Situations and Events
Author(s): Nicholas Asher and Daniel Bonevac
Source: Philosophical Studies: An International Journal for Philosophy in the Analytic
Tradition, Vol. 47, No. 1 (Jan., 1985), pp. 57-77
Published by: Springer
Stable URL: http://www.jstor.org/stable/4319729
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NICHOLAS
ASHER AND DANIEL
BONEVAC
SITUATIONS AND EVENTS
(Received 22 March, 1984)
Jon Barwiseand JohnPerryhavedeviseda new semanticprogramfor a variety
of linguistic constructions by replacing 'possible worlds' with 'situations'
(Barwise, 1981, Barwise, 1982, Barwiseand Perry, 1981a, Barwiseand Perry,
1983).1 James Higginbothamhas attacked their new 'situation semantics'
by insisting that the constructions most supportive of the Barwise-Perry
analysis- those involving naked-infinitive (NI) perception verbs- require
for their interpretation nothing beyond the resources of first-orderlogic
(Higginbotham, 1983).2 Higginbotham has argued that a semantics can
represent these constructions by quantifying over events. In this paper we
shall attempt to clarify the differences between Barwise-Perrysituation
semantics (hereafter, SS) and Higginbotham's'individual-event'semantics
(hereafter, ES). We shall argue that ES neither accounts for the relevant
usages nor succeeds, on its own terms, in presenting a coherent semantics
for NI perception verbs. We shall offer a version of SS which, in contrast,
handles these constructions adequately. Finally, we shall arguethat there is
no philosophical reason for preferringextensional semantic theories such as
ES to situation semantics.
1. SITUATION
SEMANTICS
Weshallbeginby presentingthe essentialfeaturesof the Barwise-Perry
analysis
of NI perceptioncontexts. Roughly, SS construessentencesof the form
(1)
asees4
as being 'supported'at a situations' just in case
(2)
3sCs'
(aseess&sE GE]J)
where 's' and 's" range over situations and D01
is the set of situations 'supporting' the truth of 0, which situation semanticstreatsas a bona fide sentenPhilosophical Studies 47 (1985) 57-77.
0031-8116/85/0471-0057$02. 10
(? 1985 by D. Reidel Publishing Company
58
NICHOLAS
ASHER AND DANIEL
BONEVAC
tial complement. Situations are complexes of entities standingin deterninate
relationsto each other; they arefragmentsor portionsof a world. We represent
sets of situationsby means of situation types, defined as follows: where D is a
set of individuals(the domain) and Rn a set of n-ary relations, the set S of
situation types is the set of all partialfunctions from Un(Rn X Dn) into the
set of truth values {IO,1}, where '1' representstruth. For much of this paper,
however, we shall collapse this distinction in the interests of simplifyingour
discussion.3
A full treatment of situation semantics' interpretationof NI perception
sentences requiresa characterizationof [a sees p1D.
Wewill requirea semantic
rule that interpretsthe basic syntactic structureof NI perception sentences,
which we take to be
(3)
[NPV s[NPVP]].
Providingsuch a rule requiresus to make several decisions that we cannot
defend in any detail here (Asherand Bonevac,forthcominga). First, we hold
with Barwise and Cooper (Barwise and Cooper, 1981) that most NPs are
generalizedquantifiers.With the exception of proper names, we hold that
NPs take familiesof sets as valuesin particularsituations.We shall thus extend
Barwiseand Perry'sidea of 'valueloading'(Barwiseand Perry, 1983, Barwise
and Perry, 198 ib) from singularto all NPs.
Second, we hold that an adequatesemanticsfor NI perception sentences
must contain a consistency principle, saying that a perceiversees only one
scene at a time in a given situation (Asher and Bonevac, forthcoming a,
Asher and Bonevac, forthcoming b). This allows us to simplify our general
approachto NI perceptionreports.
Third, we propose to amend situation semanticsto allow the evaluation
of quantifiers within the embedded sentence to vary. We shall therefore
define 's E ga sees oD'as
(4)
Wseej(s, a) E
I01,
where we evaluate quantifiersin 0 at a, some nonempty situation in world
w.4 We claim that our version of situation semantics does far better in ac-
counting for linguisticusage than Higginbotham'salternative.
SITUATIONS
AND EVENTS
59
2. EVENT SEMANTICS
Higginbotham'stheory takes the objects of NI perceptionto be events rather
than situations.He construesa sentence such as (1) as havingthe form, roughly, of
(5)
3 e (q (e) & see(a, e))
where 'e' rangesover events, 'see' denotes a relationbetween individualsand
events, and '?(e)' says that e is an event in which 4. Higginbothamconstrues
the NI complement 0, semantically,as a definite or indefinite descriptionof
an event. Thus, for Higginbotham,NI complementsshould function in ways
more akin to nominals than clauses. Though at odds with most syntactic
analyses of NI complements- a fact which he notes himself (p. 106) Higginbothamexploits this difference in an attempt to capture certain facts
about NI perceptionreportsnot discussedby Barwiseand Perry.
Higginbothamadopts a Davidsonianview of events and action sentences,
holding that they contain a hidden event quantification.Whethera sentence
contains an implicit event quantifier depends, for Davidson and Higginbotham, on whetherthe sentence'sVP denotes an active or transientproperty
of the subject NP. Higginbothamarguesthat all NI complementsmeet such a
criterion.
For a numberof reasons,we must complicateHigginbotham'struth conditions. First, the truth conditions should contain an additionalevent quantification. A's seeing C is itself a transient or active property of a. By Higginbotham's own criterion, then, the truth conditions of 'a sees O' should contain two implicit event quantifiers.We are also forced to this conclusion by
noting that we can embed NI reportswithin each other, as in:
(6)
John saw Marywatch Fred eat an apple.
Thus,we analyze(1) as
(7)
3 e' 3 eQ((e) & see(a, e, e'))
which is to be read, 'Thereare events e' and e such that e is an event in which
q and e' is an event in which a sees e'.
Second, the truth conditions must employ first-orderrepresentations.
Higginbothamstressesthat his analysisis significantby virtue of being firstorder (p. 101). Furthermore,he needs a symbolismmaking places for event
60
NICHOLAS
ASHER AND DANIEL
BONEVAC
variablesexplicit. ES therefore requires a translationfunction from natural
languageto a first-ordersystem of representation.Let the first-ordertranslation of k be 'T. T wfll take us from clauses in Englishto first-ordertranslations of them functioning as predicates of events. The translationfunction
in effect addsan argumentplacefor events,of which the formulais a predicate;
(Marypunched Bill)T= P(m, b, e). So the truth condition should contain an
occurrenceof '0J(e)' ratherthan '?(e)'.
Third, the truth conditions must give all quantifiers in the embedded
clause wide scope over the event quantifiers.Initially, the theory seems to
requirethat, in a situationin which
(8)
Davidsees everyonedrop to the ground
is true, there is a single event in which everyone drops, and a singleevent in
which David sees everyone drop. This in fact seems to be a perfectly natural
interpretation in a semantics with a mereological view of events, which
Higginbothamadopts (p. 113). In order to get the right predictions concerningexportationof quantifiersandveridicality,however,ES must construe
quantifiersin the embedded clause as takingwide scope over the event quantifier (p. 108). Otherwise,the exportationof 'nobody' from the complement
to preposedposition would amount to a simple logical mistake. But Higginbotham never explainswhy quantifiersin the embeddedsentence should take
wide scope. Letting the quantifiersin the complement take wide scope over
the event quantifierallows diverseevents of seeingand droppingto make (8)
true.
Despite its artificiality, then, we must demand that any quantifiersin ?
be prefixed to the left of the event quantifiers.WherepTcontains the quantifiers Q1. Q, and the quantifier-freeportion ~/, we shallconstrue(1) as
(9)
Q1 ... Qn,3e'3 e(4'T(e)& see(a, e,e')).
We shall take (9) as ES's analysisof NI perceptionsentences.
3. EVENTS VS. SITUATIONS
Higginbothamquantifies over events, construingthem as individualslacking
the structure of scenes or situations. Events are neither sets nor functions.
His proposaluses a ploy devisedby Davidsonto deal with the logical form of
action sentences (Davidson, 1980a, Davidson, 1980b, Davidson, 1980c).6
SITUATIONS
AND EVENTS
61
By introducinga new kind of individualobject into the domain of quantification, it givesa first-orderanalysisof sentencesthat seem to resista standard
approachto logical form. As we shall argue,however,Higginbotham'sstrategy
yields a theory with less expressivepower than SS. To show that SS has more
expressive power, we must (1) show that ES cannot capture distinctions
between situations and (2) reconstructDavidsonianevents as certaintypes of
situations.
In arguingfor the existence of entities such as events, Davidsonclaimsthat
we need events to give a logical analysisof action sentences, to account for
our talk about describingand redescribingactions, and to make mind-body
identity theories intelligible (pp. 164-166). As Davidson notes, it makes
sense to call his analysisof action sentencesfirst-orderonly if we can produce
a reasonablecriterion of identity for these entities. Davidsonthinks he has
such a criterion: he counts events identical if and only if they have the same
causesand the same effects (p. 179).
Davidson's criterion entails that an event may fall under severaldescriptions. For instance,consider:
(10)
Buck shoots Ed
which Davidson'sview rendersas:
( 1)
3e (shoot (Buck, Ed, e)).
Such an event may have severalcorrect descriptions.If Buck shoots Ed with
a gun, then Buck'spullingthe trigger,says Davidson,is the same event as that
of Buck's shooting Ed, modulo certainassumptionsabout causesand effects.
So (11) is truejust in case (12) is:
(12)
3e (pull (Buck, the trigger,e)).
Situation semantics, however, distinguishesbetween Buck's killing Ed and
Buck's pulling the trigger.Nothing in situationsemanticsforces their identification. Thus, situationsaremore finely individuatedentities than Davidsonian
events.
To reconstructDavidsonianevents as kinds of situations, we need to augment ES with a set of postulates telling us which descriptionsdescribeone
event. Davidson'scausal principle of individuationhelps us only if we know
just what causes and effects variousevents have. Let us call this set of postulates HI.We may specify fHby detailingthe causes and effects of each event
62
NICHOLAS
ASHER AND DANIEL
BONEVAC
or, directly,by specifyingpostulatesof the form
(13)
& 4'T(e')) +e = e'),
Ve'Ve((O'T(e)
where p and 4 are event descriptionsin English. If we include Hlwithin ES,
however, it is not clear that ES remainsa first-ordertheory. It demandsmore
resources than those found in first-orderlogic alone. Moreover,the added
resourceswill not be finitely axiomatizable,or, perhaps,even axiomatizable
at all, since HIwill be infinite and probablynot recursivelyenumerable.This
raisesa broadquestion:what counts as a first-ordersemantictheory?We shall
treat this question in detail later.
With Hlat our disposal,we can reconstructDavidsonianevents as types of
situations. We can characterizethe set of situations that support the event
descriptionsof some particularevent as the set of situations
(14)
1, = {s E S/3 e3 T('T(e) & s EI 3 e' T(e')]I & H1U {T(e)}H
4'T(e))}
where 4 and ; describe events. The set of situations correspondingto an
event e under a description0 is the set of all those situationssupportingsome
event descriptionthat HIcounts as describinge. We can think of an event e,
then, as a set containingevery situation that supportsa descriptionof e. If
this is right, then situation semanticscan express Davidsonianevents, which
turn out to be much coarserentities than scenes and situations.
4. EMPIRICAL SUPPLEMENTATION
We have pointed out that ES requiressupplementationby a set of empirical
postulatesgoverningevent identity. Thesepostulates threatenHigginbotham's
project of providinga first-orderanalysis.We shallnow arguethat ES requires
a set of postulatesgoverningnegationas well.
The most obvious way to treat a negatedNI complementis to assumethat
(74')T(e) is equivalentto 1(4T)(e), where 4T is quantifier-free.This, however,
yields incorrecttruth conditions (p. 111). Higginbotham,therefore,resortsto
antonyms. Let v be a function from first-orderformulas 4J into first-order
formulasv(4T), where v(Q) is like 4' except that it contains the antonym of
4's VP. Higginbothamtreatshis antonym function as a function from VPs to
VPs, which has the effect of our function from predicatesto predicatesin
first-orderlogic. To get accuratetruthconditions,v(4') must be strongerthan
SITUATIONS
AND EVENTS
63
v should be defined by a set of postulates of the form 'Ve(v(iT(e))
,T(e))'. This seems to make 4 and v(;) something other than strict antonyms.
But this attempt to salvage ES fails to yield an adequate treatment of a
type of inference that Higginbothamconsidersvalid. Barwiseand Perrycontend that NI perceptionverbsobey a principleof negation distribution:
-
(15)
asees}k
-(a sees q)
Higginbothamconstrues(15), where
(16)
QT=
Qn ', as
Q1...Q 3e'3 e(v(T)(e) & see(a,e, e'))
Q, ..Q
3 e 3 e (o(e) &see (a, e, e'))
where Ql is the dual of Qi. Higginbothamwants(16) to hold for all embedded
clauses.
Does Higginbotham'streatmentof negationvalidatethe negationprinciple,
as the linguistic data demand?Not in general (Asher and Bonevac, forthcoming a). Considerthe following arguments,which seem intuitivelyvalid:
(17)
(18)
Davidsees nobody in the audienceapplaud.
Daviddoes not see anybody in the audienceapplaud.
Davidsees not every frogjump.
Daviddoes not see every frogjump.
ES, as it stands, does not capture (18). We can constructa countermodelby
allowing David to see two events satisfying contradictory descriptions.To
solve this problem, Higginbothammust either build more structure into
events or adopt a constraint restrictingthe class of actual (or compossible)
events. One such constraintis
(19)
VxVeVe'Ve"Ve"'[(see(x, e, e')& see(x, e", e"'))<- e' = el'
which, roughly, says that a perceivercan see at most one event at a time. This
conflicts, however, with a mereologicalview of events, which Higginbotham
explicitly adopts (p. 113). He apparentlymust hold a principle demanding
the compatibility of events occurringat a given time. But this is impossible
to formulate in an extensional first-orderlanguage.In requiringthe compatibility of two events e and e', we are requiringin effect that any description
NICHOLAS
64
ASHER AND DANIEL
BONEVAC
of e be consistent with any descriptionof e' (given H). This seems to require
quantification over descriptions. More importantly, it requires the use of a
concept of consistency, which, by Church'stheorem, is not axiomatizable.
Again this seems to muddy Higginbotham'sclaim to a first-order,extensional
analysis.
A further problem ariseswith (17). ES validates(17) without any supplementary constraints. Since all quantifiers export, however, ES makes (17)
invertible. Some speakersfind this appropriate;many, however, hold that
(17)'s premise requires that David sees something, but that its conclusion
does not. Apparently such speakers sense an ambiguity in (17)'s premise,
taking it as equivalenteither to 'David does not see anybody in the audience
applaud' or to 'David sees everyone in the audience not applaud'.If we opt
for the strongerreading,the invertedargumentshould be invalid.ES cannot
give us the two readingswe need just becauseit attempts a first-orderanalysis;
' 3x' and 'Vx ' are equivalent.
SS's treatment of the negation principleis far superiorto that of ES. SS
assigns(15) the form
(20)
gsee (s, a)el-E L
lsee (s, a) 6 D
Recall that situations are functions. SS therefore validatesnegation distribution universallywhen, as in almost all cases, a = a'.
Becauseof SS'streatmentof negativequantifiers,'Marysees nobody laugh'
seems to be ambiguous,roughly, between 'Marydoes not see anybody laugh'
and 'Marysees everyone not laugh'. On the weaker reading,argumentssuch
as (15) will invert; on the strongerreading,they will not. 'Marysees nobody
laugh'appearsto have an interpretationmakingit equivalentto
(21)
1everybodyIs{b E D/ seeI(s, a)(I[laugh , b) = 0}.
Under this reading, (15) remainsvalid, but it no longer inverts (Asher and
Bonevac,forthcoming).This too seemsto squarewith linguisticintuition.
Note that ES treats negation in two radically different ways. When the
negation is linked to a quantifier(as in 'Oliversaw nobody leave'), it exports,
along with the quantifier,retainingits standardmeaning.When the negation
has scope only over a quantifierfree VP, however, Higginbothamappeals to
the antonym function to get correct truth conditions. SS accomplishesthis
by taking situations as partial functions into { 0, 1 }; a situation may verify,
SITUATIONS
AND EVENTS
65
refute or say nothing about a given atomic sentence. Higginbotham'sintuition
that negative quantifiers should be treated differently from negated VPs
reflects the complexity of negative quantifiersthat we have mentioned. But
a theory that can treat the phenomena properly requiresSS's notion of a
situation, which goes beyond the resources of first-orderlogic (Asher and
Bonevac,forthcomingc).
5. EVENT IDENTITY:
EMPIRICAL CONSEQUENCES
Both SS and ES capture most of the propertiescharacteristicof NI perception contexts, as Barwise and Perry describe them (pp. 376-380; Barwise
and Perry, 1981a, p. 677). But they differ with regardto certaininference
patterns. We have already seen significantdifferencesin their treatmentsof
negation. In this and the next several sections we shall show that ES lacks
the empiricaladequacyof situationsemanticswith regardto certaininferences
includingconjunctionintroduction,exportationand veridicality.
The Davidsonianview of event identity createsan importantdifficulty for
ES. Suppose that David is walking down an alley late at night. A streetlight
at the end of the alley enables him to see a man fire a gun, but darkness
hides the victim. The man firing the gun is Buck; the event of Buck'spulling
the triggeris identical to the event of Buck's shooting Ed. But David only
sees Buck pull the trigger.He does not see Ed at all. Accordingly,our intuitions lead us to conclude that
(22)
Davidsees Buck pull the trigger.
is true but that
(23)
Davidsees Buck shoot Ed.
is false. On Davidson's view of events and Higginbotham'sanalysis of NI
perceptionsentences,(22) implies(23), because
(24)
(Le)(pull(Buck, the trigger,e)) = (Le)(shoot(Buck, Ed, e)).
From (22) and (24), we can derive(23) in first-orderlogic.
To take anotherexample:
(25)
(26)
Davidsees Maryrun.
Davidsees Mary'slegs move in way W.
66
NICHOLAS
ASHER AND DANIEL
BONEVAC
(where W is the movementanyone'slegs have when they run). On Davidson's
view of events, once again the descriptions '(te) (Run (Mary, e))' and '(Le)
(Move in way W(Mary'slegs, e))' appear to pick out the same event. Consequently, (25) implies(26), a consequencethat seems simply false. It depends
where Davidis and what he sees; he could see Maryrun without seeingMary's
legs move, if there were a low wall blockinghis view of Mary'slegs but not his
view of Mary.
If these intuitions are correct, Higginbotham'sanalysisof NI perception
sentences leads to incorrect predictions. Complements to 'see', at least,
require more finely individuatedsemantic values than unstructuredDavidsonian events. In SS, in contrast, two descriptionsof the same Davidsonian
event might not be supported by the same set of situations. Thus, the inferencesfrom (22) and (24) to (23) and from (25) to (26) fail in SS.7
6. NP COMPLEMENTS
Higginbothamclaims that his construal of NI complements as NPs solves
Barwise'spuzzle of logical equivalence.ES does solve the puzzle, but not for
the reasons Higginbothamcites. His defense relies on an assertionthat the
semantic interpretation of NI complements as NPs uncovers an important
ambiguity involving conjunctive complements. Conjunction introduction
involvesinferencesof the following form:
(27)
a sees4 &a sees t
a sees (' & ;)
Higginbothamclaims that (27) is ambiguous (p. 113). Barwise and Perry
note that though(27) does not follow from their semantictheory as developed
in (Barwise,1981), it seems to be a reasonableadditionto situationsemantics
and does follow from the consistency principle that we have added to our
version of situation semantics.Higginbothamtakes the failure of (27) to be
a virtue of ES's construalof NI complementsas NPs.
Whatare the facts concerningconjunctionexploitation? Consider
(28)
John sees Maryand Fred get married.
Higginbothamis right to point out an ambiguityhere; John may see them
marry each other, or he may see two marriageceremoniesat the same time.
However,we see no such ambiguityin a sentence like
SITUATIONS
(29)
AND EVENTS
67
John saw Marysmoke and Fred fix the car.
Higginbotham's defense requires that every sentence of the form 'a sees
(p & i)' be ambiguous.But we are simply unable to get two readingsfor
(29) to parallelthe earlierexample. There is no readingof (29) invalidating
(27). The ambiguity of certainconjunctiveand quantificationalNPs does not
carry over into an ambiguity involving a conjunctive NI complement with
unambiguoussubjectNPs. Thus, ES makes an incorrectpredictionconcerning
conjunction introduction. Furthermore,this failure strongly suggeststhat NI
complementsshould not be construedsemanticallyas NPs.8
An ambiguity similar to that in (28) affects sentences containingcertain
quantificationalNPs (Lakoff, 1972). For example,
(30)
All the boys carriedthe piano upstairs
has both a group and an individualreading.This parallelismreflects the idea
that universal quantification generalizesconjunction. So Higginbotham,to
be consistent, should find universal quantification ambiguous and reject
universalimportation, which is a generalizedform of conjunction introduction. By treating embedded quantifiersas having wide scope, however, he
assignsthe same truth conditions to both premiseand conclusionin universal
importationinferences.
The possibility of two readingsfor a sentence of the form 'a sees (p & )'
apparentlyhinges on the possibility of seeing two scenes or events without
seeing their union. This does not strike us as plausiblewhen we restrict our
reports to those about seeingsat a particularinstant; for normalspeakersand
normal seers, it seems to be a physical and perhapsa metaphysicalimpossibility to see two scenes or events at one time without seeing their union.
To argue that people may do so because of their capacity to report on each
scene separatelyand their incapacity to integratethose two reportsseems to
confuse an epistemic with a non-epistemic sense of seeing. Significantly,
Higginbothamprovidesus with no examplesof the ambiguityhe alleges.9
Finally, even if there were such an ambiguity, Barwise'spuzzle would
succeed on one reading of the sentences involved. What, then, does solve
the puzzle of logical equivalence?The antonym function, by treatingnegation in a nonstandardway, precludesa derivationof (O & 4J) V (QT & v(iV))
from O' alone.
68
NICHOLAS
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7. EXPORTATION
Exportationinferenceshave the form:
(31)
a sees Q
Q(a sees
Higginbotham'sanalysiscounts all such inferencesvalid. Indeed, the premise
of (31) receives exactly the same analysis as (31)'s conclusion; on Higginbotham's analysis, exportation is really 'pseudo-exportation',since he gives
quantifierswide scope whetherembeddedor not.10
Are all embedded quantifiersin fact exportable?Many speakerscountenance exportation in all instances,but some find the exportationof universal
quantifiersquestionable:
(32)
John sees every car finish
Everycar is such that John sees it finish.11
Apparently most speakersassume that the interpretationof the quantifiers
is fixed throughoutboth premiseand conclusion.The uneasinessfelt by some
seems to stem from a sense that, when exported, the quantifiercan rangeover
a domain largerthan the one it has when unexported. Since some speakers,
at least, sense an indeterminacy with respect to quantifierinterpretations
in these sentences, the semantics should indicate that they suffer a lack of
specification. Which quantifiers export will depend upon certain semantic
or pragmaticvariables.ES cannot grant us such flexibility, since in ES the
quantifiershave the same range,regardlessof scope.
In SS exportability inferences of the form of (31) turn out to have the
structure
(33)
1Q1
a{b
E D/IP/[see] (s,a)(b)}
MalQ] b E D/Oar/Iseel (sI a)(b)}
Unlike ES, SS attributes no hidden existential quantifiersto NI perception
sentences; thus there is nothing that can prevent the conclusion of (33)
from resembling its premise.12 But SS contains an added dimension of
flexibility in its interpretationof quantifiers:quantifiersmay be interpreted
at any contextually determinedsituation a. Normally,since speakerstend to
evaluate both premise and conclusion in the same situation, we can assume
that a = a'. In that case, SS agreeswith ES that all quantifiersexport from
SITUATIONS
AND EVENTS
69
NI complements. Exportation,however, (perhapslike topicalization)imparts
an emphasiswhich suggeststhat the exported quantifiermay demandevaluation elsewhere. Intuitions concerning these cases suggest that a is almost
alwaysat least aslargein the conclusionas in the premise.This is only natural,
since the premise forms part of the conclusion's context, and intervening
premises can introduce new elements of the domain (Lewis, 1979; Kamp,
1981; Karttunen, 1976). When this occurs, SS predicts, only existential
quantifiersexport unproblematically.13We might expect, then, that existentials export in almost every context, and that universalsexport in many.14
8. VERIDICALITY
Perry and Barwise contend that NI perception contexts, like a number of
related contexts (e.g., 'see that'), are veridical. That is, they assert, (many)
inferencesof the following form arevalid:
(34)
a sees
If David sees Buck run, Buck runs. With regardto fairly simple sentences,
this principle seems unexceptionable; if Buck doesn't run, how can David
see him run?Nevertheless,(19) shouldnot be valid for all 0:
(35)
Davidsees no student cheat on the exam.
No student cheats on the exam.
(35) clearly fails. This poses a problem for any account of NI perception
verbs:how should one distinguishthe sentences p for which (34) is valid?
ES construes(34) as havingthe following form:
(36)
Q1... Qn3 e'3 e(4JT(e) & see(a, e, e'))
Q
Qn 3ei(e)
where QT=
Q, ,.. Under what circumstancesdoes (36) hold? Say that
a quantifierQ is monotonic increasing(or decreasing)just in case it validates
the inference from 'QO'and 'All k'P'(or 'All 4'0') to 'Q t. If some frogs are
green, and all green things are colored, then some frogs are colored; so
'some frogs' is monotonic increasing.Similarly, since 'No frogs chirp' and
'All birdschirp'imply 'No frogs are birds', 'No frogs' is monotonic decreasing.
70
NICHOLAS
ASHER AND DANIEL
BONEVAC
Higginbothamcorrectly observesthat (36) is valid if Q1... Q, are all monotonic increasing(p. 109).
Higginbothamseems to think that this is a necessarycondition for validity
as well. But this is plainly false. What happens to sentences with negated,
i.e., monotonic decreasing, quantifiers, such as 'no student cheats on the
exam?' 'No' is equivalent to either '- 3x' or 'Vx -'. Quantifiernegation
principles allow us to drive the negation so introduced into 'T. We can
restore the monotonic increasingcharacterof all of Q1 ... Q,nin such a way
that the inferencebecomes
(37)
Q1..Qn Ve'Ve
(T(e)
&
see(a, e, e'))
Q1...QnVe7iPT(e)
(37) is invalid, but only because its premise can be true without a's seeing
anything. If there are two negated quantifiers,two negationswill be driven
into 4; the result in this case, however, will be equivalentto 4J. We may
generalize the point: in ES, (34) is valid for all and only those sentences 0
that do not contain an odd number of negated quantifiers('no F', 'few F',
'nobody', 'nothing', etc.). We shall refer to sentences with an even number
of monotonic decreasingquantifiers,the rest of whose quantifiersaremonotonic increasing,as V-sentences.ES, then, counts (34) valid for all and only
V-sentences.
What are the facts concerningveridicality?It seems to succeedunquestionablyfor sentencescontainingonly monotonic increasingquantifiers,as Higginbotham points out. Veridicality inferences fail for sentences containing an
odd number of negated quantifiers.The speakerswe have tested feel hesitant
about the validityof veridicalityfor sentenceswith an even numberof negated
quantifiers.
Higginbotham'sanalysis,for example,counts this argumentvalid:
(38)
John sees no boy kiss no girl.
No boy kisses no girl.
These sentences are very difficult to parse.Many speakers,in fact, laugh at
sentences containingmore than one negated quantifier;this makes datahard
to collect. Nevertheless,we think that there is a readingof (38) on which it
fails, for exactly the reasonsthat (35) does.
SS renders(34) as
SITUATIONS
(39)
tlsee] (s, a)
s E II or
AND EVENTS
71
E [?]I
SS's predictions concerning veridicality depend on the relation between a
and a' and the monotonicity of the complement.'s SS validatesveridicality,
assumingthat a and a' are identical, for all V-sentences.To that extent, it
agreeswith ES. But accordingto SS, an importantambiguityaffects negated
quantifiers,which do not have the characterthat a first-orderformalization
of them would predict. SS thus validatesveridicalityfor sentencescontaining
negatedquantifierson only some of their readings.A sentencelike
(40)
John sees no boy kiss no girl
seems to have two interpretations:one, that John sees every boy kiss some
girl; the other, that John does not see any boy do something, i.e. kiss no
girl.'6 On the latter readingthe negations do not cancel, so veridicalityfails.
SS correctly predicts, then, that veridicalityinferenceswill succeed unquestionably for all embedded sentences with only monotonic increasingquantifiers, and will succeed for sentences containing even numbers of negated
quantifierson only some of their readings.
9. FIRST-ORDER
EXPRESSIBILITY
We have compared two semantic theories, one first-orderand one secondorder, and we have arguedthat the second-ordertheory handlesthe linguistic
data much better. Our comparison of ES with SS, however, leads us to
examine some more generalquestions: what counts as a first-ordersemantic
theory? What might lead one to prefer a first-ordertheory, like ES, to a
second-ordertheory? Though Higginbothamdoes not explain why a firstorder theory is, in principle, preferable, several considerationsmight be
relevant:(i) a first-ordertheory offers the hope of reducingsemanticrelations
to proof-theoreticones; (ii) a first-orderformalizationclarifiesthe ontological
commitments of a theory; and (iii) a first-ordertheory makes fewer ontological commitments than a second-ordertheory, since it quantifies only
over individuals.Second-ordertheories, in contrast,quantify over individuals
and properties,functions, or sets of individuals.How do these considerations
relateto a decision between ES and SS?
Consider first the idea that first-orderformalizationallows syntactic or
72
NICHOLAS
ASHER AND DANIEL
BONEVAC
proof-theoretic concepts to replace semantic or model-theoretic ones. Say
that a theory is a set of sentencesexpressedin a definite languagewith a welldefined consequence relation. A first-ordertheory, then, is a set of sentences
expressed in the languageof first-orderlogic with its standardconsequence
relation. In light of the strongcompletenesstheorem,if 0 is a consequenceof
a first-ordertheory 0, then 0 is derivablefrom 0 using the rulesof first-order
logic. Those who adopt a computational theory of mind may find this a
virtue. Proponentsof such a theory are committed to construingthe mind or
brain as an essentially 'syntactic engine' (Dennett, forthcoming);there is no
room in such a theory for a consequence relation that cannot be captured
syntactically. Thus, a first-ordertheory might be useful in explaining how
speakers compute semantic judgments: with the aid of some first-order
theorem prover. A higher-orderconsequence relation, in general, eludes
syntactic characterization.
ES, it turns out, does not have a first-orderconsequence relation.Higginbotham uses quantifiersthat, he confesses, cannot be expressed in a firstorder language(p. 116). After findinga way of symbolizingthese quantifiers,
he provides truth conditions for sentences containing them that employ
metatheoretic notions such as 'more A than B', 'at least as many As as Bs',
etc. Without additionalaxioms, the first-orderconsequencerelationdoes not
suffice to capture the logic of these quantifiers.Addingthe necessaryaxioms
to ES, as we shall see in a moment, simply createsother problems.
A computational theory of mind might motivate the choice of a firstorder theory. But surely not any first-ordertheory will do. It would be difficult to conceive on the computationaltheory of mind how any theory that
is not recursivelyenumerablecould be learnedor even represented.We must,
therefore, consider the nature not only of the consequence relation but of
the set of sentencesconstitutingthe theory.
There is no reason to think that ES is recursivelyenumerable.We have
seen that ES must be supplementedby a set of postulatesHI,which is probably
not recursivelyenumerable.If HIis not recursivelyenumerable,then neither
is ES. Our reasonsfor claimingthat Hlis not recursivelyenumerableare not
altogether conclusive. But, to show that HIis recursivelyenumerable,one
would need a recursivemethod that would, given any two coreferential
event descriptions, say that they are coreferential.This, on a Davidsonian
view, would require some procedurefor generatingcauses and effects when
given an event description.One can imagine such a procedure,providedthat
SITUATIONS
AND EVENTS
73
one makes a host of metaphysicalassumptionsabout the characterof events
(e.g., that there are only finitely many). The onus here, however, is on the
championof the first-ordertheory.
Second, we have seen that ES requiresa consistency principle to make
sense of negation in NI perception reports. The notion of consistency is
itself certainlynot axiomatizable,so ES cannot be either.
Finally, suppose that Higginbotham,to preservethe first-ordercharacter
of the consequence relation, were to add the necessaryaxioms for his treatment of quantifiers.He would have to add much of set theory in order to
get the truth conditions right (Barwise and Cooper, 1981). But the valid
sentencesin the languageof set theory are not recursivelyenumerable.
A second reason for preferringfirst-orderformalizationis its clarification
of ontological commitment. Quine stresses that we must translate theories
into the canonical notation of first-orderlogic before assessingtheir commitments (Quine, 1969). This, however, constitutes no reason for a blanket
rejection of higher-ordertheories; it simply calls for a first-orderregimentation for ontological purposes. In any case, Hi-ginbotham seems to adopt
an instrumentalistinterpretationof semantics that would make even firstordersemantictheoriesirrelevantfroman ontologicalpoint of view(p. 126).
A third possible reason for preferringa first-ordertheory concerns the
minimization of ontological commitment. One might argue that we can
determine the commitments of higher-ordertheories, which turn out to be
more onerous than those of first-ordertheories (Quine, 1967). Again this
seems to contradictHigginbotham'sinstrumentalism.
What are the ontological commitments of SS? And how do they differ
from those of ES? SS makes use of situation types, which are set theoretic
constructions out of properties, relations, individualsand truth values. In
fact, however, we may replace propertiesand relationswith linguistic items
- verb phrasesin the languageunder study or in some neutralmetalanguage.
Nothing in our analysiswould be altered by this replacement.We can think
of elements of situation types, then, as specifying that a sequence of individuals does or does not satisfy a certain predicate.Consequently,it is not
obvious that the formal theory of situation semanticshas ontological commitments beyond those to sets and objects in the actual world. Developing
notions of validity, consistency, etc., in the semantics of course requires
quantificationover unactualizedsituation types.
The commitments of ES, as we have construedit, are apparentlygreater
74
NICHOLAS
ASHER AND DANIEL
BONEVAC
than those of SS. ES explicitly quantifiesover individualsand events. Events,
presumably,do not reduce to complexes of individuals.Further,if ES treats
quantifierssuch as 'at least as many Fs as Gs', etc., it too makes a commitment to the ontology of set theory. Finally, defining notions of validity,
consistency, etc., which ES requiresto obtain correct empiricalpredictions,
forces quantification over individualsand events in unactualizedfirst-order
models. In a strict Davidsoniansemantics, which prohibits such quantification, characterizationsof validity and consistency may be impossible(Asher,
forthcoming).
This bringsus to a final desideratumHigginbothamespouses:extensionality. He stresses that ES is an extensional alternativeto situation semantics
and, so, avoids ontological commitments to possibilia. SS, however, is no
more committed to possibilia than ES. SS makesuse only of actualsituation
types and situations in analyzingNI perception constructions.If an NI perception report is true, a perceiversees an actual situation; this seeingis itself
an actual situation; and the quantifiersare interpretedat actual contextual
situations. ES does not fare this well; it needs a consistency principlethat
essentially contains an intensionalcontext. A satisfactorytreatmnent
of propositional attitudes forces situation semantics to quantify over possible
situations (Bonevac, 1984). But this extendibility is a virtue of SS; it provides
hope that SS can provide a unified semantic account of natural language.
Until Higginbothamcan provide a purelyextensionaltheory of propositional
attitudes,modal notions, andlogicalconcepts, the contention that a semantics
for natural language can rely on events and thus flee from intension will
remainwithout support.*
NOTES
* We owe thanks to Stanley Peters and HansKampfor inspirationand commentson
an earlierdraft of this paper. Hanno Beck and Al Martinichread an earlierdraft and
providedhelpful suggestions.We are gratefulto the Centerfor CognitiveScienceof the
Universityof Texas at Austin for its generousresearchsupportduringour work on this
project.
1 Furtherpagereferenceto Barwisewill be to Barwise(1981) unlessnoted otherwise.
2 Furtherpagereferencesto Higginbotham
will be to this article.
Barwiseand Perry have developeda plethoraof entities that go beyond the distinction between situations and situation-types.They call a situation-typepaired with a
designationof a determinatespace-timelocation a state of affairs, They also construct
courses of events, sets of states of affairs.We shall not use states of affairsor courses
of eventsin this paper,sincewe ignoremattersof tense andlocation.
SITUATIONS
AND EVENTS
75
4 Barwiseand Perry(1983) employ a discoursesituationand a set of speakerconnections. Theseareusefulin characterizinga. OthercategoriesbesidesNPs,suchas adjectives
and relative clauses, may make use of contextual situations of particularkinds. For
details,see Asherand Bonevac(1983b). The crucialsemanticrule we writeas
aaiVyls(a) iff lolcr{b E=-D/1fyDa/10,(s, a)(b) }
which says, roughly,that an NI perceptionsentenceholds of an individualin a situation
just in case the noun phrase of the embeddedsentence, evaluatedat a contextually
specifiedsituationa, holds of the set of objectssatisfyingthe verbphrase,the quantifiers
of which are evaluatedat a and the quantifier-freeremnantsof which are evaluatedat
the scene the individualsees in the originalsituation.Whenp is a propername we can
simplifythe aboveto:
IcaP 'Ys(a) iff 1'Ya/IorIJ(s,
a)(IPI).
Negatedquantifiers,such as 'no', 'nobody',etc., should also appearto the left of the
event quantifiers.The string Ql ... Qn may thus contain negation symbols as well as
' 3s, 'V's, and other quantifiers.We have been unable to understandHigginbotham's
intensionsconcerningthe exact form of r; we have thereforereconstructedthis notion
in what has seemedthe most generousway.
6 Furtherpage referencesto Davidsonwill be to Davidson(1980b) unless otherwise
noted.
7
Perhapsan alternativeto Davidson'sview of events would rid ES of at least some
incorrectpredictions.Propertytheoriststake an event to be a complexof a propertyor
relationand an individualor set of individualshavingthat propertyor standingin that
relation.See Montague(1974), Kim (1966), Brandtand Kim (1967), Goldman(1970).
Different propertiesexemplifiedby the sameindividualwould yield, on the property
theorist'sview, different events involvingthe same individualor individuals.Thus, for
the propertytheorist, the descriptionsin (24) need not pick out the same eventsif the
propertiesconstitutiveof those eventsdiffer. Thus,we can block the inferencefrom (25)
to (26) and the inference from (22) to (23) without claimingthat NI perceptioncontexts are referentiallyopaque.The propertytheorist'sevents are much closer to PerryBarwise situations than are Davidsonianevents, though situation semanticshas more
expressivepower and can presenta wider rangeof semanticvalues than either view of
events. Quantificationover events in the propertytheorist'ssense, however,would defeat Higginbotham'sstated purpose of givingan analysis of NI perceptionsentences
expressiblein first-orderlogic. Whatcompelsus to view quantificationover scenes and
situationsas higher-ordercompelsus to view quantificationoverevents,in the property
theorist'ssense,as higher-order
as well.
8 For furtherevidenceagainstHigginbotham's
view, note that a wide varietyof connectives can occur in NI complements:'although','since', 'because','even though',and 'if
not'. All modify NI complements;only 'if not', however,seemsto link NI complements.
9 Wherea past tenseseeingreportis involved,Higginbotham's
claimseemsmoreplausible,
but for differentreasons.'JohnsawMarysmokeand Fredfix his car'may be ambiguous,
insofar as 'saw' does not seem to indicate whether the events occurredat one or at
different times. We find the semanticsof tense complex, but it, ratherthan the conjunctiveNI complementitself, seemsresponsiblefor any ambiguityin these sentences.
10
Weowe the expression'pseudo-exportation'
to HansKamp.
12
This is awkward, but its natural expression, 'Every car is seen by John to finish',
uses the passivevoice. Higginbothaminsists that NI sentenceshaveno passives;we have
tried to avoid this controversy.
12 In this respect, our developmentof situation semanticsdiffers from Barwiseand
Perry's;see Barwise(1981). Little of philosophicalsignificance,however,hangson this
difference.
76
NICHOLAS
ASHER AND DANIEL
BONEVAC
13 We call a quantifierexistentialjust in case it is monotonic increasing
andpersistent;
for defmitionsof monotonicityand persistence,see Barwiseand Cooper(1981).
14 Negative quantifiers- those that are monotonic decreasingand antipersistent
export with little trouble.We can explain the validity of argumentslike (31) by noting
that, althoughSS does not universallyvalidatenegativequantifierexportations,countermodels have a peculiarform; rulingthem out requiresa revisionto SS that goes beyond
the scope of this paper.See Asherand Bonevac(forthcomingb).
Is Monotonicityfor sentencesdiffersfrom monotonicityfor quantifiers;for the details,
see Asherand Bonevac(forthcominga).
16 The second readingsoundsawkwardat first, becauseof the doublenegatives,but on
reflection it becomes apparent that this does constitute a different and perhapsthe
primaryinterpretationof (40). Arguingfor the ambiguityis difficult, since one interpretation entails the other; for a discussionof this problem, see Zwicky and Sadock
(1975). As a result, some linguistsreject such ambiguities,takingthe weakestreading
as the meaning of the expression in question (Kempsonand Cormack,1981); they
mighttake the secondreadingas the correctinterpretationof (40).
Some speakersobtain yet anotherreading- John does not see any boy kissa girl by assumingthat the secondnegatedquantifieris unintended.
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Centerfor CognitiveScience,
Universityof Texasat Austin,
Austin, TX 78712,
U.S.A.