1 Introduction
Thisbookandthesecondvolumeareaboutbeliefandcounterfactuals,aswellastheirrelation.Beliefiscentraltoepistemology. Itoccurswhenanagentsuchasapersonor,perhaps,computer programholdssomethingtobetrue.Counterfactualsfigureprominentlyinmetaphysics.Theyare if-then claims,orconditionals, aboutwhatwouldhavebeenthecaseifcertainconditionshad obtained.OneaspectoftheirrelationthatIwillfocusonisa questionintheepistemologyofmetaphysics.
InthewayIwillengagewithit,epistemologyisanormative discipline.Iwillstudy how agents should believe,asopposedto what they do believe.Moreprecisely,Iwillstudyhowagents shouldbelieveonthehypothesisthattheyhavecertainendssuch asholdingtrueandinformativebeliefs.InthewayIwillengage withit,metaphysicsissubordinatetoepistemologyinsofaras metaphysicalthesesarenecessaryconditionsforthesatisfiability ofepistemologicalnorms.Givenaninstrumentalistunderstanding ofnormativity,thismeansthatmetaphysicalthesesarenecessary conditionsforthepossibilityofattainingendsfromepistemology.Howexactlythis“transcendental”metaphysicsissupposed toworkisacomplicatedmatter.Iwilltrytoexplainitinthis introduction.
Broadlyspeakingwecandistinguishfourapproachestounderstandingbelief.RepresentationalistssuchasFodor(1975)andMillikan(1984)claimthatholdingabeliefconsistsinthepossession ofamentalrepresentationwithapropositionalcontent.Dispositionalistsandtheirpredecessors,behaviorists,claimthatholding abeliefconsistsincertainactsordispositionstoact,suchasthe dispositiontoactasifthepropositionalcontentofthebeliefwas
BeliefandCounterfactuals:AStudyinMeans-EndPhilosophy.FranzHuber,OxfordUniversityPress. ©OxfordUniversityPress2021.DOI:10.1093/oso/9780199976119.003.0001
true.Aparticularversionthereofisinterpretationism(Davidson 1984).Accordingtoit,anagentholdsabeliefif,andonlyif,a charitableinterpretationoftheagent’sactsordispositionstoact requiresattributingthisbelieftotheagent.
Eachoftheseviewscanbecombinedwithafunctionalistunderstandingofbelief,butfunctionalismcanalsobedefendedonits own.Itsaysthatholdingabeliefconsistsintheagent’smental statestandingintherightcausalrelationstosensorystimuli,acts ordispositionstoact,andothermentalstatessuchasdesires. Whileconsideringbeliefstohavepropositionalcontentsisnot essentialtoallofthesepositions,theyallarecompatiblewithdoing so.Thesameistrueofprimitivism,whichpostulatesbeliefasa primitivementalstatethatdoesnotadmitoffurtheranalysis.These propositionalcontentshaveacertain“conceptualstructure.”The detailsofthisstructurewilldependonone’sviewofpropositions (Stalnaker1984),butminimallyitwillcomprisethestructureof logicandsettheory.Itisthisminimalconceptualstructurethat thepresentprojectpresupposes.
Anapproachtounderstandingbeliefthatthisbookrejectsis eliminativism(Churchland1981).Thelatterflatlydeniestheexistenceofbeliefs.Onthisview,beliefsareaconvenientfictionwe ascribetoourselvesandothersinoureverydayconceptionofthe mind,our“folkpsychology.”However,onthisview,themature sciencethatwilleventuallyreplacethisprescientificviewofthe mindwillholdthattherearenobeliefs.Everyotherpositionthat getsridofbelief—forinstance,byreplacingitwithprobabilistic degreeofbelief(Jeffrey1970)—isalsorejectedbythisbook.Itis anassumptionofthepresentprojectthattherearebeliefs,andthat anagentcanhaveendsthatareattainedif,andonlyif,sheholds certainbeliefs(whosepropositionalcontentsmay,butneednotbe requiredtobetrue).
Thereexistatleasttwokindsofconditionals(Adams1970; Briggs2019):indicativeconditionalsandcounterfactual,or subjunctive,conditionals(althoughnoteverybodyiswillingto identifycounterfactualandsubjunctiveconditionals;seeBennett
2003).Eachcanbeapproachedinatleasttwoways.Onone viewconditionalsexpresspropositionsthataretrueorfalse (Stalnaker1968;Lewis1973a).Onanotherviewconditionals donotexpresspropositionsthataretrueorfalse;theydonot havetruthvalues.Instead,theyexpresstheutteringorthinking agent’sinternalstateofmindratherthanapropositionaboutthe externalreality.Thelatter“expressivist”viewisprominentfor indicativeconditionals(Adams1975;Edgington1995),butsome alsoadoptitforcounterfactualconditionals,orcounterfactuals forshort(Edgington2008;Spohn2013;andSpohn2015,whose accounthasitthatcounterfactualsexpresspropositionsrelativeto theagent’sconditionalbeliefsandapartition).Inthisbookandthe secondvolumeIwillbeconcernedprimarilywithcounterfactuals. Indicativeconditionalswillplayarolemainlyinsofarasthey expressconditionalbeliefs.WhileIthinkthisistherightview, andIwillassumeitthroughoutthisbook,nottoomuchhingeson thisassumption:ifitwasfalse,Ijustwouldnotsaymuchabout indicativeconditionals.
Incontrasttothis,muchhingesontheassumptionthatcounterfactualsexpresspropositionsthataretrueorfalse.Thepresent projectassumescounterfactualstohavetruthvalues.However,I hastentoaddthatthisassumptiondoesnotbringwithitwhatis knownas“modalrealism”(Lewis1986a).
Afactualornon-modallanguageallowsonetosay that somethingisthecase:itisraining;thestreetsarewet.Amodallanguage orsystemofrepresentationpresupposesafactuallanguageand additionallyallowsonetosay how somethingfactualisthecase: itcouldberaining;probablyitis;ifitwas,thestreetswouldbe wet.Ofcourse,whatisamodalclaiminonelanguagemaybe afactualclaiminanother.Foreachfactuallanguagethereisat mostonelinguistic,conceptual,orrepresentationalentitythat accuratelyandmaximallyspecifically—thatis,ascompletelyas thefactuallanguageallows—describesorrepresentsreality.Iwill callthisentitythe actualfactual“world” forthefactuallanguage considered.
Theactualfactualworldisnotreal.Touseadangerouslyloaded term,itisan idea—amind-dependentconstructsomewhatsimilartoastatedescription(Carnap1947a).Besidestheactualfactualworldtherearemanymerelypossiblefactualworlds,that is,descriptionsorrepresentationsthatmaximallyspecificallybut inaccuratelyrepresentreality.Thesefactualworldsincludeevery descriptionorrepresentationthefactuallanguageorsystemof representationallowsfor.(Whichonestheseareisitselfsomething thatneedstobelearned,andwewillseeinchapter6howtodo so.)Factualworldsgiverisetofactualpropositionsthatwecan formallyrepresentassetsoffactualworlds.Somuchforafactual language.
Inamodallanguagewecansaymorethaninafactuallanguage. Inadditiontobeingabletosaythatitisnotraining,wecansaythat itcouldhavebeenraining,thatitprobablywasnot,butthat,ifit hadbeen,thestreetswouldhavebeenwet.Modalpropositionscan beformallyrepresentedassetsof modalworlds. Modalworldsconsistofafactualcomponent,whichisafactual world,plusonemodalcomponentforeachmodality.Inourcase themodalcomponentofamodalworldspecifieswhatcouldand wouldhavebeeninitsfactualcomponent.Themodalcomponent doesnot specifywhatcouldandwouldhavebeeninreality.Instead, itspecifieswhatcouldandwouldhavebeeninsomefactualworld, whichmayormaynotbetheactualfactualworld.Thismeans thatmodalpropositionsarenotaboutrealitybutaboutideas. Furthermore,foranyfactualworldthereisatmostonemodal componentthataccuratelyandmaximallyspecificallydescribes whatcouldandwouldhavebeeninthisfactualworld.Thismodal componentisdeterminedbythefactualworldandthelanguageor systemofrepresentation.Realityhasasayinthisonlyinsofarasit hasasayinwhichfactualworldisactual,andwhichlanguageone isspeaking.
Onthisview,factualandmodalworldsarerelativetoalanguage orsomeotherformofrepresentation.Theyarenotrealinany language-,thought-,orrepresentation-independentsense.Wetalk
andthinkaboutandconceptualizeandrepresentrealityintermsof whatisandwhatisnot,intermsofwhatcouldbe,andintermsof whatwouldhavebeen.Andwedosobecausewefindituseful.Yet these nots, coulds,and wouldsarenotpartofreality.Theybelong tothelanguageorsystemofrepresentationweusetodescribeor representreality,andthustotherealmofthemental.Asitsname suggests,theonlythingthatisreallyrealisreality.
Supposeitisneitherrainingnorsnowing,butthatitcould havebeenraining,andthatthestreetswouldhavebeenwetifit hadbeen.Onthepresentviewthereisnothinginrealitythatis describedby,correspondsto,ormakestruethese nots, ors, ands, coulds,and woulds.Theyaretiedtoourrepresentationofreality inthoughtandlanguage—andneedlesstosay,wecannotthink, letalonetalkaboutrealitywithoutsomerepresentation.Justas thinkingandtalkingaboutrealityaredependentonalanguage orsystemofrepresentation,soistruth.Thisiswhytheseclaims andthoughtscanhavetruthvalueswithouttherebeinganything inrealitythatmakesthemtrue.Whatistrueandwhatisnottrue, andwhatcouldbetrueandwhatwouldhavebeentruedependon realitybecausetheactualfactualworlddependsonreality.Yetwhat istrue also dependsonthelanguageorsystemofrepresentation thatthesepropositionsbelongto.Counterfactualsandothermodal claimscanexpresstruths,andnotmerelybeliefsorconditional beliefs,withouttherebeinganymodalrealitythatmakesthemtrue. Thereasonisthattheycanbeunderstoodasclaimsaboutideas.
Insum,thepresentview—whichIwillcallidealismaboutalethic modality,thatis,themodalitythatpertainstowhatistrue—isa thirdoptionbetweentherealistandexpressivistviews.Likethe expressivist,themodalidealistdoesnotlocatethemodalitiesin realitybutinthemind.Liketherealist,themodalidealistdoesnot interpretthemodalitiesasexpressingdoxasticstatesbutaspropositionsthataretrueorfalse.Ofcourse,whatcountsasaproposition isradicallydifferentontherealistandidealistaccounts.Modalities are ideas.However,theyarenotideaswithreality.Theyare our ideas. We conceptualizerealityintermsof couldsand woulds,and
wedosofortheexactsamereasonthatweconceptualizereality intermsof nots, ors,and ands:becausewefindituseful.Different beingswhoalsothinkortalkaboutrealitymayconceptualizeor representitindifferenttermsorideas—say,becausetheyhave differentabilitiesandlimitations,orbecausetheyhavedifferent ends.Thereisnorightorwronghere,justamoreorlessusefulfor variouspurposes.
Inchapter5Iwillarguethatsomethingsimilaristrueofdeontic modalitythatexpresseswhatshouldoroughttobe.Ratherthan correspondingtosomedeonticreality,itreducestowhatwemight desireandwhichmeans-endrelationshipsobtain.Whatisreal areourdesiresandbeliefs.Moreprecisely,whatisrealisour having desiresandourholding beliefs.Theirpropositionalcontents arenot.
Counterfactualsareaboutwhatwouldhavebeenthecaseif certainconditions—conditionsthatmaywellbecontrarytofact— hadobtained.Anagentbelievesapropositionif,andonlyif, sheholdsittobetrue(whichdoesnotimplythatshehasor shouldhavetheendofholdingtruebeliefs).Anagentbelievesa propositionconditionalonanother(orthesame)if,roughly,she holdstheformerpropositiontobetrueontheassumptionthat thelatteris.Chapter5willpresentanaccountofthenatureof conditionalbelief.Fornowitisenoughtodistinguishitfromthe agent’sbeliefinthecorrespondingcounterfactual(Leitgeb2007). Thereare,however,circumstancesinwhichaconditionalbeliefis relatedtothebeliefinthecorrespondingcounterfactual.Thisisso becausesomecounterfactualsimply singulardefaultconditionals, andbecauseaconditionalbeliefisrelatedtothebeliefinthe correspondingdefaultconditional.
Adefaultconditionalisan if-then claimaboutwhatis usually, normally,or typically thecaseifcertainconditionsobtain,where normalityisunderstoodinapurelydescriptivesense(Bear& Knobe2017).Normally,ifTweetyisabird,itcanfly.Thismeans Tweetycanflyinthemostnormalworldsinwhichitisabird.It ismorenormalforTweetytobeabirdandbeabletoflythanfor
ittobeabirdandnotbeabletofly.Oftendefaultconditionalsare inferredfrom genericdefaultrules suchasthatbirdscannormally fly,butpenguinscannot.Inthiscasethedefaultconditionalthat, normally,Tweetycanflyifitisabirdcanbeinferredonlyifone hasnoinformationaboutTweetythatcontradictstheclaimthatit canfly.Forinstance,onecannotinferthatitismorenormalfor Tweety-the-penguintobeabirdandbeabletoflythanforittobe abirdandnotbeabletofly.
Similarly,thedefaultrulethatpresidentsnormallydonottweet doesnotallowonetoconcludethatitismorenormalforTrump tobepresidentandnottweetthanitisforhimtobepresidentand tweet—justasthegenericinformationthat,statisticallyspeaking, presidentsarelikelymaledoesnotallowonetoconcludethat thefirstfemalepresidentislikelymale.Genericdefaultrulesand statisticalinformationareformulatedintermsofgenericvariables thataredefinedonapopulationofindividuals.Singulardefault conditionalsandclaimsaboutsingle-caseprobabilitiesareformulatedintermsofsingularvariables(Huber2018:ch.10).The questionofunderwhatconditionstheformerlicenseinferencesto thelatterisavariantofthereferenceclassproblem(ibid.).
Adefaultconditional α ⇒ γ istrueintheactualworldif,and onlyif, γ istrueinallpossibleworlds(i)inwhich α istrueand(ii) thataremostnormalfromthepointofviewoftheactualworld.We willseeinthisintroductionthatthereareseveralcounterfactuals. Someofthem(butnotall,asthesecounterfactualsmaycontradict eachother)implythecorrespondingdefaultconditionals.Tosee why,let α γ beacounterfactualofthiskind. α γ istrue intheactualworldif,andonlyif,(1) γ istrueinallpossible worldsinwhich α istrueandthataremostnormal;and—ifthe actualworldisitselflessnormalthanthemostnormalworldsin which α istrue—(2) γ istrueinallpossibleworldsinwhich α istrueandthatareatleastasnormalastheactualworld.The counterfactual α γ thussaysthat,normally—andevenifthings arenotnormal,aslongastheyarenotlessnormalthantheway thingsactuallyare—if α istrue,thensois γ.
Theactualworldmay,butneednotbeamongthepossible worldsthataremostnormalfromitspointofview.Ifitis,the counterfactual α γ istrueintheactualworldif,andonlyif, thedefaultconditional α ⇒ γ is.Otherwisethecounterfactualmay befalsewhilethedefaultconditionalistrue.However,theconverse casecannotoccurforacounterfactualofthiskind.
Idaiscertainthatitismorenormalforittobesunnyon Wednesdayandhertohavelunchintheparkthanforittobe sunnythatdayandhernottohavelunchinthepark.Thismay bebecausesheiscertainthatshewouldhavelunchintheparkifit wassunnyonWednesday.InthissituationIdashouldbelievethat shewillhavelunchintheparkontheassumptionthatitissunnyon Wednesday.Whenanagentiscertainofadefaultconditional,but no“overriding”information,sheshouldbelieveitsconsequent,or then-part,ontheassumptionthatitsantecedent,or if-part,istrue. Thisnormativeprinciplerelatingbeliefinadefaultconditional andconditionalbeliefisanapproximationofthe royalrule.Some counterfactualsimplythecorrespondingdefaultconditionals,and anagentmaybelieveadefaultconditionalbecauseshebelievesthe correspondingcounterfactual.Therefore,thisapproximationalso connectsbeliefinsomecounterfactualsandconditionalbelief.This connectionwillbeexploredinchapters7and10.
Theplanfortheremainderofthisbookandthesecondvolume isasfollows.Inchapter2IwillfirstdiscusswhichagentsIam focusingon,aswellaswhichcognitiveendsIamassumingthemto have.ThenIwilldescribehowthisrelatestoconditionalbeliefand beliefrevision.Chapter3willfirstpresenttheAGMtheoryofbelief revision(Alchourrón,Gärdenfors,&Makinson1985).ThenIwill focusontheproblemofiteratedbeliefrevision.Inchapter4Iwill showhowthisproblemfindsasolutioninrankingtheory,which wasintroducedinSpohn(1988)andismostcomprehensively discussedinSpohn(2012).
Chapter5willfirstanswerthequestionofwhyconditional beliefsshouldobeytherankingcalculus.ThenIwilldiscussthe underlyingviewofnormativity.Iwillconcludewithanoteonthe
logicofconditionalobligations,whichisidenticaltothelogicof conditionalbeliefs.Inchapter6Iwillconsidertwosmallapplicationsofrankingtheorytoproblemsinepistemologyandthephilosophyofscience.Thefirstexplainshowconceptscanbelearned inrankingtheory.Thisincludeslogicallearningasaspecialcase. Thesecondexplainshowconditionalinformationasconveyedby indicativeconditionalscanbelearned.Theseapplicationsillustrate howrankingtheorycanbefruitfullyappliedtotacklephilosophical problemsthathaveprovendifficultforBayesianism.Iwillconclude thischapterbydissolvingaworryraisedbyWeisberg(2015).
Inchapter7Iwillturntothelogicofcounterfactualsandtryto explainhowIthinkwecanandshouldengagewithsomephilosophicalproblems.Centraltothisviewofhowtophilosophize areaninstrumentalunderstandingofnormativity,orrationality, accordingtowhichoneoughttotakethemeanstoone’sends,and theuseofformalmethodsinestablishingmeans-endrelationships. Theviewismotivatedbyadeepmistrustofintuitions.WhileI maynotalwaysbeabletohidemyfrustrationswithsomeofthe morespeculativeversionsofintuition-basedphilosophy,myaim isaconstructiveone:topointoutonewayofengagingwithsome philosophicalproblemsthatdoesnotoverlyrelyonintuitions.
Philosophersinterestedincounterfactualsoftenconsideritdecisivewhichcounterfactualsintuitivelyseemtobetrue.However, subjectiveintuitionsvaryacrossphilosophersandwithinphilosophersacrosstime(Knobe&Nichols2008).Iwanttosupplement thisintuition-basedmethodologywithwhatmaybecalleda“principled”accountofthelogicofcounterfactuals.Specifically,Iwill proposeanormativeprinciple,theroyalrule,thatindirectlyrelates defaultconditionalsandcounterfactualstoconditionalbeliefs.
Thegeneralideabehindtheroyalruleisthat,absentfurther information,alethicmodalityconstrainsorguidesdoxasticmodality,thatis,themodalitythatpertainstobelief.Anapproximation ofitintermsofdefaultconditionalssaysthatanagentshould believeaproposition C ontheassumptionthatsheiscertainofthe proposition A,aswellasthedefaultconditionalthat,normally,if
A,then C,butnooverridinginformation.Theideaisthat,absent overridinginformation,defaultconditionalsconstrainorguide conditionalbeliefs.Moreprecisely,theroyalrulesaysthatone oughttodisbelieveaparticularpropositiontoaparticulargradeon theassumptionthatitis,inapurelydescriptivesense,abnormalto thisgradeforthispropositiontobetrue,butnostrongerorfurther information.
TheroyalruleisaqualitativeversionofLewis’s(1980)“principal principle”thatrelateschanceanddegreeofbelief.Thelatterprinciplesaysthatanagent’sinitialdegreeofbeliefinaproposition C oughttobeequalto x giventhatthechanceequals x that C istrue and,perhaps,further“admissible”informationbutnoinadmissibleinformation.Withthehelpofacoupleofassumptionsabout whatinformationisadmissible,theprincipalprincipleentailsthat chancesbehavehowanagent’sinitialconditionaldegreesofbelief oughttobehave.Now,initialdegreesofbelief—and,giventheratio formula,initialconditionaldegreesofbelief—oughttoobeythe probabilitycalculus.Witness,forinstance,theDutchBookargumentduetodeFinetti(1937)andRamsey(1926)(hereitistricky torelyonJoyce’s[1998;2009]gradationalaccuracyargument,as Joyce[2009:279]appealstotheprincipalprincipleindefenseofhis assumptionsaboutinaccuracy).Therefore,chancesdosoaswell.
Thus,probabilism—thatis,thethesisthatdegreesofbeliefought toobeytheprobabilitycalculus—andtheprincipalprinciplehave aconsequencethatisaboutchances,thatis,thatchancesareprobabilities.Whilethisclaimispresumablyalsoinagreementwith oursubjectiveintuitions,thereisnoneedtoappealtothelatterin ordertodefendthisclaim.Probabilismandtheprincipalprinciple dothisforus.Thisillustrateshowtwonormativeprinciplesfrom epistemologycanentailametaphysicalthesis.
Supposethat,inaddition,wecanjustifybothprobabilismand theprincipalprinciple.Accordingtoinstrumentalism,whatone oughttodoistakethemeanstoone’sends.Thus,tojustifya normativeprincipleistoshowittobeameanstoattainingsome endonemayhave.Probabilismcanperhapsbejustifiedbythe
DutchBookargument,andtheprincipalprinciplecanperhapsbe justifiedinsomeotherway(Pettigrew2013).Ifso,thethesisthat chancesareprobabilitiesisaconsequenceofprobabilismandthe principalprinciple,whichinturncanbejustifiedbybeingshownto bemeanstoattainingendsonemayhave.Intuitionsarecertainly usefulasheuristicsinarrivingatthesenormativeprinciplesand inconsideringvariousmetaphysicaltheses.However,atnopoint doesonehavetoappealtointuitionsinordertodefendthemetaphysicalthesis.
Theupshotofthiswayofengagingwithsomephilosophical problems—of means-endphilosophy—isthefollowing.Themetaphysicalthesisthatchancesareprobabilitiesisanecessaryconditionforthepossibilityofattainingcertainendsonemayhave. Giventhatonehastheseends,oneoughttosatisfythosenorms. Yetonecansatisfythosenormsonlyifthingsareacertainway. Means-endphilosophythustellsonewhatmetaphysicalthesesone iscommittedtobypursuingvariousends.
InthesamewayIwanttousetheroyalruleandthethesisthat beliefsoughttoobeytherankingcalculustoderivesomepropertiesofdescriptivenormality.Giventhetruthconditionsstated intheprecedingparagraphs,thesepropertiesdeterminesomeof thelogicalpostulatessatisfiedbydefaultconditionalsandcounterfactuals.Thesepostulatesareexpectedtoapproximatethelogical postulatesphilosophershaveproposedonthebasisofsubjective intuitions.However,wedonothavetorelyonthoseintuitions inordertosupportthesepostulates.Instead,weobtainthemas consequencesoftwonormativeprinciplesfromepistemologyplus assumptionsaboutthetruthconditionsofdefaultconditionalsand counterfactuals.
Thisisthesenseinwhichtheaccountofthelogicofcounterfactualswillbeprincipled.Ofcourse,tobeconvincedbythis means-endargumentoneneedstoaccepttheassumptionsmade, aswellaspursuetheendsthenormativeprinciplesaremeansto attaining.Thosewhodonotaregiveninformationaboutameansendrelationshipforwhichtheymayhavelittleornouse.
Inordertocarryoutthisargumentindetailthefollowing ingredientsareneeded.First,weneedatheoryofconditional beliefs.Spohn’s(1988)theoryofrankingfunctionswilltellus howconditionalbeliefsoughttobehave.Theconditionaltheory ofconditionalbelieffromchapter5willtelluswhattheyare. Second,weneedapreciseformulationofthenormativeprinciple thatrelatesdescriptivenormalitytoconditionalbelief.Wewillget thisintheformoftheroyalruleinchapter7.Third,weneedan argumentthatestablishesthethesisthatconditionalbeliefsshould obeytherankingcalculus.Thiswillbetheconsistencyargument fromchapter5.Finally,theveryprinciplerelatingdescriptive normalitytoconditionalbelief,theroyalrule,needstobejustified aswellbybeingshowntobeameanstoattaininganendonemay have.Thiswillbeattemptedinsection8.1.
Intheremainingsectionsofchapter8Iwillconsidertwosmall applicationsoftheresultingtheorytoproblemsinmetaphysicsand thephilosophyofscience.ThefirstapplicationconcernsLewis’s (1973b)definitionofcausationintermsofcounterfactuals.Itturns outtobeaspecialcaseofSpohn’s(2006a)definitionofcausationintermsofrankingfunctionsmodulotheinterpretationof thelatter.ThesecondapplicationconcernsaproblemforLewis’s (1979)“systemofweightsorpriorities”governingoverallsimilarity betweenpossibleworldsthatarisesfromanapplicationofArrow’s (1951)impossibilitytheorem.Ifirstlearnedofthisproblemfrom ThomasKroedelinKonstanzinJuly2009.Morreau(2010)raises it,too.Therelevantsection,8.3,reliesonjointworkwithThomas Kroedel(Kroedel&Huber2013).Theseapplicationsillustratehow rankingtheorycanbefruitfullyappliedtotacklephilosophical problemsthathaveprovendifficultforthesimilarityaccountof counterfactuals(Stalnaker1968;Lewis1973a).
Thegoalofchapter9istoshowthattherank-theoreticnormality accountofcounterfactualsisbettersuitedfortheorizingabout causalitythanthesimilarityaccountofcounterfactuals,aswellas thestructuralequationsframework(Spirtes,Glymour,&Scheines 2000;Pearl2009).Asmentioned,counterfactualsareclaimssuchas
thefollowing:ifIdahadnothadcoffeeinthemorning,shewould havebeentiredatnoon.Theyareaboutwhatwouldhavebeenthe case(Idawouldhavebeentiredatnoon),ifcertainconditionshad obtained(ifIdahadnothadcoffeeinthemorning).Assuggested bytheterm‘counterfactuals,’theseconditionsmaywellbecontrary tofact—infact,Idahadcoffeeinthemorning.Causalclaimsare claimsaboutonepropertyoreventbeinganeffectofanother propertyorevent.Ida’sbeingalertatnoonisaneffectofherhaving coffeeinthemorning.Inotherwords,herhavingcoffeeinthe morningcauses,orbringsabout,thatsheisalertatnoon.
Counterfactualsarecloselyrelatedtocausality(Collins,Hall,& Paul2004;Paul&Hall2013).Acausalclaimisoften(e.g.,inLewis 1973b;1979;2000)saidtobeshorthandforamorecomplicated claiminvolvingaspecificcounterfactual.ThecausalclaimthatIda’s beingalertatnoonisaneffectofherhavingcoffeeinthemorning isoftensaidtobeshorthandfor,oratleastcloselyrelatedto,the followingthreeclaimsessentiallyinvolvingaspecificcounterfactual.First,Idahadcoffeeinthemorning.Second,Idawasalertat noon.Afterall,onlypropertiesthatareinstantiatedoreventsthat takeplacecanbecausesoreffects.Third,the“causal”(orbetter: Briggs’s2012moregeneral“interventionist”)counterfactual:ifIda hadnothadcoffeeinthemorning,shewouldhavebeentiredat noon.
Thecausalcounterfactualis“forward-looking.”Itsantecedent isaboutthepotentialcause:whetherornotIdahadcoffee.Its consequentisaboutoneofitsallegedeffects:whetherornotIdawas alert.Theseforward-looking,causalcounterfactualsaretobeused inthestudyofcausality.However,thereareothercounterfactuals thatrelatetocausalityinadifferentandsometimesopposingway, andstillothersthatdonotrelatetocausalityatall.Forinstance, youmaywonderwhetherIdahadcoffee.Youfigure:ifIdahadnot beenalertatnoon,shewouldnothavehadcoffeeinthemorning. Thatis,youreasonfromtheabsenceofoneoftheallegedeffects back totheabsenceofthepotentialcause.Causalcounterfactuals reasonintheoppositedirectionfromthepotentialcause forward
tooneofitsallegedeffects.Theyholdfixedwhatis“causally upstream”:evenifIdahadnotbeenalertatnoon,shewould stillhavehadcoffeeinthemorning.Thiscausalcounterfactual contradictsthepreviouscounterfactual.Moreover,itisalsotrue thatifIdahadnotdrunkanything,shewould,trivially,alsonot havehadcoffee.However,thiscounterfactualisnotrelatedto causalityatall.
Thenon-causalcounterfactualsoftheformerkindarecalled “backtracking”counterfactuals,thoseofthelatterkind“spurious” (Menzies2008).Thequestioniswheretodrawthelinebetween causalcounterfactualsontheonehand,andbacktrackingand othernon-causalcounterfactualsontheother(Woodward2003).
Thestate-of-the-artrepresentationofcausalcounterfactualsare causalmodelswithstructuralequations(Haavelmo1943;Halpern &Pearl2005;Pearl2009;Spirtesetal.2000).However,structuralequationspresupposeratherthanprovideananswertothe questionofwheretodrawthelinebetweencausalandnon-causal counterfactuals.Theyalsodonotcaptureallaspectsofcausation (Hiddleston2005).Thelatterproblemhasledtothedevelopmentofso-called“extendedcausalmodels”(Halpern2008;2016; Halpern&Hitchcock2010;2013).Thesecontaintwoelements representingtwoseeminglydistinctmodalities.Thefirstelement arestructuralequationsthatrepresentthe“(causal)laws”ofthe model.Thesecondelementisarankingfunction(or,inlater versions,anorderingrelation)thatrepresentsnormality.
Onegoalofchapter9istoshowthatthesetwoseeminglydistinct modalitiescanbeunifiedintoonemodalitybyadoptingthetheory ofcounterfactualsfromchapter7.Itistobenoted,though,that normalityinextendedcausalmodelsisunderstoodtoincludenondescriptive,normativeelements(Hitchcock&Knobe2009).These areexplicitlyexcludedfromthewaynormalityisunderstoodhere. Theunificationwillbeachievedbyformulatingtwoconstraints. Theseallowustosubsumeextendedcausalmodelswiththeirtwo modalitiesunder“counterfactualmodels”thatcontainjusttheone modalityofdescriptivenormality.
Thetwoconstraintsturnouttobeformallypreciseversionsof Lewis’s(1979)“systemofweightsorpriorities”thatgovernsoverall similaritybetweenpossibleworlds.ThissystemisLewis’s(1979) answertothequestionofwheretodrawthelinebetweencausaland non-causalcounterfactuals.Itappealstothemodel-independent notionofa“lawofnature.”Thetwoconstraintsappealtothemodelrelativenotionofa“necessarilytruedefaultconditional.”Thelatter differsfromthenotionofalawofnature(Woodward2003:ch.6) andcorrespondstowhatisrepresentedbyastructuralequation. Menzies(2004)arguesthatsuchmodel-relativityisunavoidable.If so,thetwomodel-relativeconstraintsmightbeviewedasananswer tothequestionofwheretodrawthelinebetweencausalandnoncausalcounterfactuals.However,withoutameans-endargument forthisclaimIcanonlyrefrainfrommakingit.BothLewis’s(1979) answerandthetwoconstraintslocatethedifferencebetweencausal andnon-causalcounterfactualsnotintheirtruth-conditionsbutin whatisheldfixedindeterminingoverallsimilarityanddescriptive normality,respectively.Iwillassumethismuchtobecorrect.
Chapter10willbringtogethertheviewofconditionalbeliefs developedinchapters2–6andtheviewofcounterfactualsdevelopedinchapters7–9byfocusingonthequestionwhatoneshould believeaboutwhatwouldhavebeenthecase.Thiswillbedone byconsideringconditionsunderwhichdefaultconditionalsand counterfactualscanbetestedempirically.(ForthetimebeingI willbracketthatwhatis,strictlyspeaking,directlyaccessibleis restrictedtotheagent’sinternalstateofmindandexcludesthe externalreality.)
SupposeItellyouwhatIdahadforbreakfastMondaythrough Thursday,andwhethershewastiredatnoononthesedays.You willhavenodifficultyinferringthatIdawouldhavebeentired atnoononFriday,ifshehadnothadcoffeeonFridaymorning. Myinterestliesinidentifyingconditionsunderwhichonecan— withaparticularformofreliability—inferthetruthvaluesof counterfactualsfrom“empiricallyaccessible”information.Iwill dosobystatingaverysimpletheorem.Animplicationofthis
