Metasemantics and Singular Reference Ori Simchen University of … · 2015-11-14 · Metasemantics...
Transcript of Metasemantics and Singular Reference Ori Simchen University of … · 2015-11-14 · Metasemantics...
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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