A Problem for Actualism About Possible Worlds (McMichael)

8/12/2019 A Problem for Actualism About Possible Worlds (McMichael)

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ThePhilosophical eview,XCII, No. 1 (January1983)A PROBLEM FOR ACTUALISM ABOUT

POSSIBLE WORLDSAlanMcMichaelI. INTRODUCTIONT he notion fa possibleworldhasmanyusesin the formal

philosophyof language. Its primaryuse, of course,is in theinterpretation f sentencesabout necessity nd possibility. prop-ositionis necessary f and only if it is true in all possibleworlds;possibleifand only f truein some possibleworld. One advantageof thepossibleworlds nterpretations its extensionality.he inten-sional notions of necessity nd possibility re replaced by quan-tifiers ver possible worlds. The language in whichthese quan-tifiers ppear, sometimescalled world theory, an be given anordinaryTarski semantics.A second advantage of the possibleworlds nterpretations purelyheuristic. t ust seems to help ourmodal thinking o imagineotherpossibleworlds.However, thenature ofpossibleworlds s thesubjectof a familiarcontroversy, he dispute between actualism nd possibilism. necommon position in this controversy,which I shall call atomisticactualism,eems to methe mostplausible.Nevertheless, shall showthat t is open to serious objection. It fails to providean adequateinterpretation orcertainmodal sentences, ssumingthatweadoptstandard rules of interpretation. hus we must either rejectatom-istic ctualism, ven though, s I shall argue inthe next section, healternatives re not attractive, r reject the standard semantics,despite its practicalsuccesses.

II. POSSIBILISM AND ACTUALISM'According to the possibilists,possible worlds are concrete en-tities. n thisrespect,they re like the concreteuniversewhichwe'The possibilism-actualismistinctionhouldnotbe confusedwith hepossibilism-modalismistinction. possibilistnthe senseofthe seconddistinctions a personwhobelieves hatnecessityndpossibilityre ana-lyzablentermsfquantificationver ome ind fentities.Whether eorshe s a possibilistnthefirstensedepends n whether hose ntitiesre

taken obe actually xistingrmerely ossible.49

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ALANMCMICHAELinhabit.For the possibilist, hisconcreteuniverse s the ctualworld.(In sayingthat possible worldsare concrete,the possibilists notsayingthat theyare made of actual concretethings.Manyworldscontainnonactual oncrete things, uch as individual dragons andunicorns.)Accordingto thepossibilism f David Lewis, thisworld's ctualityis a merelyrelativematter.2This world is indeed actual withre-spectto itself, ut everyother world s actual withrespectto itself.So all worlds are on an ontological par. This postulationof on-tologicalparity,while perhaps it can be consistentlymaintained, sprima acie absurd. The apparent absurditymaynot be sufficientreason for dropping Lewis' theory altogether,but it is enoughreason to prefera consistent lternative.A second formof possibilism akes the notionof actuality o beabsolute.Thus thisworld is distinguished romothersby thenon-relativeproperty f actuality. n the most plausibleversionof thisview,the propertyof actuality s takento be simpleand irreduci-ble.3Another-way o put theview is to saythatall possibleworldshave being, ut onlythisworldhas existencer actuality.Many phi-losophers have found thistwo-tieredMeinongian ontologyquiteincomprehensible. am inclined to reject it also, provided thatsome actualistalternative an be found.Actualistswho believe in possible worldsview themas existingabstract ntities.The actual world is notactual merely n thesensethat texists-all possibleworlds exist-but rather n thesense thatthis concreteuniverse correspondso it.Robert Stalnaker s an actualistwho givesserious considerationto the view thatpossibleworlds are irreducibleabstractentities.4He suggests hattheterm world' s infactmisleading:there sonlyone world, this one. However, there are many 'ways the world

2Lewis,CounterfactualsHarvard University ress, 1973), 84-91.3This second formof possibilism s usuallyadopted as a view about allpossible objects, rather than merelyabout all possible worlds. See, forexample, thetheory f possiblescontained n Terence Parson'sNonexistentObjectsYale University ress, 1980). Meinong,and possiblyLeibniz,heldsimilarviews.4Stalnaker, PossibleWorlds, Nous 10 (1976), 65-75. Stalnakerdoes notexplicitlyndorse this view,buthe does defend it againstobjections. amgratefulfor his commentson thismatter, n which he pointsout thathismain thesesare (a) thatactualismdoes not require reductionof possibleworldsand (b) thatreductionof propositions opossibleworldshas certain

advantagesover the reversereductionof possibleworldsto propositions.50

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A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDSmighthave been' or 'world-states,'nd they re whatwe mean bythe term possibleworlds.'These world-statesre abstract ntitiesdistinctfromthisconcreteuniverse.We mightthink of themasspeciallydeterminateproperties.One of the world-statess actualin thesense that t is exemplifiedyour concreteworld.This worldstate is 'the way the world is.' None of the other world-statessexemplified.Thus the notionof actualitydoes not remainunex-plained, as itdoes in theabsolutistformof possibilism, ecause inconstruingworldsas a kindof property, heactuality-nonactualitydistinction ollapses into the exemplification-nonexemplificationdistinction.On the view in question, possible worlds are basic properties.They are notpropertiesthatmightbe reduced to simplerproper-ties,or to propertiesand relations.This particularaspect of theview s one I findunattractive. he decisionto treatpossibleworldsas basic clasheswithall commonly ccepted patterns f reduction.Reductionproceeds from ablesand chairsto atoms,notviceversa.Since this worldcontainstablesand chairsas parts, t too is com-plex. But since the stateof this world,the waythe world is,mustsomehowencode thecomplexinterrelationsfthisworld'sparts, talso is complex,a complexofproperties nd relations.Finally,ustas the stateof this world is complex, so too are the otherworld-states.AlvinPlantingais an actualistwho takesworldsto be complexstates-of-affairs.5state-of-affairssa proposition-likentity. xam-ples are Karpov'sbeingworld hess hampionnd Plantinga'shavingclimbed ountEverest. he former tate-of-affairsbtains,he latterdoes not. Both states-of-affairs,owever, repossible. hat is,eachis such that it could have obtained. Not everypossible state-of-affairs s a world,onlythosethatare maximal. state-of-affairsismaximal fand only ffor nystate-of-affairs', either t simpossi-ble forS toobtainand S' not to obtain,or it s impossibleforbothSand S' to obtain.That is,S ismaximal fand only ffor nystate-of-affairs ', S either ncludes ', or S precludes'. Speaking loosely,maximal state-of-affairss one which scompletely eterminate.6A

5Plantinga,TheNature fNecessityOxfordUniversity ress,1974), IV. 1.6This is only oosely correctbecause a maximal possiblestate-of-affairsmay nclude a state-of-affairsf somethingbeingF without ncluding,forany ndividualX, thestate-of-affairsf X's beingF. The importance fthispointwillbecome clear in the nextsection.51



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ALANMCMICHAELpossibleworld s a state-of-affairshich sbothmaximal and possi-ble. Although all these worldsexist,ust one of them s actual nthesense that it obtains. Thus the distinction etween actuality ndnonactuality s merely the distinction etween obtainingand notobtaining.As in Stalnaker's theory,worlds,being abstract bjects,exhibit dualitywhichaccounts for the distinction.There are two other actualisttheorieswhichare very imilar oPlantinga's.One, espoused by RobertAdams, saysthatworldsaremaximal onsistentetsofpropositions.7 set of propositions s con-sistentfand only f t spossible for ll itsmembers o be true.Sucha set is maximal if and only if for every propositionp, the setcontains eitherp or the negation ofp. The actuality-nonactualitydistinctions based on thetrue-false uality f propositions: ne ofthe worlds is actual because it contains all the true propositions.According to the remaining actualist theory, worlds are in-terpretedodeltructures.uine has proposed a viewof this ort.8Hehas construedworlds as certainset-theoretic tructures epresent-ing possiblearrangements f physicalparticles.One of these struc-tures,presumably,represents he arrangementof particles n theactual world. Quine's theory seems more parsimoniousthan theothers. It does not, after all, refer to propositionsor states-of-affairs.Nevertheless, t rests on the same ontologicalbasis as thetwo other theories. Quine's model structures re interpreted.hatmeans the featuresof those structures re associatedwithproper-ties and relations hatare taken to be fundamental.But suchprop-erties and relationsare theverycomponentsof Plantinga's tates-of-affairs nd Adams' propositions.This agreement on an on-tologicalbasisoutweighs ll the differences etweentheviews.Thethree views offerequally promising nterpretationsf modal dis-course.Consequently, lump all threeunder the same title: tomis-ticactualism.

I believe that ome form f atomistic ctualism s correct.For thepresent, shall adopt Plantinga'sversion. Accordingly, ur modalsemantics ssumes the followingform:(1) 'It is possiblethatA' is true fand only f there s a possible

7Adams, Theories of Actuality,Nous 8 (1974), 211-231.8Quine, PropositionalObjects, n Ontological elativityColumbia Uni-versity ress, 1968).52



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A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDSworld Wsuch thatW includes thestate-of-affairsxpressedbyA.

(2) 'It is necessarythatA' is true if and only fevery possibleworldW includes the state-of-affairsxpressedbyA.9Itmightbe objectedthatour semantics scircular, ince thenotionsof a possibleworld and of nclusionhavebeen defined nterms faprimitive nderstandingofpossibility. he chargeofcircularitysnot effective, owever,since we are by no means trying o definepossibilitynd necessity.We are simply rying o givean extensio-nal semanticsfor those notions, n the hope that itwill prove il-luminating. t is wrong to thinkthatdefinition s the onlywaytoilluminatea notion.

III. THE ITERATED MODALITIES OBJECTION

Atomistic ctualismprovidesadequate interpretations ormanystatementswhich eem orequirequantification vernonactualpos-sible objects.Consider:(3) It is possible thattherebe someone who is not actual.

Let S be the state-of-affairshere eing omeone who s not ctual.Then according to the possibleworldsanalysis, 3) is true if andonlyif:-(4) There is a possible world W which includes the state-of-affairsS.

Since the original statement s surelytrue,theremust be such aworld W. But the existenceof such a world squitecompatiblewithatomistic ctualism.S is a generalstate-of-afflars;o constituent fit s a merelypossibleobject.Thus (4) does notrequirethatWhavea merelypossibleobjectas a constituent.Of course, actualistsmustdeny thatW containsany instance fthe existentially eneralized state-of-affairs. On the one hand,any nstanceofS that nvolves n actualobjectX isa state-of-affairs

91am interestedrimarilyn logicalnecessitynd logicalpossibility.However, ftherangeofpossibleworldsssuitablyestricted,1) and (2)can be applied to statementsnvolving therkinds of necessity ndpossibility. 53o



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ALANMCMICHAELthat ould notpossibly btain.W is possible, o cannot ncludesuchan instance.On theother hand, W cannotincludean instanceof Sthat nvolves nonactual bject,sinceactualistsdeny thattherearesuch things.Therefore,W includes S, but not any instance of S.This does not,contrary o appearances, contradict hemaximalityof W. Since the actualist denies the existence of the relevant n-stancesof S, there is nothingthat W is missing.There are problems,however, n the interpretationf iteratedmodalities.Consider the sentence:

(5) It is possiblethattherebe a personX whodoes not exist nthe actual world, nd who performs omeactionY,but whomightnot have performedY.This sentence s surelytrue.For example,JohnF. Kennedycould(logically)have had a second son whobecomesa Senator,althoughhe mighthave chosen to become an astronaut nstead.This is aninstanceof iteratedmodalitybecause we are talking bout what ispossiblypossible.On the possibleworldsanalysis, 5) is true ust in case:

(6) There is a world W which includes the state-of-affairsfthere being someone X who does not exist in the actualworld,and who performs ome actionY,and therebeingaworld W' whichincludes the state-of-affairsfX existingand not performing ctionY.Unfortunately,t is difficult o see how thistruth-conditionan bemet.We have seen how therecan be a worldW which ncludesthestate-of-affairshere eingomeone who snot ctual.This is a gener-al state-of-affairs;tdoes not have the nonactual individualX as aconstituent. ut sinceX is not an actual individual, t s difficultosee how there can be anotherworldW' which ncludes the state-of-

affairs fhisexisting.Because X is notactual, t seemsthatthere sno such state-of-affairss X's existing, o nothingcan include it.The reasoning is that if there were such a state-of-affairss X'sexisting, hen X would be a constituent f it and so, by actualistprinciples,be an actual individual-contrary to our hypothesis.One mightobjectthatalthoughthere s no state-of-affairsfX'sexisting, here ndeed could be. So in thisotherpossibleworldW,there is such a state-of-affairs. lso, there are maximal possible54



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A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDSstates-of-affairsn W which include the state-of-affairsf X'sexisting.

But thistacitly cknowledgesthat the states-of-affairsxistingnone worldcan be distinct rom hose nanotherpossibleworld, ndhencethepossibleworldswhichexistfrom hepointofviewofoneworldare distinct rom hosewhichexistfrom he pointof viewofanother. To acknowledge this is to give up the extensionality fpossibleworlds semantics, inceit s beingclaimedthatthepossibleworldsquantifierwithin he context there s a worldWsuchthatWincludes ' does not have a range identical to that of thequantifier n the outside.That is, theydon'tbothrangeoversomeone universalsetof possibleworlds.But if we have to giveup theextensionalityf thepossibleworldsapproach,we might s welldowithout t.The foregoingobjection is formalized n theAppendix of thispaper,usinga freemodal logicwith uantifiers or ndividuals ndfor states-of-affairs.IV. Do ESSENCES HELP?

Plantingaappears to avoid the iteratedmodalitiesproblembythe introduction fessences.1He holds thatthere can be states-of-affairs f the formX existsven if there s no corresponding ndi-vidualX. This doctrine s nottrivial.n speakingofstates-of-affairsof the form X exists, lantinga allows only proper names to besubstitutedfor the variable 'X', not definitedescriptions.Thuswhile t s true that here s a state-of-affairshe resentingof ranceexistsven thoughthere s no presentKingofFrance,this s notaninstanceof Plantinga'sdoctrine.The state-of-affairshe resent ingofFranceexists s not of the formX exists. tates-of-affairsf theformX existsre states-of-affairsf genuine individualexistence,notmerely tates-of-affairsf the existenceof a unique individualsatisfyinguch-and-such description.

'0Kit Fine triesto do without t. See his Postscript o Worlds, imes,ndSelvesby Fine and A. N. Prior (Amherst,Massachusetts:University fMassachusettsPress,1977). Fine exploressome oftheconsequencesofoneof theviewswhich s prominentn thispaper,namely, hat tates-of-affairsthat containindividualsas constituentsmayexistonlycontingently.Essences are introduced in TheNatureofNecessity,. 2. But a moreimportanttreatmentfor our purposes is contained in ActualismandPossibleWorlds, Theoria 2 (1976), 139-160.55



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ALANMCMICHAELHow can there be a state-of-affairsf the formX exists n theabsence of an individualX? Plantingamaintainsthat a state-of-

affairsof the formX existss not a compound of the property fexistenceand some individualX. Rather, t is a compound of thepropertyof existenceand some individualessence. Essences, ac-cording to Plantinga, exist of necessity, ut an essence does notnecessarily orrespondtosome actual individual.Yet each essence,whether there is a corresponding individual or not, entersintosome one state-of-affairsf the formX exists.Plantingatakesessences to be a certainkindof property:(7) E is an essence if and onlyif it is possible that somethinghaveE necessarily, nd necessarily nythingwhichhasE isidentical to that thing. (Possible worlds analysis:E is anessence if and onlyifthereis some worldW such thatforsomeobjectX whichexists nW, 1) X has theproperty ineveryworld nwhichX exists, nd (2) for nyworldW' and

object Y which exists in W', if Y has E in W', then Y isidenticaltoX.)A property is an essence of Socrates,forexample,ifSocrates hastheproperty essentially,nd necessarily nythingwhich hasE isidentical to Socrates. (7) leaves room,on the otherhand, forunex-emplifiedssences,essenceswhich are not essencesof anything.Anessence is a property which could have been an essence ofsomething.Pretty learly hereare essencesin the senseof (7). For example,the property f beingidentical o Socrates s an essence of Socrates.Socrateshas thispropertyn everyworld nwhich he exists, nd itis impossible for somethingelse to have this property.The ex-pressionforthis essence,however,containsa propername foranindividual.Since on thepresentviewthisname isan expressionforthe essence of Socrates,the whole expressionrepresentsno analysisof thatessence. The questionnaturally rises whether here s anyinterestingense in whichessences can be analyzed. More specifi-cally,we may ask: are essencesqualitativen the sense thatthey recompoundsof general roperties, roperties hatdo not themselvesinvolveeither ndividualsor theiressences?An affirmativenswerto this question would bolster Plantinga'sposition,for it wouldmean that the essences of nonactual individuals,unexemplified

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A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDSessences,need notbe swallowedwhole, butmaybe understood ntermsof theirparts. I shall try o show,however,that ndividualessences cannot be qualitative.There are twostrongargumentsagainstthe viewthatessencesare qualitative.The first s the argumentfrom ymmetricalorlds:there are possibleworlds thatare entirely ymmetrical.n each oftheseworlds, n individual on one side oftheaxis ofsymmetryasexactlythe same general properties,both intrinsic nd relational,as its correspondent on the other side of the axis of symmetry.Assuming thatessences are qualitative, t followsthatifthe indi-viduals in one of these pairs have individualessences, theybothhave thevery ame essence-which is impossible.We have shown,therefore, hat there could have been individuals that lack indi-vidual essences. The problem forthe qualitativeessences view isthat the possible existence of such individuals cannot be in-terpreted, bviously, n termsof unexemplified ssences.

One mightobject thatthe case of symmetricalworlds s ust toospecial tounderminetheessencestheory.Two pointscan be madeinresponse.First, tseems tome,on thecontrary, hat hetheoreti-cal impossibility f adequate interpretationsn the case of sym-metricalworlds does suggest that the essences view yields thewrongtruth-conditions ormodal statementsngeneral.Secondly,it is not clear thatsymmetricalworldsare only a special difficulty.Couldn'tI have existed in a symmetrical orld?If so, then n thatworld, share allmygeneralpropertieswithmycorrespondent. oneitherof us can have a qualitative ndividualessence there.But ifI have an individual essence in the actual world,then I have itnecessarily. hus thefact hat don'thave an individualessenceinthe symmetricalworld impliesthat I don't have an individual es-sence in thisworldeither.The same goes forother ndividuals: findividualessencesare qualitative, hen an individualthat an existin a symmetricalworld has no individual essence in the actualworld.2The second argument,which I shall call the argument fromlikeness,equiressome new terminology. efine therole f an indi-vidual tobe theconjunctionofall itsgeneralproperties.Recall that

'2An argumentfrom ymmetrical orlds lso appears inRobertAdams'paper Actualism nd Thisness, Synthese9 (1981), 3-42.

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ALANMCMICHAELgeneral propertiesare ones thatdo not involveeither ndividualsor individualessences. They maybe either ntrinsic rrelational.For example, being descendentfAbeLincoln s not general,butthere re many ssociatedeneralrelationalproperties, uchas beinga descendentf famousnational eader.Noticethatrolesare maximalin the sense thatforany general propertyP, an individual'sroleincludesitherP or -P (Q includes P =dfnecessarily,nything hatexemplifiesQ exemplifies ). In fact, olesmaybe definedas maxi-mal possiblequalitativeproperties:R is a role fand only f 1) it spossible for something to exemplifyR, and (2) for any generalproperty , eitherR includesP or R includes -P. This definitiongoes beyond the previousdefinition, orit encompasses not onlythe roles of actual individuals,but also roles thatare not actuallyexemplified.In addition to an individual'sactual role,thereare manyotherroles it could have exemplified.However, since roles are maximalqualitativeproperties,each one of an individual'spossible rolesmustinclude thatindividual'sessence, given the assumption thatroles are qualitative. It followsthatthe disjunctionf all an indi-vidual's possible roles is an essence, since (1) the individualcouldnotexistwithoutfilling ne of theroles in thedisjunction, nd (2)no other individual could exemplify he disjunctionwithoutex-emplifying he original individual'sessence-which is impossible.Call roles R and S compossiblef it is possible for there to beindividualsX and Y such thatbothX fillsroleR and Y fillsrole S.Then the argument from likeness is: if two roles R and S aresufficientlylike, thennecessarily nything hatfillsrole R couldhave filledrole S and viceversa.But thereare compossibleroles Rand S such that (A) R and S are sufficientlylike, and (B) it ispossible for there to be distinct ndividuals X and Y such thatXexemplifiesR and Y exemplifies . From(A) and thefirst remise,itfollowsthat fR and S include essences,thentheymust ncludethesameessence. From (B), it followsthat ifR and S include es-sences, theymust include distinctssences. Thus R and S cannotinclude essences. But assumingthatessences are qualitative, ndgiventhatR and S are roles,eitherbothR and S includeessences,or necessarily, nythingexemplifyingR or S lacks an individualessence. Since R and S do not include essences,anything hatex-emplifies itherR or S lacksan individualessence.But since R and58



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A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDSS are possiblyexemplified, t followsthattherecould have beenindividualsthatlack individualessences-the same conclusionasthatreached in the argumentfromsymmetricalworlds.There are fancierversionsof thisargument.The rolesR and Sneed not themselvesbe sufficientlylike, theyneed onlybe con-nected by a chain of roles R, R1, R2, . . , Rn, S such that eachrole is sufficientlyikethenextone in thechain.The intermediaterolesneed notbe compossiblewitheach otheror withR and S.13One mightobject thatno such rolesR and S can be foundthatare sufficientlylike,or that re connectedbya chainofroleseachof which is sufficientlyike its neighbor. It seems to me, on thecontrary, hat t s easyto conceiveof such roles.R and S mightberolesof identicaltwins r,betteryet,rolesof twoelectrons reatedin the same collisionof particles.Neither does it seem rightto object that such roles R and Spresent special case thatdoes notunderminetheessencestheory.This objectioncan be metwith hesame responseas the ikeobjec-tionto the symmetricalworldsargument.I conclude fromthese argumentsthatwe mustrejectthe ideathat essences are qualitativeproperties.The alternativeview ofessences sthat ssencesareHaecceities,propertieswhichnecessarilycharacterize ingle ndividualsbut which renotreducibletogener-al properties.Perhaps Plantinga'sactualismcan be based on es-sences of this sort.14Assumingthe failureof the qualitativees-sences view, the existence of Haecceities certainlyfollows.For

'31n IdentityThrough Possible Worlds: Some Questions (Nous 1(1967), 1-8),RoderickChisholmseems to be sayingthata chain of suffi-ciently ikerolescan be constructed etweentheactual role ofAdam andthe actual role of Noah. I am not convincedthatthiscan be done in thecase of Adam and Noah. However, I thinkthatthe argumentfrom ike-ness can be supportedbymore plausible examples.14The term 'haecceity',however, is not Plantinga's. I derive it fromDavid Kaplan's How to Russell a Frege-Church, ournal fPhilosophy2(1975), 716-729. There Kaplan says, The doctrinethatholds that tdoesmake sense to ask-without reference ocommonattributes r behavior-whether his s the same individual n anotherpossibleworld, . ., I callHaecceitism. ny propertywhichdoes thedutyof distinguishingn indi-vidual-without referenceto general attributes-I call an haecceity.hisusage springsnaturally romKaplan's. However, tmaynotbe compatiblewiththe much older usage of Duns Scotus. Allan Back has told me that

Scotus' haecceitiesare probablynot properties.59



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A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDSThe Kripke semantics s, on the face of it,a possibilist emantics,sincewe can identifywithinta set ofall possibleobjects, ctual andnonactual.15This isomorphism s one of the signs that Plantingais havingtroublewiththe actualistprogram. Another sign is thathe hasdeparted from the usual actualistbasis. Typicallythe actualistre-ducesworldsto existing ndividuals,generalproperties, nd gener-al relations.To introduce primitivepropertieseach of which isspecific o some nonactual object seems tantamount o acceptanceof possibilism.Yet this s preciselywhat Plantingadoes.Finally,Plantinga s in theunfortunate ositionof beingunableto givea singleexample of an unexemplified ssence. Is theprop-ertyof being identicalto SherlockHolmes, for example, such anessence? It seems not to be. From the stories,we do indeed knowwhatsome of Holmes' propertiesare supposed to be. But underPlantinga'sHaecceitism, hisknowledgeseemsinsufficiento graspan essence. We don't knowenough of Holmes' propertiesto pickhim out uniquely n anypossibleworld.Hence the example fails.'6

V. MUST WE TAKE POSSIBLE WORLDS SERIOUSLY?Atomisticactualism is threatenedby the problem of iteratedmodalities.It is easy to see how worlds can include there beingindividualsother than those which there actuallyare. But those

individualscould be otherwisethan they are in theirrespectiveworlds.This suggests hatthereare yetotherworldswhich ncludetheir existence. However, it seems that a world can include theexistenceof somethingonly if that thing s a constituent f thatworld.Since atomistic ctualismholds thatthereare no nonactualpossibleindividuals,nonactualpossibleindividuals re notconstit-uents of anything.The theory f essencespromiseshelp. Accordingto thattheory,a world can include thestate-of-affairsfsomenonactualpossible's'5See Plantinga's Actualism nd PossibleWorlds, 155. Speakingstrick-ly,Plantinga'ssemantics s isomorphiconlyto thatversionof the Kripkesemanticswhichrequirestheextensionof a predicate n a world tobe a setofn-tuplesof thingsthatexistn thatworld.'6Plantingahimself eachesa similar onclusion.See TheNature fNeces-sity, ILL.3-4,wherehe discussesfictional reatures.

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ALAN MCMICHAELexistingwithout ontaining hatnonactualpossible as a constituent.It need onlycontain an unexemplified ssence. Unfortunately,hismaneuver fails. The theoryof essences has two forms.One form,the theory of qualitative essences, is vulnerable to certain argu-ments.A second form,Haecceitism, eems not to solveour originalproblem. There is no good reason to believe that there are unex-emplifiedHaecceities. Haecceities seem to depend fortheirexis-tenceon the ndividualsthey haracterize.But toremove the prob-lem of iterated modalities, we need unexemplified essences.Haecceitieswill not do.Myconclusion is that atomistic ctualism s in conflictwith tan-dard possibleworldsemantics, n accountof theproblemof iter-ated modalities. f we retain atomistic ctualism,which have ar-gued is the most reasonable conceptionofpossible worlds, henwemustrejectthe standard semantics, s representedby principles 1)and (2). I see no other wayout.One might espondthatthe problemof teratedmodalities risesonlybecause we are discussing particularlyealisticorm f actual-ist semantics.To be sure, an actualistmust reject the idea of therereally eing onactual possibles. Nevertheless, e or she isentitled oemploy a semanticswhich includes so-callednonactual possibles.Acceptance of a possibilist's emanticsdoes notnecessarily nvolvecommitment o the possibilist's ntology.The nonactualpossibleindividuals whichappear in the semanticsmightbe construed,forexample,as numbersor sets. f thereare enough ofthese so-calledpossibles, nd if they re related n therightways, hen the seman-ticswhich ncludes them may indeed prove adequate, in the senseof providinga correct distribution f truth-values, ven thoughtherereallyare no nonactual possibles.Mymain objectionto thisapproach is that t involves unsolveddifficulties.t should be clear that the construction f such a non-realistic emantics s a sleightof hand that has neveractuallybeenaccomplished. In order to give such a semantics, he number ofnonactual possiblesand theirrelationshipsmustbe determined. tis not clear how this s to be done.17

171n On WhatThere Is, Quinementionshepossibilist'sifficultyfdetermining,orexample, he number f possiblemen in a particulardoorway. he same ort fdifficultys nvolvednattemptingoconstructa nonrealisticctualist emantics.62



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A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDSIt is true that Saul Kripke has given a semanticsformodal logic,one that can plausibly be construed as a nonrealistic ctualist e-

mantics.However, to give a semanticsformodal logic sonly to givetheform f a semanticsfor modal language.Whatwe are ultimatelyinterested n, I believe, is to give truth-conditions or some nicemodal fragment f a natural anguage. Kripke'ssemantics s usefulfor nvestigating he notionof logical validityn a modal language.It does not supply conditions for truth.When I say that to give anonrealisticactualist semantics the number and relationshipsofnonactual possible individuals must be determined, mean that tmust be determined if the semantics s to provide us with truth-conditions. agree that a semanticsfor modal logichas been givenwithout uch a determination.'8My secondaryobjection s thatquestionsofrealismwillhaunt usanyway. f a nonrealistic semantics s actuallyconstructed, hensince it contains nonrealisticelements, the problemwill arise ofdistinguishingwhataspectsofthe semantics re ofgenuinesignifi-cance and what aspects are purelyartificial.We willwanta methodfor factoring ut the artificial spects.But a nonrealistic eman-tics coupled with a method of factoringout is just a realisticsemantics.An analogous situation arises in the use of spatial coordinatesystems.Given a particular oordinatesystem, he factthatan ob-ject A has coordinates (X, Y, Z) has no significance utside thatsystem.However, the fact that anotherobjectB with coordinates(X', Y', Z') is separatedfromAbythesquare rootof (X' - X)2 + (y'- y)2 + (Z' - Z)2 units s of ndependent significance.t holdsinallcoordinate systems assumingabsolute ength nd discounting ela-tivistic ffects).The problemof distinguishinguch invariant ea-tures fromartificial nes is ust as important s finding coordi-nate system hat works.

My complaintwiththe approach of nonrealistic emantics s thatit seems to be based on the assumptionthat generation f a correctdistributionftruth-valuess theonly emanticgoal. The economysought by realistic emantics s a second semanticgoal and is alsoworthyof pursuit. We don't just want a modal semantics that18Compare Plantinga'sdistinction etween pure and applied emantics,The NatureofNecessity,II.4.

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ALAN MCMICHAEL'works. We also want one thatisolates the invariantfeaturesofmodal reality.

In summary, question the approach of nonrealistic emanticsfor two reasons: (1) It involves unsolvedproblemsconcerning henumber and relationshipsof nonactual possibles. (2) Even if anadequate nonrealisticsemantics is constructed,we will want totransformt ntoa realistic emantics y factoring ut itsartificialfeatures.Given the undesirability f nonrealistic emantics, ur originalproblem remains. We cannot retain atomistic ctualism,neitherPlantinga'sversionnoranyoftheothers,without evising tandardmodal semantics.19APPENDIX: FORMALIZATION OF THE ITERATED MODALITIES

OBJECTION

I shalluse 'p' and 'q' as variablesforstates-of-affairs,x'and 'y' sindividualvariables. Inclusion of a state-of-affairsby a state-ofaffairs willbe representedusingthenecessity perator: LI(p -> q).Also, some symbolswill be givenspecial interpretations:Wp: p is a possibleworld@: the actual worldEp: the state-of-affairsexistsEx: the individualx existsCxq: the individualx is a constituent f state-of-affairs

In addition to standardaxioms and rulesfor freequantificationalS5, I shall use the following:1. Definitionof a world-

LO(Wp -> Kp & (q)[LI(p -> q) v LI(p -> -q)])2. Constituency-

OI1(q)(x)( q & LI[q -> Ex] -> Cxq)191wish to thank Marvin Belzer,James Fahey,Kit Fine, Edmund Get-tier,Alvin Plantinga,Melinda Roberts,Eleonore Stump,and the editors fThe Philosophical eview for their comments on earlier versionsof thispaper.

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A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDSNecessarily, f a possible state-of-affairsncludes the exis-tenceof some individual,then that ndividual s a constitu-ent of the state-of-affairs.t is interesting o note, on theotherhand, that a state-of-affairsan exclude he existenceof an individualwhich s not constituentfit. For example,thestate-of-affairs= theresexactlyne ndividual nd t sanelectronxcludes theexistenceof x = Socrates. We have O q(I think) nd we haveLI(q -> -Ex), but we do nothaveCxq.

3. Actuality f Constituents-LI(q)(x)(Cxq -> LI[@ --> Ex])Necessarily, nyconstituent f a state-of-affairsustbe anactuallyexistingthing.This axiom can be regarded as aconsequence of twoothers:3a. Actuality f all possible constituents f an actual state-of-affairs-

(q)LI(x)(Cxq -> L[[@ --> Ex])3b. Necessaryexistenceof states-of-affairs-LIE-, where the blank is filledbyany states-of-affairsterm.This validatesthe Barcan formulaand itsconverseforstates-of-affairs:

(p)FE( .p. . Ex)' is the translation f 'x does not exist in theactualworld'.We mayproceed:

(2) Wp & Li[p (-> x)(3 y)(-LI[@ -> Ex] & Pxy& (3q)[Wq &LI(q -> Ex & -Pxy)])] & Ep* AssumptionEI)*-In freelogic, part of an El assumption s existence of the in-;tantiated tem.)

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ALANMCMICHAEL(3) Cp 2, Simp,DefWorld(4) p AssumptionC)(5) Li[p > (3x)(3y)(-][@ --> Ex] & Pxy& (3q)[Wq & Li(q ->Ex & -Pxy)])] 2, Simp(6) (3x)(3y)(-LI1[@ -> Ex] & Pxy& (3q)[Wq & Li(q -> Ex &-Pxy)]) 4, 5, Necessity,P(7) -Li[@ -> Ex] & Pxy& (3q)[Wq & Li(q -> Ex & -Pxy)] &

Ex & Ey AssumptionEI, EI)(8) (3q)[Wq & Li(q -> Ex & -Pxy)] 7, Simp(9) Wq & Li(q -> Ex & -Pxy) & Eq AssumptionEI)

(10) Li(q -> Ex) 9, Simp, . .(11) O q 9, Simp,DefWorld(12) Cxq 10, 11, Constituency*(*-To applytheaxiomsin thisand thenextstep,wemustalso use'Ex' and 'Eq'.)(13) Li(@ -> Ex) 12, ActofConstits(14) -Li[@ ->Ex] 7, Simp

Sincethecontradictionomposed of 13) and (14) occursonlywith-in El and O subproofs, t sAssumption 1) alonewhich sresponsi-ble for the contradiction.Kit Fine avoids the contradiction y rejecting3b, thenecessaryexistenceof states-of-affairs.n theresultingmodal theory, tates-of-affairs uantifiersdo not commute withthe modal operators(that s,theBarcan formula nd itsconversedo nothold for tates-of-affairs). onsequently, nyworldtheory erivedfrom his heo-ryof states-of-affairsillcontainineliminableoccurrencesof themodal operators,withtheirattendantopaque contexts, nd so itwillnot be truly xtensional.Of course,this s no drawback tall if,because of theproblemsraisedin thetext,no satisfactoryxtensio-nal worldtheory s possible.Virginia olytechnicnstitutend State University

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A Problem for Actualism About Possible Worlds (McMichael)

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