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ReasoningwithAttitude ReasoningwithAttitude FoundationsandApplicationsof InferentialExpressivism LUCAINCURVATI AND JULIANJ.SCHLÖDER OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwide.Oxfordisaregisteredtrademarkof OxfordUniversityPressintheUKandincertainothercountries. PublishedintheUnitedStatesofAmericabyOxfordUniversityPress 198MadisonAvenue,NewYork,NY10016,UnitedStatesofAmerica.
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Toourparents 4.6Weakassertions,epistemicmodalassertions,andevidence116
7.1Traditionalexpressivismabouttruth
9.3Moderateassertionandmoderaterejection
Preface Words,sentences,andlanguagesareendowedwithmeaning.Language allowsustoconveythoughtsabouteventsoccurringindistantplaces,andto coordinateonactionstobeundertakenbyourfutureselves.Butwhatdoes themeaningoflinguisticexpressionsconsistin?Alongstandingviewinthe historyofphilosophy,tracingatleastasfarbackasPlato’sCratylus,identifies themeaningofanexpressionwithwhatitstandsfor—itsreference.This viewisknownasreferentialismandhasbecomesomethingofaparadigm withinthestudyofmeaning.Thisisnodoubtdue,atleastinpart,tothe successofformalsemantics,whichhasovertheyearsprovidedincreasingly sophisticatedreferentialanalysesofthecontributionofalargenumberof expressionstothemeaningofthesentencesinwhichtheyoccur.
Thisisnottosaythatreferentialismhasgoneunchallenged.Onestrand ofoppositioncomesfromtheexpressivistanalysisofmoralvocabulary. Expressivismemergedintheheydayoflogicalpositivismasanattemptto reconcilemoraldiscoursewithanempiricistmetaphysicsandhassincethen hadmanyreincarnations.Thesereincarnationssharetheideathatmeaning istobeexplainedintermsofspeechacts,whichprovidelinguisticexpression toourinnerlives.Anotherstrandofoppositiontoreferentialismcomesfrom theinferentialistanalysisoflogicalvocabulary.Inferentialismhasitsroots inWittgenstein’sremarksinthe PhilosophicalInvestigations thatmeaningis use,andtakesthemeaningofexpressionstobeexplainedintermsoftheir roleininferences.
Acentralcontentionofthisbookisthat,theirdifferencesnotwithstanding,expressivismandinferentialismarebestseenasopposingreferentialism onthebasisofthesamepragmatistinsight:thatsemanticexplanations shouldnotgobeyondwhatisneededtoexplaintheroleofwordsinour practices.Expressivistsfocusontheattitudesthatwordsareusedtoexpress; inferentialistsfocusontheinferencesthatwordsareusedtodraw.Inthis book,welaythefoundationsforinferentialexpressivism,atheoryofmeaning whichcountenancesbothaspectsofourlinguisticpracticeandexplains meaningintermsoftheinferenceswedrawinvolvingtheattitudeswe express.
Inferentialismandexpressivismfacechallengesoftheirown.Thehistory ofethicalexpressivismanditsmanyreincarnationsis,atleastinpart, thehistoryofthestruggletoaccountforthebehaviourofexpressionsin embeddedcontexts.ThisisthecoreofwhatisknownastheFrege–Geach Problem.Inferentialism,foritspart,hasremainedlimitedinscope,somuch sothatdoubtshavebeenrightlyraisedaboutitsabilitytoprovideatheory ofmeaningforexpressionsotherthansimplelogicalconstantssuchas and and or.
Wearguethat,byjoiningforces,expressivismandinferentialismcan meettheirkeychallenges.Byexplainingmeaninginferentially,wecontend, expressivistscansolvetheFrege–GeachProblem.Theproblem,asweshow, arisesnotonlyinmeta-ethics,butinseveraldomainsinwhichanexpressivistanalysisiscalledfor.Theresourcesofinferentialismaffordexpressivists themeansofsolvingtheproblemacrosstheboard.Byenrichingtheirrepertoirewithattitudeexpressionsofvariouskinds,inturn,inferentialistscan providesemanticanalysesofavarietyoflinguisticitemsgoingwellbeyond thesimplelogicalconstants.Wedemonstratethisbyprovidingapplications oftheinferentialexpressivistapproachtoadiverserangeoflinguisticitems, includingepistemicmodals,probabilityoperators,conditionals,moralpredicates,thetruthpredicate,andpropositionalattitudepredicates.
ReferentialsemanticsistypicallycarriedoutinaTarskianmodeltheoreticframework.Wearguethatinferentialistexpressivistsemantics isbestcarriedoutinwhatwecalla multilateral proof-theoreticframework. Thisframeworkmakesuseofinferencerulesinvolvingformulaedecorated withsignsstandingforspeechactsexpressingattitudes.Weobtainthis frameworkbyextendingstandard bilateral frameworks,whichincludesigns forassertionandrejection,withsignsforspeechactssuchasweakand strongassertion,approvalanddisapproval,andsupposition.Adoptingthis frameworkopensupthepossibilityofdistinguishingbetweentwonotions oflegitimateinference:legitimateinferenceaspreservingcommitmentand legitimateinferenceaspreservingevidence.Onceproperlyincorporated intotheframework,thisdistinctionmotivatesprincipledrestrictionsonthe meta-rulesofclassicallogicandleadstoauniformsolutiontopuzzlesand paradoxesof,amongothers,truth,epistemicmodality,andconditionals.At thesametime,thetheoriesthatwedevelopcanaccountforthelinguisticdata intherelevantdomainsthathavepreoccupiedsemanticistswhilstvalidating allclassicallyvalidarguments.Theprospectsforaresearchprogramme combiningexpressivismandinferentialismarebrightindeed.
Asshouldbeclear,then,therearedifferentthemesrunningthroughthis book:thepragmatistthemeconcerningtheshapeoursemanticexplanations shouldtake;thefoundationalthemeconcerninghowtocombineexpressivismandinferentialismintoanoveltheoryofmeaning;theexpressivist themeconcerninghowtheresultingapproachhastheresourcestosolve theFrege–GeachProblem;theformalsemanticsthemeconcerninghowthe approachcanbeappliedtoproviderichsemantictheoriesofnotionsfrom avarietyofdomains;thelogicalthemeconcerninghowtosolvesemantic andepistemicparadoxesofvariouskinds.Althoughwedeemthesethemes tobeintertwinedandcomplementary,wehopethateachofthemwillbeof interestinitsownright.
Wenowprovideanoutlineofthestructureofthebookandofthecontent ofitstenchapters.Inthefirsttwochapters,weprovideopinionatedintroductionstothesemanticframeworksofexpressivismandinferentialism, theirappealingfeatures,andthedistinctiveproblemstheyface.Weargue thatbothexpressivismandinferentialismarebestmotivatedonthebasis oftheiradherencetoapragmatistapproachtosemantictheorizing.Expressivism,inparticular,complieswiththemeta-theoreticalprinciplewedub the PragmatistRazor,whichunderwritesourchallengestovariousformsof referentialismthroughoutthebook.Wealsomakeastartonsolvingsomeof theproblemsexpressivismandinferentialismareconfrontedwithbutargue inChapter1thattosolvetheFrege–GeachProblemexpressivistshadbetter becomeinferentialists,andinChapter2thattosolvetheProblemofLimited Applicabilityinferentialistshadbetterbecomeexpressivists.
InChapter3,weshowhowtocombineexpressivismandinferentialismintoinferentialexpressivism.Ourpointofdepartureisthebilateralist approachtomeaningwhich,weargue,isbestunderstoodasaformof inferentialexpressivismaboutnegation.Wegoontopresenttheinferential expressivistsolutiontotheFrege–GeachProblemasappliedtothecase ofembeddingsofnegationinconditionalantecedents.Weconcludethe chapterbyarguingthatbilateralismfacestheproblemofweakrejectionsand thattosolvethisproblem,bilateralistsshouldbecomemultilateralists.
InChapter4weshowhowtheextensionfrombilateralismtomultilateralismopensupthepossibilityofsolvingtheProblemofLimitedApplicability. Inparticular,weextendthebasicmultilaterallogicofthepreviouschapter intoanepistemicmultilaterallogicandusethislogicasthebasisforan
inferentialexpressivistexplanationofthemeaningoftheepistemicmodal might.Wenotethatthestrategyusedtoexplainthemeaningof might isan applicationofageneral multilateralmethodology forprovidinginferential expressivistexplanationsofthemeaningoflinguisticitems.
Theremainingchaptersapartfromtheconcludingonedetailapplications ofthemultilateralmethodologytoarriveatinferentialexpressivistaccounts offurtherpiecesofvocabulary.WebeginbyprovidinganinferentialexpressivistaccountofmoralvocabularyinChapter5.Weshowthatthisaccount hastheresourcestoaddressaparticularlystrongversionoftheFrege–Geach Problem,tosolvetheWishfulThinkingProblemforethicalexpressivism, andtoaccountformoralmotivation.
WethenturntoattitudeascriptionsinChapter6.Wegiveaninferential expressivistsemanticsforascriptionsofvariouskindsofattitudesandshow thatthissemanticsiscompatiblewithwhatwedeemtobethecorrectshape ofasolutiontotheManyAttitudesProblemforexpressivism.Wegoonto discussthequestionofrealismaboutthemindfromthepointofviewof inferentialexpressivism.
InChapter7,weprovideaninferentialexpressivistaccountofthetruth predicate.Weprovethattheresultingtheoryoftruthhastheresourcesto provideaprincipledsolutiontothesemanticparadoxesandtheirrevenge versions.Thetheory,moreover,canbeprovablyshowntoshareprofound similaritieswithsupervaluationalapproachestotruth.
InChapter8,wetackleconditionals.Weextendthemultilateralframeworksoastoincludenotonlysignsforcategoricalspeechacts,butalsofor conditionalones.Wethenexplainthemeaningofconditionalsintermsof suchbinaryspeechacts.Weshowthattheresultinginferentialexpressivist accountofconditionalshasseveralattractivefeatures.Notably,itavoids Gibbard’scollapseproblemandCurry’sParadoxinanaturalway.
Asafinalapplicationofthemultilateralmethodology,wepresentin Chapter9aninferentialexpressivistaccountofepistemicusesofprobabilisticvocabulary.Wegiveaninferentialexpressivistanalysisof itisprobablethat whichaccountsforseverallinguisticdataconcerningprobability expressionsandavoidstheFrege–GeachProblem.Weendthechapterby explaininghowtheaccountcanbeextendedtoexpressionsofcomparative probabilityandtoquantitativeprobabilitytalk.
WeconcludethebookinChapter10byillustratingtheroadaheadfor theinferentialexpressivistapproachtomeaning.Wepresentanumberof
furtherpossibleapplicationsoftheapproachandoutlinehowonemaygo aboutcarryingouttheseapplications.
Someofthechaptersarebasedonmaterialthathasappearedelsewhere,thoughofteninaverydifferentform.Chapter3drawson‘Weak rejection’(AustralasianJournalofPhilosophy,2017),Chapter4drawson ‘Weakassertion’(PhilosophicalQuarterly,2019)and‘Epistemicmultilateral logic’(ReviewofSymbolicLogic,2022a),Chapter5drawson‘Inferential expressivismandthenegationproblem’(OxfordStudiesinMetaethics,2021), andChapter7drawson‘Inferentialdeflationism’(PhilosophicalReview, Forthcoming).Wearegratefultotheeditorsandpublishersforpermission tousematerialfromthesearticles.
On13June2014the LoLaDay tookplaceattheUniversityofAmsterdam. Duringthismeeting,severalmembersoftheLogicandLanguage(LoLa) groupoftheInstituteforLogic,LanguageandComputationgavetalkson aspectsoftheircurrentresearch.Webothpresentedmaterialonthespeech actofrejection.Havingdiscoveredthatwewerebothworkingonwhatwe consideredanunjustlyneglectedtopic,wedecidedtoexchangenotes.So beganthecollaborationthatledtothisbook.WewouldliketothankFranz BertoandRobertvanRooijfororganizingthatmeetingasheadsofLoLaat thetime.
Overtheyears,thematerialinthisbookhasbenefittedfromconversations andfeedbackfrommanyfriendsandcolleagues.Weareespeciallygrateful toMariaAloni,DanielAltshuler,NicholasAsher,BahramAssadian,Dorit Bar-On,FranzBerto,AriannaBetti,JustinBledin,PaulBloomfield,Lwenn Bussière,TimButton,MatthewChrisman,MariangelaCocchiaro,Paul Dekker,ImogenDickie,CianDorr,RaquelFernández,FilippoFerrari, StephenFinlay,SalvatoreFlorio,MelissaFusco,ManuelGarcía-Carpintero, LewisGordon,MagdalenaKaufmann,AngelikaKratzer,ManfredKrifka, AlexLascarides,HannesLeitgeb,BillLycan,MichaelLynch,Matthew Mandelkern,TeresaMarques,ThomasMüller,JulienMurzi,CarloNicolai, AlejandroPérezCarballo,FrancescaPoggiolesi,HuwPrice,GregRestall, DaveRipley,LucasRosenblatt,MarcusRossberg,LorenzoRossi,Giorgio Sbardolini,ThomasSchindler,LionelShapiro,StewartShapiro,Sebastian Speitel,UnaStojnić,MartinStokhof,ChristineTiefensee,RobertvanRooij, FrankVeltman,JackWoods,andHeddeZeijlstra.Wewouldalsoliketo
thankPeterOhlinandtheteamatOxfordUniversityPressfortheirhelp andsupportthroughoutthewritingandproductionprocess.
Wehavepresentedsomeofthematerialinthisbookinanumberof forums.WearegratefultotheorganizersandaudiencesoftheMathematical LogicColloquiumattheUniversityofBonn,theTheoreticalPhilosophyColloquiumatUtrechtUniversity,thePLMMasterclasswithAngelikaKratzer attheUniversityofSalzburg,thePhilosophyColloquiumattheUniversity ofGothenburg,theNewYorkPhilosophyofLanguageWorkshop,theXIV AnnualMadisonMetaethicsWorkshop,theSemanticsandPhilosophyin Europe11ConferenceattheUniversityofWarsaw,theHigherSeminar inTheoreticalPhilosophyatUppsalaUniversity,theMondayColloquium attheUniversityofBonn,theWorkshoponPropositions,Properties,Sets, andOtherAbstractObjectsattheUniversityofAmsterdam,theSPAGAD2 WorkshopandtheMini-WorkshoponDiscourseoftheZAS(Berlin),the LogicColloquiumattheMunichCenterforMathematicalPhilosophy, theLogicColloquiumandPhilosophyColloquiumattheUniversityof Konstanz,theLondonGroupforFormalPhilosophy,theWorkshopon ClassicalandNon-ClassicalApproachestoParadoxesattheUniversityof BuenosAires,thevonWeizsäckerColloquiumattheUniversityofTübingen, thePhilosophyofHybridRepresentationsreadinggroupattheUniversityofBarcelona,theLogicColloquiumattheUniversityofConnecticut, theVarietiesofPhilosophicalExpressivismWorkshopattheUniversityof Mannheim,andtheRhinelandExpressivismWorkshopattheUniversityof Bonn.WearealsogratefultotheaudiencesoftheEXPRESSWorkshops onBilateralApproachestoMeaningandonExpressivistApproachesto Meaning,whichweorganizedattheUniversityofAmsterdamtogetherwith LwennBussièreandGiorgioSbardolini.
ThisworkhasreceivedfundingfromtheEuropeanResearchCouncil (ERC)undertheEuropeanUnion’sHorizon2020researchandinnovation programme(grantagreementNo.758540)withintheproject Fromthe ExpressionofDisagreementtoNewFoundationsforExpressivistSemantics (EXPRESS).TheERCfundingmadeitpossibletodevoteourselvesfulltime tothisprojectandtopublishthebookopenaccess.Wearedeeplygrateful. Finally,beforewebegin,somewordsfromeachofusindividually.
FromLuca: ThankyoutoJulianforbeingsuchawonderfulcollaborator andforbeingsomuchfuntoworkwith;toTimSmileyforintroducingme torejectionwhenIwasagraduatestudent;totheCambridgepragmatists forinfluencingmeinwaysthatIamonlynowfullyrealizing;toSarahfor
hercontinuousloveandnotmindingtoomuchmetestingheracceptability judgementsaboutembeddedepistemicmodals;toTommasoforbringingso muchjoytomylife;andtomyparentsforalwaysbelievinginme.
FromJulian:IamgratefultoLucaforbeing,overtheyears,anoutstanding advisor,supervisor,colleague,andco-author;toRaquelFernández,Alex Lascarides,andPaulDekkerfortheirteachingswhichhavestayedwithme morethantheymightknow;toYu’anforherloveandtolerationoflatenights working;andtomyparentsfortheirunwaveringsupport.
3.1.CoordinationprinciplesinBasicMultilateralLogic
Expressivism Thisbookpresentsanddevelops inferentialexpressivism,anovelapproach tothestudyofmeaningwhichcombineselementsoftheinferentialist andexpressivistprogrammes.Thischapterintroducesexpressivismandthe challengesitfaces.Thenextoneintroducesinferentialism.
Bothexpressivismandinferentialismcomeinlocalandglobalvarieties. Globalapproachestomeaningtaketheircentraltenetstoapplyacrossthe board;localapproachesrestrictattentiontosomespecificsetofexpressions orsomeparticularareaofdiscourse.Historically,expressivismoriginatedas anapproachtothemeaningandfunctionofmoralvocabulary,sowefocus inthischapteronethicalexpressivism,butmuchofwhatwesaycanbeeasily appliedtoexpressivisttreatmentsofotherareas.Weshallindicatewhenthis isnotthecase.
Webeginbyintroducingsomekeydistinctionswithinthetheoryof meaningwhichwillbeusefulintheremainderofthebook.Wethenpresent whatwesee(andareoftenseen)asthetwomainconcernsthathave beenparticularlyinfluentialintheemergenceanddevelopmentofethical expressivism.Weexplainhowtherelatedviewofspeakersubjectivismcan beseenasanearlyattempttodealwiththeseconcerns.Accordingto ethicalsubjectivism,themeaningofmoralvocabularyconsistsin reports ofattitudes,andtheconstitutivefunctionofmoralstatementsistoreport theseattitudes.Speakersubjectivismfacestheproblemofaccountingfor thephenomenonofmoraldisagreement.Thisproblemmotivatesthefocus on expressions ofattitudes,whichisthecentralinnovationofexpressivism. Traditionalethicalexpressivismtakesthemeaningofmoralvocabularyto consistinexpressionsofattitudes,andthefunctionofmoraljudgementsto bethatofexpressingtheseattitudes.
Traditionalexpressivismfacesanumberofproblems,whichwealso introduceinthischapter.Ofthese,theso-called Frege–GeachProblem is perhapsthebestknown,andtheonethathashistoricallybeenregarded asathorninthesideofexpressivism.Indeed,sophisticatedandhybrid formsofexpressivismhavebeendeveloped,atleastinpart,inresponseto
ReasoningwithAttitude:FoundationsandApplicationsofInferentialExpressivism.LucaIncurvatiand JulianJ.Schlöder,OxfordUniversityPress.©OxfordUniversityPress2023. DOI:10.1093/oso/9780197620984.003.0001
thisproblem.Oneofthecentralcontentionsofthebookisthatinferential expressivismoffersthebestavailablesolutiontothisproblem,asitarisesnot onlyintheethicaldomain,butinotherdomainsaswell.
1.1Semantics,postsemantics,andmeta-semantics Thisbookisconcernedwiththetheoryofmeaning.Philosophershave historicallyassigneddifferentmeaningsto‘theoryofmeaning’.Thecentraldistinctionhere,whichhasbecomecustomaryinrecentyears,isthat betweensemanticsandmeta-semantics(Kaplan1989a).
Semantics isconcernedwiththeassignmentofsemanticvaluestothe expressionsofalanguage.Semantictheoriesaretypically compositional: theyassignsemanticvaluestothesimpleexpressionsofthelanguage, anddeterminethesemanticvalueofcomplexexpressionsasafunctionof thesemanticvalueofthesimplerones.Thecompositionalityofsemantic theoriesisintendedtoaccountforthefactthatspeakerscanunderstandand producecomplexexpressionswhichtheyhaveneverencounteredbefore.
Instandard, referential semantictheories,expressionsareassigneddenotationsastheirsemanticvalues.Thatis,areferentialsemantictheoryspecifiesamapping ⋅ fromexpressionstotheirdenotations.Thus,forinstance, thesemantictheorycomputesthesemanticvalueof Andrearests byassigningAndreaasthedenotationof Andrea,therestingfunction—thatisthe functionmappingthethingsthatresttothevalue1andallotherthingsto thevalue0—asthedenotationof rests,anddetermininghowthesesemantic valuescombinetodeterminethesemanticvalueofthesentence.Insymbols, andusingthelambdanotationtorepresentfunctions:
Andrea = Andrea rests =��x.x rests
Andrearests = 1iffAndrearests
Typically,therestingfunctionistakentorepresentthepropertyofresting, andthevalues1and0torepresenttruthandfalsity.Underthisinterpretation,thesemantictheoryspecifiesthetruthconditionsof Andrearests on thebasisofthemeaningofitscomponents.
StandardsemantictheoriesinthetraditionofRichardMontague(1970) orDavidLewis(1970)typicallyassignsemanticvaluestothesimple
semantics,postsemantics,andmeta-semantics3
expressionsrelativetoan indexi,an n-tuplewhoseelementsaretypically takentorepresentthecircumstancesofevaluation.Accordingly,the semanticvalueofasentencewouldbeafunctionfromindicesto0or1. Suppose,forinstance,thattheindexincludeselements w and t,standing, respectively,fortheworldandtimeofevaluation.Thenthesemanticclauses ofourtoyexamplelookasfollows.
t,w = Andrea rests t,w =��x.x restsat t and w
Andrearests t,w = 1iffAndrearestsat t and w
Todealwithindexicalphenomenainlanguage,itiscustomarytoalsotake the contextofutterance intoaccount.Onthestandardpicturegoingback toDavidKaplan(1989b),thisisdonebyrelativizingsemanticvaluesto aparameter c,representingthecontext.ThisiswhatLewis(1980)calls the variable-but-simple-semantic-value approachtosemantics.Onthis approach,semanticvaluesarevariablebecausetheychangefromcontextto context,atleastforsomesentences,suchasthosecontainingindexical vocabulary;theyaresimplebecausethesemanticvaluesofsentences aremerefunctionsfromindicestotruthvalues.Onthe constant-butcomplicated-semantic-value approachtosemantics,bycontrast,semantic valuesareconstantacrosscontexts;theyarecomplicatedbecausethey arefunctionsfromindicesandcontextstotruthvalues.Theconstant-butcomplicated-semantic-valueapproachhasrecentlybeenrevivedinthework ofBrianRabern(2012),SethYalcin(2014),andPaoloSantorio(2019) amongothers.
Thereferentialsemantictheorycomputesasemanticvalueforeach sentenceofthelanguage.Supposing,forsimplicity,thatwehavesettled forthevariable-but-simple-semantic-valueapproach,thesemantictheory specifies,foreachsentence,theconditionsunderwhichthesentencereceives value1(representingtruth)atacontextandatanindex.ThisiswhatJohn MacFarlane(2003)callsthe semanticsproper.Thenextstageistodefine suitablenotionsoftruthandvalidityforthelanguage,thestageMacFarlane callsthe postsemantics.AsMacFarlaneputsit,attheendofthedayweare interestedintruth simpliciter (perhapsrelativizedtoacontext),ratherthan truthatanindex.Butthesemanticsproperaffordsthemeanstodefinetruth simpliciter intermsoftruthatanindex:wecantakeasentencetobetrue simpliciter justincaseitistrueattheindex ic ofthecontextofutterance.
Andrea
Incasetheindex i includesaworldandatime,forinstance, ic willinclude theworldandtimeofthecontextofutterance.Asforvalidity,accordingto thestandarddefinition(andsuppressingcontextsensitivityforsimplicity) anargumentisvalidjustincase,foreveryindex i,ifthepremissesofthe argumentaretrueat i,thentheconclusionistrueat i.Logicaltruthisthen definedasthespecialcaseinwhichthesetofpremissesisempty,thatisby sayingthatasentenceislogicallytruejustincaseitistrueateveryindex.
TheformalsemantictheoryjustdescribedassignsAndreato Andrea andtherestingfunctionto rests (relativetoanindex i).Moreover,it assigns Andrearests afunctionfrom i tothevalues0and1(relativeto theparameter c)asitssemanticvalue.Asnoted,itiscustomarytointerpretthefunctionsassignedtopredicatesasrepresentingthecorresponding properties,sothattherestingfunctionrepresentsthepropertyofresting. Similarly,itiscustomarytointerpretthemembersoftheindexasrepresentingthecircumstancesofevaluationandtheparameter c asrepresenting thecontextofutterance.Finally,thevalues1and0aretypicallyinterpreted asstanding,respectively,fortruthandfalsity.However,allofthisisnot partofthesemantictheory,butratherofthe interpretedsemantictheory: thesemantictheoryunderaparticularinterpretation.Onewayoflooking atthesituationistoconsidertheformalsemanticsasprovidingamodel,and theinterpretationasspecifyingwhattheelementsofthemodelaretaken torepresent.Whattheelementsofthemodelaretakentorepresentisthe answertotheInterpretationQuestion.
InterpretationQuestion. Whatdoesthesemanticvalueofanexpression represent?
Ofcourse,theinterestofasemantictheorytypicallyliesinitscapacityto explainfactsthatbelongtothedomainbeingmodelled,soitistypically interpretedsemantictheoriesthataretheobjectsofinterestsofsemanticists andphilosophers.Thus, referentialists,whoholdthatthemeaningofan expressionisgivenbyitsreferent,willtypicallytake,forinstance,the semanticvalueofapredicatetobeafunction,andthisfunctiontorepresenta property.Nonetheless,itisimportanttoalwayskeeptrackofthedistinction betweensemantictheoryasanabstractstructureanditsinterpretation.
Sofar,wehavepresentedsemantics(whichincludesthesemanticsproper, thepostsemantics,andtheirinterpretation).Thisisonesenseof‘theory ofmeaning’.Anothersenseisprovidedby meta-semantics,thestudyof
semantics,postsemantics,andmeta-semantics5
foundationalquestionsaboutsemantics.Meta-semanticquestionsabound. Herewehighlightanumberofmeta-semanticquestionsthatwillbeparticularlyrelevantintheremainderofthebook.Weuseourtoyexamplefrom standardreferentialsemanticsasarunningexample.
ThesemantictheorytellsusthatAndreaisthesemanticvalueof Andrea andtherestingfunctionisthesemanticvalueof rest.Butwhatmakesitthe casethatthisisso?Onecentralmeta-semanticquestionisthe metaphysical questionofwhatmakesitthecasethatanexpressionhasthesemanticvalue itdoes.
MeaningDeterminationQuestion. Invirtueofwhatdoesanexpression havethesemanticvalueitdoes?
AsemantictheorydoesnotprovideananswertotheMeaningDeterminationQuestion—nordoesitintendto.Atheorywhoseaimistoprovide ananswertotheMeaningDeterminationQuestionisknownasa foundationalsemantics (Speaks2021)—ineffect,abranchofmeta-semantics.1One influentialanswertotheMeaningDeterminationQuestionisprovidedby representationalism.Accordingtorepresentationalism,anexpressionhasthe semanticvalueitdoesinvirtueofwhatitrepresents.Thus,forinstance, Andrea hasthesemanticvalueitdoesbecauseitpurportstorepresent Andrea,and rests hasthesemanticvalueitdoesbecauseitpurportsto representthepropertyofresting.
TheMeaningDeterminationQuestionistobedistinguishedfromthe questionofwhat led toanexpressionhavingthesemanticvalueitdoes. Thisquestionconcernstheetiologyofmeaning.Ofcourse,itisinprinciple possibletothinkthatthenaturalhistoryofanexpression is whatmakes itthecasethatithasthesemanticvalueitdoes.Butthispointofviewis notforceduponus.Forinstance,onemayacceptagame-theoreticaccount oftheoriginsofmeaning,wherebyexpressionscometohavethesemantic valuestheydoasaresultofsomecoordinationgame.Thisiscompatiblewith thinking,forinstance,thatwhatmakesitthecasethatexpressionshavethe
1FollowingStalnaker(1997),ithasbecomerelativelycommontocontrastfoundationalsemantics with descriptivesemantics (García-Carpintero2012).Thisisunfortunate,becauseitmakesitsound asif(first-order)semanticsisamerelydescriptiveenterprisewithoutanyexplanatoryambitions,a descriptionwhichmostworkingsemanticistswouldlikelyresist,asnotedbySzabo(2019).AsSzabo pointsout(andStalnakerhimselfstresses),semantictheoriescruciallypurporttoexplainspeaker productivity.Thefactthatsemantictheoriesarecompositionalis,asnoted,intendedtoaccount forthis.
