinis, three-piece suits, and broken glasses
that are shattered all over the floor. We have to recognize a wider
range of counting criteria, then, that guarantee compliance with (32)
in one way or other.



Assuming counting criteria, the proposition expressed by 31(a) would
still be exemplified by Teapots, even if we grant that teapots can
have proper parts that are also teapots. The specification of
denotations for sentences with numerals would now have to make
reference to teapots that can be counted, call them "numerical
teapots". Representations like 31(b) and its kin should then be
understood along the lines of 33(b):



(33)


a.
There are three teapots.
b.
l*s* [?]*x* [*x*
[?]*p* *s* & |{*y*:
*y* [?]*p* *x* &
numerical-teapot(*y*)(*w**s*)}| =
3]
 


If Teapots contains nothing but three individuals that are numerical
teapots in the actual world, 33(b) is true in Teapots. But then none
of the proper subsituations of Teapots can contain three individuals
that are numerical teapots in the actual world. Any such situation
contains at least one teapot that is a proper part of one of the
teapots in Teapots, hence can no longer contain three numerical
teapots.



In contrast to Teapots, Teapots & Scissors (Case Four below) does
not exemplify 31(b). Teapots & Scissors has parts where 31(b) is
not true: take any part that has just the scissors or just a part of
the scissors in it, for example. But Teapots & Scissors is not a
minimal situation in which 31(b) is true.



**Case Four: Teapots and Scissors**




|  |  |
| --- | --- |
| teapots and scissors | Teapots & Scissors has three teapots and a pair of scissors
and nothing else in it. |



Definition (29) has the consequence that Teapots does not exemplify
the proposition 34(b) below, even though 34(b) is true in Teapots.



(34)


a.
There are two teapots.
b.
l*s* [?]*x* [*x*
[?]*p* *s* & |{*y*:
*y* [?]*p* *x* &
teapot(*y*)(*w**s*)}| = 2]
 


34(b) is true in Teapots, since Teapots contains a plural individual
that contains exactly two teapots. However, 34(b) is not exemplified
by Teapots. Teapots has parts in which 34(b) is not true without being
a minimal situation in which 34(b) is true. More generally, if
sentences of the form *there are n teapots* denote propositions
of the kind illustrated by 34(b), then those propositions can only be
exemplified by situations that have exactly *n* teapots.
Likewise, if *there is a teapot* is interpreted as in 35(b)
below, the proposition it expresses can only be exemplified by
situations with exactly one teapot, even though it can be true in
situations with more teapots.



(35)


a.
There is a teapot.
b.
l*s* [?]*x* [*x*
[?]*p* *s* & |{*y*:
*y* [?]*p* *x* &
teapot(*y*)(*w**s*)}| = 1]
 


The predicted exemplification properties of sentences with numerals
are welcome, since they suggest that (29) might indeed capture the
relation between propositions and situations that we are after: The
situations exemplifying the proposition expressed by *there is a
teapot* are all situations that have a single teapot in them,
hence are literally minimal situations containing a teapot. In
contrast, the situations exemplifying the proposition expressed by
*there is mud* are all situations that contain mud and nothing
else, hence do not have to be minimal situations containing mud.



The major consequence of (29) is that if a proposition has
exemplifying situations at all, the set of its exemplifying situations
must be either homogeneous or quantized in the sense of Krifka 1992. A
set of situations is quantized iff it doesn't contain both a
situation *s* and a proper part of *s*. A set of
situations is homogeneous iff it is closed under the parthood
relation, that is, whenever it contains a situation *s*, it
also contains all parts of *s*. As argued in Krifka's
work, algebraic notions like homogeneity and quantization might
capture linguistically important aspectual distinctions like that
illustrated in (36) (see the entry on
 tense and aspect).



(36)


a.
Josephine built an airplane.
b.
Josephine flew an airplane.
 


The proposition expressed by 36(a) seems to be exemplified by minimal
past situations in which Josephine built an airplane, and this set of
situations is quantized. On the other hand, the proposition expressed
by 36(b) seems to be exemplified by all past situations that contain
airplane flying by Josephine and nothing else, and this set of
situations is homogeneous. Homogeneous sets cannot be used as counting
domains, however, and this requires adjustments with examples like
37(b).



(37)


a.
Josephine built an airplane just once.
b.
Josephine flew an airplane just once.
 


37(b) cannot quantify over all situations that exemplify the
proposition *Josephine flew an airplane*, since this would give
us a quantification domain that violates the Counting Principle (32).
We have to impose a counting criterion, then, and the topological
notion of self-connectedness seems to be relevant here, too (see von
Fintel 2004a,b). As a result, 37(b) might quantify over maximal
self-connected situations exemplifying the proposition expressed by
*Josephine flew an airplane*.



We are now in a position to see how exemplification can be used for
the analysis of donkey sentences. Look again at (38) and (39):



(38)
Whenever a man saw a donkey, the man greeted the donkey.
(39)
Whenever snow falls around here, it takes ten volunteers to remove
it.


(38) and (39) quantify over parts of a contextually salient topic
situation. The antecedents of the conditionals tell us more about what
those parts are. In (38) quantification is over situations
exemplifying the proposition expressed by *a man saw a donkey*,
which are all situations that contain a single man and a single
donkey. Those situations can then be taken to be resource situations
for the definite descriptions *the man* and *the donkey*
in the consequent of (38). (39) also quantifies over parts of the
topic situation that exemplify the antecedent proposition, but as in
the case of 37(b), considering all exemplifying situations would
violate the Counting Principle, and we therefore need a counting
criterion. (39) might then quantify over maximal self-connected
situations exemplifying the proposition expressed by *snow falls
around here*. Those situations include complete snowfalls, then,
and if it does indeed snow a lot around here whenever it snows, (39)
might very well wind up true.



Not all propositions that look like perfectly acceptable candidates
for sentence denotations have exemplifying situations. Consider 40(b),
for example:



(40)


a.
There is more than five tons of mud.
b.
l*s* [?]*x* [mud(*x*)(*s*)
& *f*ton(*x*) > 5]
 


Whenever there is a situation that has more than five tons of mud in
it, there are parts that have just five tons or less. But none of
those parts can be part of any minimal situation with more than five
tons of mud, since there are no such situations.



In a situation semantics, it often happens that there are several
options for assigning subtly different propositions to sentences, and
sometimes the options are hard to distinguish on truth-conditional
grounds. Insisting on both adequate truth-conditions and adequate
exemplification conditions might help narrow down the field of
candidates. 40(a) can also be paraphrased as saying that the total
amount of mud in some contextually salient resource situation weighs
more than five tons. The denotation of 40(a) could be (41), then,
which includes a contextualized maximalization condition:



(41)
l*s* [?]*x* [*x*
[?]*p* *s* & [*x* =
s*z* mud(*z*)(*s*')] &
*f*ton(*x*) > 5]


(41) is true in a situation *s* if it contains all the mud of
some salient resource situation *s*' (possibly the actual
world as a whole), and that mud weighs more than 5 tons. (41) is
exemplified by the mud in *s*', provided it weighs more
than five tons. Sentences may contain noun phrases that provide
anchors for the maximalization condition. (42) is a case in
question:



(42)


a.
There is more than five tons of mud in this ditch.
b.
l*s* [?]*x* [*x*
[?]*p* *s* & *x* =
s*z* [mud(*z*)(*w**s*)
& in(this ditch)(*z*)(*w**s*)]
& *f*ton(*x*) > 5]
 


42(b) is exemplified by the mud in this ditch, as long as it weighs
more than five tons.



Maximalized interpretations for *more than n* and similar kinds
of indefinites like *at least n* are discussed in Reinhart
1986, Kadmon (1987, 1990, 2001), Schein 1993, and Landman (2000,
2004). Some of the original observations go back to Evans 1977. As
noted by Reinhart and Kadmon, *more than n* noun phrases
produce maximality effects of the kind illustrated in (43):



(43)
There was more than 5 tons of mud in this ditch. The mud was
removed.


(43) would be considered false in a situation where there was in fact
7 tons of mud in this ditch, but only six tons were removed. This
judgment can be accounted for by assuming that utterances of the
second sentence in (43) are about a particular past situation that
exemplifies the first sentence. This situation can then serve as a
resource situation for the interpretation of the definite description
*the mud*. If sentences like 42(a) have maximalized
interpretations, it follows that the mud that was removed was all the
mud in the ditch.



There are other numeral expressions that trigger maximalization. (44)
is an example:



(44)


a.
There were between two and four teapots on this shelf.
b.
l*s* [?]*x* [ *x*
[?]*p* *s* & *x* =
s*z*
[teapots(*z*)(*w**s*) & on(this
shelf)(*z*)(*w**s*)] & 2 [?]
|{*z*: teapot(*z*)(*w**s*)
& *z* [?]*p* *x* }| [?] 4]
c.
There were between two and four teapots on this shelf. They were
defective.
 


44(c), too, would be considered false in situations where only some of
the teapots on the shelf are defective. Even simple numeral phrases
like *four teapots* can have maximalized interpretations.



(45)
There were four teapots on the shelf. They were defective.


Intuitions for (45) are not so clear, but (46) brings out a sharp
difference between simple and complex numeral phrases.



(46)


a.
Every time I sell two teapots on a single day, I am entitled to a
$5 bonus.
b.
Every time I sell more than two teapots on a single day, I am
entitled to a $5 bonus.
c.
Every time I sell between two and five teapots on a single day, I
am entitled to a $5 bonus.
 


Imagine that I sold exactly four teapots yesterday. 46(a) has an
interpretation where I am entitled to a $10 bonus. On this reading,
our quantification domain is some set of non-overlapping situations
that are minimal situations in which I sold two teapots on the same
day. Regardless of how we pair up yesterday's four teapot sales
to construct an acceptable counting domain, we always end up with
exactly two bonus-qualifying situations. This shows that numeral
expressions like *two teapots* do not obligatorily have
maximalized interpretations. 46(a) contrasts with 46(b) and (c). 46(c)
has no interpretation where I qualify for a $10 bonus if I sold four
teapots yesterday. And 46(b) has no interpretation where I get $10
dollars if I sold six, for example. We can conclude, then, that
numeral expressions of the form *more than n NP* or *between
n and m NP* trigger denotations that are obligatorily maximalized,
but this is not the case for simple numerals of the form *n
NP*.



Returning to the donkey sentences we looked at earlier, we now
understand why 47(a) and (b) (repeated from above) do not simply
quantify over minimal situations in a naive sense:



(47)


a.
When a cat eats more than one can of Super Supper in a day, it
gets sick.
b.
Whenever there are between 20 and 2000 guests at a wedding, a
single waiter can serve them.
 


The antecedents of 47(a) and (b) involve maximalization. For 47(a),
for example, the proposition expressed by the antecedent could be
48(b):



(48)


a.
When a cat eats more than one can of Super Supper in a day
...
  

When the amount of Super Supper a cat eats within a day is more than
one can ...
b.
l*s* [?]*x* [?]*y*
[cat(*x*)(*s*) &
*f*day(*s*) = 1 & *y* =
s*z*
[Super-Supper(*z*)(*w**s*) &
eat(*z*)(*x*)(*s*)] &
*f*can(*y*) > 1]
 


48(b) restricts the situations quantified over to those whose temporal
extension is a day, which could be a calendar day, or, more plausibly,
a 24-hour period. The maximality condition can then pick out all the
food eaten during such a period by the relevant cats, regardless of
whether they ate just a little more than what comes in a can or much
more than that. There is no pressure to keep the portions small.
However, Fox & Hackl (2006) have drawn attention to a class of
cases where there *is* pressure to keep amounts small in
sentences with *more than n* noun phrases. (49) below would be
such a case:



(49)
Whenever the ballot count showed that a candidate had won more
than 50% of all votes, the winning candidate appeared on TV five
minutes later.


(49) suggests that candidates appeared on TV five minutes after it
became clear that they had won the majority of votes. If 500 votes
were cast in all, for example, and the ballot count showed at 8:00 pm
that one of the candidates had won 251 votes, the winning candidate is
claimed to have appeared on TV at 8:05 pm. This judgment is expected
if (49) quantifies over situations that exemplify the proposition
expressed by its antecedent. Factoring in maximalization triggered by
*more than 50% of all votes*, the antecedent can be paraphrased
as (50):



(50)
The ballot count showed that the number of votes won by a
candidate was more than 50% of all votes.


The exemplifying situations for the proposition expressed by (50) are
minimal ballot count situations that establish that one of the
candidates has carried the majority of votes. If there are 500 ballots
in all, the exemplifying situations are all situations where 251
ballots have been counted.



The last case to discuss concerns negative quantifiers.



(51)


a.
There is no teapot.
b.
l*s* ![?]*x*
teapot(*x*)(*s*)
 


51(b) is exemplified by the situations in which it is true. This makes
the situations exemplifying negative sentences a rather disparate
batch that do not resemble each other in any intuitive sense. If we
want to quantify over situations exemplifying the propositions
expressed by negative sentences, as we do in (52) below (repeated from
above), contextual restrictions for the topic situation must play a
major role, including those contributed by the topic-focus
articulation and presuppositions (Kratzer 1989, 2012; von Fintel 1994,
2004a). Exemplification is not expected to make any contribution here,
which is the result we want to derive.



(52)
Whenever nobody showed up, we canceled the class.


This section discussed and tested a particular possibilistic account
of the relation between a proposition and its exemplifying situations.
The test cases were conditionals that quantify over situations that
are "minimal" in a way that is responsive to specific
properties of their antecedents: the presence of count nouns versus
mass nouns, telic versus atelic verb phrases, modified versus
unmodified numerals, negative versus positive quantifiers. The account
showed the right responsiveness in interaction with independently
motivated interpretations for the sentences involved. Interestingly,
once possible maximalizations are factored into sentence denotations,
the exemplification account spelled out in definition (29) coincides
with the naive minimalization account in most cases. The only
systematic exceptions seem to be atelic antecedents, including those
involving negation. Contrary to initial appearance, then, the
naive minimalization accounts found in most existing analyses of
donkey sentences within a possibilistic situation semantics are close
to correct (but see section 9 for discussion of another potentially
problematic case, example (61)).


## 8. Exemplification and exhaustive interpretations



Minimal interpretations of sentences are a common phenomenon and are
not only found in the antecedents of donkey sentences. Among the most
widely discussed cases are exhaustive answers to questions, or more
generally, exhaustive interpretations (Groenendijk & Stokhof 1984,
Bonomi & Casalegno 1993, Sevi 2005, Schulz and van Rooij 2006,
Spector 2006, Fox 2007, Fox & Hackl 2006; see also the entry
 implicature).
 Here is an illustration.



(53)



|  |  |
| --- | --- |
| Josephine:  | Who caught anything? |
| Beatrice: | Jason and Willie did. |




We tend to understand Beatrice's answer as suggesting that Jason
and Willie were the only ones who caught something. This is the
exhaustive interpretation of Beatrice's answer. Non-exhaustive
or "mention some" answers are often marked with special
intonation or particles, as in (54), for example:



(54)



|  |  |
| --- | --- |
| Josephine:  | Who caught anything? |
| Beatrice: | Jason and Willie did for sure. |




In this case, Beatrice indicates that she does not mean her answer to
be understood exhaustively. In combination with Groenendijk and
Stokhof's 1984 analysis of questions, the exemplification
relation allows a strikingly simple characterization of exhaustive and
non-exhaustive answers. If we import Groenendijk and Stokhof's
analysis into a situation semantics, the extension of
Josephine's question in (54) is the proposition in (55):



(55)
l*s* [l*x* [?]*y*
caught(*y*)(*x*)(*s*) = l*x*
[?]*y*
caught(*y*)(*x*)(*w*0)]


(55) describes possible situations in which the set of those who
caught something is the same as the set of those who caught something
in the actual world. Since question extensions are propositions, they
can be exemplified. Suppose Jason, Willie, and Joseph are the only
ones who caught anything in the actual world. Then (55) is exemplified
by all minimal situations in which Jason, Willie, and Joseph caught
something. If nobody caught anything in the actual world, then any
actual situation exemplifies (55). Bringing in the Austinian
perspective, we can now say that answers to questions are always
understood as claims about the actual situations that exemplify the
question extension. Via their exemplifying situations, then, question
extensions determine possibly multiple topic situations that answers
are understood to make claims about. When an answer is interpreted as
exhaustive, the proposition it expresses is understood as
*exemplified* by the topic situations. When an answer is
interpreted as non-exhaustive, the proposition it expresses is
understood as being merely *true* in the topic situations. We
have, then:



(56)



|  |  |
| --- | --- |
| **Question extension** | A proposition. The set of situations that answer the question in
the same way as the actual world does. |
| **Austinian topic situations**  | All actual situations that exemplify the question
extension. |
| **Exhaustive answers** | Propositional answers that are understood as exemplified by the
topic situations. |
| **Non-exhaustive answers** | Propositional answers that are understood as true in the topic
situations. |

 


The proposition expressed by Beatrice's exhaustive answer in
(53) is understood as exemplified by the topic situations determined
by Josephine's question, and that implies that Jason and Willie
were the only ones who caught anything. In contrast, Beatrice's
non-exhaustive answer in (54) is understood as being true in the topic
situations, and that allows for the possibility that there were others
who caught something.



It might be useful to consider a few more possible answers that
Beatrice might have given in response to Josephine's question
and find out what the exemplification approach would predict if the
answers are understood exhaustively:



(57)


a.
Two cats did.
b.
Between two and five cats did.
c.
Nobody did.
 


The proposition expressed by 57(a) is exemplified by minimal
situations in which two cats caught something. If the topic situations
are of this kind, they, too, are minimal situations in which two cats
caught something. But then the only ones who caught anything in the
actual world are two cats. Building in maximalization, the proposition
expressed by 57(b) is exemplified by minimal situations in which a
bunch of two to five cats that consisted of all the cats that caught
something in some salient resource situation caught something. If the
topic situations are of this kind, then only cats caught something,
and there were between two and five of them. For 57(c), the set of
situations that exemplify the proposition it expresses coincides with
the set of situations in which it is true. Consequently, there is no
difference between an exhaustive and a non-exhaustive interpretation.
The topic situations include the actual world, and what is being
claimed about them is that nobody caught anything.



The examples discussed suggest that the notion of minimality that is
needed for the analysis of donkey conditionals also accounts for
exhaustive interpretations of answers. A third area where what looks
like the same notion of minimality shows up is Davidsonian event
predication.


## 9. Situation semantics and Davidsonian event semantics



Situations and events seem to be the same kinds of things. If
situations are particulars, so are events. If situations are built
from relations and individuals standing in those relations, so are
events. We don't seem to need both of those things. We
don't seem to need both situation semantics and Davidsonian
event semantics (see entries
 Donald Davidson
 and
 events).



The core of a Davidsonian event semantics are predications like the
following:



(58)
swim(Ewan)(*e*)


(58) is the classical Davidsonian formalization of the tenseless
sentence *Ewan swim*. The predication in (58) is standardly
read as "*e* is a swim by Ewan". Crucially, this
formula is not understood as '*e* is an event that
contains a swim by Ewan' or as "*e* is an event
*in* which Ewan is swimming". In other words, unlike the
basic predications in situation semantics, Davidsonian basic
predications have a built-in minimality condition. This is a major
difference between situation semantics and Davidsonian event
semantics, maybe *the* difference. Without the minimality
condition, we couldn't do many things we want to do with a
Davidsonian semantics. As an illustration, consider the following
example:



(59)


a.
Ewan swam for 10 hours.
b.
[?]*e* [swim(Ewan)(*e*) &
*f*hour(*e*) = 10]
 


If the simple predication *swim(Ewan)(e)* in 59(b) could be
understood as "*e* is an event in which Ewan
swims", then 59(b) could describe an event where Ewan swam for
just five minutes, but a lot of other things went on as well in that
event: He rode his bike, his sister slept, his mother harvested
shallots, his father irrigated fields, and taken together, those
activities took a total of 10 hours. 59(a) doesn't describe
events of this kind, hence 59(b) couldn't be a formalization of
59(a). The standard way of understanding 59(b) is as saying that there
was a swim by Ewan that took 10 hours.



But what is a swim by Ewan? A swim is typically a self-connected
situation in which someone is swimming, and which is
"minimal" in a sense that it excludes other activities
like riding a bike, sleeping or farm work. It doesn't exclude
parts of the actual swimming, like movement of arms and legs. Most
importantly, a swim by Ewan doesn't *literally* have to
be a minimal situation in which Ewan is swimming, which would be a
very short swim, if there are minimal swimming situations at all. The
relevant notion of minimality is by now familiar: a swim by Ewan is a
situation that exemplifies the proposition "Ewan is
swimming". This suggests that the exemplification relation can
be used to actually define basic Davidsonian event predications within
a situation semantics. The exemplification relation relates possibly
very complex sentences to their exemplifying situations. Davidsonian
event predications emerge as those special cases where the sentences
that are related to exemplifying situations are atomic.



If verbs have an event argument, as Davidson proposed, then simple
sentences consisting of a verb and its arguments always involve
Davidsonian event predication, and hence exemplification. Importing
Davidsonian event semantics into situation semantics, the proposition
expressed by 59(a), for example, might be formalized as follows:



(60)
l*s* [past(*s*) & [?]*e*
[*e* [?]*p* *s* &
swim(Ewan)(*e*) & *f*hour(*e*) =
10] ]


The formula in (60) incorporates the usual notation for Davidsonian
event predication. Within a situation semantics, this notation is just
a convenient way to convey that *swim(Ewan)(e)* is to be
interpreted in terms of exemplification: we are not talking about
situations in which Ewan swims, but about situations that exemplify
the proposition "Ewan swims".



If Davidsonian event predication is part of the antecedent of a
conditional, exemplification may come in more than once when
determining the situations the conditional quantifies over. This is
crucial for examples like (61):



(61)
Whenever a man rides a donkey, the man gives a treat to the
donkey.


(61) quantifies over situations that contain just one man and just one
donkey, but it does not seem to quantify over minimal donkey rides.
There is no pressure to keep the rides short and multiply the treats
accordingly. A single shift from descriptions of merely verifying to
exemplifying situations would not yield the correct quantification
domain for (61). If we tried to keep the situations small enough so as
to contain no more than a single man and a single donkey we would have
to keep the rides short as well. However, if the antecedent of (61)
contains Davidsonian event quantification, we can keep the situations
quantified over small enough to prevent the presence of more than one
man or donkey, but still big enough to contain complete donkey rides.
The proposition expressed by the antecedent of (61) would be (62):



(62)
l*s* [?]*x* [?]*y*
[man(*x*)(*s*) & donkey(*y*)(*s*)
& [?]*e* [*e* [?]*p*
*s* & ride(*y*)(*x*)(*e*)] ]


If the domain for the event quantifier in (62) is established on the
basis of some suitable counting criterion, it could quantify over
maximal spatiotemporally connected donkey rides. The proposition in
(62) can then be exemplified by minimal situations that contain a
single man *x* and a single donkey *y* and a maximal
spatiotemporally connected event of riding *y* by
*x*.



The goal of bringing together situation semantics and Davidsonian
event semantics, at least in certain areas, is pursued in a number of
works, including Lasersohn (1988, 1990), Zucchi (1988), Portner
(1992), Cooper (1997), and Kratzer (1998).