1
IndeterminacyinCausation
EricSwanson
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.
3
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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