Chalmers It is widely believed that for all or at least for all entertainable it is knowable a priori that actually It is even more widely believed that for all such it is knowable that actually There is a simple argument against th ID: 34515
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Premises(2)and(3)appeartobeinstancesofcoreprinciplesofthelogicsgoverningKandA:Ap!Apand(Kp!p).PerhapsonecandenythattheEnglishword`actually'satises(2),butitishardtodenythatthereisatechnicaltermthatworksthisway.Denying(3)appearstorequireallowingthattherecanbeknowledgeoffalsepropositions(althoughmoreonthislater).Premise(4)followsfromtwoprinciplesgoverningentertaining:entertainingapropositionrequiresentertainingitsconstituents,andknowingapropositionrequiresentertainingthatpropo-sition.Ifristrue,sothatno-oneentertainsq,thentherstprincipleentailsthatno-oneen-tertainsr$Ar(ofwhichqisaconstituent),andthesecondprinciplethenentailsthatno-oneknowsr$Ar.Someonemightobjecttotheseprinciplesbyholdingthatknowledgeisdisposi-tionalwhileentertainingisoccurrent,orthatentertainingisnotasubpropositionalnotion.Onecanstraightforwardlygetaroundtheseworriesbyreinterpreting`Ep'as`Someoneentertainsapropositionofwhichpisaproperorimproperconstituent',andreinterpreting`Kp'as`Someoneoccurrentlyknowsp',or`Someoneknowspwhileentertainingp'.TheconclusionfollowsfromthepremisesbyclassicallogicandtheweakmodallogicK(infact,byminimallogicandbytheversionofKonwhichtheoremsofminimallogicarenecessary).From(3)and(4),onecanderive(K(r$Ar)!((r$Ar)&:r)).From(1)and(2),onecanderive(K(r$Ar)!Ar).Fromthesetwoclaimsonecanderive(K(r$Ar)!(r&:r)),fromwhichtheconclusionfollows.Theoriginalversionoftheconclusionisthenegationofaninstanceofthekeythesisthatforallp,itisknowablethatp$Ap.Evenifwemakethemodicationsabove,themodiedconclusionthatitisnotoccurrentlyknowablebyhumansthatr$Arisnolessinteresting,asthestandardreasonsforholdingthatitisknowableapriorithatp$Aparealsoreasonsforholdingthatitisoccurrentlyknowablebyhumansthatp$Ap(atleastwhenthepropositionisentertainablebyhumans).Itisworthnotingthattherearealsoversionsoftheargumentthatdonotrelyonthenotionsofconstituencyorofentertaining.Theargumentrequiresonlyatruepropositionrthatsatises(4):thatis,suchthatrnecessitates:K(r$Ar).Forexample,ifonerejectsthenotionofconstituencybecauseonetakespropositionstobesetsofpossibleworlds,onecansimplytakertobeanytrueproposition(apairofworldsincludingtheactualworldandoneother,forexample)suchthat:Krholdsinallr-worlds.ThenassumingthatAristhenecessaryproposition,rwillsatisfy(4),andtheconclusionfollows.Anotherversionoftheargument,relevantforsomeonewhoacceptsconstituencybuthasdoubtsaboutentertaining,takes`Eq'tomean`Someoneknows(p$Ap)forsomepofwhich2 Giventhesurprisingconsequences,onemaywanttoexaminetheoptionsforrespondingtotheargumentinmoredetail.Anumberoftheavailableoptionsaretiedtodi erentavailableviewsofthesemanticsof`actually'andofthewayitbehavesinepistemicandmodalcontexts.Whatwemightcalltheface-valueviewof`actually'holdsthatthereisapropositionexpressedby`Ap'suchthat`KAp'and`Ap'aretruei thispropositionisknownornecessary(andlikewiseforother`A'-involvingsentences).Giventheface-valueview,theconclusion(5)followsdirectlyfromthestandardprinciplesabove(Ap!Ap,therecanbenoknowledgeoffalsepropositions)andtheexistenceofatruepropositionthatsatises(4).AparticularlyclearillustrationisprovidedbytheRussellianface-valueview,whichcombinestheface-valueviewwiththeclaimsthat`p'expressesaRussellianpropositionpandthat`Ap'expressestheRussellianpropositionp(@)holdingthatpistrueintheactualworld-state@.3IfristheRussellianproposition:Eq,whereqisaRussellianpropositionthatisnotactuallyentertained,thenitiseasytoseethatiftheRussellianpropositionr$r(@)isentertainedinaworld,itisfalseinthatworld.Sothepropositioncannotbe(occurrently)known,andgiventheface-valueview,(5)follows.TheRussellianface-valueviewallowsadiagnosisofthesurprisingconsequencesabove.Ifthisviewiscorrect,itispossibletousethesentence`r$Ar'toexpressknowledge.Wemightsaythatsomeoneknowsasentencewhentheyknowthepropositionitexpressesintheworldofknowledge(perhapsaspresentedundertheguiseofthesentence).Inthissense,itispossibletoknow`r$Ar'.Butifonedidso,inapossibleworldw,thesentencewouldexpressapropositionr$r(w)distinctfromthepropositionr$r(@)thatitactuallyexpresses.Onemightsaythatthesentence`r$Ar'issemanticallyfragile:thepropositionitexpressesdependsonwhetherspeakersattempttoknowwhetherthesentenceistrue.4Semanticfragilityyieldsanaturalexplanationoftheunknowabilityofthepropositioninquestion:onecouldknowthesentence,butifonedid,itwouldexpressadi erentproposition(thatis,apropositiondistinctfromthepropositionitactuallyexpresses).Itcanalsoexplainthefailureofclosureofknowabilityunderlogicalentailment:onecouldusethetheentailmenttoderivethesentence`p$Ap',but sentences,butwecanextendittopropositionsbysayingthataproofofapropositionpinasystemLisanabstractsequenceofinterpretedsentencessuchthatthesequenceisaproofinL(invirtueofthelogicalformofthesentences)ofasentencethatexpressesp.3Itisnotobviousjustwhatitistoknowapropositionabouttheactualworld@inanotherpossibleworld.Williamson(1987)raisesquestionsaboutthisnotioninrespondingtoEdgington(1985),whoinvokesthenotioninaddressingFitch'sparadoxofknowability.Soames(2007)givesanaccountonwhichsuchknowledgeinvolvesasortofcompletedescriptivespecicationof@.4 @inthisway.Ifoneweretoundergotheprocessonewoulddemonstratenot@butadi erentworld-statew.Onemighttherebycometoknowthepropositionp$p(w)apriori,butonewouldnottherebycometoknowthepropositionp$p(@)apriori.SoSoames'argumentfails.Assumingthatthisprocessistheonlywaytocometoknowsuchpropositionsapriori(whenpisnotitselfknowableapriori),thenthenaturalconclusionisthat(forsuchp),theRussellianpropositionp$p(@)isknowableapriorii itisknownapriori.SemanticfragilityisnotlimitedtoaRussellianviewofpropositions.Ifoneholdsanobject-involvingFregeanview,onwhichthepropositionexpressedbyasentenceisaFregeanpropositionwiththereferentsofsimpleexpressionsinthesentenceasconstituents,onewillalsobeconfrontedwiththeissueofsemanticfragility.Ifthisviewiscombinedwiththeviewthattheactualworld-stateispartoftheextensionof`actually',thensentencessuchas`r$Ar'willbesemanticallyfragile,justasontheRussellianview.Ifthisviewiscombinedwithaface-valuesemanticsfor`actually',thenitwillyieldconsequencesanalogoustothoseoftheRussellianface-valueview.6Ofcourse,thefactthatsemanticfragilityprovidesadiagnosisofthesurprisingconsequencesneednotmakethoseconsequenceseasiertoaccept.Onemightstillwanttoholdthatp$Apisalwaysknowableapriori,oratleastthatitisalwaysknowable.Todoso,oneneedsanalternativeviewofthesemanticsof`actually'.Oneclassofalternativeviewsholdsthatthesentencesinquestionarenotsemanticallyfragile,sothat`r$Ar'expressesthesamepropositioninallworlds.Forexample,onemightholdthat`actually'isaprimitiveoperator,orthatthesentencesinquestionexpresstheirprimaryintensions,orthat`Ap'expressesthesamepropositionas`p'.Buttoavoidtheconsequences,onewillstillbeleftwithadicultchoicebetweendenying(2)anddenying(3),andgiventhestandardprinciplesmentionedabove,onewillstillbeleftdenyingtheface-valueview.7Thenaturalupshotisthattoavoidtheconclusion,rejectingsemanticfragilityislessimportantthanrejectingtheface-valueview. 6Allthisappliestotheobject-involvingFregeanviewinChalmers(forthcoming),onwhichsentencesexpressenrichedpropositions:structuredtwo-dimensionalentitiesinvolvingbothprimaryintensionsandextensionsascon-stituents.Giventhat`r$Ar'expressesanenrichedpropositionwiththeactualworld@asaconstituentandgivenface-valuesemanticsformodalandepistemiccontexts,(5)follows.Topreservestandardtwo-dimensionalclaimsabouttheapriorityof`p$Ap'(e.g.DaviesandHumberstone1980),oneneedstoinvokenotionsofsententialandpropo-sitionalaprioritythatcomeapartfromaprioriknowabilityofaproposition(seeChalmersforthcoming,notes24and25).7Aviewthatrejectssemanticfragilityandholdsthatthesentence`Ap$p'isalwaystruewhenutteredwillprobablyholdthatthatApistrueataworldi pistruethere,andwillalmostcertainlyholdthisbiconditionalacross6 thatthereisathirdreadingof`actually'—perhapsthecanonicalphilosophicalreading–onwhich(2)istrueand(5)isfalse,sothat(3)isfalsealso.Iamsympathetictothepluralistviewmyself,butevenonthepluralistview,theexistenceofareadingof`actually'onwhichtheargumentissoundisenoughtoraisemanyoftheoriginalissues.Forexample,therearguablyremainsanintuitionthatforallp,thepropositionexpressedby`pi inthisveryworld-statep'istrivial,knowable,andknowableapriori.Ifso,thereremainsthequestionofhowtoreconcilethisintuitionwiththeargumentagainstit.Analternativewayofrespondingtotheargumentistoacceptitsconclusionwhileholdingontoaversionoftheoriginalthesisthatp$Apisalwaysknowable,byarguingthatthereisasenseof“knowable”inwhichapropositionmaybeknowableeventhoughitisnotmetaphysicallypossiblethatitbeknown.Oneversionofthisstrategyappealstoagentivepossibility(whatispossibleforanagent,wherethismightbeunderstoodassomethinginthevicinityofwhattheagenthasthecapacitytodo),holdingthatapropositionisknowablewhenitisagentivelypossibleforsomeonetoknowit,whiledenyingthatagentivepossibilityentailsmetaphysicalpossibility.9Thispositionfacesanobviouschallenge,however,inthattheoriginalargumentmightbereformulatedintermsofagentivepossibility,andthecaseforthefourkeypremisesremainsstrongwhentheyarereadthisway.Anotherattempttondadi erentsenseof“knowable”isinspiredbythetwosensesof“prov-able”discussedearlier.Accordingtothisproposal,apropositionisknowable(apriori)i thereexistsaconclusive(apriori)justicationforit.Itwouldtakesomeworktomakethisproposalprecise,butanaturalthoughtisthatajusticationisroughlyanalogoustoaproof:anabstractstructureofpropositionsandevidence,standinginrelationsofsupport,groundedinevidenceoratleastinknownorjustiedpropositions.Onecouldthensaythatanapriorijusticationisonegroundedonlyinnon-experientialevidenceorinpropositionsthatareknown/justiedapriori,andaconclusivejusticationisajusticationappropriateforknowledge.Ine ect,thisanalysisyieldsnonmodalnotionsofjustiability,knowability,andaprioritythataredistinctfromthemorefamiliarmodalnotions,andthatareinsteadanalogoustothestandard 9Fara(2010)developsastrategyofthissortinrespondingtoFitch'sparadox.Inasimilarspirit,onemightalsousetheproposalinthenextparagraphtorespondtoFitch'sparadox.OnecouldconsistentlyholdthatthereexistsaconclusivejusticationfortheFitchpropositionp&:Kp,invirtueofthereexistingseparateconclusivejusticationsforpand:Kp,althoughitisimpossibletousethisjusticationtoknowtheproposition.Insofarasthisnotionyieldsanonmodalnotionofknowabilityanalogoustothestandardnonmodalnotionofprovability,itmightalsoyieldasenseinwhichtheFitchpropositionisknowable.8 Hazen,A.1978.Theeliminabilityoftheactualityoperatorinpropositionalmodallogic.NotreDameJournalofFormalLogic19:617-22.Humberstone,I.L.1982.Scopeandsubjunctivity.Philosophia12:99-126.Soames,S.2007.Actually.ProceedingsoftheAristotelianSociety,SupplementaryVolume81:251-77.Williamson,T.1987.Ontheparadoxofknowability.Mind96:256-61.10