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IndeterminacyinCausation

EricSwanson

ericsw@umich.edu

Thisisn’tthefinalversionofthispaper;

pleaseconsulttheofficialversioninPhilosophicalQuarterly.

Abstract:Iarguethattherearesomecausalrelataforwhichitisindeterminatewhetheronecaused

theother.Positingindeterminacyincausationhelpsusdefendcontestedprinciplesinthelogicof

causationandmakespossiblenewwaysofthinkingaboutthetheoreticalimpactofsymmetriccausal

overdetermination.Iclosebydiscussingamendmentsofcurrenttheoriesofcausationthatwould

helpexplaincausalindeterminacy.

Keywords:causation,indeterminacy,counterfactuals,additivity,distributivity,overdetermination

Philosophersoftenassumethattheactualfactsprovidedeterminateanswerstoallthecausal

questionswemighthave.Iargueherethatthisassumptionisnotonlyunwarrantedbutfalse.Section

1offersexamplesofcausalstructuresthatgiveusreasontopositindeterminacyinthecausalfacts.

Accordingtotherightdiagnosesofthesecases,Iargue,therearesomecausalrelataforwhichitis

indeterminatewhetheronecausedtheother.Theconsequencesofpositingindeterminacyin

causationarewide-rangingandimportant.Insection2,Iarguethatindeterminacyincausationhelps

usseewhyacontestedprinciplegoverningtheadditionofcausesisinfactvalid.Insection3,Iuse

indeterminacyincausationtodefendaprinciplethatgovernsthedistributivityofcauses,drawingon

parallelsbetweenindeterminacyincausationandindeterminacyincounterfactualstoconstructone

kindoftheorythatcanpredictindeterminacyincausation.Section4developstheviewthat

symmetriccausaloverdeterminationgivesrisetoindeterminacyincausation,anddrawsoutsome

respectsinwhichthisviewishelpfulforethicsandforadvocatesofnon-reductiveontologies.Iclose

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bydiscussingsomewaysinwhichcurrentnon-counterfactualtheoriesofcausationcouldbe

amendedtocountenanceindeterminacyincausation.

1. ThePhenomenon

Thefollowingcaseillustratessomefeaturesofcausalindeterminacy.

THELONELYSUPERSTARS:Lastyear,AlplayedontheAngels,andBettyplayedontheBrewers.Neither

oftheirteamswonthechampionship;athirdteam—theCardinals—didinstead.Butthings

couldhavebeendifferent.Indeed,thingsverynearlyweredifferent:Alverynearlydecidedto

playfortheBrewers,andBettyverynearlydecidedtoplayfortheAngels.Neitherwouldever

playfortheCardinals.Soifthey’dbeenteammates,theymighthaveplayedfortheAngels,and

theymighthaveplayedfortheBrewers.Andiftheyhadbeenteammates,whethertheyboth

playedfortheAngelsorbothplayedfortheBrewers,theteamtheybothplayedonwouldhave

wonthechampionship.

Inthecaseasdescribed,AlandBetty’splayingondifferentteamswascausallyrelevanttothefact

thattheCardinalswonthechampionship.1Theirplayingondifferentteamswasalsocausally

relevanttothefactthatboththeAngelsandtheBrewerslost:ifAlandBettyhadbeenteammates,

oneofthoseteamswouldnothavelost.

It’snotsoobvioushowweshouldanswertwofurtherquestions:

1. WasAlandBetty’splayingondifferentteamscausallyrelevanttotheAngels’loss?

2. WasAlandBetty’splayingondifferentteamscausallyrelevanttotheBrewers’loss?

1Iuse‘causalrelevance’forthe“broadandnondiscriminatory”causalrelation(Lewis1973a:559)thatisthetargetof

mostmetaphysicians’theoriesofcausation.ForstylisticreasonsIsometimesalsouseotherterms(like‘cause’and‘causaldependence’)torefertothisrelationortoitsinverse.

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Answeringbothquestions‘no’lookswrong.Supposeweweretryingtogiveacausalexplanationfor

theAngels’loss.WewouldlikelyciteBetty’sdecisiontoplayfortheBrewersaspotentiallycausally

relevant.Similarly,wewouldlikelyciteAl’sdecisiontoplayfortheAngelsaspotentiallycausally

relevanttotheBrewers’loss.AlandBetty’splayingondifferentteamsmadeabigdifferencetothe

outcomeforeithertheAngelsortheBrewers.Butweshouldnotanswerbothquestions‘yes,’either.

AlandBetty’splayingondifferentteamsmadeadifferencetotheoutcomeforonlyoneofthe

teams—theonethatwouldhavewoniftheyhadplayedonthesameteam.So,forexample,itis

counterintuitivetosaythattheirplayingondifferentteamswascausallyrelevanttotheAngels’loss,

becauseevenifAlandBettyhadplayedonthesameteam,it’spossibletheAngelswouldhavelost

regardless.SimilarlyfortheBrewers:it’spossiblethattheywouldhavelostevenifAlandBetty

hadn’tplayedondifferentteams.Tobesure,wedon’thaveabasisforsayingwhichteamwouldhave

wonthechampionship,ifAlandBettyhadplayedonthesameteam.Butitwouldbeamistaketo

counttheirplayingondifferentteamsascausallyrelevanttobothteams’losses.Onlyoneoutcome

couldhavebeenaffectedbytheirplayingonthesameteam.

AmuchmoreattractiveoptionistosaythatitisindeterminatewhetherAlandBetty’splayingon

differentteamsiscausallyrelevanttothefactthattheAngelslost,andalsoindeterminatewhether

theirplayingondifferentteamsiscausallyrelevanttothefactthattheBrewerslost.Theactualfacts

donotsettleallofourcausalquestionsinthiscase,becausethosefactsdonotmaketheirplayingon

differentteamscausallyrelevanttoboththeAngels’lossandtheBrewers’loss,andalsodonotmake

theirplayingondifferentteamscausallyrelevanttoneithertheAngels’lossnortheBrewers’loss.All

thisnotwithstanding,AlandBetty’splayingondifferentteamsiscausallyrelevanttothefactthatthe

AngelsandtheBrewersbothlostthechampionship,becauseifthey’dplayedonthesameteam,the

AngelsortheBrewerswouldhavewon.

WhileTHELONELYSUPERSTARSsuggeststhatitcanbeindeterminatewhatcausedwhatwhenthe

causalrelataarefacts,onemightwonderwhethercausalindeterminacycanoccurwithothercausal

relata.Onthiswayofthinking,apparentcausalindeterminacyisatleastinpartduetothecausal

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relata,andfactsallowforakindofindeterminacyexcludedbyparticularslikeeventsandagents.2

ButaddingdetailstoTHELONELYSUPERSTARShelpsshowthatthisisn’tthecase.SupposethatAland

Bettyhadanargumentthatwascausallyrelevanttotheirdecisiontoplayondifferentteams.In

particular,supposethattheargument—anevent,notafact—causedAltoplayontheAngels,and

causedBettytoplayontheBrewers.Then,onmyview,itisindeterminatewhethertheargument

wascausallyrelevanttotheAngels’loss,andindeterminatewhethertheargumentwascausally

relevanttotheBrewers’loss,forreasonsanalogoustothosediscussedearlier.Supposefurtherthat

Carl—anagent,notaneventorfact—provokedtheargument.ThenitisindeterminatewhetherCarl

wascausallyrelevanttotheAngels’loss,andindeterminatewhetherhewascausallyrelevanttothe

Brewers’loss.Socausalindeterminacylookstobeindependentofourviewsaboutthecausalrelata.

IsthekindofindeterminacyatplayinTHELONELYSUPERSTARSandthesevariationsonit

metaphysical,semantic,orepistemic?Ifitisepistemic,thenourignorancealoneexplainswhyweare

reluctanttosayeitherthatAlandBetty’splayingondifferentteamsiscausallyrelevanttothe

Brewers’loss,orthatitisnotcausallyrelevanttotheirloss.Onsuchviewstheremustbesome

determinatefactofwhichweareignorant:itmustbeeitherdeterminatelytrueordeterminately

falsethatAlandBetty’splayingondifferentteamsiscausallyrelevanttotheBrewers’loss.To

sustainthislineoneneedsaverystrongnon-reductiveviewoncausation,accordingtowhichbrute

causalstructuremakesitthecasethattheAngels,say,weredeterminatelycausallyunaffectedbyAl

andBetty’splayingondifferentteams.3Sincewecanfreelyadddetailswhilepreservingthe

symmetrybetweenAlandBetty’scausalcontributions,suchviewswouldevenhavetoholdthatthe

causalfactsdonotsuperveneonthenon-causalfacts.4

Withoutarguingagainstanti-reductionismhere,Iproceedontheassumptionthatthe

indeterminacyinquestionismetaphysical,semantic,orsomecombinationofthetwo.(Itakethis

assumptiontobeextremelyplausible,butevencommittedanti-reductionistsshouldbeinterestedin

seeinghowthedialecticproceedsgiventheassumption.)Ifwethinkofthiskindofindeterminacyas

2Thankstoananonymousrefereeforpressingthispoint.3Alternatively,onecouldpositbrutecounterfactualfactsorstructure(asinHawthorne2005:404-5),andholdthatitis

thesuperveniencebaseforthecausalstructure.Iwon’targueagainstanti-reductionisttheoriesofcounterfactualshere.(Thankstoananonymousrefereefordiscussion.)

4Forcausalanti-reductionistviewsandarguments,seeArmstrong1983;Tooley1987;Woodward1990;andCarroll1994;fordiscussionseeCarroll2009andHall2006&2013:67-9.

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metaphysical,thenwewillsaythatincaseslikeTHELONELYSUPERSTARS,forsomecandethereisno

factofthematteraboutwhetherccausede.Ifwethinkofindeterminacyinthe‘causal’factsas

semantic,thenwewillsaythattherearemultiplepreciserelationsthat‘cause’andrelatedlocutions

coulddenote,giventhefactsabouthowdenotationsarefixed.Foronesetofsuchrelations,R1,Aland

Betty’splayingondifferentteamsbearsarelationinR1totheAngels’loss,andnottotheBrewers’

loss.Foranotherset,R2,AlandBetty’splayingondifferentteamsbearsarelationinR2tothe

Brewers’loss,andnottotheAngels’loss.Inclinationstothinkaboutcausationinamoreorless

robustlyrealistwaymightinclineatheoristtowardpositingmetaphysicalorsemantic

indeterminacy.Buttheupshotforthemetaphysicsofcausationissignificanteitherway,for

accordingtobothpositsthereisnorelationthatisdistinctivelyeligibletobethereferentof

‘causation.’

Bothkindsofindeterminacycanbemodeledinwaysthatallowfor‘precisifications’or

‘resolutions’ofindeterminacy,subjectconstraintsimposedbypenumbralconnections(Fine1975).

Inthemetaphysicalcase,wecanthinkoftheseprecisificationsasneither‘determinatelycorrect’nor

‘determinatelyincorrect’waysofrepresentinghowthingsare(Barnes&Williams2011:115).Inthe

semanticcase,wecanthinkoftheseprecisificationsasprovidingdenotationsfor‘cause’thatare,

again,consistentwiththefactsabouthowdenotationsarefixed(vanFraassen1966;Fine1975;

Keefe2000).Eitherwaytherewillbeconstraintsonhowthingsstandaccordingtothe

precisifications.Forexample,accordingtotheprecisificationsonwhich‘AlandBetty’splayingon

differentteamscausedtheAngels’loss’istrue,‘AlandBetty’splayingondifferentteamscausedthe

Brewers’loss’comesoutfalse.Thisisbecause‘AlandBetty’splayingondifferentteamscausedat

mostoneteam’sloss’isdeterminatelytrue,andsotrueaccordingtoeveryprecisification.These

constraintsonprecisificationsareimportantinpartbecausetheymakeavailablesubtle,easily

overlookedpositionsonthelogicofcausation,towhichInowturn.

2. CausalAdditivity

CarolinaSartorio(2006)arguesagainstthefollowingprinciple:

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CausalAdditivity:Ifccausede1,andccausede2,thenccausede1∧e2.

(Althoughsimilarprinciplescanbearticulatedforothercategoriesofcausalrelata,forsimplicityI

supposehenceforththatthecausalrelataareconjoinableanddisjoinablefactsandthatthereis

causationbyomission(followingSartorioamongmanyothers,andpaceAronson1971,Dowe2000,

andBeebee2004).)SartoriooffersthefollowingcaseasacounterexampletoCausalAdditivity:

BATTLEFIELD:IamatthebattlefieldandIseethatsomeofoursoldiersareabouttobe

slaughteredbytheenemy.Icouldsaveanyoneofthem,butonlyoneofthem(Ionly

haveonebulletleft).Icannotgetmyselftochoosewhichonetosavesotheyalldie.

(2006:374)

OnSartorio’sview,foreachsoldier,thefactthatIdidnotshootiscausallyrelevanttothefactthat

thatsoldierdied,becauseIcouldhavesavedanyoneofthesoldiers.Butifweread‘allofthose

deaths’collectively—notdistributively—thenmynotshootingisnotcausallyrelevanttoallofthose

soldiers’dying:‘althoughIcausedeachofthedeaths,Ididn’tcausetheirsum’(374).Thisisbecause

somesoldierswouldhavediedwhateverIdid;thefactthatsomedieiscausallyindependentofme.

IagreewithSartorio’sjudgmentthatIamnotresponsibleforthesoldiers’dyingconstrued

collectively.ButIthinkwedobettertosaythat,foreachsoldier,itisindeterminatewhetherIam

causallyrelevanttothefactthatthatsoliderdied.5Supposethatthefamilyandfriendsofonesoldier

saidthatIwascausallyresponsibleforthefactthatthatsoldierdied.Iwouldbewithinmyrightsto

contrastthesituationIwasin—onewhereIcouldnotpossiblysavemorethanonesoldier—witha

situationinwhichtherewasonlyonesoldierIcouldhavesaved,andforsomereasonIfailedtoact.

Inthelattersituation,Iamdeterminatelycausallyrelevanttothefactthatthesoldierdied.In

Sartorio’ssituation,Iamnot,sinceIcansaveatmostoneofthemanysoldiers.

ThisdiagnosisalsomakesSartorio’sexampleconsistentwithCausalAdditivity.Onmyview,itis

indeterminatewhetherccausede1,indeterminatewhetherccausede2,…,andindeterminate

whetherccauseden.Butitisdeterminatelyfalsethatccausede1,e2,…,anden.Eventhoughforeach

5SaraBernsteinarguesindependentlyforasimilarconclusioninherforthcoming,focusingonomissionsandcausal

proportionalityassourcesofcausalindeterminacy.

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evente1,e2,…,en,thereissomeprecisificationaccordingtowhichccausedthatevent,thereisno

precisificationaccordingtowhichccausedalltheeventse1,e2,…,en.Soalthoughtheantecedentofa

substitutioninstanceofCausalAdditivityisindeterminate,andtheconsequentfalse,thereisno

precisificationaccordingtowhichtheantecedentistrueandtheconsequentfalse.Sartorio’scaseis

thusnotacounterexampletoCausalAdditivity.

Sartoriolaterarguesthat‘[i]tisagoodthingthatAdditivityfailswhenitdoes’(380)onthe

groundsthatifAdditivitydidnotfail,eachoneofuswouldbecausallyrelevantnotonlyto‘the

individualdeathsofpeopleindistantplaces’butalsoto‘allthosedeathstakencollectively’(384).But

onmyview,again,whatIdoisnotdeterminatelycausallyrelevanttothefactthatanyparticular

distantpersondies,becauseIcouldnotpossiblysavethecollectiveconsistingofallthepeoplewho

wouldbesavedifIweretointervene.Rather,foreachofthosedistantpeople,itisindeterminate

whetherwhatIdoiscausallyrelevanttothefactthatthatpersondiesinthewaythattheydo.And,

again,thewaysinwhichwhatIdoisindeterminatelycausallyrelevanttothosefactsdonotmakeme

responsiblefortheallthedeathstakencollectively.

RobertaBallarinarguesforanotherwaytosaveCausalAdditivity.OnBallarin’sapproach,there

aredisjunctiveeffects,where‘thoughaneventorfact,C,isneitheracauseofaneffect,E1,noracause

ofadistincteffect,E2,itisnonethelessacauseofthedisjunctiveeffect(E1orE2)’(2014:22).In

Sartorio’sBATTLEFIELD,Ballarinholdsthat‘youcauseoneofthesoldierstodie,butnoparticular

soldierissuchthatyoucausehisdeath….Thisiscausationofamerelydisjunctiveeffect,wherea

disjunctiveeffect,butnoneofitsdisjuncts,hasbeencaused’(27).BallarinthuspreservesAdditivity

bynottriggeringit:ifforeachsoldier,Iamdeterminatelynotcausallyrelevanttothefactthatthat

soldierdies,thenthere’snointerestingsumofmyrelevantcausalresponsibilitiestospeakofinthe

firstplace.

TherearetwomaincomponentstoBallarin’sargumentinfavorofcountenancingdisjunctive

effects.Ontheonehand,sheisconcernedtopreserveplausibleprinciplesinthelogicofcausation—

CausalAdditivityandCausalDistributivity,whichIdiscussinthenextsectionofthispaper.

Appealingtoindeterminacyincausationgivesusanotherwaytopreservethoseprinciples.Onthe

otherhand,Ballarindrawsanalogiesbetweencausationandthedenotationsofintensionaltransitive

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verbs:‘thereareessentiallydisjunctiveeffectsinthesamesenseinwhichthereareessentially

disjunctiveobjectsofbelieving,wanting,andowing,butnotofmeeting,kicking,andkissing’(23).6

Butthedenotationsofintensionaltransitiveverbshavemanypropertiesnotsharedbycausation.7So

it’snotclearthatweshouldtakeBallarin’sanalogyverystrictly—thatis,it’snotclearthatweshould

seetheanalogyasgivinguspositivereasonstocountenancedisjunctiveeffects.Perhapsit’sbetter

seenasacorrectivetothethoughtthatdisjunctiveeffectsare‘anewkindofspookyentity,merely

disjunctivethings’(34).Theanalogyhelpsusseethattheyarenospookierthanthe‘thingsweowe’

whenweowesomeoneapennybutnoparticularpenny.Soconstrued,Ballarindoesn’tofferpositive

argumentsforherviewoverviewslikemine.Moreover,Ballarin’saccounthassomecounterintuitive

consequences.Forexample,inTHELONELYSUPERSTARS,Ballarin’saccountwouldmakeit

determinatelyfalsethatAlandBetty’splayingondifferentteamswascausallyrelevanttotheAngels’

loss.SoacompletecausalexplanationofthatlosswoulddeterminatelynotincludethefactthatAl

andBettyplayedondifferentteams.Onmyaccount,bycontrast,wecansaythatacompletecausal

explanationoftheAngels’losswouldcitethefactthatit’sindeterminatewhetherAlandBetty’s

playingondifferentteamswascausallyrelevanttoit.Withappropriateattentiontopenumbral

connections(Fine1975),thisallowsustoavoidcontradictingtheplausibleprinciplethatthe

conjunctionofacompletecausalexplanationofϕandacompletecausalexplanationofψisa

completecausalexplanationofϕ∧ψ.

3. CausalDistributivity

Ballarinalsoarguesthaton‘theclassicalLewisiancounterfactualaccountofcausation,’in

BATTLEFIELDIam‘acauseofthebigeventthatisthesumofallthreedeaths,withoutbeingacauseof

anyofthecomponentdeaths’(32–3).Andso,shecontends,Lewis’s1973analysisofcausation

invalidates

6Asarulesemanticsforintensionaltransitiveverbsdonotappealto“disjunctiveobjects,”dueinparttoskepticismabout

theexistenceofdisjunctiveobjects(see,e.g.Lewis1970:218–9andWright2002:424).Foradetailedapplicationanddefenseofdisjunctiveobjects,seeAkiba2015.

7Fordiscussionofpropertiesofintensionaltransitiveverbssee,e.g.Moltmann1997.

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CausalDistributivity:Ifccausede1ande2,thenccausede1orccausede2.

Inalimitedsense,however,thisisunfairtoLewis,becauseifwesupplementLewis’sanalysisof

causationwithRobertStalnaker’ssemanticsforcounterfactuals(1968;1980),theresultingtotal

theorypredictsindeterminacyincausationinsuchawaythatwevalidateCausalDistributivity.

ToseetherelevantcontrastsbetweenLewis’sandStalnaker’stheoriesofcounterfactuals,

considerQuine’sclassicBizet/Verdicounterfactuals(1950:15):

(1) IfBizetandVerdihadbeencompatriots,BizetmighthavebeenItalian.

(2) IfBizetandVerdihadbeencompatriots,VerdimighthavebeenFrench.

LewisandStalnakeragreethat(1)and(2)arebothtrue.Andtheyalsoagreethat(3)istrue.

(3) IfBizetandVerdihadbeencompatriots,BizetwouldhavebeenItalianorVerdiwould

havebeenFrench.

Buttheydisagreeabout(4)and(5).

(4) IfBizetandVerdihadbeencompatriots,BizetwouldhavebeenItalian.

(5) IfBizetandVerdihadbeencompatriots,VerdiwouldhavebeenFrench.

Lewisholdsthattheyarebothfalse(1973:80);Stalnakerholdsthattheyarebothindeterminate—

‘neithertruenorfalse’—dueto‘indeterminacyinthelanguage…evenafterallthefactsarein’(1980:

101).Lewis’scommitmenttotheirfalsityisadirectresultofthetruthof(1)and(2)andhis

commitmentto

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CounterfactualDuality:‘Ifithadbeenthatϕ,itmighthavebeenthat ψ’istrueiff‘Ifithadbeenthat

ϕ,itwouldhavebeenthat¬ψ’isfalse(Lewis1973b:80–1;otheradvocatesincludeBigelow&

Pargetter1990:103;Bennett2003:192;andHájek2009).

GivenCounterfactualDuality,inotherwords,thetruthof(1)makes(4)false,andthetruthof(2)

makes(5)falseaswell.StalnakerrejectsCounterfactualDuality,andendorsesprinciplesinthelogic

ofcounterfactualsthatLewishastoreject—mostimportantlyforourpurposes,

CounterfactualDistributivity:ϕ⟥→(ψ∨χ)⊧(ϕ⟥→ψ)∨(ϕ⟥→χ)8

Thesedifferentapproachestocounterfactualsmakeallthedifferencewhenweconsider

Lewis’s1973analysisofcausation.Onthatanalysis,causationistheancestralofthe‘causal

dependence’relation,whereevente‘dependscausally’onadistincteventciffcandeoccurandifc

hadnotoccurred,ewouldnothaveoccurred.9IfwecombinethistheorywithLewis’stheoryof

counterfactuals—inparticular,withLewis’sendorsementofCounterfactualDuality—thenwe

predict,asBallarinargues,thatfornosoldierinBATTLEFIELDaremyactionscausallyrelevanttothe

factthatthatsoldierdied,althoughmyactionsarerelevanttothefactthatallthesoldiersdied.

Similarly,inTHELONELYSUPERSTARSwepredictthatthefactthatAlandBettyplayedondifferent

teamsisnotcausallyrelevanttothefactthattheAngelslost,andalsoisnotcausallyrelevanttothe

factthattheBrewerslost,althoughitiscausallyrelevanttothefactthattheAngelsandBrewerslost,

takencollectively.ThuseitherofthesecaseswouldconstituteacounterexampletoCausal

Distributivity.

Lewis’s1973analysisofcausationvalidatesCausalDistributivity,however,ifwe

supplementitwithStalnaker’ssemanticsforcounterfactuals,oranyotherplausiblesemanticsfor

counterfactualsthatvalidatesCounterfactualDistributivity.

8Thisisaxiom5inStalnaker’saxiomatizationofhislogicofcounterfactuals,C2(1968:48).9ForbroadlysimilarapproachesseeLyon1967andthetheoryof“dependence”inHall2004.

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Proof.Supposethatciscausallyrelevanttod∧e.ThenbyLewis’s1973theoryofcausation,ifchad

beenfalse,d∧ewouldhavebeenfalse.Soifchadbeenfalse,dwouldhavebeenfalseorewould

havebeenfalse.GivenCounterfactualDistributivity,itfollowsthateither(i)ifchadbeenfalse,d

wouldhavebeenfalse,or(ii)ifchadbeenfalse,ewouldhavebeenfalse.AndbyLewis’s1973theory

ofcausation,itfollowsthateither(i)ciscausallyrelevanttodor(ii)ciscausallyrelevanttoe.

Thisdoesnotmeanthatifciscausallyrelevanttod∧ethenwehavethetruthof‘ciscausally

relevanttod’orthetruthof‘ciscausallyrelevanttoe.’Whatwehave,rather,isthetruthoftheir

disjunction.Theclaimsmaybothbeindeterminate,buttheywillbeindeterminateinsuchawaythat

theirdisjunctionistrue(justasitmaybeindeterminatewhetherthisleafisgreen,andtruethatthe

leafiseithergreenornotgreen).

ThisapproachissimilartoStalnaker’sresponsetoanargumentthatLewisoffersinsupportof

CounterfactualDuality.Lewisasksustosupposethattherewasnopennyinmypocket,andthatI

didn’tlookinmypocket.Then,Lewissays,(6)‘isplainlyfalse’(1973:80).

(6) IfIhadlooked,Imighthavefoundapenny.

Lewisarguesthatanysemanticsfor‘might’counterfactualsonwhichCounterfactualDualityis

invalidwillpredictthat(6)istrue.StalnakercapturesLewis’sreadingof(6)byholdingthatits

‘might’hasa‘quasi-epistemicreading,’relativeto‘whatwouldbecompatiblewith[myknowledge]if

Iknewalltherelevantfacts’(1980:101).IfIknewalltherelevantfacts,Iwouldsaythatitcouldn’tbe

thatifIhadlooked,Iwouldhavefoundapenny—or,equivalentlyonStalnaker’sapproach—thatitis

falsethatifIhadlooked,I(quasi-epistemically)mighthavefoundapenny.

Stalnaker’sapproachdoesnotvalidateCounterfactualDualitybecauseStalnakermaintainsthat

‘Ifthereissomeindeterminacyinthelanguage,therewillstillremainsomedifferentpossibilities,

evenafterallthefactsarein,andso[quasi-epistemic]possibilitywillnotcollapseintotruth.’For

example,thereisenoughindeterminacyinthelanguagethatboth(4)and(5)areneithertruenor

falseevenrelativeto‘whatwouldbecompatiblewith[myknowledge]ifIknewalltherelevantfacts.’

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ThisishowStalnakermanagesto‘agreewithLewis’saccountthatIfA,itmightbethatBistrueifand

onlyifIfA,itwouldbethatnot-Bisnottrue’(101)whiledenyingCounterfactualDuality:some

‘would’counterfactualsareneithertruenorfalsealthoughthe‘might’counterfactualsthatareprima

faciedualtothemaretrue.IfweadoptStalnaker’ssemanticsforcounterfactuals,wecansaythatthe

indeterminate(4)and(5)areanalogoustotheindeterminate(7)and(8):

(4) IfBizetandVerdihadbeencompatriots,BizetwouldhavebeenItalian.

(5) IfBizetandVerdihadbeencompatriots,VerdiwouldhavebeenFrench.

(7) IfAlandBettyhadbeenteammates,theywouldhaveplayedfortheAngels.

(8) IfAlandBettyhadbeenteammates,theywouldhaveplayedfortheBrewers.

ThisiswhatallowsustosaythatitisindeterminatewhetherAlandBetty’splayingfordifferent

teamsiscausallyrelevanttothefactthattheAngelslost,andthatitisindeterminatewhetherAland

Betty’splayingfordifferentteamsiscausallyrelevanttothefactthattheBrewerslost,butthatitis

truesimpliciterthatAlandBetty’splayingfordifferentteamsiscausallyrelevanttothefactthatthe

AngelsandtheBrewerslost.

AtthispointLewis,andmanysympatheticwithhisviewsoncounterfactuals,mightarguethat

Stalnaker’ssemanticsreliesonanobjectionableprinciple:

TheLimitAssumption:Foreverypossibleworldiandnon-emptypropositionA,thereisatleast

oneA-worldminimallydifferentfromi(Stalnaker1980:89;seealsoPollock1976:18–20;

Herzberger1979;Lewis1981:228;andWarmbrōd1982).

AsLewisputshiscomplaint,‘wehavenorighttoassumethattherealwaysareasmallestantecedent-

permittingsphereand,withinit,asetofclosestantecedent-worlds’(1973:20).Fortunatelyitis

possibletoreconcileStalnaker’ssemanticswithfailuresofthelimitassumption,byappealingto

orderingsupervaluationism,anextensionoftraditionalsupervaluationism(Swanson2012;2014).

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WecantherebysecurethevalidityofCausalDistributivity,givenacounterfactualtheoryof

causation.10

Orderingsupervaluationismsubsumestraditionalsupervaluationism,handlingnotonlycasesin

whichtherearemultiple‘tied-for-best’precisifications,butalsocasesinwhichforeach

precisification,anotherisbetter.Intuitively—andputtingthepointintermsofsemantic

indeterminacyforthesakeofitsfamiliarity—ifasweconsiderbetterandbetterprecisificationsofa

sentence,weeventuallycometoaboundarywithinwhichalltheprecisificationsaretrue,thenwe

canabstractawayfromthecompetitionbetweenprecisifications,andfromthedifferencesbetween

thosecompetingprecisifications,andsaythatthesentenceisorderingsupertrue.Thisisnotso

differentfromtheintuitivethoughtbehindtraditionalsupervaluationism:ifasentenceistrueonall

‘admissible’precisifications,thenwecanabstractawayfromthecompetitionbetween

precisifications,andfromthedifferencesbetweenthoseprecisifications,andsaythatthesentenceis

supertrue(vanFraassen1966:486–7;Fine1975:278).Stalnakerdeploystraditional

supervaluationismtohandlecasesinwhichmultipleantecedentworldsareequallyclosetothe

worldofevaluation:heseestraditionalsupervaluationismasapost-semanticmechanismwithwhich

wecan‘reconcilethedeterminacyofabstractsemantictheorywiththeindeterminacyofrealistic

application’(1980:89).ThisapproachallowsStalnakertopreservehislogicforcounterfactualseven

whentherearemultipleequallycloseantecedentworlds.

Orderingsupervaluationismservesexactlythesamepurpose,butwithabroaderrangeof

application.WecangiveStalnaker’ssemanticsforcounterfactuals,andhandleviolationsofthelimit

assumption(anduniquenessassumption)inthepost-semantics,viaorderingsupervaluationism.

Whenforagivencounterfactualtherearenoantecedentworldsthatareclosesttotheworldof

evaluation,weineffectaskwhether,asweconsiderantecedentworldsthatcomecloserandcloserto

theworldofevaluation,weeventuallycometoaboundarywithinwhichalltheantecedentworlds

arealsoconsequentworlds.Ifso,thecounterfactualisorderingsupertrue.Ifasweconsider

antecedentworldsthatcomecloserandclosertotheworldofevaluation,weeventuallycometoa

10TheoriesaccordingtowhichcounterfactualdependenceissufficientforcausationwillalsosecurethevalidityofCausalDistributivity,aslongastheyconnectindeterminacyincounterfactualstoindeterminacyincausationintheappropriateways.

14

boundarywithinwhichalltheantecedentworldsareworldsinwhichtheconsequentisfalse,then

thecounterfactualisorderingsuperfalse.Otherwiseitisindeterminate.Moreprecisely:the

counterfactualisinterpretedrepeatedly,relativetoselectionfunctionsthatyieldworldsthatare

closerandclosertotheworldofevaluation.Iftheselectionfunctionassociatedwithprecisificationa

yieldsaworldthatisclosertotheworldofevaluationthantheselectionfunctionassociatedwith

precisificationb,thenaisabetterprecisificationofthecounterfactualthanbis.Thecounterfactualis

orderingsupertrueiffthereissomeprecisificationofthecounterfactual,i,suchthatthe

counterfactualistrueaccordingtoalltheprecisificationsthatareatleastasgoodasi.Itisordering

superfalseiffthereissomeprecisificationofthecounterfactual,i,suchthatthecounterfactualisfalse

accordingtoalltheprecisificationsatleastasgoodasi.And,again,itisindeterminateotherwise.

WhatisattractiveaboutthisapproachisthatitnotonlyletsusgetStalnaker’slogicfor

counterfactualswhentherearemultiple‘tied-for-closest’antecedentworlds—italsoletsusget

Stalnaker’slogicwhenforeveryantecedentworldanotheriscloser(forfurtherdiscussion,see

Swanson2012).Inparticular,wegettheorderingsupervalidityofCounterfactualDistributivity,

repeatedbelow.

CounterfactualDistributivity:ϕ⟥→(ψ∨χ)⊧(ϕ⟥→ψ)∨(ϕ⟥→χ)

Lewis’stheoryofcounterfactualsdoesnotvalidateCounterfactualDistributivity:ifasweconsiderϕ

worldsthatcomecloserandclosertotheworldofevaluation,weneverreachaboundarywithin

whichalltheϕworldssareψworlds,oralltheϕworldsareχworlds,thenitmaybethatϕ⟥→(ψ∨

χ)eventhough¬(ϕ⟥→ψ)∧¬(ϕ⟥→χ).ButStalnaker’stheory,supplementedwithordering

supervaluationism,wouldmakeanygivenprecisificationofCounterfactualDistributivitytrue.

Relativetoaparticularselectionfunction,ϕ⟥→(ψ∨χ)⊧(ϕ⟥→ψ)∨(ϕ⟥→χ).Asaresult,any

instanceofCounterfactualDistributivityisorderingsupertrue,andsimilarlyforCausalDistributivity.

Butofcourseitispossiblethatitisneithersupertruenorsuperfalsethatϕ⟥→ψ,andneither

supertruenorsuperfalsethatϕ⟥→χ,whileitissupertruethat(ϕ⟥→ψ)∨(ϕ⟥→χ).Thuswecan

usealogicofcounterfactualsthatvalidatesCounterfactualDistributivitytoprovidealogicof

15

causationthatvalidatesCausalDistributivity—anduseorderingsupervaluationismasapost-

semanticrepairmechanismwhenweencounterfailuresofthelimitassumption.

Itmaybehelpfulalsotoseehoworderingsupervaluationismhelpsinaparticularcasewherethe

limitassumptionfails.

SELECTINGATEAM:Everyplayerwhoisatleastsixfeettallisselectedfortheteam.Everyplayerwhois

lessthansixfeettallandwhoseheightexpressedininchesisarationalnumberisalsoselected

fortheteam.Everyplayerwhoislessthansixfeettallandwhoseheightexpressedininchesis

anirrationalnumberisnotselectedfortheteam.

Inthisexample,aplayer’sbeingatleastsixfeettallisdeterminatelynotcausallyrelevanttoher

beingselectedfortheteam,byLewis’slights,becauseonLewis’ssemanticsforcounterfactualsit’s

determinatelyfalsethatifthatplayerhadn’tbeenatleastsixfeettallshewouldn’thavebeenselected

fortheteam.OnStalnaker’ssemantics,supplementedwithorderingsupervaluationism,this

counterfactualcomesoutindeterminate:asweinterpretthecounterfactualrelativetoselection

functionsthatyieldantecedentworldsthatarecloserandclosertotheworldofevaluation,wenever

cometoaboundarywithinwhichallthoseantecedentworldsarealsoworldsinwhichthe

consequentistrueorworldsinwhichtheconsequentisfalse.Sothecounterfactualisneither

orderingsupertruenororderingsuperfalse;itisindeterminate.Soit’salsoindeterminate,given

Lewis’s1973analysisofcausation,whethertheplayer’sbeingatleastsixfeettalliscausallyrelevant

toherbeingselected.

MuchofthisdialecticcanbereplayedforLewis’s2000theoryofcausation.Incasesthat

demonstratehowthisaccountinvalidatesCausalDistributivity,cinfluencesd∧ewithoutinfluencing

dandwithoutinfluencinge.Wegetthisstructurewhen,roughlyspeaking,iftherewerealterationsof

ctherewouldhavebeenalterationsofd∧e,butiftherewerealterationsofctherewouldn’t

necessarilyhavebeenalterationsofdandtherewouldn’tnecessarilyhavebeenalterationsofe.On

Lewis’stheoryofcounterfactuals,insuchcasesitwillbefalsethatcinfluencesd,andfalsethatc

influencese;onStalnaker’stheoryboththoseclaimswillbeindeterminate.

16

NoneofthisistosaythatwemusthaveeitherLewis’s1973theoryofcausationorhis2000

theorytogettherequisitekindofindeterminacyincausation.Rather,itistoillustrateonewayin

whichthatindeterminacycanbecapturedbyanimportanttheoryofcausation,supplementedbya

particulartheoryofcounterfactuals.Totheextentthatwelikecounterfactualtheoriesofcausationin

thefirstplace—whetherforomissions,forHall’snotionof‘dependence’(2004),withmoredefense

thanLewisoffers(Coady2004),orwithelaborationsandamendmentsthatLewisdoesnotoffer

(Paul2000)—it’sgoodthattheypredictindeterminacyincausation.Thisisnotapointagainstother

generalapproachestotheorizingaboutcausation.Butaswemakeamendmentsandfillindetails,

withinsuchapproaches,topredictindeterminacyincausation,weareaimingtoemulatethisfeature

ofcounterfactualtheories.

4. SymmetricOverdetermination

JonathanSchafferpresentsthefollowingdilemma:

Whenc1andc2areoverdeterminingcausesofe,arec1andc2eachcausesofe

individually,orarec1andc2onlyacauseofecollectively?(2003:24)

Schafferarguesforthefirstview(‘individualism’)inpartonthegroundsthataccordingtothesecond

view(‘collectivism’)either“(i)c1(/c2)individuallycausesnothing,inwhichcasethepowerofc1∨c2

isamysteriousemergentpower;or…(ii)c1(/c2)individuallycausespartofe,inwhichcaseitishard

tounderstandhowc1individuallycanfailtocountasacauseofe”(38).Allowingforindeterminacy

incausationgivesus(asitwere)aThirdWay:wecansaythatitisindeterminatewhetherc1is

causallyrelevanttoe,andindeterminatewhetherc2iscausallyrelevanttoe,butdeterminatelytrue

thatc1∨c2iscausallyrelevanttoe.Wethusavoidsayingthatc1∨c2hasemergentcausalpowers,

andalsoavoidsayingthatc1(orc2)isacauseofpartofe.Schaffer’sotherargumentsfor

individualismdon’tgeneralizetothisposition.Indeed,Ithinktheysuggestthatwedosignificantly

17

bettertopositindeterminacyinsymmetricoverdeterminationcasesthantoendorseindividualism.

I’llconsidereachofSchaffer’sargumentsinturn.11

Schafferarguesthat‘individualoverdeterminersplaythepredictive,explanatory,manipulative,

andmoralrolesofcauses’(29).MyresponsetoSchaffer’sargumentaboutthepredictiverolesof

causesisrelevanttoSchaffer’sotherarguments,soIbeginbylayingoutthatresponseindepth.If

tworockssimultaneouslyshatterawindow,Schafferwrites,‘knowledgethatrock1isthrownatthe

window(onanaccuratetrajectory,withenoughforce)issufficienttolicenseapredictionthatthe

windowwillshatter’(29).Whilethat’strue,thepredictiveroleofcausalthoughtisn’texhaustedby

ourabilitytopredictwhatwillhappenifaneventoccurs.Wealsowanttouseourknowledgeof

causalfactstohelpuspredictwhatwouldhavehappenedifsaideventhadn’toccurred.Knowledge

likethathelpsuslearnabouthowthingswork,helpsusthinkaboutresponsibility,andhelpsus

makeinformedchoicesabouthowtodealwithsimilarphenomenainthefuture.Inthisparticular

example,theknowledgeweshouldnotoverlookisthatinterveningtopreventrock1fromreaching

thewindowwouldnothavepreventedthewindowfromshattering.Toknowthis,weneedtoknow

morethanthatit’sindeterminatewhetherrock1causedthewindowtoshatter.Butifweknowin

additionsimplythatthefactthatrock1wasthrownorrock2wasthrownwascausallyrelevanttothe

window’sshattering,thenweknowthatinterveningonjustonerock’spathwouldnothavebeen

enoughtosavethewindow.Theunderlyingproblemhereisthatindividualismmakessymmetric

overdeterminationtoosimilartojointcausation.Toseethis,supposethatanotherwindowwould

nothaveshatteredunlesstwo(other)rockshitit.Thoserocksarebothdeterminatelycausally

relevanttotheshatteringofthewindow,andinterveningtopreventeitherrockfromreachthe

windowwouldhavepreventedthewindowfromshattering.ButifSchafferwererightabout

individualism,thenthejointcausationcasewouldhavethesamecausalstructureasthesymmetric

overdeterminationcase.Countenancingindeterminacyincausationgivesusanintuitivewaytodraw

distinctionsherethatareimportanttopredictivecausalreasoning.

11IdonotconsiderSchaffer’sargumentsfromconversationalpragmaticshere,becausediscussingthecomplexitiesofthe

interactionbetweenindeterminacy,pragmatics,andthejudgmentsofordinaryspeakerswouldleadusfarafield.

18

Nowletusturntoexplanation.Insomecontextsandforsomepurposes,itwillsufficetoanswer

thequestion‘Whydidthewindowshatter?’bysaying‘Becauserock1wasthrownatit,’asSchaffer

observes(29).Butinothercontexts,andforotherpurposes,thisexplanationisincompletein

problematicways.Ifwearetryingtopreventorgetcompensationforwindowshatterings,for

example,itwillbeimportanttodescriberock2’scausalrole.Butasbeforeweshouldavoidgivinga

descriptionoftherocks’causalroles(individuallyandcollectively)thatassimilatesthecausal

structureofsymmetricoverdeterminationtoacausalstructureassociatedwithjointcausation.

Countenancingindeterminacyincausationmakesthatpossible.Withrespecttomanipulation,

Schafferobservesthat‘werec1differentinanyofmanyways,thenewouldhavebeendifferentinany

ofmanyways’(29).Butwhetherwehaveacaseofsymmetricoverdeterminationoracaseofjoint

causationaffectshowandtowhatextentmanipulatingc1affectse.

Finally,countenancingindeterminacyincausationraisesfascinatingmoralquestions,onlysome

ofwhichIamabletopursuehere.Whileit’struethat,asSchafferwrites,‘anagentwhoperformsc1is

liabletopraiseorblamefore’(30;seealsoGoldman1999),thenatureofthepraiseorblameis

affectedbythepresenceandcausalroleoftheoverdeterminingcause.Icanbestmakethecasefor

thisthesisthroughexamples.First,supposethatwebothworkhardonourcollectiveproject,which

turnsouttobeasuccess.Buteitheroneofusworkinghardwouldhavesufficedforthatsuccess.We

bothdeservepraise,butneitherofus,Ithink,deservespraiseinquitethewaythatwewouldasthe

solecauseofthesuccess.Second,IrisMarionYoungarguesthat‘Politicalresponsibilityinrespectto

structuralinjustice…oftenrequirestransforminginstitutionsandthetaskstheyassign.Thisis

everyone’staskandnoone’sinparticular’(2004:385,emphasisadded).Agiveninstitutioncouldbe

transformedwithouteveryone’sintervention,andmanygroupsthatwouldsufficetotransformsuch

aninstitutionareonaparwitheachother.Sothefailuretotransformaninstitutionissymmetrically

overdeterminedbymanygroups’omissions.Toholdeverygroupthatwouldsufficetoeffectsucha

transformationaswholly,determinatelyresponsibleforthefailuretobringaboutthetransformation

isinconsistentwithordinarypractice,and,Ithink,inconsistentwithourreflectivejudgmentsabout

howtoapportionblame.ThisispartofYoung’spoint,Itakeit,whenshewritesthattransforming

19

institutionsistheresponsibilityofnooneinparticular.12Third,RobertGoodinoffersacaseofa

terroristgang,themembersofwhichhavedifferentrolesandresponsibilities—thereis‘the

mastermind,thedetonator,thedecoy,thepassivemember,etc.’Goodinsuggeststhat‘Lesserdegrees

ofresponsibilityfalltothose…whoplayedwhatwereonlyveryminorroles,inthesensethatthe

basicplot—theoveralloutcome—wouldhavebeenlittlechangediftheyhadbeenomitted

altogether’(1987:181).Similarly,insymmetricoverdeterminationcasesthefactthatthe‘overall

outcome’wouldhavebeennodifferentifoneoftheoverdeterminingcauseshadnotoccurredaffects

thesenseinwhichtheindividualoverdeterminersareresponsiblefortheoutcome.Whilethereare

manywaysinwhichindeterminacyincausationmightimpactmoraljudgments,countenancingitis

animportantsteptowardexplainingthesemoraldistinctions.

Schafferalsoarguesthat‘individualoverdeterminersandtheireffectsareconnectedbycomplete

processes’(33),andthereforedeservetocountascauses.Countenancingindeterminacyincausation

changesthedialecticherequiteabit.Wemightsay,forexample,thatindeterminacyincausationcan

arisewhenit’sindeterminatewhetheraprocessiscomplete.Incasesofsymmetric

overdetermination,thisindeterminacywouldariseifitwerenotpossibleforboththeprocess

associatedwithrock1andtheprocessassociatedwithrock2tobecompletewithrespecttothe

shatteringofthewindow.Inlightofthispossibility,wearenotyetinagoodpositiontosaytowhat

extenttheconnectionbetweensymmetricoverdeterminersandtheireffectsresemblesthe

connectionbetweenordinarycausesandtheireffects.Beforeworkingonthatquestion,weneedto

workoutthebestwaytoreconcileprocessviewsoncausationwithindeterminacyincausation.

JonathanLivengood(2013)offersfurtherreasonstorejectindividualism,althoughhis

argumentsdon’tdistinguishstraightforwardlybetweencollectivismandcountenancing

indeterminacy.Livengoodshowsthatseveralrecentcharacterizationsof‘singular’or‘actual’

causationintermsofstructuralequations13counteveryabstentionasacauseofthewinner’svictory

insimple-majorityelections,andcounteveryvoteasacaseofthevictoryinallsimple-plurality

electionswithmorethantwocandidates—howeverthevotesweredistributed.Individualismisthe

12SeealsoSaraBernstein’sdiscussionofcharitycasesinherforthcoming.13Inparticular:Hitchcock2001;Woodward2003;Halpern&Pearl2005;andHall2007.

20

culprit.Thesecharacterizationsandotherslikethemshouldberevisedtoallowforindeterminacy,

therebyavoidingwholesalecollectivismandthedangerofmakingnoabstentionscountascauses.14

ButIwanttocautionagainstthetemptationtothinkofvotesincasesofoverdeterminationas

‘instancesofaweakspeciesofcausation,callitpartialcausation,orcontributorycausation,orcausal

influence’(Goldman1999:206).Overdeterminersdon’t‘weakly’or‘partially’causeaneffect:tosay

thatisagaintoassimilatesymmetricoverdeterminationtojointcausation.Rather,thecausalfacts

simplydon’tsettlequestionsaboutwhichoverdeterminercausedtheeffect.

TreatingsymmetricoverdeterminationinthewaythatIhavedevelopedhereopensupan

interestingpossibleresponsetoLauriePaul’sworrythat‘nonreductionismgeneratesmassive

amountsofsymmetriccausaloverdetermination’(2007:278;seealsothediscussioninHall&Paul

2013:155–61).Thecounter-intuitivenatureofpervasivesymmetricoverdeterminationleadsPaulto

arguethatnon-reductionistsshouldholdthatmacro-andmicro-levelobjectscanshareproperty

instances,andthat,givenatheoryofpropertyinstancecausationliketheoneshedevelopsinher

2000,‘causalresponsibilityisshared,notoverdetermined’(85).Paul’sresponse,andthatofsome

otherswhohaveworkedonthisproblem(e.g.Wilson2011),isineffecttoarguethatweshould

endorseapackageofviewsthatdoesnotleadtosymmetriccausaloverdetermination.Such

packages,elegantastheyare,aren’tforcedonthenon-reductionistwhocountenancescausal

indeterminacy.Shemaysayinsteadthatforeach‘level’or‘layer’itisindeterminatewhetherfactsat

thatlevelcausedagiveneffect,butthatitisdeterminatelytruethatthesumoflayerscausedthe

effect.

5. AccountingforIndeterminacyinCausation

Thereismuchworktobedoneinamendingvarioustheoriesofcausationtoaccountforcausal

indeterminacy.Hereareacoupleofexamples.Supposewehavearegularitytheoryofcausation

accordingtowhichccauseseiffcandearefacetsofanappropriatepatternofsuccession.Onsucha

14Suchrevisionsmightalsohelptheseapproachesavoida“modalcost”thatLivengoodnotes:“Insteadofattendingto

counterfactualdependenceonlyintheactualcircumstances,theindividualistmustattendtocounterfactualdependenceincounterfactualcircumstancesaswell”(324).

21

view,whatwoulditbeforittobeindeterminatewhetherccausese?Presumablyitwouldhavetobe

indeterminatewhethercandearefacetsofanappropriatepatternofsuccession.Such

indeterminacymightcomefromanyofseveraldifferentsources.Forexample,itmightbe

determinatewhattheappropriatepatternsofsuccessionare,butindeterminatewhethercandeare

facetsofone.Itmightbedeterminatethatcandearefacetsofapatternofsuccession,but

indeterminatewhetherthepatternisappropriate.Itmightbedeterminatethatcandearefacetsof

something,butindeterminatewhetherthethingtheyarefacetsofisapatternofsuccession(though

ifitisapatternofsuccession,say,itisanappropriateone).Whilethisisjustatoyexampleofa

regularitytheory,itshouldbeenoughtomakeitclearthatextendingregularitytheoriesto

accommodatethecasesdiscussedhereisn’tatrivialmatter:ataminimum,therearemanychoice

pointsfortheregularitytheorist.Hereisanotherexample.Supposewehaveaprocesstheoryof

causationaccordingtowhichcandearepartofacausalprocessifftheyarepartof‘aworldlineofan

objectthatpossessesaconservedquantity’(Dowe1995:323).Whatwoulditbeforittobe

indeterminatewhethercandearepartofacausalprocess?Again,indeterminacycouldinprinciple

creepinatseveralpoints:itmaybeindeterminatewhethercandearepartofaworldlineofan

object,indeterminatewhethertheworldlinepossessesacertainquantity,indeterminatewhether

thequantityisconserved,andsoon.Finally,wecouldenhancestructuralequationmodelsbyusing

supervaluations(Schaffer2016),fuzzysets(Palumbo,Romano,&Vinzi2008),orsomeother

approachtorepresentindeterminacy.HalpernandHitchcock2010and2013discusssomeother

possiblesourcesofindeterminacyinstructuralequationmodels.Itisinterestingtoaskwhetherone

representationoftherelevantindeterminacieswouldsufficeand,ifnot,howmultiple

representationsofindeterminacywouldinteract.

Onereasonwhythereissomuchworktobedonehereisthatit’snotindeterminacypersethat

matters.Rather,weshouldaimtocapturethelogicalrelationshipsthatallowindeterminacyin

causationtodotheworkI’veoutlinedhere,validatingprincipleslikeCausalAdditivityandCausal

Distributivity,andhandlingconsideredjudgmentsaboutsymmetricoverdeterminationinanelegant

way.Onewaytoexplainthisistoanalyzecausationintermsofcounterfactuals,andtoadopta

Stalnakeriansemanticsforcounterfactuals.Whetherornotweshouldusecounterfactualsin

22

analyzingcausation,thecorrelationsbetweenindeterminacyincounterfactualsandindeterminacyin

causationarestriking.Theoriesofcausationshouldaimtopredictandexplainthem,and,asI’ve

suggested,philosophersingeneralshouldaimtoexploitthem.15

UNIVERSITYOFMICHIGAN,UNITEDSTATES

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