MetasemanticsandSingularReference*

OriSimchenUniversityofBritishColumbia

ForthcominginNoûs

1.Introduction

Metasemanticsisconcernedwithhowthesemanticallysignificantbecomes

endowedwithitssemanticsignificance.Ifsemanticsisoftheusualtruth-

conditionalsort,thenaprincipalissueformetasemanticsishowsubsentential

expressionsbecomeendowedwiththeirdistinctivecontributionstothetruth-

conditionsofwholesentencesinwhichtheypartake.Metasemanticsasitis

ordinarilyunderstoodisthemetaphysicsofsemanticendowment,wherethelatter

iscastintruth-conditionalterms.1Itisbeholdentosemanticsinsofarasitattempts

toarticulatedeterminantsforsemanticendowment.

Therearedistinctwaysofconceivingofthemetasemanticproject,however.

Animportantchoicepointconcernswhethertothinkofsemanticendowmentas

emergingdirectlyfromconditionssurroundingtheproductionoremploymentof

theitemssemanticallyendowed(e.g.causalrelationsbornetoportionsofspeakers’

*ForhelpfuldiscussionofthismaterialIamindebtedtoaudiencesatUBC,UniversityofBologna,BarIlanUniversity,UCSantaCruz,LundUniversity,TelAvivUniversity,PrincetonUniversity,UniversityofAlberta,andtothefollowingindividuals:MahradAlmotahari,RobertaBallarin,PaulBartha,YuvalDolev,EliDresner,DeliaGraffFara,LizHarman,RobertHirsch,EmmanuelGenot,JustineJacot,TomKelly,KathrinKoslicki,JamesMartin,ChrisMole,HowardNye,ErikOlsson,AlanRichardson,GideonRosen,ChrisStephens,AbeStone,MaxWeiss,andtwoanonymousreferees.IgratefullyacknowledgethesupportoftheSocialSciencesandHumanitiesResearchCouncilofCanada.1Semanticendowmentmaybemulti-layered.Thetype‘this’isgovernedbyacertainsemanticrule–acharacter–thatspecifiessemanticvalues–contents–oftokensofthetypeintheirrespectivecontexts.Onemetasemanticissuethatcouldberaisedinlightofthissemanticproposalishowthetype‘this’cametobeassociatedwithitscharacter.Adifferentmetasemanticissueishowagiventokenof‘this’cametobeassociatedwithitsparticularcontributiontotruth-conditions,theindividualdemonstratum.InwhatfollowsIfocusexclusivelyonmetasemanticissuesofthesecondkind.

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environment),ortothinkitintermsofconditionssurroundingtheinterpretive

consumptionorreceptionofsuchitems(e.g.facilitationofgoodexplanationsof

speakers’verbalbehavior).Thefirstgeneralapproach–callitproductivism–is

takenbythelikesofDonnellan,Kaplan,Kripke,andearlyPutnam,amongmany

others.Thesecondapproach,interpretationism,istheoneusuallyassociatedwith

DavidsonandLewis.Myaimistoofferapartialarticulationanddefenseofa

generalproductivistorientationtothesubjectbyarguingagainstmetasemantic

interpretationism.Iwillmakeacasefortheclaimthataninterpretationist

orientationtometasemanticsisseverelyflawedwhenitcomestosingular

reference.MyargumentwillbecastagainstaLewisianversionofmetasemantic

interpretationismcommonlyknownasreferencemagnetism,buttheconsiderations

Iofferaregeneral,sointheAppendixIadjustmyoverallargumenttosuita

Davidsonianframeworkaswell.Iendbydrawingageneralmoralfor

metasemanticsanditsrelationtotruth-conditionalsemantics.

Fromaproductiviststandpoint,metasemanticsprimarilytargetsconditions

ofproducingoremployinganitemofsignificance.Ingeneral,thesortofproduction

metasemanticsisconcernedwithisproductionofitemsofsignificancequa

significant.Inadifferentterminology,weareconcernedwithproductionof

symbolsratherthanthatofsigns.2Whatdistinguishesproductivismasa

metasemanticorientationisthattheitem’sproductionquasignificantdepends

directlyonconditionssurroundingtheitem’sproductionormanipulationbythe

2Cf.Wittgenstein1961,at3.32:“Thesign(‘Zeichen’)iswhatcanbeperceivedofasymbol.”Extending‘perceive’tocoverintrospection,thedistinctioncanbeextendedtocovermentalitemsaswell.

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speakerorwriterquainsignificant.Whatmakesitthecasethataspokenreferential

tokenofanoun,say,hasthesignificanceithas,isdetermineddirectlybythe

circumstancesunderwhichthetokenwasphoneticallyproduced.Some

productivistapproachesappealtoreferentialintentionsofspeakerstoexplainhow

areferringtokenemployedonaparticularoccasioncomestorefertowhatitrefers

to,asinDonnellan’s(1966)treatmentofreferentiallyuseddescriptionsorKaplan’s

(1989)treatmentofdemonstrativepronouns.3Otherproductivistapproaches

appealtothecausalhistoryoftheitemofsignificancevis-à-visthethingtowhichit

referswithoutparticularemphasisonreferentialintentions.Soforcertainversions

oftheapproachwhatdeterminesthesemanticcontributionofatokentotruth-

conditionsonagivenoccasionofuseisthereferentialintentionwithwhichitis

employedorsomethingsimilar,whereasforotherversionswhatdeterminesitisa

morebasiccausaldependenceoftherepresentation–beitatokenofalinguistic

typeoraparticularmentalrepresentation–ontheitem(s)represented.4

Productivismmaybecontrastedwithinterpretationism,ametasemantic

orientationwherebyendowmentwithsemanticsignificanceemergesdirectlyfrom

conditionssurroundingtheinterpretiveconsumptionoftheitemsthusendowed.

UnderthisgeneralrubricwehaveinthefirstinstancetheDavidsonianappealto

considerationsoffitofassignmentofsemanticvaluestosubsententialexpressions

3Thisdoesnotpreclude–andmostoftenincludes–therequirementthattheagentbeappropriatelycausallylinkedtotheindividualthereferentialintentionspecifies.Forfurtherdiscussionofsuchdetailsregardingnames,seeChapter3ofSimchen2012.4Whetherornotcausal-historicalrapportwithamorphologicalitemissufficientforcausal-historicalrapportwithanintendedreferentneednotconcernus.Ialsonoteinpassingthatateleosemanticaccountwherebysemanticendowmentarisesfromthediachronicallyshapedfunctionoftheproduceditemtorepresenttotheitem’sconsumersisadifferentsortofproductivistaccount.Fordiscussionoftheroleofconsumershere,seeMillikan1989andespecially1990.

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withspeakers’overalllinguisticbehaviorandattitudesincontext–thelatter

themselvessubjecttofurtherinterpretability–soastoengenderexplanatorily

suitable(‘interpretive’)truth-conditionsforwholesentencesincontext.Butmy

focushereisontheLewisianappealtoaconstraintofworldlynaturalnessinthe

assignmentofsemanticvaluestosubsententialexpressionsthatmaximizesoverall

truthfortheglobaltheoryinwhichtheexpressionsembed.Beyondimportant

differencesamonginterpretationistapproaches,anunderlyingthemethatunites

themisthatendowmentwithsignificanceisamatteroftheitemsthusendowed

beingregardableinacertainway,whethersuchregardingfacilitatesanaccountof

therationalityofthespeaker’slinguisticbehaviorinhisorherworldly

surroundings(Davidson),orwhetheritalsofacilitatesanexplanatorilysuperior

theoreticalcaptureofthewaytheworldis(Lewis).Eitherway,endowmentwith

significancedoesnotemergedirectlyfromconditionssurroundingtheproduction

oremploymentoftheiteminquestionbutfromconditionssurroundingtheirpost-

productionassessment.5InLewis’scasetheshapeoftheworldandtheshapeofour

5Forinterpretationismtheitem’sregardabilityundervariousconstraintsdeterminesitssemanticendowmentdirectly.Thisshouldbedistinguishedfromaproductivistalternativewherebytheitem’ssemanticendowmentisshapedbyintentionsonthesideoftheproducerthatincludetheintentionthattheitemberegardedinacertainway.Onthelatterproductivistalternativetheitem’sregardabilityentersintodeterminingsemanticendowmentonlyindirectly,viaconditionsofproductionthatincludetherelevantintentiononthesideoftheproducer.Hereisarecentendorsementofsuchanidea(notforthepurposeofpromotinganyparticularmetasemanticposition)inHeck2014:

Successfulcommunicationrequiresthespeakerandheraudiencetoconvergeonareferent.Butthespeakerdoesnotutterthedemonstrativeandthenconsultthecontextualcuestofigureouthowtointerpretherownwords.Rather,inplanningherspeech,shehasalreadydecidedwhatobjecttoassignasvalueofthecontextualparameterthatfixesthereferentofthedemonstrative,thatis,whichobjectsheintendsheraudiencetointerpretherasspeakingabout.(343)

Andhereisarecentendorsementoftheideathatpotentialuptakebyacooperativeaudienceistobetakenintoaccountwithinabroadlyintention-basedproductivistaccountofdemonstrativereferenceinKing2014:

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theoryoftheworldtogetherconspiretomakeitthecasethatourpredicateshave

thesignificancetheyhave–apost-productionaffair.

InwhatfollowsIwillarguethatthelatterapproachcomesupshortin

handlingacertainunder-exploredthreatofreferentialindeterminacy,akindof

indeterminacythattargetssingularreferenceinparticular.Thebottomlinewillbe

that(1)referentialindeterminacyofthetypetobediscussedarisesonlyinan

interpretationistsetting–productivismisimmunetoit–and(2)aLewisian

antidoteintermsofeligibilityofinterpretationcharacterizedbyappealingto

naturalnessforpropertiesisincapableofdealingwiththeproblem.

2. ReferenceMagnetism

Ibeginbysketchingmyprimarytarget.Lewisianreferencemagnetismisin

thefirstinstanceathesisaboutthesemanticvaluesassignedtopredicates.6,7The

Isuggestwesaythatthevalueofauseofademonstrativeinacontextisthatobjectothatmeetsthefollowingtwoconditions:1)thespeakerintendsotobethevalue;and2)acompetent,attentive,reasonablehearerwouldtakeotobetheobjectthatthespeakerintendstobethevalue.Wecanabbreviatethisbysayingthatanobjectoisthevalueofanoccurrenceofademonstrativeincontextjustincasethespeakerintendsotobethevalueandthespeakersuccessfullyrevealsherintention.[Hereafootnoteisadded:“Notethataspeakercansuccessfullyrevealherintentioneventhoughherhearerfailedtofigureoutwhatsheintended.Thehearercouldbeinattentive,incompetent,etc.”–OS](225)

6TheapproachhasbeenextendedbySider(2011)tocoverassignmentsofsemanticvaluestoexpressionsotherthanpredicates,notablyquantifiers,butthisextensiondoesnotaffectthemainfocushere,whichissingularreference,beyondLewis’seffortsundertheoriginalproposal.7ForpresentpurposeswesetasideimportantquestionsregardingLewis’smetasemanticorientationthatmatteragreatdealtoLewisscholarship.See,inparticular,Weatherson2012andSchwartz2014.InLewis1984wecomeacrossthefollowingcaveat:

IshallacquiesceinPutnam'slinguisticturn:Ishalldiscussthesemanticinterpretationoflanguageratherthantheassignmentofcontenttoattitudes,thusignoringthepossibilitythatthelattersettlestheformer.Itwouldbebetter,Ithink,tostartwiththeattitudesandgoontolanguage.ButIthinkthatwouldrelocate,ratherthanavoid,theproblem;whereforeImayaswelldiscussitonPutnam'sownterms.(222)

IneverythingthatfollowsweacquiesceinLewis’sacquiescence.

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idea,inanutshell,isthatcertainoverallinterpretationsofourlanguageintothe

worldareobjectivelybetterthanothersduetotheirhighereligibility,thelatter

understoodintermsofmaximizationofnaturalnessintheassignmentofsemantic

valuestopredicates.ThethesiswasinitiallyproposedasanantidotetoPutnam’s

model-theoreticargument,anargumentpurportingtoshowthatundercertain

minimalassumptionsaboutrealisttruth,thedistinctionenshrinedbyrealistsofall

stripesbetweenepistemicidealityandmetaphysicaltruthcannotbesustained.

Putnam’sargumentturnsonthe(almost)inevitableavailabilityofanoverall

interpretationofourlanguageintotheworldthatrendersanepistemicallyideal

theorytrueoftheworld.Theargumentexploitsabasicpointaboutmodel-theoretic

interpretation.

Assumewiththerealistthattheworldisatotalityofmind-independent

things.(Forpresentpurposesweneednotenterthefrayoftryingtoprecisifythe

darknotionofmind-independence.)LetTbeourepistemicallyidealtheoryina

first-orderextensionallanguage.Twouldbeatleastconsistent,soitwouldhavea

model.UndercertainminimalassumptionsaboutTandthesizeoftheworld,T

wouldhaveamodelmofexactlythesamesizeastheworld.Byexploitingthe

existenceofabijectionfromthedomainofmintotheworlditselfwecandefinea

modelmwofTthathastheworlditselfasitsdomain.SotheepistemicallyidealT

turnsouttobetrueoftheworldafterall–thereisnowayforitnottobetrueofthe

worldunderminimalassumptions.Thedistinctionbetweenepistemicidealityand

realisttruthcollapses.

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HereishowLewis(1984)respondstothisargumentintermsofeligibility:

“Whenwelimitourselvestotheeligibleinterpretations,theonesthatrespectthe

objectivejointsinnature,thereisnolongeranyguaranteethat(almost)anyworld

cansatisfy(almost)anytheory”(227).Letusfleshthisoutabit.Theinterpretation

Putnam’sargumentappealstoinforcingthepronouncementsofepistemicideality

tocomeouttrueoftheworldmayverywellassign,ifwehappentobeepistemically

unlucky,highlygerrymanderedsemanticvaluestoourpredicatesthatdonot

respectobjectivejointsinnature.Recallthatmwwasdefinedintermsofabijection

fromthedomainofmintothedomainofmw.Thebijectionitselfwasarbitrary;allit

didwasensurethatthestructureimposedbyTonmisreplicatedinmwregardless

ofindependentfeaturesoftheindividualsinthedomainofmw.Butthedomainof

mwisjustthetotalityofworldlythings.FromtheLewisianstandpointthemisstep

inPutnam’sargumentisthefailuretodistinguisharbitraryinterpretationsofTfrom

intendedones,onesthatrespectthestructurethatalreadyinheresintheworld

itself.Itisonlythelatterthatarerelevantfortheassessmentoftherealistpoint

thatTmightbefalseoftheworld.Twouldbefalseoftheworldifitsohappensthat

ithasnomodelisomorphictothewaytheworldreallyis.8

ThisisundoubtedlyaformallyadequateresponsetoPutnam’sargument.9It

reliesonacertainideathatthosewithKantianleaningsmayfindspookyand

unilluminating–theideathattheworldhasitsowninherentstructure

8Wemaysteerawayfromcontroversysurroundingtheimpliedsuggestionthatthewaytheworldreallyisisamodelbyparaphrasingasfollows:Twouldbefalseifithappensnottohaveamodelisomorphictoamodelrepresentingthewaytheworldreallyis.9LewiscreditsMerrill(1980)withthegeneralidea.

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independentlyofourconceptualinvolvementinit.10Theprosandconsofthisidea

liebeyondourpresentconcern.Thequestionbeforeusiswhetheranythinginthis

proposedantidotetoPutnam’sargumenttouchesonreferenceunderstoodinits

commonsingularvariety.CanLewisianconsiderationseffectivelyblock

indeterminacyinsingularreference?SupposeIsay‘Thisisanicepieceoffruit’with

respecttoaparticularappleinafruitstall,aparadigmcaseofsingularreference.I

wouldhavethoughtthatIwasreferringtotheparticularappleinthestall.Can

LewisianconsiderationsruleoutthatIwasactuallyreferringtotheexoplanetAlpha

CentauriBb,somefourlightyearsaway,ortothenumber17?11

Aninitialthoughtisthattheycan.ConsiderthefollowingpassagefromLewis

1983:

Naturalnessofpropertiesmakesfordifferencesofeligibilitynotonlyamongthepropertiesthemselves,butalsoamongthings.CompareBrucewiththecat-shapedchunkofmiscellaneousandever-changingmatterthatfollowshimaround,alwaysafewstepsbehind.Theformerisahighlyeligiblereferent,thelatterisnot.…ThisisbecauseBruce,unlikethecat-shapedchunk,hasaboundarywelldemarcatedbydifferencesinhighlynaturalproperties.WhereBruceends,therethedensityofmatter,therelativeabundanceofthechemicalelements,…abruptlychange.Notsoforthechunk.(372)

Thereisametasemanticideaimplicitherethatneedstobedrawnout.How

differencesineligibilityforpropertiesaresupposedtocarryovertodifferencesin

eligibilityforthingsisillustratedbycomparingBrucethecatwithacat-shaped

10ThuswereadinPutnam1990:“WhatLewis’sstoryclaimsisthattheclassofcatscriesoutforalabel,whiletheclassofcats*doesnotcryouttobenamed.Ratherthansolvingtheproblemofreference,whattheideaofaconstraintbuiltintonatureandof‘eliteclasses’doesistoconfusethematerialistpicturebythrowinginsomething‘spooky’.”(38)11Asshouldbeclearfromtheensuingdiscussion,theexampleofdemonstrativereferenceisselectedasawayofdramatizingindeterminacyinsingularreference.Nothingimportanthangsondistinctivefeaturesofdemonstrativereferencebeyondutilityforsingularreference.Anyreferentiallyusedsingulartermwoulddojustaswellforpresentpurposes,suchasareferentialuseof‘Bruce’tospeakofaparticularcat.

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chunkofmatterfollowingBrucearound(assumingthechunkisnotjustanothercat

stalkingBruce).NaturalpropertiesmarkBruce’sboundary,wearetold,butthe

samecannotbesaidfortherelativelyarbitrarychunkbehindBruce.Supposethisis

so.Startingwithacorpusofsentencesheldtobetrue,letonebe‘Brucehasan

organicsurface’,where‘organicsurface’appliestotheoutermost10micronthick

layerofamoreorlesscontiguousbodymostlyconstitutedbyorganicmolecules.

Assumingthat‘organicsurface’alreadystandsforarelativelynaturalproperty,

‘Bruce’willrefertothecatratherthantherelativelyarbitrarychunkofmatter

behindhimonpainoffalsifyingthesentence.Butthisstrategyofrulingoutthe

chunkinfavorofBruceastheintendedreferentfor‘Bruce’extendsbeyondcases

wherethechoiceisbetweenacatandagerrymanderedchunkofmatter.It

generalizestocaseswherethechoiceisbetweentwothingswhoserespective

boundariesareequallywelldemarcatedbydifferencesinnaturalproperties.

ConsiderBruceandBruce’sstalkerLenny,acatalwaysthreefeetbehindBruce.

Holding‘Brucehasacenterofmassatx,y,z,t’tobetrueandholdingthe

interpretationofthepredicatefixedwilldecidewhether‘Bruce’referstoBruceorto

Lenny,dependingonwhichofthetwocatshasacenterofmassatx,y,z,t.Sothe

moregeneralmetasemanticideaimplicitinthistalkofeligibilityforthingsisthat

holdingtheinterpretationofpredicatelettersfixedwillalsofixtheinterpretationof

singularterms,givenacertainallocationoftruth-conditionstosentences.

Gobacktotheearlierexampleof‘Thisisanicepieceoffruit’wherethe

intendedreferentfortherelevantoccurrenceof‘this’isanappleratherthana

planetoranumber.Anycandidateforbeingtheintendedinterpretationofthe

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languagewouldneedtorespectthat.Considerthreerivalinterpretations.Each

assignsthesetofallandonlypiecesoffruitto‘isapieceoffruit’,thesetofalland

onlyplanetsto‘isaplanet’,andthesetofallandonlynumbersto‘isanumber’.12

Butoneinterpretationassignstheappleinthestallto‘this’asusedonthat

particularoccasion.AsecondassignsAlphaCentauriBb.Thethirdassignsthe

number17.Onlyonthefirstinterpretationwill‘Thisisapieceoffruit’betrueif

andonlyiftheappleisapieceoffruit.Onthesecondinterpretation‘Thisisapiece

fruit’willbetrueifandonlyifAlphaCentauriBbisapieceoffruit.Onthethird

interpretation‘Thisisapieceoffruit’willbetrueifandonlyifthenumber17isa

pieceoffruit.Soontheassumptionthatallocationoftruth-conditionstosentences

istobeasofthefirstinterpretation,wecanruleoutthesecondandthird

interpretationsasunintended.Consideringonlythesethreerivalinterpretations,

weseemtohavemanagedtosecurethedeterminacyof‘this’asusedontherelevant

occasiontorefertotheappleratherthantoAlphaCentauriBborthenumber17.So

far,sogood.

Here,however,isanaggingthought.Considerthesecondinterpretation,the

oneassigningAlphaCentauriBbto‘this’asusedonthatparticularoccasion.We

assumedthatonthesecondinterpretation‘Thisisapieceoffruit’comesouttrueif

andonlyifAlphaCentauriBbisapieceoffruit,‘Thisisaplanet’comesouttrueif

andonlyifAlphaCentauriBbisaplanet,and‘Thisisanumber’comesouttrueif

12OurdiscussionconcernsLewis’santidotetoPutnam-stylereferentialindeterminacyinanextensionalsetup,sowhatisheldfixedistheassignmenttothepredicatelettersofso-calledeliteclasses–extensionsofnaturalpropertiesandrelations–ratherthanthepropertiesandrelationsthemselves.Referentialindeterminacyargumentscanbetailoredtosuitricherlanguagesaswell.SeeChapter2ofPutnam1981andHaleandWright1997.

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andonlyifAlphaCentauriBbisanumber.Thisisbecauseweassumedthattheway

inwhich‘Thisisapieceoffruit’,forexample,comesouttrueonthefirst

interpretationisthesameasthewayinwhich‘Thisisaplanet’comesouttrueon

thesecondinterpretation;andweassumedthatthewayinwhich‘Thisisaplanet’

comesoutfalseonthefirstinterpretationisthesameasthewayinwhich‘Thisisa

pieceoffruit’comesoutfalseonthesecondinterpretation,andsimilarlyforthe

othercases.Inshort,weassumedthatbeingtrueorfalseforwholesentences,asa

functionoftheinterpretationofsubsententialexpressions,isunivocallyfixed.But

thismightbechallengedinturn.Whatiftruthforsentencesasafunctionofthe

interpretationofsubsententialexpressionsisitselfopentoindeterminacy?The

suggestionmayseemoutrageous,sure,butnomoresothantheoriginalsuggestion

ofreferentialindeterminacy.Ifthelattergotaphilosophicalhearing,thenthe

formershouldgetoneaswell.Mightitbethatforasentenceoftheformφttobe

trueisforsomethingotherthantheintendedinterpretationofttobeamongthe

thingsintheintendedinterpretationofφ?Ifso,thenthestrategyappealedtoabove

forrulingoutthesecondandthirdinterpretationsasunintendedmaynotbe

availableafterall.Forsupposethatitisafeatureoftruthforsentences–as

opposedtoafeatureoftheinterpretationsof‘this’andof‘isapieceoffruit’–that

‘Thisisapieceoffruit’comesouttrueontheinterpretationthatassignsAlpha

CentauriBbto‘this’andassignsallandonlypiecesoffruitto‘isapieceoffruit’.And

suppose,correlatively,thatitisafeatureoffalsitythat‘Thisisaplanet’comesout

falseontheinterpretationassigningAlphaCentauriBbto‘this’andallandonly

planetsto‘isaplanet’.Ifthesearesomehowliveoptions,thentheyspelltroublefor

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theabovestrategyofrulingoutthesecondandthirdinterpretationsasunintended

duetogettingthetruth-conditionswrong.

3. Scrambled-Truth-in-a-Model

Beforediscussingtheseoptionsfurtherletusfillinsomeofthedetailsby

focusingonasimplefirst-orderextensionallanguageL.Besidestheusualfirst-

orderlogicalvocabulary,Lcontainsonlyconstantsciandpredicatelettersofvarious

aritiesPjn.Amodelmisdefinedintheusualwayas<M,ℑ>,whereMisauniverseof

discourseandℑaninterpretationfunctionthatassignstoeachconstanttamember

oftheuniverseMandtoeachpredicateletterφofaritynasubsetofthenth

CartesianpowerofM(ann-placerelation).

Wehavethefamiliarinductivedefinitionoftruth-in-a-model(⊨).Letusonly

concernourselveswiththeatomicsentencesφ(t1,…,tn).Therelevantclauseinthe

definitionof⊨,wheremis<M,ℑ>,is:

m⊨φ(t1,…,tn)iff<ℑ(t1),…,ℑ(tn)>∈ℑ(φ).

Inthefulldefinitionoftruth-in-a-modelaprovisionwouldbemadeforthe

assignmentofvaluestofreevariablesbeforeageneralclauseforatomicformulasis

given,apointtowhichIreturnbrieflybelow.

NowletmLbe<ML,ℑL>,whereMListheintendeddomain(‘L’for‘Lewis’).We

assumethatforanyℑ,ℑ≠ℑL,ℑisnomoreeligiblethanℑLasanoverall

interpretationofthelanguagewhenitcomestothepredicates.ℑListhusmaximally

eligiblebyLewisianstandards.

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Nowapreliminaryobservation:thereisaninterpretationℑʹ,ℑʹ≠ℑL,that

agreeswithℑLontheassignmenttoeverypredicateletterinthelanguage.Simply

defineℑʹ(φ)=ℑL(φ)foreverypredicateletterφandletƒ:ML→MLbeanontrivial

permutationonML,definingℑʹ(t)=ƒ(ℑL(t))foreveryconstantt.Wheremʹis

<ML,ℑʹ>,thereisnoguaranteeofcoursethatthesamesentenceswillcomeouttrue

inmLandmʹ.

Wenowdefineanewnotion:scrambled-truth-in-a-model(⊨σ).For

m=<M,ℑ>weletthescramblerσ:M→MbeapermutationonM.Thedefinitionof⊨σ

islikethatof⊨exceptfor:

m⊨σφ(t1,…,tn)iff<σ(ℑ(t1)),…,σ(ℑ(tn))>∈ℑ(φ).13

Truth-in-a-modelbecomesaspecialcaseofscrambled-truth-in-a-modelwhenσis

theidentityfunction.

Claim:ForanysentenceSofL,mL⊨Siffmʹ⊨ƒ-1S.

Proof:Theonlycasestoconsideraretheatomicsentences.Oncetheclaimis

establishedforthose,extensiontothegeneralcasebyinductiononcomplexityis

routine.Fromourdefinitions,

mʹ⊨ƒ-1φ(t1,…,tn)iff

<ƒ-1(ℑʹ(t1)),…,ƒ-1(ℑʹ(tn))>∈ℑʹ(φ)iff

<ƒ-1(ƒ(ℑL(t1))),…,ƒ-1(ƒ(ℑL(tn)))>∈ℑL(φ)iff13Weassumethatwherethetermsarevariablesthedefinitionrelativizestoanassignmentsofvaluestothevariables:

m,s⊨σφ(v1,…,vn)iff<σ(s(v1)),…,σ(s(vn))>∈ℑ(φ).

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<ℑL(t1),…,ℑL(tn)>∈ℑL(φ)iff

mL⊨φ(t1,…,tn). ☐

Remark1:mLandmʹ,whileagreeinginalltheassignmentstothepredicateletters,

disagreeintheirassignmentstotheterms.(Recallthatƒisnontrivial.)Itis

indeterminatewhichofℑLandℑʹisintended,andsoindeterminatewhichofmLand

mʹisintended.Assumingthatsingularreferenceismodeledbytherestrictionof

interpretationfunctionstoconstants,singularreferencegoesindeterminateeven

understrongLewisianassumptions.

Remark2:Asimilarargumentcanbegivenforlanguageswithnoconstantsby

focusingontheusualprovisionforinterpretingvariables.LetLʹbejustlikeLexcept

withouttheconstants.LettingℑLʹagreewithℑLoneverysigninLʹ,weletmLʹbe

<ML,ℑLʹ>.GivenanyassignmentsofvaluesfromMLtothefreevariablesv,by

analogousconsiderationstothoseaboveforanyopenformulaφ(v1,…,vm)ofLʹ,

mLʹ,s⊨φ(v1,…,vm) iffmLʹ,sʹ⊨ƒ-1φ(v1,…,vm),wheresʹisthecompositionƒ°s.Byinduction

onsyntacticcomplexityitcanthenbeshownthatforanysentenceSofLʹ,mLʹ⊨Siff

mLʹ⊨ƒ-1S.Thesignificanceofthisparticulardetailwillemergeinthenextsection.

Remark3:Thepresentargumentdiffersfromfamiliarindeterminacyarguments

originatingfromQuineandPutnam,withfamiliarresponsesbyLewis,Devitt,and

others.Theotherargumentstakeforgrantedthattruthperseistobemodeledby

truth-in-a-modelandthenproceedbypermutingassignmentstothenon-logical

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vocabularyinatruth-in-a-modelpreservingway.14Notsointhepresentcase.The

ideathatsententialtruthistobemodeledbytruth-in-a-modelisnotsacrosanct,a

factexploitedtodrivethepresentthreatofreferentialindeterminacy.

4. InterpretationistReplies

Howwouldtheinterpretationistproceedhere?Theinterpretationistbegins

withtruth-conditionsforwholesentences.Theinterpretationofourpredicate

lettersisalreadypresumedtobefixedandbeholdentomaximalnaturalness.The

challengeistosaywhatselectswhethertobetrueforsentencesisasof⊨orasof

⊨ƒ-1.IfsomethingalreadyselectswhetherreferenceisasofℑLorasofℑʹ,then

startingwithtruth-conditionsforsentencesmightdeterminewhethertobetrueis

asof⊨orasof⊨ƒ-1.15Alternatively,startingwithtruth-conditionsforsentences,

whetherreferenceisasofℑLorasofℑʹwilldepend,inturn,onwhethertobetrue

isasof⊨orasof⊨ƒ-1.ToborrowanimagefromDavidson,startingwithtruth-

conditionsandtryingtosolveforwhatgeneratesthemisliketryingtosolveasingle

equationwithtwovariables,referenceandtruth.

Interpretationismprioritizestruthoverreference.Referenceisunderstood

astheassignmentofsemanticvaluestoexpressionsingeneratingtruth-conditions

14FordetailsseeHaleandWright1997.Takingforgrantedthattruthperseistobemodeledbytruth-in-a-modelappliesequallytoargumentsthatproceedbyconstructionofdeviantinterpretationsthatarearguablysimplerthantheintendedoneandtoargumentsthatconceiveofalternativesemanticpropertiesandrelationsthatdifferfromoneanotherintheirpatternsofinstantiation.SeeWilliams2007andHawthorne2007.15‘Might’becausedifferencesamongbijectionsmaynotbesignificantenoughtobelinguisticallymanifestable,inwhichcasetheresolutionalludedtointhetextwouldnotwork.Henceforthwerestrictourselvestodifferencesthatareprimafacielinguisticallymanifestable.

16

forsentences.TheLewisianinterpretationistunderstandsthistobeconstrainedby

considerationsofnaturalnessintheassignmentofsemanticvaluestopredicates,

assignmentsthatcarvenatureatthejoints.Crucially,howsubsentential

expressionsaretobeinterpretedisbeholdentoobjectivejointsinnature.Butmore

fundamentally,howsubsententialexpressionsaretobeinterpretedisconstitutive

oftheexpressionshavingtheirsignificancetobeginwith.Theargumentofthe

previoussectionsuggeststhatsuchanapproachleavessingularreference,thekind

ofreferencewithwhichweengageineverydaylifeinspeakingofapplesatthefruit

stallorofindividualcats,radicallyunder-determined.

AtthispointwemightconsideraQuineanreaction.Hopingtoallayconcerns

aboutindeterminacyinsingularreference,theQuineaninsistsontheeliminability

ofsingularterms.Dispensingwithsingulartermsdispenseswithwhateverafflicts

them.Butheretwopointsshouldbeborneinmind.First,ifsingularreferenceis

importantpre-theoretically,thentheQuineanattitudewillfailtoengagewiththe

problemathandinasatisfactoryway.Anditseemsveryimportantpre-

theoretically:weseemtocaredeeplyaboutwhatinparticularwethinkandtalk

aboutinourthoughtandtalk.Indeed,weseemtocareaboutthisevenwhentruth

andfalsityarenotatissue.16Second,inlightofRemark2above,evenifatsome

levelourlanguagewereentirelybereftofsingulartermsitwouldbeindeterminate

whatmakesitthecasethataclaimoftheform∃xψx,e.g.,comesouttrue,whatthe

semanticmechanismisviawhichsuchtruthisaccomplished.Asnotedabove,given

16SeeSimchen2013fordiscussionofcasesoftruncatedutterancesthatarereferentialdespitehavingonlysubsententialsignificance.(Onemaythinkofsuchcasesasplayinganon-negligiblecommunicativeroleinbringingtopicsintoconversationalsalience.)

17

anassignmenttothefreevariableswecanconsideranassignmentthatisthe

compositionoftheoriginalassignmentandtheinverseofthescrambler.Itisthen

easilyshownbyappealingtotherelevantsemanticclausegoverningexistential

quantificationthatmLʹ⊨∃xψxiffmLʹ⊨ƒ-1∃xψx.Butthemechanismviawhich∃xψxis

madetrueinmLʹisthatsomethinginthedomainML,callito,fallsintheLewisian

interpretationofψ.Themechanismviawhich∃xψxismadeƒ-1-scrambled-truein

mLʹ,bycontrast,isthatsomethinginMLpotentiallyotherthano–theƒofo–hasan

imageunderƒ-1thatfallsintheLewisianinterpretationofψ.AQuineanattitude

mightproclaimthisadistinctionwithoutadifference,butthoseofuswhowishto

maintainarealistattitudeaboutsemanticfactswouldconsideratmostoneofthese

alternativestobecorrect.17

AsagainsttheQuineanattitudeofindifference,letusberemindedwhat

thingswouldbelikeiftruthwerebettercapturedby⊨ƒ-1thanby⊨.Isay‘Thisisa

nicepieceoffruit’standingatthefruitstallinmyneighborhoodgrocer.Itso

happensthat‘this’asspokenbymeasIconsiderajuicyAmbrosiaappleinthestall

reallyreferstotheexoplanetAlphaCentauriBb,somefourlightyearsaway.Italso

happensthatformysentencetobetrueisforanimageoftheexoplanetundersome

bijectionoftheuniverseontoitselftobeanicepieceoffruit.Loandbehold,the

imageinquestionisjusttheappleIamholdinginmyhand,whichisanicepieceof

fruitindeed–afortuitouscosmiccoincidence.

17Adiscussionofvariableelimination,asinQuine1960andelsewhere,wouldtakeustoofarafield,butpredicate-functorlogic,withitsderelativization(orcropping)functor,seemstoosyntacticallyalientoplayasignificantmodelingroleinnaturallanguagesemantics.ForacleardiscussionoftheissuethatalsoincludesastraightforwardmodeltheoryforPFL,seeDahllöf1999.

18

Butagain,‘this’isasingulartermandourinsistentQuineanproposesthatwe

dowithoutthose.Weadjusttheexampletoaccommodatetheinsistence.Looking

throughthestallIsay‘Thereisanicepieceoffruithere–Icanjustfeelit’.Ignoring

thetreatmentof‘here’,myfirstsentencemightbemadetruebythefactthat

somethingsomewhereintheuniverse–exoplanetAlphaCentauriBb–issuchthat

itsimageunderacertainbijectionoftheuniverseontoitselfisacertainappleinthe

stallhereinmyneighborhoodgrocer,fourlightyearsawayfromtheexoplanet,

whichhappenstobeanicepieceoffruit.Thisshouldstrikeusasnolessabsurd

thantheoutlandishalternativeoutlinedwithrespectto‘Thisisanicepieceoffruit’.

IfIamright,theinterpretationisthasnoobviouswayofdoingjusticetoour

inclinationtoregardsuchalternativesaswildlyimplausible.

Mighttheinterpretationistappealtosomegeneralconsiderationof

simplicityfavoringtruth-in-a-modeloverscrambled-truth-in-a-model,thereby

allowingustoweedoutasunintendedcertainoverallinterpretationsofour

languagethataremaximallyeligiblewithrespecttothepredicates?Afterall,the

definitionofscrambled-truth-in-a-model,withitsappealtoascramblerσ,seems

morecomplicatedthanthatoftruth-in-a-model.Unfortunately,sucharesponseis

oflimitedreach.Foronething,truth-in-a-modelcanbeconstruedasaspecialcase

ofscrambled-truth-in-a-model,asnotedabove,wherethescramblerisidentity.

Andwewouldbehardpressedtofindanon-ad-hocwayofregardingidentityas

somehow‘simpler’thanƒ-1.Thechallengeistospelloutawayinwhichtheidentity

function,allonitsown,issimplerthananarbitrarynontrivialpermutationofthe

domain.Againstthebackgroundofcomparingpermutationsofthedomain,identity

19

isnotobviouslysimpler:itisonepermutationamongmany,butonethatrequiresa

furtherconditiontospecify.Butthenagain,againstsuchabackgroundidentityis

notbeingconsidered“allonitsown”.18Howtothinkofthecomparativesimplicity

ofidentitybutnotagainstanysuchbackgroundisunclear.19

Onemightappealtosomeformallydesirablepropertythattruth-in-a-model

possessesandscrambled-truth-in-a-modellacks,suchasinvarianceunder

isomorphism.20Thefollowingexpressestherequirementfortruth-in-a-model:

(i) Ifm⊨S,thenforanym*=<M*,ℑ*>isomorphictom,m*⊨S.

Thestrictanalogof(i)forscrambled-truth-in-a-modelfailsbecausethescramblerσ

isapermutationonMandthereissurelynoguaranteethatforeverytermtand

everysuchm*,ℑ*(t)∈M.Sothereisnoguaranteethatσ(ℑ*(t))iswelldefined.But

therelevanceoftherequirementofinvarianceunderisomorphismtothesupposed

advantageoftruth-in-a-modeloverscrambled-truth-in-a-modelformodelingtruth

perseisnotobvious.Letusassumethatundertheauspicesofabstractmodel

theory(i)hasaclearadvantageoverthescrambledvariant(ii):

18ItmightbetemptingtoappealtodegreesofKolmogorovcomplexityhere,butnoticethattherelevantissueisnotwhichdescriptionofafunctionissimpler,but,rather,whichfunctionissimpler.Itisthelatterratherthantheformerthatisrelevanttothequestionathandofwhetherornottruth-in-a-model(oridentity-scrambled-truth-in-a-model)issimplerthanƒ-1-scrambled-truth-in-a-model.Howwearetoproceedfromcomputationalsimplicityinspecifyingthingstosimplicityinthethingsthemselvesremainsunclear.(Forwhatit’sworth,Mathematicians’verdictsofsimplicityareoftenshapedbyhowmuchisrequiredtospecifythings,soe.g.amonoidmightbeconsideredsimplerthanagroupduetotheabsenceoftheinversecondition.Bysuchastandardanon-arbitrarypermutationwillnotbesimplerthananarbitraryone.)19InthespiritofthepreviousdiscussionoftheQuineanattitudeofindifferenceitmightbeclaimedthattruth-in-a-modelandidentity-scrambled-truth-in-a-modelareafteralldistinct,thelatterbutnottheformeroperatingviatheworkingsoftheidentityfunction.ThepointdeservesamorethoroughtreatmentthanIcanofferithere,butsufficeittosaythatoncethecomparisonwiththeneighboringscramblednotionisbroughtintosalience,itbecomesunclearwhethertheformerconstrualshouldbeprivilegedoverthelatter.ThankstoJamesMartinforraisingthisissue.20ThankstoMaxWeissforemphasizingthis.

20

(ii) Ifm⊨σS,thenforanym*=<M*,ℑ*>isomorphictom,m*⊨σ*S,whereσ*ish°σ°h-1andh:M→M*istheisomorphism.21

Suchanadvantageof(i)over(ii)fromthepointofviewofabstractmodeltheory

doesnotimmediatelyentailwithoutfurtherargumentaclearadvantagefortruth-

in-a-modeloverscrambled-truth-in-a-modelasthebettercaptureoftruthpersefor

oursentences.Andsuchanargumentseemslikeaverytallorderindeed.

Butevenifwesetallthisaside,comparethesuggestedappealtosimplicity

withthefollowingpossibleresponse–notattemptedbyPutnam–totheLewisian

appealtoreferencemagnetismasthesavingconstraintontheintended

interpretationofthelanguageoftheepistemicallyidealtheoryT.Theideathatto

betrueforTistobetrueinsomemodelwiththeworlditselfasthedomainis

certainlylocallysimplerthantheideathattobetrueforTistobetrueinamodel

withtheworlditselfasthedomainandwithaninterpretationfunctionthatrespects

theworld’spreexistingstructure.22Thus,ablindappealtosimplicitywoulddrive

theshockingconclusionthatTisguaranteedtocomeouttrueoftheworldafterall,

sothatthedistinctionbetweenepistemicidealityandrealisttruthcannotbe

sustained.Butsuchanappealtosimplicityisclearlyotiose.Thequestionposedby

21Claim:Scrambled-truth-in-a-modelhas(ii).

Proof:Weshowthatifm⊨σφ(t1,…,tn),thenforanym*=<M*,ℑ*>isomorphictom,m*⊨σ*φ(t1,…,tn),whereσ*ish°σ°h-1andh:M→M*istheisomorphism.Extensiontothegeneralcasebyinductionon

syntacticcomplexityisagainroutine.Form=<M,ℑ>,m⊨σφ(t1,…,tn)iff<σ(ℑ(t1)),…,σ(ℑ(tn))>∈ℑ(φ)iff(†)<h(<σ(ℑ(t1))),…,h(σ(ℑ(tn)))>∈ℑ*(φ).

Ontheotherhand,foranytermt,ℑ*(t)=h(ℑ(t)),soℑ(t)=h-1(ℑ*(t)).Substitutingin(†)yields:(†ʹ)<h(σ(h-1(ℑ*(t1)))),…,h(σ(h-1(ℑ*(tn))))>∈ℑ*(φ).

Weobservethath°σ°h-1,i.e.σ*,isapermutationonM*,so(†ʹ)obtainsiffm*⊨σ*φ(t1,…,tn)bythedefinitionofscrambled-truth-in-a-model. □22‘Locally’becausetheideaoftheworldbeingatotalityofthingswithnoinherentstructure,whatwithmindsimposingstructureonthistotality,mayverywellturnouttohaveramificationsofenormouscomplexityonaglobalscale.

21

Putnam’sargumentiswhetherornotTcouldreallybefalse.Suchanissuehas

ramificationsthatarefar-reachingenoughtotrumpanyknee-jerkappealto

simplicitythatwouldfavorthelocallysimpleraccountofwhatitisforTtobetrue.

Inthepresentcase,too,ifsingularreferenceisasofℑʹratherthanasofℑL,

thenthisprovidesuswithamplereasontosetasideaconsiderationofsimplicity

thatwouldfavortruth-in-a-model(oridentity-scrambled-truth-in-a-model)overƒ-1-

scrambled-truth-in-a-modelasthebettercaptureoftruthforoursentences.After

all,whenIsay‘Thisisanicepieceoffruit’whileattendingtotheappleinmyhand,it

hadbetterturnoutthatwhatIsayistrueornotdependingonhowthingsstandin

thevicinityoftheapple.If‘this’asspokenatthefruitstallreallyreferstoAlpha

CentauriBb,thenblindlyfollowingsomelocalsimplicitycriterionwouldmakewhat

Isaytrueorfalsedependingonhowthingsstandwithsomethingotherthanthe

applesomefourlightyearsaway.

Theinterpretationistmighttrytoshiftsomehowtoaconsiderationof

simplicityregardingreferenceandtruthtakentogether.Butnoticethatthematter

isnotasclearasonemighthavehoped.Weseemtohavenogroundsforsupposing

thatsingularreference,takenonitsown,issimpleronewayoranother:the

hypothesisthatreferenceisasofℑʹisnolesssimplethanthehypothesisthat

referenceisasofℑL.Andasseenabove,weseemtohavenoreasontosupposethat

simplicityconsiderationsautomaticallytrumpwhenitcomestotruth-in-a-model

(oridentity-scrambled-truth-in-a-model)overƒ-1-scrambled-truth-in-a-model.How

exactlysimplicityconsiderationsaresupposedtotrumpwhenitcomestoreference

andtruthtakentogetherisfarfromclear.

22

PerhapsthethoughtisthatLewisianconsiderationsofnaturalnessmaybe

takentoruleoutscrambled-truth-in-a-modelinfavoroftruth-in-a-modeldirectly.23

ButnaturalnessasconceivedbyLewisdoesnotapplysmoothlyhere:welacka

workablesenseofwhattheequivalentofnaturaljointsmightbeoutsidethenatural

order.Lewis(1983:375-6)doesemploytheapparatusofnaturalpropertiesto

solvetheKripke-Wittgensteinproblem,butherecaremustbetakennottodraw

unintendedconclusions.ThequestionposedbyKripke’sWittgensteiniswhat

determinesthatbyaddingwemeantoaddratherthantoquadd.Lewis’sansweris

thatthepropertyofaddingismorenaturalthanthepropertyofquadding.This

shouldnotbemistakenfortheclaimthatthefunctionofadditionismorenatural

thanthefunctionofquadditionandthattherefore‘addition’referstotheoneand

nottheother.Inthefirstplace,afunctionisnotapropertybutanindividual,and

whileLewisdoeshavesomethingtosayabouteligibilityforindividualsintermsof

demarcationoftheindividual’sboundariesbymorenaturalproperties(as

discussedinSection2),functionsclearlylackboundariesintherelevantsense.Such

anaccountformathematicalindividualswouldneedanotionofnaturalnessfor

mathematicalpropertiesthatLewisdoesnotprovide.Forsomeindicationofthe

difficultyhere,considerwhichismorenaturalintherelevantsense–beinga

naturalnumberorbeingareal?Sinceeverynaturalisarealandnottheotherway,

thenaturalsarecertainlymoreexclusive,whichmightsuggestthattheyaremore

eliteintherelevantsense.Butbythatcriterionthetranscendentalsarealsomore

exclusivethanthereals–arethey,too,moreelite?Orisitthatbeingofthesame

23Thankstoananonymousrefereeforraisingthis.

23

cardinalityastherealsprecludesthetranscendentalsfrombeingmoreelite?The

pointisnotthatwecouldnotdreamupacriterioncomewhatmay.Thepointis

thatsuchworkisfarfromtrivialandclearlynotastraightforwardextensionofthe

Lewisianapparatusofnaturalness.TherelevantcontextinLewis1983makesclear

thatLewis’sfocusisonnaturalnessinthepsychologyofaddingascomparedwith

thepsychologyofquadding.Thefocusisnotonnaturalnessininterpreting

mathematicallanguage,appealingsomehowtothecomparativenaturalnessofthe

additionfunction.Thefocusisonnaturalnessininterpretingtheattitudes

undergirdingthementalactivityofadding.Thevariouscasesofaddingare

supposedtoenjoygreaterobjectivesimilaritythanthevariouscasesofquadding.

Insum,attemptingtoruleoutscrambled-truth-in-a-modelbyappealingtoLewisian

naturalnessisproblematic.ThereisnostraightforwardextensionoftheLewisian

apparatustothecaseathand.

Letmeconcludethissectionbyconsideringonelastinterpretationist

responsetotheaboveargumentthatreliesontherolereferenceplaysintheoverall

explanationofwhysentenceshavetheirtruth-conditions.24Theresponsebuildson

anideafoundinSider2011:

FollowingJ.RobertG.Williams(2007,section2)wecanderivethedoctrineofreferencemagnetismfromawell-motivatedandmoregeneraldoctrineabouttheoreticalvirtue.Thisdoctrineistheonedefendedinsection3.1:explanatorytheoriesmustbecastinjoint-carvingterms.

AsIwilldevelopit,thecrucialassumptionofthederivationisthatreferenceisanexplanatoryrelation–onecanexplaincertainfactsbycitingwhatwordsreferto.Butifreferenceweregivenabizarreinterpretation,thenreference-involving“explanations”wouldnotinfactbeexplanatory,sincetheywouldbecastinbadlynon-joint-carving

24ThankstoMahradAlmotaharifordiscussionhere.

24

terms.(27-28)

Theinterpretationistwantstosaythatpartofthereasonwhy‘Thisisapieceof

fruit’hasitstruth-conditionsisthat‘this’referstotheapple.Thefactthat‘this’

referstotheappleplaysacertainroleintheexplanationofsemanticendowmentfor

thesentence.Butthisseemsnotsounderthedeviantinterpretationthathas‘this’

refertotheplanet.Forundertheproposedalternativeschemeitdoesnotmatter

what‘this’referstoaslongasthescramblermapsitontotheapple.Inthisway

truth-conditionsfor‘Thisisapieceoffruit’seeminsensitivetowhatever‘this’refers

to.Itwouldseemtoprecludereferencefromplayingitsrequisiteexplanatoryrole.

Thereplytotheinterpretationististhatundertheƒ-1-scrambled-truth-in-a-

modelschemethetruth-conditionsfor‘Thisisapieceoffruit’arejustassensitiveto

whatever‘this’happenstoreferto.Nothingprecludesthereferencerelationfrom

playingacriticalexplanatoryroleinwhysentenceshavetheirtruth-conditions.

Indeed,ifsententialtruthisasofƒ-1-scrambled-truth-in-a-model,thenthereference

relationthattakes‘this’totheplanetratherthantheapplehasasmuchofan

explanatoryroletoplayintheassociationofsentenceswiththeirtruth-conditions

asthereferencerelationthattakes‘this’totheapplehasifsententialtruthisasof

identity-scrambled-truth-in-a-model.Whethersententialtruthisonewaywhile

referenceisasofℑL,orsententialtruthisanotherwaywhilereferenceisasofℑʹ,

theallocationoftruth-conditionstosentenceswillbethesame(modulothe

ambiguityabouttruth).Sententialtruthbeingthesecondwaydoesnotpreclude

singularreference(asmodeledbyℑʹ)fromplayingitsexplanatoryroleifweassume

thatsententialtruthbeingthefirstwaydoesnotprecludesingularreference(as

25

modeledbyℑL)fromplayingitsexplanatoryrole.Inbothcasesthereferenceof

‘this’partiallyexplainswhythesentencehasitstruth-conditions.Theexplanatory

roleofreferenceundertheƒ-1-scrambled-truth-in-a-modelschemeisinnoway

diminished.

5. ProductivismRedux

Thingsaredifferentundertheauspicesofmetasemanticproductivism.

Productivismprioritizesreferenceovertruth.25Whatdeterminessemantic

significanceforsubsententialexpressionsareconditionssurroundingtheir

productionandmanipulationbyspeakersorwriters.Crucially,theirsignificanceis

fixedpriortoraisingandsettlingquestionsabouthowtheyshouldbeinterpreted.

ProductivismcanthusdirectlyruleoutmʹormL(orboth)asunintended–

whichevergetsantecedentlyproducedreferencewrong.Referenceisdetermined

bytheconditionssurroundingtheproductionofthereferringitems,whichallows

ustoselectinterpretationsasintendedanddiscardothersasunintended.26For

example,onareferential-intention-basedproductiviststory,‘this’asspokenwith

respecttoaparticularappledependsforitssemanticendowmentonthespeaker’s

25Itmightbethoughtthatthecontrastbetweenproductivismandinterpretationismdoesnotcoincidewithacontrastbetweenallottingexplanatoryprioritytosemanticendowmentforsubsententialexpressionsasopposedtoallottingittosemanticendowmentforfullsentences(asisthewontofbothDavidsonianandLewisianvarietiesofinterpretationism).Thismightbesoasapurelyconceptualmatter,butconsiderationsIofferinSimchen2013tellagainsttheoptionofaproductivistaccountthatallotsexplanatoryprioritytosemanticendowmentforfullsentences.AndfamiliarQuineanconsiderationsregardingtheevidentialsituationforinterpretationdeemaninterpretationistaccountthatallotsexplanatoryprioritytosemanticendowmentforsubsententialexpressionsunpromisingaswell.See,e.g.,Quine1968andDavidson1977.ThankstoEliDresnerandLizHarmanfordiscussion.26Eventhoughourfocushereisonsingularterms,thisisnolesstrueforpredicates.SeeSimchen2015forimportantramificationsofthispointforinterpretationingeneralandinlegalcontextsinparticular.

26

intentiontorefertotheapple,whichplausiblydepends,inturn,onacausal-

historicallinkoftherightsortobtainingbetweenspeakerandapple.Bycontrast,no

suchreferentialintentionsexisttobackup‘this’asproducedontherelevant

occasionreferringtoAlphaCentauriBbortothenumber17.27

Productivismalsohasresources,whichinterpretationismlacks,toexplain

directlywhysententialtruthisbettermodeledbytruth-in-a-model(thelimitcaseof

scrambled-truth-in-a-modelwherethescramblerisidentity)thanbyscrambled-

truth-in-a-modelwithnorestrictiononthescrambler.Sententialtruthislocalas

perproducedreferenceinawaythatscrambled-truth-in-a-modelwithno

restrictiononthescramblerignores.Localityinthiscontextshouldbethoughtofas

directdependence.If‘Thisisapieceoffruit’expressesatruth,thengiventhatthe

referenceof‘this’isalreadytotheappleinthestall,wenaturallyandintuitively

requirethatthetruthinquestionshouldturndirectlyonhowthingsstandwiththe

appleinquestion,ratherthanturndirectlyonhowthingsstandwithanindividual

otherthantheappleinstead.Inthelimitcaseofscrambled-truth-in-a-modelwhere

thescramblerisidentitythisintuitiverequirementoflocality-per-referenceontruth

isclearlyrespected.28Thisiswhyweconsidertruth-in-a-modelabettertheoretical

captureofsententialtruththanscrambled-truth-in-a-modelwithnorestrictionon

thescrambler.Undertheauspicesofproductivism,referenceissettledanddecides

27Howtothinkofreferentialintentionsandotherdereattitudesdirectedatnumbersisvexing.SuggestiveworkonthetopicwithinabroadlyproductivistoutlookcanbefoundinKripke1992.28Hereisacasethatviolatestheintuitiverequirementoflocality-per-referenceontruth(wheresuchlocalityis,onceagain,amatterofdirectdependence):Supposethattruthisdeterminedbymicrophysicalgoingsonandyetsingularreferenceisinvariablytomacrothings.Onsuchaview,whattrefersto–amacrothing–isnotidentical(butmerelycoincides,letussay)withthatwhosefallingunderφmakesφtcomeouttrue–amolecularlattice.Whilethereisasenseof‘local’accordingtowhichtruthinsuchacasestillabidesbytheintuitiverequirement–themacrothingandthelatticeareatthesameplaceatthesametime–thatisnotthesenserelevantfortherequirement.

27

theinterpretationofsingularterms.Wearetheninagoodpositiontoappealtoan

intuitiverequirementontruth–locality-per-reference–toargueagainstthe

suitabilityofscrambled-truth-in-a-model.Productivismisataclearadvantagehere.

Aswesaw,foraninterpretationistlocalityconsiderationsmightdeliverthewrong

result,giventhatreferenceisnotantecedentlysettled.Ifsingularreferenceisasof

ℑʹratherthanasofℑL,thenintheinterestofmaintainingthedistributionoftruth-

conditionsoversentencesthebettercaptureoftruthcouldeasilyviolatethe

locality-per-referencerequirement.Notsoundertheauspicesofproductivism.29

Letmeconcludebyhighlightingthesheerintuitiveplausibilityofa

productivistoutlookinmetasemanticsascomparedwithinterpretationism.

Metasemanticinterpretationismisasurprisingdoctrineeasilymistakenfora

benignanduncontroversialone.Thedoctrinemaintainsthatthesignificanceof

expressionsisconstitutedbytheirinterpretability,whetherbyanactuallinguistic

actororbyanidealizedversionthereof.Talkofconstitutionemphasizesthe

distinctlymetaphysicalflavoroftheview,thatitisametasemanticdoctrine

targetingthecreationofendowmentwithsignificance,theconditionssurrounding

itsemergence.Suchtalkservestodistinguishtheviewasdiscussedherefroma

mildandratherplausibledoctrineintheepistemologyofunderstanding.Therecan

benoseriousquestionastowhetherinterpretationplaysacrucialrolewhenit

comestosemanticuptake.Howelsemightwecometoappreciatethesignificance29Thecommittedinterpretationistmighttrytoarguethattheadvantagejustdiscernedforproductivismoverinterpretationismisillusory.Productivism,itmightbeclaimed,isjustanothertheoreticalcapture,ametasemantictheory,towhichreferencemagnetismappliesinturn.SomeLewisiansarecertainlydrawntosucha“justmoremetasemantictheory”moveagainstaproductivistorientation,shiftingfromreference-magnetisminmetasemanticstowhatSider(2011)callsmetametasemantics.Thematterdeservesaseparatediscussionthatcannotbeundertakenhere,butseeChapter1ofSimchenunpublished.

28

ofdemonstrativepronouns,say,ifnotbyconstructinginterpretations,understood

asempiricalconjecturesofasort?Theconjecturalaspectofsuchanendeavoris

broughtintosharpreliefincataphoriccontexts,caseswheretheaudiencehasto

keeptrackandbacktracktoearlierportionsofthediscourseinlightofwhat

happenslater.Thisallconcernstheepistemologyofunderstanding.Metasemantic

interpretationism,ontheotherhand,isnotanepistemologicaldoctrinebuta

metaphysicalone.Thequestionitsetsouttoanswerisnothowwecometoknow

whatexpressionsmean,but,rather,howitisthattheymeanwhattheydo,whatitis

thatconferssignificanceuponthem.Aspeakerbegins‘Shewasunsureatfirst’and

thenstopsshort,forwhateverreason,ofcompletingtheutterancewith‘butthen

Amymadeuphermindtoleave’.30Letusassumethattheutteranceissudden

enoughandoutofthebluetoleavetheaudienceinthedarkastothesignificanceof

‘she’.Twometasemanticquestionsimmediatelyarise.First,does‘she’asspokenon

thatoccasionsucceedinreferringtoanyoneinparticular?Second,assumingthat

‘she’doessucceedinthisway,whatmakesitthecasethatitstandsforAmyrather

thanforanyoneelse?Productivismtypicallygivesanaffirmativeanswertothefirst

question.Anditwouldtypicallyappeal,aspartofitsanswertothesecondquestion,

tofactsconcerningthehistoryofthespeakervis-à-visAmythatenterintothe

productionofthetokenontherelevantoccasion:forexample,thatitwasAmythat

thespeakerhadinmindastheintendedreferentfortheproducedtokenof‘she’.

Interpretationismmightgiveanaffirmativeanswertothefirstquestionaswell.But

asananswertothesecondquestiontheinterpretationistwouldappealtofeatures30Forfurtherdiscussionofsuchphenomenaandtheirrelevanceformetasemantics,seeSimchen2013.

29

ofthelargerdiscourseinwhichthetokenembedsandtheavailabilityofaglobal

interpretationofthatdiscoursethatmaximizesspeakerrationalityandtruthgiven

thecircumstancesofthespeaking.

Myaiminthispaperhasbeentodemonstratethatinterpretationismis

confrontedwithadistinctivechallengeconcerningsingularreferencethatthe

Lewisiandoctrineofreferencemagnetismisnotequippedtohandle.Theproblem

raisedpivotsonthenatureofbeingtrueforsentences.Butextendingreference

magnetismtothepredicate‘true’isoflittleuse.Itcanbeagreedonallsidesthat

‘true’asappliedtosentencesstandsforbeingtrueasappliedtosentences.The

threatofindeterminacydiscussedinthischapterproceedsbytargetingthenature

ofbeingtrueforsentences,notbytargetingtheconnectionbetweenthepredicate

‘true’andbeingtrue.Andreferencemagnetismissilentonthenatureofsentential

truth.

Thereremainsthepossibilityoffutureextensionsandelaborationsofthe

Lewisianoutlookinlightoftheabove,supplementingreferencemagnetismwitha

directengagementwiththenotionofsententialtruth.31Butproductivismalready

goesacertaindistancetowardsengagementwiththeissue,andwithoutthe

unnaturalsubjugationofreferencetotruth.Metasemanticproductivismiseasily

andnaturallyinformedbyanintuitiverequirementthattruthforsentencesbelocal-

per-reference.Language-worldrelationspertainingtosyntacticallycomplex

31Itmightbearguedonessentialistgroundsthatitisoftheverynatureofsententialtruththatitisbettermodeledbytruth-in-a-modelthanbyscrambled-truth-in-a-model.Butiftheforegoingiscorrect,metasemanticproductivismallowsustoavoidsuchanindependentheavy-dutyessentialistcommitmentregardingthenatureofsententialtruth.Undertheauspicesofproductivismtherequirementthattruthbelocal-per-referenceisnaturalandhighlyintuitivebycomparison.ThankstoGideonRosenfordiscussionhere.

30

expressionsofacertainsortturnouttodependonlanguage-worldrelations

pertainingtosyntacticallysimplerconstituentsratherthantheotherwayaround.

Butforinterpretationistreconstructionstothecontrary,thisisexactlyhowthings

shouldbe.

Ibeganthispaperbynotingtheobviousfactthatmetasemanticsisbeholden

tosemantics.Semanticsstudiesthewhatofsemanticendowmentwhile

metasemanticsstudiesthehow.Buthavingcomethisfarwecannowappreciate

thatatadifferentlevelsemanticscanbeseenasbeholdentometasemanticsaswell.

Throughthecomparisonwithscrambled-truth-in-a-model,truth-in-a-modelisseen

asanobviousnaturalchoiceforabasicsemanticnotion.32Thehistorical

metamathematicaldevelopmentoftruth-in-a-modelintheworkofTarski,Vaught,

andothers,shouldnotblindustothefactthatutilizingthenotionfornatural

languagesemanticsisparticularlycompelling–inawaythatutilizingscrambled-

truth-in-a-modelwithnorestrictiononthescramblercouldneverbe.Thisissoto

theextentthatmodel-theoreticsemanticsisalreadytacitlycommittedtothenatural

andintuitiverequirementthattruthbelocal-per-reference.Thislocality

requirement,Ihaveargued,sitsillwithametasemanticswherebywholesentences

andtheirtruth-conditionsareearlierintheorderofmetasemanticexplanationthan

thereferenceofsingularterms,thelatterbeingasubsequentabstraction.IfIam

right,model-theoreticnaturallanguagesemantics,withitsformalarticulationof

32Lestitbesuspectedthattheissueraisedinthischapterispeculiartomodel-theoreticsemanticswhileatruth-theoreticapproachissomehowimmunetoit,Iofferanadaptationofthesituationtoatruth-theoreticsettingintheAppendixbelow.

31

truth’slocality-per-reference,alreadyexhibitsatacitcommitmenttoanon-

interpretationistmetasemantics.

32

Appendix:ScrambledTruth

Weshowtheavailabilityofanotionofscrambledtruthinatruth-theoretic

settingbyconsideringafirst-orderextensionaltoylanguageLH.Interpretation

beginswithempiricalhypothesesaboutLHintheformofT-sentences.33Saywehave

amassedthefollowingT-sentences,amongothers:

− ⌜SOCRATESADAMOKELEV⌝istrueiffSocratesishumanorSocratesisadog.34

− ⌜FIDOLOADAM⌝istrueiffFidoisnothuman.

− ⌜MASHEHUADAMVELOKELEV⌝istrueiffsomethingishumanandnotadog.

− ⌜SOCRATESKELEVOMASHEHUADAMVEKELEV⌝istrueiffeitherSocratesisadogorsomethingisbothhumanandadog.

Ouraimistogiveadefinitionofthetruthpredicatethatentailsthese.Thefirst

interpretivetaskistodiscernsemanticallysignificantunitswithinthem.Saywe

concludethat⌜SOCARATES⌝and⌜FIDO⌝areterms,⌜ADAM⌝and⌜KELEV⌝are

one-placepredicates,andthelogicalparticlesareasfollows:the⌜MASHEHU⌝

constructionisexistentialquantification,the⌜VE⌝constructionisconjunction,the

⌜O⌝constructionisdisjunction,andthe⌜LO⌝constructionisnegation.Sothe

logicalformof⌜SOCRATESADAMOKELEV⌝isrenderedmoreexplicitby

unpackingthedisjunction:⌜SOCRATESADAMOSOCRATESKELEV⌝.Andthe

logicalformof⌜MASHEHUADAMVELOKELEV⌝isrenderedmoreexplicitby

33SeeDavidson1974.34Cornerquotesareutilizedthroughouttominimizeuse-mentionconfusion.

33

addingavariabletobeboundbythequantifier:⌜MASHEHUvvADAMVELOv

KELEV⌝.Wethusaddvariablestotheinventoryofterms,⌜xi⌝foreachi.

Nextwehavethesemanticclausesfordenotationofatermrelativetoa

sequenceandapplicationofapredicate.Foranysequencesandanyi,⌜xi⌝denotes

orelativetosiffoistheithmemberofs.Foranysequencesandnamen,ndenoteso

relativetosiffeithern=⌜SOCRATES⌝ando=Socrates,orelsen=⌜FIDO⌝and

o=Fido.Finally,foranypredicateP,PappliestooiffeitherP=⌜ADAM⌝andois

human,orelseP=⌜KELEV⌝andoisadog.

Nextcomesaninductivedefinitionofsatisfactionbyasequence.Forany

formulaFofLHandanysequencesdrawnfromthedomainUthatLHisusedtotalk

about,Fissatisfiedbysiffeither1.Fisanatomicformula⌜tP⌝wheretdenoteso

relativetosandPappliestoo;orelse2.Fisaformula⌜LOG⌝forsomeformulaG

andGisnotsatisfiedbys;orelse3.Fisaformula⌜GVEH⌝forsomeformulasG

andHandbothGandHaresatisfiedbys;orelse4.Fisaformula⌜GOH⌝and

eitherGissatisfiedbysorHissatisfiedbys;orelse5.Fisaformula⌜MASHEHUxi

G⌝whereGhas⌜xi⌝freeandthereisasequences*thatdiffersfromsinatmostthe

ithplacesuchthatGissatisfiedbys*.Finally:asentenceSofLHistrueiffforany

sequencesofU,Sissatisfiedbys.

Wenowdefinescrambledtruthasfollows.LetµbesomepermutationonU

suchthatµ(Socrates)=Fidoandµ(Fido)=Socrates.Foranysequencesandanyi,

⌜xi⌝scrambledlydenotesµ(o)relativetosiffoistheithmemberofs.Forany

sequencesandnamen,nscrambledlydenotesorelativetosiffeither

n=⌜SOCRATES⌝ando=Fido,orelsen=⌜FIDO⌝ando=Socrates.Foranypredicate

34

P,PappliestooiffeitherP=⌜ADAM⌝andoishuman,orelseP=⌜KELEV⌝andois

adog,asbefore.

Nextcomestheinductivedefinitionofscrambledsatisfactionbyasequence,

theonlydifferencefromsatisfactionbyasequencebeingthefirstclause:forany

termtandpredicateP,⌜tP⌝isscrambledlysatisfiedbysifftscrambledlydenoteso

relativetosandPappliestoµ–1(o).AsentenceSofLHisscrambledlytrueiffforany

sequencesofU,Sisscrambledlysatisfiedbys.

Claim:ForanysentenceSofLH,SistrueiffSisscrambledlytrue.

Theproofisobviousfromthedefinitionsbuttedious.Letusillustrate,however,

withrespecttoacoupleofsentences,firstanatomicsentenceandthenonethatis

syntacticallymorecomplex.

FirstweshowthatforanysequencesofU,⌜SOCRATESKELEV⌝issatisfied

bysiff⌜SOCRATESKELEV⌝isscrambledlysatisfiedbys.⌜SOCRATESKELEV⌝is

scrambledlysatisfiedbysiff⌜KELEV⌝appliestotheimageunderµ–1ofthe

scrambleddenotationof⌜SOCRATES⌝relativetos,i.e.theimageunderµ–1ofFido,

i.e.Socrates.So⌜SOCRATESKELEV⌝isscrambledlysatisfiedbysiffSocratesisa

dog,whichholdsiff⌜SOCRATESKELEV⌝issatisfiedbys.

NextweshowthatforanysofU,⌜MASHEHUx17x17ADAMVELOx17

KELEV⌝issatisfiedbysiff⌜MASHEHUx17x17ADAMVELOx17KELEV⌝is

scrambledlysatisfiedbys.First,ssatisfies⌜MASHEHUx17x17ADAMVELOx17

KELEV⌝iffthereisasequences*thatdiffersfromsinatmostthe17thplacesuch

that⌜x17ADAMVELOx17KELEV⌝issatisfiedbys*.Thelatterholdsiffboth⌜x17

ADAM⌝and⌜LOx17KELEV⌝aresatisfiedbys*,whichholdsiff⌜x17ADAM⌝is

35

satisfiedbys*and⌜x17KELEV⌝isnotsatisfiedbys*,whichholdsiffsomethinginU

ishumanandnotadog.WenowshowthatsomethinginUishumanandnotadog

iff⌜MASHEHUx17x17ADAMVELOx17KELEV⌝isscrambledlysatisfiedbys.

Suppose,first,thatsomethinginUishumanandnotadogandassumeforreductio

that⌜MASHEHUx17x17ADAMVELOx17KELEV⌝isnotscrambledlysatisfiedbys.

Thenforanysequencesʹthatdiffersfromsinatmostthe17thplace,⌜x17ADAMVE

LOx17KELEV⌝isnotscrambledlysatisfiedbysʹ.Soforanysuchsequencesʹ,either

⌜x17ADAM⌝isnotscrambledlysatisfiedbysʹ,orelse⌜LOx17KELEV⌝isnot

scrambledlysatisfiedbysʹsothat⌜x17KELEV⌝isscrambledlysatisfiedbysʹ.Sofor

anysuchsequencesʹ,either⌜ADAM⌝doesnotapplytotheimageunderµ–1ofthe

scrambleddenotationof⌜x17⌝relativetosʹ,whichisjusttheoccupantofthe17th

placeinsʹ,orelse⌜KELEV⌝appliestothatoccupant.Thisimpliesthateverything

inUiseithernothumanoradog,contradictingourassumptionthatsomethinginU

ishumanandnotadog.Therefore,ifsomethinginUishumanandnotadog,then

⌜MASHEHUx17x17ADAMVELOx17KELEV⌝isscrambledlysatisfiedbys.Finally,if

⌜MASHEHUx17x17ADAMVELOx17KELEV⌝isscrambledlysatisfiedbys,thenfor

somesequences**thatdiffersfromsinatmostthe17thplace,⌜x17ADAMVELOx17

KELEV⌝isscrambledlysatisfiedbys**,soboth⌜x17ADAM⌝and⌜LOx17KELEV⌝

arescrambledlysatisfiedbys**,so⌜x17ADAM⌝isscrambledlysatisfiedbys**and

⌜x17KELEV⌝isnotscrambledlysatisfiedbys**,sotheimageunderµ–1ofthe

scrambleddenotationof⌜x17⌝relativetos**–whichisjustthe17thmemberofs**

–ishumanandnotadog,andsosomethinginUishumanandnotadog.This

completesthedemonstrationthat⌜MASHEHUx17x17ADAMVELOx17KELEV⌝is

36

satisfiedbysiff⌜MASHEHUx17x17ADAMVELOx17KELEV⌝isscrambledlysatisfied

bys.

37

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