Logical integrity: from Maximize Presupposition!

32 Pages·2017·0.26 MB·English

[lastmodified: November29,2018]
Logical integrity: from Maximize Presupposition!
to Mismatching Implicatures
Contents
1 Introduction 1
2 LogicalIntegrity(firstversion) 4
3 MaximizePresupposition! andrelatedphenomena 10
4 Mandatoryimplicatures 19
5 LogicalIntegrity(finalversion) 28
6 Looseendsandopenproblems 30
7 Conclusion 33
1 Introduction
Inthisstudyanovelgeneralization,labeledLogicalIntegrity(hf. LI),isputforthwhichyieldsa
unifiedaccountofsome fairlybroadclassofacceptability judgments. Thegeneralizationisbuilt
withthefollowingstatementatitscore,statedprotematthespeech-actlevel.
(1) LI’score condition. Asentenceφ mustnotbe utteredincontextC ifithasan alternativeψ
suchthat(i)φ contextuallyentailsψ inC,but(ii)φ doesnotlogicallyentailψ.
ItwillbearguedthatLI,whichconsistsof(1)coupledwithasuitable“projectionrecipe”,1 makes
adequate predictions for a broad array of examples which has so far been chopped up by three
distinct analyses that happen to capture more or less mutually incompatible generalizations: the
Maximize Presupposition! principle originating in Heim (1991), the Presupposed Ignorance system
in Spector & Sudo (2017) and the Mismatching Implicature approach of Magri (2009a). It is
furthermorearguedonthebasisofnovelevidencethatthepredictionsmadebyLIaresuperiorto
each of these three piece-meal analyses individually considered (in some cases it is shown that
salient modifications of the analyses would not solve the relevant problems either). As both the
empirical landscape and inter-connections of the proposed analyses in the literature are somewhat
complicated,inthisintroductorysectionanoverviewoftherelevantfactsisprovidedfollowedby
theoutlineoftherestofthepaper.
Heim(1991)sketchedaprincipleoflanguageuseaccordingtowhich,giventhechoicebetween
twocompetingforms,allelseequal theonewiththestrongerpresuppositionmustbeusedunless
1Seethediscussioninsections2.2and5.
1
its presupposition is not known to be true. This principle was taken up in subsequent literature
(Percus 2006, Sauerland 2008, Schlenker 2012, a.o.) and is standardly referred to as Maximize
Presupposition! (hf. MP). As an example, in (2a) ‘all’ is blocked by ‘both’ because the latter
triggersastrongerpresupposition(thatJohnhasexactlytwoarms)whichissatisfiedinthecontext.
In contrast in (2b) ‘all’ is available because this time the presupposition of ‘both’ (that John has
exactlytwofingers)contradictsbackgroundassumptionsrenderingthe‘both’-sentenceunusable.
(2) [Context: Johnhastenfingersandtwoarms.]
a. Johnbroke{#all,(cid:51)both}ofhisarms.
b. Johnbroke{(cid:51)all,#both}ofhisfingers.
An alternative account of the oddness of ‘all’ in (2a) is given by (1) above. Note that the ‘all’-
sentence in (2a) does not logically entail the ‘both’-sentence: since it is not a logical truth that
John has two arms, it is logically possible that John has more than two hands and broke all of
them in which case the ‘all’-sentence is true but the ‘both’-sentence is not (more specifically, the
‘both’-sentence is undefined due to presupposition failure). On the other hand, on the contextual
assumptionthatJohnhasexactlytwohandsthetruthofthe‘all’-sentenceguaranteesthetruthofthe
‘both’-sentence, i.e., the argument in (3) is valid. Put differently, the ‘all’-sentence contextually
entailsthe‘both’-sentenceinanycontextinwhichitistakenforgrantedthatJohnhasexactlytwo
hands.
Johnhasexactlytwoarms
(3) Johnbrokeallofhisarms
∴Johnbrokebothofhisarms
Hence on the assumption that ‘all’ and ‘both’ compete, an assumption that LI shares with MP,
it is predicted by (1) that the ‘all’-sentence in (2a) should be blocked by its ‘both’-alternative in
anycontextinwhichitisassumed thatJohnhastwohands. The“core”examplesofMP arethus
explained by LI as well as MP. However there is a delicate difference in predictions: MP, unlike
LI,reliescruciallyontheconditionthatthepresuppositionsofthealternativesbecommonground.
Asarguedin section3.4.1,MP-type effectscanarise even whenthepresupposition ofthestronger
alternativeisnot knowntobetrue,afactthatLIaccountsforwithoutfurtheradobutisproblematic
forMP.
As quickly pointed out above, MP as a principle of language use is assumed to kick in to
decidebetweenasetofalternativesonlywhenallelseisequal betweenthethem. Whatdoesthis
restictionamounttoinpractice? Severalargumentsintheliterature(seeinparticularPercus2006
andSchlenker 2012)pointtothe conclusionthatinthe contextofMP allelseisequal when(and
only when) the relevant competitors are “equally informative”, roughly in the sense that neither
competitorcan betrue withouttheother beingtrueas well. Hence iftwo sentences arenot equally
informative,MPcannotbecalledupontodecidebetweenthem. Recently,Spector&Sudo(2017)
(hf. S&S)haveproblematizedthisconclusion. ThecrucialexamplediscussedbyS&Sis(4).
(4) [Context: allstudentssmoke.]
#Johnisunawarethatsomestudentssmoke.
ALT={Johnisunawarethatallstudentssmoke}
2
Assumption: ‘α isunawarethatφ’presupposesthatφ istrueandassertsthatitisnotthecase
thatα believesφ tobetrue.
Theunacceptabilityofthe‘some’-sentencein(4)isreminiscentoftheMP-effectin(2a)because
here as well the unacceptable sentence has an alternative, the ‘all’-sentence, with a stronger
presupposition (that all students smoke) which is satisfied in the given context. Nevertheless
MP cannot account for the oddness of the ‘some’-sentence in (4) if it is restricted by equal-
informativeness. The reason is that (in contrast to the alternatives in (2a)) the alternatives in (4)
arenot equallyinformative. InasituationinwhichallstudentssmokeandJohnissurethatsome
students smoke but is uncertain as to whether all students do the ‘some’-sentence in (4) is false
but its ‘all’-alternative is true. Furthermore, this particular situation is not contextually ruled out
in (4) (since nothing is assumed regarding John’s epistemic state) therefore the two competitors
arenotequallyinformativeinthatparticularcontext. S&Stake(4)atfacevalueandproposethat
theequal-informativenessconditionofMPmustbedropped. Theycalltheresulting,moregeneral
principlePresupposedIgnorance. SincePIisnotcontrolledbyequal-informativenessitcanaccount
for(4): the‘some’-sentencehasanalternativewithastrongerpresuppositionwhichissatisfiedin
thecontextandthatisenoughforPItoruleitoutinthatcontext. ButbythesamelogicPIgenerates
toomany “falsenegatives”,incorrectly ruling outcertain sentencesasinfelicitous. S&S,therefore,
introduce a novel implementation of the exhaustivity operator which can be inserted to “rescue”
certainsentencesfromoddnessincertaincontexts.
Asithappens, (1)canaccountfor theoddnessofthe‘some’-sentence in(4)withoutanymodi-
ficationbeingnecessary. Notethatthe‘some’-sentencedoesnotlogicallyentailits‘all’-alternative:
inasituationinwhichonlysomestudentssmoke,the‘some’-sentencemaybetrue(dependingon
John’sepistemicstate)butthe‘all’-sentenceiscertainlynot,becauseitspresuppositionisfalse. On
theotherhandonthecontextualassumptionthatallstudentssmoke,thetruthofthe‘some’-sentence
immediatelyguaranteesthetruthofits‘all’-alternative. Thatistosay,thefollowingargumentis
valid.
Allstudentssmoke
(5) Johnisunawarethatsomestudentssmoke
∴Johnisunawarethatallstudentssmoke
LI,therefore,predictsthatanycontextinwhichitisassumedthatallstudentssmokeisacontext
in whichthe ‘some’-sentence isinfelicitous, which is the desiredprediction. However, there is a
differenceinpredictionsbetweenPIandLI:PI(likeMP)dictatesapreferencesforalternativeswith
stronger presuppositions while no such preference is encoded by LI. As argued in section 3.4.2,
alternativeswithlogicallyindependent presuppositionsalsoenterintoakindofcompetitionthatis
verysimilarto(4),afactthatcanbemadetofollowfromLIbutisproblematicforPI(andMP).
Finally,ahighlyconsequantialmechanismofexhaustificationismotivatedinMagri(2009a,b,
2011) on the basis of examples including (6). The generalization that Magri’s system (call it
Mismatching Implicatures, hf. MI) captures, for the simple cases, is that a sentence is odd in a
contextinwhichitisequallyinformativewithoneofitslogicallynon-weakeralternatives. Thus
inthecontextof(6)the‘some’-sentenceandits‘all’-alternativeareequallyinformative,sincethe
possibilityofJohngivingonlysomeofhisstudentsanAiscontextuallyruledout,andaspredicted
by this generalization ‘some’ cannot be felicitously used. Note that since there is no difference
3
betweenthepresuppositionsofthetwoalternativesin(6),MP/PIareinapplicableinthiscaseasa
matterofprinciple.
(6) [Context: Johngavethesamegradetohisstudents.]
#JohngavesomeofhisstudentsanA.
ALT={JohngaveallofhisstudentsanA}
Insection 4,(6)isembedded inthelargerparadigm andacompact summaryofMagri’s proposal is
provided. ItisshownthattheparadigmcanbecapturedbyLIwithoutfurtherado,thusreinforcing
theintuitionthat(2),(4)and(6)havethesamesource. Furthermore,basedonsomeobservations
regarding thearchitecture ofMagri’s proposal,several obstaclesfor itas itstands and forpossible
extensionsofittoMPeffects(seealsoSingh2009)arediscussedinthesamesection. Insection5a
modifiedversionoftheinitialversionofthegeneralization(asputforthinsection2)ismotivatedon
thebasisofasetofproblematicdatapointsdiscussedintheearliersections. Section6isconcerned
withseverallooseendsandopenproblemsforthepresentaccount.
2 LogicalIntegrity(firstversion)
2.1 Backgroundassumptions
The set of propositions that are “taken for granted” by the interlocutors at a particular point in a
conversation is the common ground (or, the background assumptions). The set of those possible
worldsthatarecompatiblewiththebackgroundassumptionsisthecontextset(or,globalcontext
(seebelow),or,simply,context). Atrivalenttreatmentofpresuppositionsisassumedthroughout,
wherethethirdtruth-value‘#’representspresuppositionfailure. Thepresuppositionofasentenceis
satisfiedinacontextiffthesentenceisdefined(doesnotdenote‘#’)atevery“point”inthatcontext.
Within a trivalent setting, the classical, bivalent notion of entailment can be generalized in
differentways(see,e.g.,Chemlaetal.2017). Thediscussionbelowreliesalmostexclusivelyonthe
followingnotionofentailment,giveninthegeneralizedformasitwillbeappliedtobothproposition-
andproperty-denotingexpressions. Forsimplicitythedefinitionisgivenformodel-theoreticobjects
ratherthanobject-languageexpressions.
(7) If X and X are two objects of a type τ type that “ends in t” and can take n arguments,
1 2
X entails X , X (cid:15) X , iff for all type-appropriate sequences of objects Y ,...,Y , if
1 2 1 2 1 n
X (Y )...(Y )=1thenX (Y )...(Y )=1.
1 1 n 2 1 n
Another,strictlyweakernotionofentailment,whichwewillhaveoccasiontouseinitsbidirectional
forminsection3,isthatofStrawson-entailment(vonFintel1999).
(8) If X and X are two objects of a type τ type that “ends in t” and can take n arguments, X
1 2 1
Strawson-entailsX iffforalltype-appropriatesequencesofobjectsY ,...,Y ,ifX (Y )...(Y )=
2 1 n 1 1 n
1thenX (Y )...(Y )∈{#,1}.
2 1 n
This study relies on Schlenker’s (2009) theory of local contexts. Under this approach, given a
sentenceφ andaglobalcontextC,eachoccurrenceofaproperty-orproposition-denotingconstituent
of φ, α, can be mapped to a model-theoretic object of the same semantic type, it’s local context,
4
denotedlc(α,φC). Thereis noneedtoget intothebolts andgearsof Schlenker’s theory here. In
(9)alltherelevantfactsareaggregated.
(9) Foranyproposition-denotingexpressionsφ andψ,property-denotingexpressionsα andβ,
individual-denotingexpressionυ,andgeneralizedquantifierQ,
a. lc(ψ, [φ∧ψ],C)=lc(ψ, [φ →ψ],C)=λw.w∈C∧ φ w =1
(cid:74) (cid:75)
b. lc(ψ, [φ∨ψ],C)=λw.w∈C∧ φ w =0
(cid:74) (cid:75)
c. lc(β, [Q(α,β)],C)=λw.λx.w∈C∧ α w(x)=1
(cid:74) (cid:75)
d. lc(φ, [υ is(un)awarethatφ],C)=λw.∃w(cid:48) ∈C: w=w(cid:48)∨w∈DOXw(cid:48)
υυυ
Notethatforanyconstituentitslocalcontexthasthesamesemantictype. Hencethedifferenttypes
in(9b)and(9c). Onceaworkingnotionoflocalcontextsisavailable,entailmentcanberelativized
tocontexts,localandglobal.
(10) If X , X and C are three objects of a type τ type that “ends in t” (the latter being the
1 2
context)andcantakenarguments,X contextuallyentailsX inC,X (cid:15) X ,iffforalltype-
1 2 1 C 2
appropriate sequences of objects Y ,...,Y , if X (Y )...(Y )=1 and C(Y )...(Y )=1
1 n 1 1 n 1 n
thenX (Y )...(Y )=1.
2 1 n
Putdifferently,X (cid:15) X iffX ∧C (cid:15)X (assuminggeneralizedconjunction). Foranyexpressionφ
1 C 2 1 2
andcontextC, φ ∧Ccanbethoughtofasthecontextualmeaningofφ inC.
(cid:74) (cid:75)
Perhaps some words need to be said pertaining to (9d). According to (9d), the local context
of the clausalcomplement of ‘(un)aware’ relative to the (global)contextC is the unionof C with
the set of all words that are compatible with what υ possibly believes to be true. The informal
justificationisthis. Givenφ,thetaskistoidentifyallandonlythoseworldsatwhich oneneedsto
knowthedenotationofφ inordertocomputethedenotationofthefullsentence. Since‘(un)aware’
isfactive,weneedtoknowwhetherφ holdsattheworldsinCand,since‘(un)aware’isdoxastic,
weneedtowhetherornotφ istrueateveryworldwhichiscompatiblewithυ’sbeliefs(attheworld
ofevaluation).2
Afinalpointregardingthewaywithwhichthetheoryoflocalcontextswillbeusedinthisstudy
isworthstressing.3 Eventhoughtheprimarymotivationbehindthistheoryistogiveanexplanatory
accountofpresuppositionprojection,localcontextscanbeusedforavarietyofdifferentpurposes.
There istechnically noreason for atheory that useslocal contextsfor some purposeor otherto use
itforpresuppositionprojectionaswell. Assuch,itisverymuchpossibletouselocalcontextsin
a framework in which presupposition projection is handled in some other fashion. In particular,
nothinginwhatfollowshangsontheassumptionthatlocalcontextsaretheengineofpresupposition
projection. In fact, wewon’thavemuchoccasionto talkaboutprojection inanydetailedwayat all;
we can afford to simply rely on well-established descriptive generalizations. On the other hand,
in this study local contexts are worked heavily as information sources relative to which certain
conditionscanbechecked.
2Thedefinitiongivenin(9d)differsfromSchlenker(toappear). Thedifferenceisimmaterialformypurposeshere.
3Seealso(Spector&Sudo2017: fn.32),whichmakesthesamepoint.
5
2.2 Theproposal
Theproposedgeneralizationisintroducedintwosteps. Inthissubsectionthefirstversion,LI,is
formulated(explicitlyin(19))anditspredictionsregardingtherelevantexamples,asubsetofwhich
was discussed in section 1, are rigorously investigated. However, certain problematic facts will
motivateamodificationtothefirstversion,leadingtothefinalversionoftheproposal,LI*,spelled
outinsection5.
As pointed out in section 1, the core of LI is the statement in (11), repeated from (1). It
dictatesthatforasentencetobeacceptable,acertainbalancemustbehitbetweenthecontextual
informationitconveysandthepatternoflogicalentailmentthatitentersintowithits(independently
characterized)alternatives.
(11) A sentence φ is unacceptable in context C if it has a logically non-weaker alternative ψ
whichitcontextuallyentailsinC.
The statement in (11), coupled with the definitions of logical and contextual entailment in the
previoussection(i.e.,(7)and(10)respectively),yieldsthefollowinggeneralization.
(12) a. Let φ and ψ be two competing forms and C some context. If it is logically possible
for φ to be true and ψ to be “untrue” (i.e., either false or undefined) then this must be
contextuallypossibleinCaswell,otherwiseφ isunacceptableinC.Abitmoreformally,
b. Let φ and ψ be alternatives such that ∃w∈W : φ w =1∧ ψ w ∈{0,#}. Then, φ is
acceptableincontextConlyif∃w∈C: φ w =1(cid:74)∧(cid:75) ψ w ∈{(cid:74)0,(cid:75)#}.
(cid:74) (cid:75) (cid:74) (cid:75)
Tounpackthereasoningcompressed(11),supposeφ andψ aretwocompetingsentences. According
tothedefinitionin(7),ψ islogicallynon-weakerthanφ (i.e.,φ (cid:54)(cid:15)ψ)iffitispossibleforφ tobetrue
andψ tobeuntrue. Assumeψ isinfactlogicallynon-weakerthan φ. Accordingto(11),φ cannot
be used in a context C if, in C, φ contextually entails ψ. By contraposition, if φ is acceptable in
somecontextC,thenφ doesnot contextuallyentailψ inC.Theconsequentofthisconditional(i.e.,
φ (cid:54)(cid:15) ψ)effectivelyboilsdowntoanexistentialclaim,inlightofthedefinition(10): Ccontainsat
C
leastoneworldinwhichφ istrueandψ iseitherfalseorundefined. Ifthispossibilityiscontextually
ruled out, φ is unacceptable. The examples worked through below illustrate the breadth of this
proposal.
Tobeginwith,considertheclassicMPeffectin(13).
(13) [Context: Johnhasexactlytwostudents.]
#Johninvitedallhisstudents.
ALT={Johninvitedbothhisstudents}
The‘all’-sentencein(13)doesnotlogicallyentailthe‘both’-alternative;whilethetruthof‘all’is
sufficient to guarantee that ‘both’ is not false, it is not sufficient to guarantee that it is true: in a
worldinwhichJohnhassevenstudentsandinvitedallofthem,‘all’istruebut‘both’isundefined.
Therefore,accordingto(11),the‘all’-sentencein(13)canonlybeusedifitiscontextuallypossible
thatitistruebutthe‘both’-alternativeiseitherfalseorundefined. Asjustmentioned,thetruthof
the ‘all’guarantees thatthe ‘both’is not false,therefore the requirementboils downto thatit must
becontextuallypossiblethat the‘all’-alternativeis trueandthe ‘both’-alternative isundefined; in
6
otherwords,itmustbecontextuallypossiblethatJohnhasmorethantwostudentsandheinvitedall
of them. But the context given in (13) entails that John has exactly two students, thus ruling this
possibilityout. Thereforethe‘all’-sentencein(13)ispredictedtobeblocked. Inthesamecontext,
the‘both’-sentenceispredictedtobevacuouslyacceptabletotheextentthatitlacksanon-weaker
alternative.
Next,considerasimpleMagricase.
(14) [Context: Johnalwaysgivesthesamegradetohisstudents.]
#JohngaveanAtosomeofhisstudents.
ALT={JohngaveanAtoallofhisstudents}
Obviouslythe‘some’-sentencein(14)doesnotlogicallyentailits‘all’-alternative. Therefore,the
‘some’-sentence is predicted to come with the requirement that it must be contextually possible
thatitistrueandthe ‘all’-alternativeiseitherfalse orundefined. Butsincethe two sentencescarry
thesamepresupposition(thatJohnhasstudents),itisimpossiblefor‘some’tobetrueand‘all’be
undefined. Therefore,itmustbecontextuallypossiblethat‘some’istrueand‘all’isfalse;inother
words,itmustbecontextuallypossiblethatJohnhassomestudentsandgaveanAtosomebutnot
allofthem. Thispossibilityisruledoutbythecontextspecifiedin(14),hencethe‘some’-sentence
is correctly predicted to be blocked. In the context of (14), the ‘all’-sentence is predicted to be
vacuouslyacceptabletotheextentthatitlacksanon-weakeralternative.4
Consider now the example brought forth by Spector & Sudo (2017) which, as pointed out in
section1,isproblematicforMaximizePresupposition!. Theexampleisrepeatedin(15a)andthe
assumedlexicalentryisgivenin(15b).
(15) a. [Context: allstudentssmoke.]
#Johnisunawarethatsomestudentssmoke.
ALT={Johnisunawarethatallstudentssmoke}
b. unaware w =λPλx:P(w)=1.¬Bw[P]
x
(cid:74) (cid:75)
c. Foranyworldw,individualx andpropositionP, Bw[P]iffx believesPtobetrueinw.
x
The ‘some’-sentence in (15a) does not logically entail its ‘all’-alternative: in a world in which
onlysomestudentssmoke,‘some’maybetruebut‘all’iscertainlyundefined. Therefore,‘some’
is predicted to come with the requirement that it must be contextually possible that it is true and
‘all’iseither falseorundefined. Now, it isimpossibleforthe‘some’-sentence tobetruewhenits
‘all’-alternative is false.5 Therefore, the requirement boils down to that it must be contextually
possiblethatthe‘some’-sentenceistrueandits‘all’-alternativeisundefined;inotherwords,itmust
becontextuallypossiblethat somebutnotallstudentssmokeand Johnisunsureasto whetherthat
anystudentsmokes(i.e.,¬B [∃]). Thispossibilityisruledoutbythecontextof(15a),hencethe
J.
‘some’-sentenceispredictedtobeblocked.
Importantly,for(15a)onemustalsocheckthatthe‘all’-sentenceisnotincorrectlyruledout:
4Seesection6.2foradiscussionofanimmediateconsequenceofthispredictionpertainingtohomogeneity.
5‘α isunawarethatφ’canbeanalyzedinasφ∧¬B (φ),whereunderliningmarksthepresupposition. Itimmediately
α
followsthatifφ (cid:15)ψ,whenever‘α isunawarethatφ’istrue,‘α isunawarethatψ’iseithertrueorundefined: the
clausalcomplementof‘unaware’isaStrawson-downward-entailingenvironment.
7
(16) [Context: allstudentssmoke.]
(cid:51)
Johnisunawarethatallstudentssmoke.
ALT={Johnisunawarethatsomestudentssmoke}
The novelty here is that, in contrast to (13) and (14), the two competitors in (15a) are logically
independent. Havingshownearlierthatthepresuppositionallystrongeralternative(i.e.,the‘all’-
sentence) blocks the presuppositionally weaker one (i.e., the ‘some’-sentence), in light of the
acceptabilityof(16)wemustnowmakesurethattheoppositedoesnothold. Itisstraightforward
to check that (11) predicts the ‘all’-sentence to come with the requirement that it is contextually
possiblethatallstudentssmokebutJohnonlybelievesthatsomestudentssmoke. Thispossibility
isnotruledoutin(16)(sincenoassumptionismaderegardingtheepistemicstateoftheattitude
holder,John),hence‘all’isindeedpredictedtobeacceptableinthespecifiedcontext.6
Letusnowlookathow(11)fairswiththepositivecounter-partof‘unaware’.
(17) [Context: allstudentssmoke.]
(cid:51)
Johnisawarethatsomestudentssmoke.
ALT={Johnisawarethatallstudentssmoke}
As pointed out by S&S, ‘aware’ does not show the same behavior as ‘unaware’. In a context
in which it is common ground that all students smoke, ‘aware...some...’ is fine, (17), but
‘unaware...some...’ is not, (15a). This is as things should be, according to (11): the ‘some’-
sentencein(17)doesnotlogicallyentailits‘all’-alternative(i.e.,thatJohnisawarethatallstudents
smoke), therefore it is predicted to come with the requirement that it must be contextually possible
that ‘some’ is true while ‘all’ is either false or undefined. In contrast to the previous examples,
hereagenuinelydisjunctiverequirementisgenerated becausethetruthof‘some’in(17)isindeed
compatiblewithbothfalsity and undefinednessofits‘all’-alternative;thustherequirementisthatit
must be contextually possible that the ‘some’-sentence in (17) is true and either not all students
smoke or all students smoke but John does not believe so. Given the background assumptions
in (17), the second possibility is not contextually ruled out and therefore the ‘some’-sentence is
predictedtobeacceptable.
Importantly, every effect so far discussed (and those that will be discussed in the following
sections)canbereconstructed“locally”.
(18) a. #Noprofessorwhohasexactlytwostudentsinvitedallofthem.
b. #Ifallstudentssmoke,Johnisunawarethatsomestudentssmoke.
c. #EitherJohngavehisstudentsdifferentgrades,orhegavesomeofthemanA.
Take(18a)(thesamepointcanbemadewiththeothertwoexamples). Theproblemhereisthat,at
root, the sentence logically entails its ‘both’-alternative, indeed the two are logically equivalent.
The reason is that the presupposition triggered by ‘both’ in the sentence ‘no professor who has
exactly two students invited both of them’ is filtered through the restrictor and boils down to the
6Theacutereadermightobjectthatevenifthispossibilityiscontextuallyruledout(e.g.,inacontextinwhichitis
commongroundthat(i)allstudentssmokeand(ii)eitherJohnthinksallstudentssmokeorhethinksthatnostudent
smokes),the‘all’-sentence(i.e.,Johnisunawarethatallstudentssmoke)isstillacceptable. Indeedthisfactcannotbe
accountedforby(11)butitwillbeoneofthewelcomedpredictionsofLI*insection5.
8
presupposition that every professor who has exactly two students has exactly two students, which is
tautologous. Consequently, at the sentential level there is no truth-conditional difference between
the sentence in (18a) and its ‘both’-alternative. For our purposes this means that (11) no longer
predictsanycontrasttoarise,contrarytofact. Thisisbecause(11)isaglobalconditionthatapplies
tosentencesatrootand,assuch,itisblindtotheinternalconstitutionofsentences. Iftwosentences
areglobally synonymous then(11)doesnot “see”thedifferencebetween thetwotobeginwith, let
alonepredictingonetobeblockedbytheother.
However,correctpredictionsaremadeif(11)ischeckedagainstthelocalcontextofthescope
expression‘invitedallofhisstudents’. Thelocalcontextofthescopeof‘no’in(18a)ispredicted
to be that function which maps each world w in the context-set to the set of individuals that are
professorswithexactlytwostudentsinw. Forsimplicity,wecanturnthisfunctionintothesetS=
{(cid:104)w,a(cid:105):w∈C∧ professorwhohasexactlytwostudents w(a)=1}. Nowrelativetothiscontext,
the weaker altern(cid:74)ative ‘λx.x invitedallofx’sstudents’ co(cid:75)ntextually entails the logically stronger
‘λx.x invitedbothofx’sstudents’; indeed, the two are contextually equivalent in the sense that
for any (cid:104)w,a(cid:105)∈S, λx.x invitedallofx’sstudents w(a)= λx.x invitedbothofx’sstudents w(a).
(cid:74) (cid:75) (cid:74) (cid:75)
Thereforethe‘all’-alternativeispredictedtobeblocked.
I take the moral of (18) to be that (11) must be supplemented with a projection recipe. For
the moment, I’d like to propose (19) as a solution. This same form of “localization” in the face
of the challenge raised by the data in (18) has also been proposed by Singh (2011) for Maximize
Presupposition!, Spector & Sudo (2017) for Presupposed Ignorance, and Schlenker (2012) for
MandatoryImplicatures(forthelatter,seealsosection3.2).7
(19) LogicalIntegrity,LI.(firstversion)
a. Projection principle. Asentenceφ isunacceptablein context Cifit containsaproperty-
or proposition-denoting constituentβ whichviolates CCin itslocal contextwith respect
tooneofitsalternativesβ(cid:48).
b. Core Condition, CC. A property- orproposition-denoting expression β violates CCin
(its local) context C w.r.t. β(cid:48) iff β(cid:48) is logically non-weaker than β and β contextually
entailsβ(cid:48) inC(i.e.,β (cid:54)(cid:15)β(cid:48) butβ (cid:15) β(cid:48)).
C
In a nutshell, LI checks CC, which is effectively the level-neutralized version of (11), for every
constituent (of the relevant type) of a given sentence, including the whole sentence.8 Since a
sentenceisruledoutassoonasaCC-violationisdetected,everysentenceruledoutby(11)isruled
7Althoughtheprojectionrecipe(19a)isadoptedbythementionedauthorswithoutfurtherado,thereissomechoice
involvedinformulatingit. Forexample,onecouldrequirethatonlythesmallestproperty-orproposition-denoting
constituent that contains a certain alternative-triggering item (such as ‘some’) not to violate CC. This formulation
accountsforthebasicfacts,butletmebrieflypointoutwhyitfailsingeneral. Consider(15a)fromabove. Thesmallest
constituentthatcontains‘some’in(15a)istheembeddedclause‘somestudentssmoke’. Thelocalcontextofthis
expressionisλw.∃w(cid:48)∈C: w=w(cid:48)∨w∈DOXw(cid:48). InthiscontextthereisnoviolationofCC(seefn. 8): toaccountfor
J.
theoddnessof(15a)oneneedstocheckCCattheroot.
8Inthecaseof‘(un)aware’therearenowtwoconstituentstobetakenintoaccount,thewholesentenceandtheembedded
clause. Theembeddedclause,however,isnotruledoutbyLIineithercase. Thereasonisthatthelocalcontextofthe
embeddedclauseincludetheworldscompatiblewithJohn’sbeliefs,andnocontextualrestrictionisputonthese;in
particular,therequirementgeneratedbyLI(thatitbecontextuallypossiblethatsomebutnotallstudentssmoke)isnot
ruledoutbythelocalcontexts.
9
outbyLI;buttheconverseisnottrue,e.g. everysentencein(18)isruledoutbyLI.Wewillseethat
insomecasesLIpredictsfalsenegatives. ThisproblemisaddressedbyLI*formulatedinsection5.
3 MaximizePresupposition! andrelatedphenomena
3.1 Outline
Insubsection3.2thebare-bonesofthetheoryofMaximizePresupposition! (hf. MP)arelaidout.
Theproblemwiththerequirement,oftenassociatedwithMP,thatforittobeactivatedtherelevant
alternatives must be “equally informative” is discussed in some detail. Some relevant facts are
reviewed in subsection 3.3 and it is argued, building in particular on Spector & Sudo (2017) (hf.
S&S),thatfactspointinopposingdirectionsregardingwhetherequal-informativenessisanecessary
conditionofMP.S&S’ssolutiontothispuzzleisbrieflysummarizedinthesamesubsection,and
subsection3.4closesbyadiscussionoftwodatapointsthatareproblematicforS&S’sproposal.
3.2 Strawson-equivalentalternatives: StandardMP
Considerthefollowing,fairlystandardformulationofMPinwhichthe“allelseequal”provisois
explicitly cashed out as equal-informativeness. (Throughout this section attention is focused on
sentencesatrootandthereforetheformulationin(20)isnotlocalized.)
(20) MaximizePresupposition!. Letφ andψ betwoalternativessuchthatthepresuppositionof
ψ is strongerthan φ. InanycontextC in whichthe following two conditions aremet, one
mustuseψ.
a. Thepresuppositionsofbothφ andψ aresatisfied.
b. φ andψ areequallyinformative.
There are at least two salient ways to precisify the notion of equal-informativeness. The option
which has been adopted most widely in the literature is that of contextual equivalence: φ and
ψ are contextually equivalent in C iff there is no world w in C in which one alternative is true
and the other is not, ∀w∈C: φ w =1⇔ ψ w =1.9 An alternative, which is strictly stronger
and has also sometimes been(cid:74)uti(cid:75)lized, is th(cid:74)at(cid:75)of contextual identity: φ and ψ are contextually
identicalinCiffthereisnoworldwinCinwhichthetwoalternativesdeliverdifferenttruth-values,
∀w∈C: φ w = ψ w. As pointed out immediately below, the choice between the two is in fact
(cid:74) (cid:75) (cid:74) (cid:75)
mootatleastfortheclassicexamplesthathavebeenusedtomotivateMP.
HerearetwoclassicexamplesthatMPhasbeentraditionallyappliedto.
(21) a. #Asunisshining. ALT={Thesunisshining}
b. #AllofJohn’seyesareopen. ALT={BothofJohn’seyesareopen}
As an example, the unacceptability of (21b) is accounted for as follows. The ‘both’-alternative
in (21b) has a stronger presupposition which is satisfied in normal contexts. Furthermore, the
two alternatives are equally informative in normal contexts in the sense that they cannot convey
9Thisisthebidirectionalversionofcontextualentailmentasdefinedinsection2.1.
10