Deep theorizing about possibility requires theorizing about possibleobjects. One popular approach regards the notion of a possible objectas intertwined with the notion of a possible world. There are twowidely discussed types of theory concerning the nature of possibleworlds: actualist representationism and possibilist realism. Theysupport two opposing views about possible objects. Examination of theways in which they do so reveals difficulties on both sides. There isanother popular approach, which has been influenced by the philosophyof Alexius Meinong. The Meinongian approach is relevant to theorizingabout possible objects because it attempts to construct a generaltheory of objects other than ordinary concrete existing objects.Independently of the debate about the nature of possible worlds orabout Meinongianism, it is not always as straightforward as it may atfirst appear to determine whether putative possible objects are indeedpossible. Another category of object similar to that of a possibleobject is the category of a fictional object. Although initiallyattractive, the idea that fictional objects are possible objectsshould not be accepted blindly. An important instance of theoreticalusefulness of possible objects is their central role in the validationof two controversial theorems of a simple quantified modal logic.

• 1. What They Are
• 2. Possible Worlds
  • 2.1 Possibilist Realism
    • 2.1.1 Modal Counterpart Theory
    • 2.1.2 Modal–Dimensionalism
    • 2.1.3 Specificity Problem
  • 2.2 Actualist Representationism
    • 2.2.1 Nesting Problem
    • 2.2.2 Essence Solution
    • 2.2.3 Other Solutions
• 3. Without Possible Worlds
  • 3.1 Subsistence vs. Existence
    • 3.1.1 Theory of Non-Existent Objects
    • 3.1.2 Theory of Encoding
• 4. Unicorns
• 5. Fictional Objects
• 6. Quantified Modal Logic
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. What They Are

Possible objects—possibilia (sing.possibile)—are objects that are possible. What it is tobe an object—which is a basic and universal metaphysicalcategory—will not be discussed but will be simply assumed asunderstood. What it is to be possible is the focus. Possibility of anobject should be understood in tandem with another notion, namely,actuality. The two notions are related at least in the following way:(i) every actual object is a possible object. A more controversialrelation between the two notions is expressed as follows: (ii) notevery possible object is an actual object, that is, some possibleobject is a non-actual object.

There is a wide-spread conservative view on objects, which says thatany object is an actual object. In other words, the adjective‘actual’ is redundant, for it excludes no object. Fromthis it follows that non-actual possible objects are not objects, thatis, they are nothing. Thus on this view, the adjective‘possible’ is equivalent to ‘actual’ whenapplied to objects and (ii) is false. This makes the notion of apossible object, or equivalently the notion of an actual object,uninteresting. The notion of an object is the basic notion and doesall the work. There is another conservative view on objects, whichdoes not deal in actuality or possibility directly. It deals inexistence instead. It is the view that any object is an existingobject. On this view, the following analog of (ii) is false: not everyobject is an existing object, that is, some object is a non-existingobject. This view makes the notion of an existing object equivalent tothat of an object; existence adds nothing to objecthood. If we combinetalk of actuality and talk of existence, we obtain five alternativeconservative views with varying degrees of conservatism:

(1) is a stronger claim than the other four. (2) and (3) are strongerthan (5) and (4), respectively. (1)-(3) give characterizations of allobjects, whereas (4) and (5) are more limited in scope. When the verb‘exists’ is understood with the most comprehensive domainof discourse (assuming the availability of such a domain), (5) isknown asactualism. If the domain of discourse for‘exists’ is stipulated to consist only of actual objects,(5) is trivial and compatible withpossibilism, the positionwhich says that some object is outside the domain consisting of allactual objects;cf. (ii). Most of those who advertise theirpositions as actualist hold not only (5) with the most comprehensivedomain of discourse in mind but also (1), and therefore (2)-(4) aswell. There are some theorists who hold (5), or at least do not deny(5), but deny (1). They do so by denying (3), that is, by maintainingthat some object is a non-existing object. Such a view is one versionof Meinongianism. But let us start with actualism and possibilism.

We shall first examine possibilism. It is superficially the mostcommonsensical position. It is superficially commonsensical to holdthat some objects are not actual: e.g., Santa Claus, the Fountain ofYouth. If we understand this view in terms of existence, that is, asthe claim that there are—that is, there exist—some objectsthat are not actual, we have possibilism. As we have noted,‘exist’ here should not mean “actually exist”but should be understood with a larger domain of discourse in mind.Such a domain is the domain containing not only actual objects butalso non-actual possible objects as genuine objects. To flesh out theidea of such a domain as proposed by the best-known version ofpossibilism, it is necessary to start with the idea of a possibleworld. After we articulate and examine possibilism as couched in thepossible-worlds framework, we shall discuss versions of actualism alsocouched in the possible-worlds framework. We shall then examine othertheories outside the possible-worlds framework.

2. Possible Worlds

According to the framework of possible worlds, all alethic modalstatements involving possibility are existential quantifications overpossible worlds and all alethic modal statements involving actualityare singular statements about a particular possible world, namely, theactual world (Kripke 1959, 1963a, 1963b). For example, to say thatJulius Caesar was possibly not assassinated is to say that JuliusCaesar was not assassinated at some possible world, and to say thatJulius Caesar was actually assassinated is to say that Julius Caesarwas assassinated at the actual world. Likewise with existence: to saythat Julius Caesar possibly existed is to say that Julius Caesarexisted at some possible world, and to say that Julius Caesar actuallyexisted is to say that Julius Caesar existed at the actual world.Assuming that the actual world is a possible world, it follows that ifJulius Caesar actually existed, he possibly existed.

In general, any object that actually exists possibly exists. Assumingthat actuality (of an object) is nothing but actual existence andpossibility (of an object) is nothing but possible existence, thisgrounds the plausible conceptual connection between actuality andpossibility noted earlier: (i) every actual object is a possibleobject. The overall philosophical merit of the possible-worldsframework cannot be judged without close scrutiny of its metaphysicalfoundations. Specifically, the two key questions which need to beasked are: “What are possible worlds in general?” and“What is the actual world in particular?” Metaphysicaltheorizing about possible worlds goes back at least to Leibniz, butthe contemporary theorizing is pursued largely on two distinct fronts;possibilist realism and actualist representationism.

2.1 Possibilist Realism

Possibilist realism takes non-actual possible objects to be (real,genuine) objects; it takes their metaphysical status to be on a parwith that of actual objects. When possibilist realists assert,“Non-actual possible objects exist”, their word‘exist’ has the same linguistic meaning as when actualistsassert, “Actual objects exist”. Possibilist realistsbelieve that some domains of discourse with respect to which‘exist’ may be understood include more than actualobjects, whereas actualists deny it. Thus according to possibilistrealism, to call an object non-actually possibly existent is merely todeny its inclusion in a particular realm—call it‘actuality’—and affirm its inclusion in some otherrealm. That other realm is no less a realm of existence than actualityis a realm of existence. All realms of existence are metaphysically ona par with one another. Every token use of the existence predicate isto be understood with respect to some realm of existence, eitherexplicitly or implicitly.

What distinguishes actuality from all other realms? The leading answeris due to David Lewis, who is the proponent of the best-known versionof possibilist realism, namely, modal counterpart theory.Lewis’s view on actuality is known as the indexical theory ofactuality (Lewis 1970). The basic idea is that actuality for us is therealm which includes us, and more generally, actuality forxis the realm which includesx. But there are many differentrealms which include us: this room, this building, this town, thiscontinent, this planet, this galaxy, this minute, this hour, this day,this month, this year, this century, etc. So, to fix our actuality asa unique realm which includes us, Lewis takes the largestspatiotemporal whole which includes us. More precisely, actuality forus is the maximal spatiotemporally related whole of which we are(mereological) part. In general, actuality forx is themaximal spatiotemporally related whole of whichx is part.For anything to exist non-actually-for-x but possibly is forit to be part of some realm outside actuality forx, that is,to be part of some maximal spatiotemporally related whole of whichx is not part. Note that this is a reductionist view ofexistence, both actual and non-actual possible. Existence is firstrelativized to a maximal spatiotemporally related whole, and thenexistence in such a whole is defined reductively in terms of(mereological) parthood. Lewis characterizes possible worlds asmaximal spatiotemporally related wholes. Actuality is the actualworld, and all other maximal spatiotemporally related wholes arenon-actual possible worlds.

A possible object is simply a part of a maximal spatiotemporallyrelated whole (Lewis 1986). (Strictly speaking Lewis prefers to say“analogically spatiotemporal” instead of“spatiotemporal” but we shall let that pass.) By mostcriteria, Lewis’s possible worlds, hence also his possibleobjects, fall under the label ‘concrete’ rather than‘abstract’. Every non-actual possible object (apart frompure Cartesian egos, perhaps) is a spatiotemporal object and bears nospatiotemporal relation to any actual object, or to any possibleobject exiting at any possible world at which it does not exist. Thismakes non-actual possible objects as real as non-actual possibleworlds. It is worth while to remind ourselves that this does not makeit automatically true to say that non-actual possible objects exist,even if we accept non-actual possible worlds. Whether it is true tosay so depends on the domain of discourse with respect to which theexistence predicate is to be understood.

2.1.1 Modal Counterpart Theory

On Lewis’s modal counterpart theory, every possible object isconfined to one possible world. Indeed, Lewis defines a possibleobject as an object all of whose parts exist at some single possibleworld (Lewis 1986: 211). This conception of a possible object forcesLewis to resort to his counterpart theoretic account of modalityde re (Lewis 1968). According to any possible-worlds theoryof modality, to say that you could have been the leader of a religiouscult is to say that at some possible world you are the leader of areligious cult. According to Lewis, to say that at a possible worldyou are the leader of a religious cult is to say that at that possibleworld there is a counterpart of you, that is, someone who resemblesyou to sufficient degrees in relevant respects, who is the leader of areligious cult. The counterpart relation is a similarity relation inmost cases (but arguably not in all cases). As such, it is not anequivalence relation. This affords Lewis ample theoreticalmaneuverability but at the same time causes him some theoreticaltrouble. For example, as Lewis himself admits, his counterparttheoretic account of modality either yields the consequence that everyactual object necessarily exists or yields the consequence that someactual object is not identical to itself (Lewis 1983: 32). There isalso a famous complaint voiced by Saul Kripke (Kripke 1972:344–45, note 13). It in effect says that whether someone otherthan you is the leader of a religious cult at some possible world isirrelevant to whether you could have been the leader of a religiouscult. Lewis’s reply to this is that thede re characterof the possibility is preserved by the stipulation that the person whois the cult leader is the counterpart of you, rather than thecounterpart of someone else, at an appropriate possible world. For anattempt to avoid counterparts and still retain a broadly Lewisianrealistic framework, see McDaniel 2004.

A significantly different counterpart theory is proposed by DeliaGraff Fara (Fara 2008, 2012). Fara analyzes modalityde re interms of sortal sameness rather than similarity. She clearlydistinguishes sortal sameness (e.g., “is the same boatas”) from identity (“is identical with”), and thisqualifies her analysis as a version of counterpart theory: a givenboat is F at a world if and only if at that world something that isthe same boat as--rather than identical with--that given boat is F.This also somewhat alleviates Kripke’s famous complaint againstcounterpart theory. Suppose that a boatB is actually made upof a hunk of woodW and a small plankP is a properpart ofW. It is intuitively sensible to hold thatBis identical withW, thatB could have lackedP as a part, and thatW could not have lackedP as a part. But this intuitive view appears internallyincoherent. IfB is identical withW andWcould not have lackedP as a part, then it appears thatB also could not have lackedP as a part; in otherwords,B withoutP appears to be an impossibleobject. On Fara’s analysis,B could have lackedP if and only if at some possible world, somex issuch thatx is the same boat asB andxlacksP, andW could have lackedP if andonly if at some possible world, somey is such thaty is the same hunk of wood asW andy lacksP. Sincey may not be the same boat asx(e.g.,y may not be a boat at all), there is not even anappearance of inconsistency with the latter lacking (a counterpart of)P and the former not lacking it. Thus, even ifB isidentical withW andW could not have lackedP,B could have lackedP, i.e.,BwithoutP is a possible object even thoughW withoutP is not. Whereas Lewis invokes similarity, which is relativeto contextually shifting respects, Fara invokes sortal sameness, whichis less shifty. Fara’s counterpart theory also interestinglyavoids denying the necessity of identity.

Independently of his counterpart theory, Lewis’s definition of apossible object has some peculiar consequences, given that existencein general is understood as bearing of the part-of relation to thewhole that constitutes the domain of discourse. Take any two possibleworldsw₁ andw₂. Lewis wantsto assert that bothw₁ andw₂exist in some sense. So for the assertion to be true, it must be truerelative to a domain of discourse which contains as a sub-domain somewhole of which bothw₁ andw₂are part. Not both are part of a single possible world or of its part.The smallest whole of which they both are part is the (mereological)sum ofw₁ andw₂. So, somedomainD containing such a sum as a sub-domain must count asan acceptable domain of discourse for the evaluation of an existenceclaim. Consider a proper partp₁ ofw₁ and a proper partp₂ ofw₂. Let Gerry be the sum ofp₁andp₂. Then it is true to say that Gerry existswhen the domain of discourse isD. So, there is a sense inwhich Gerry exists. In fact it is the same sense in whichw₁ andw₂ exist. But Gerry isnot a possible object, according to Lewis’s conception, forGerry does not have all of its parts at a single possible world. Thisis peculiar. Gerry is an object which exists in the same sense inwhich possible worlds exist but Gerry is not a possible object.Since—as sanctioned by the universality of mereologicalsummation, which Lewis accepts—Gerry is an object, Gerry is animpossible object. But there is nothing impossible about Gerry anymore than there is about the sum ofw₁ andw₂. Perhaps the sum ofw₁ andw₂ is an impossible object, too. But this ideaflouts the initially plausible principle of recombination forpossibility of objects, which says that ifx is a possibleobject andy is a possible object independent ofx,then the totality consisting exactly ofx andy is apossible object. Defenders of Lewis’s theory may take this tomean that the principle of recombination, despite its initialplausibility, is to be rejected. There is another unexpectedconsequence of Lewis’s theory. If the sum ofw₁ andw₂ is an impossibleobject, then the sum of all possible worlds is an impossible object,for the former is part of the latter and no impossible object is partof a possible object. But this makes the domain in which all possibleworlds reside, or “logical space”, an impossible object.This appears unwelcome. Lewis does consider an alternative conceptionof a possible object, which says that a possible object is an objectevery part of which exists at some possible world or other (Lewis1986: 211). This allows a possible object to have parts at differentpossible worlds. Lewis, who accepts the universality of mereologicalsummation, does not deny that possible objects in this sense are asreal as possible objects in his preferred sense. He however dismissesthem as unimportant on the ground that we do not normally name them,speak of them, or quantify over them. But given that sets of possibleworlds and sets of possible objects figure in important philosophicaldiscussions concerning the identity of propositions and properties,these sets seem important. If the sum of the members of an importantset is important, then Lewis’s dismissal appears hasty. Again,defenders of Lewis may stand this line of reasoning on its head andconclude that the sum of the members of an important set is not alwaysimportant.

A useful overview of various issues concerning Lewis’spossibilist realism, as well as actualist representationism, is foundin Divers 2002, which is the first systematic attempt to defend partsof Lewis’s theory since Lewis 1986. Cameron 2012 presents adefense of Lewis’s reductive analysis of modality. Loux 1979 isthe standard anthology of classical writings in modal metaphysics in1963–79.

2.1.2 Modal–Dimensionalism

Lewis’s is the most developed version of possibilist realismbased on possible worlds. As a result, discussion of possibilistrealism almost always focuses exclusively on Lewis’s version.There are, however, other versions of possible-worlds-basedpossibilist realism, and one of them deserves a brief mention. Assumethat the universe is spread out in three-dimensional space andpersists through one-dimensional time. The non-Lewisian version ofpossibilist realism in question may then be called‘modal–dimensionalism’. It says that in addition tothe four physical (spatiotemporal) dimensions, the universe has modaldimensions. Possible worlds are points in modal space as defined bythe modal axes just as physical spatiotemporal points are points inphysical spacetime as defined by the four physical spatiotemporalaxes, and possible objects “persist” through possibleworlds. A version of modal–dimensionalism is what W. V. Quineargued against when he took himself to be arguing against a typicalpossibilist realism (Quine 1976), and it is arguably the view manypossible-worlds theorists adumbrated, however vaguely and inchoately,as the representative possibilist realist theory before Lewisforcefully articulated his own version.

Modal–dimensionalism differs from Lewis’s theory in anumber of important respects but the most striking is the absence ofcounterpart theory. Modal–dimensionalism eschews counterpartsand proposes that to say that you are the leader of a religious cultat a possible world is to say that you yourself exist at that worldand are the leader of a religious cult at that world. Anotherdifference between modal–dimensionalism and Lewis’s theoryis that unlike the latter, the former avoids the mereologicalconception of the existence of a possible object at a possible world.According to modal–dimensionalism, just as a temporally orspatially persisting object is (arguably) not part of the temporal orspatial points or regions at which it exists, a modally persistingobject is not part of the possible worlds at which it exists.Modal–dimensionalism also differs from Lewis’s theory innot being a thoroughly reductionist theory. It does not analyze thenotion of a possible world in mereological terms but leaves it aslargely primitive (Yagisawa 2002, 2010, 2017). This enablesmodal–dimensionalists to allow the possibility of there being noconcrete object, whereas on Lewis’ theory, if there is noconcrete object, there is no possible world. For a different attemptto reconcile possibilist realism with the possibility of thenon-existence of anything concrete, see Rodriguez-Pereyra 2004.

Though free from some difficulties inherent in Lewis’stheoretical machinery, modal–dimensionalism has its ownobstacles to overcome, not the least of which is to make substantivesense of the idea of an object’s persisting not just in physicalspace and time but in modal space. One idea is to mimic the“endurantist” approach to temporal persistence and saythat a possible object persists through many possible worlds by havingall of its parts existing at each of those worlds. Another idea is tomimic the “perdurantist” approach to temporal persistenceand say that a possible object persists through many possible worldsby having different parts (world stages) at different possible worldsand being the modal-dimensional “worm” consisting of thoseworld stages. Note that this does not make the object mereologicalpart of a possible world at which it exists. It only makes each of theobject’s world stages part of the object. Lewis, in contrast,has it that a possible object has all of its parts at a singlepossible world (where they are mereological part of that world) andtherefore does not persist through different worlds at all. Despitethese differences, Lewis, speaking of the “perdurantist”version of modal–dimensionalism, says that it is but anotational variant of his own theory. He then proceeds to criticize it(Lewis 1968: 40–2). Lewis formulates his opposition tomodal–dimensionalism more carefully in Lewis 1986: 213–20.Achille Varzi derives Lewis’s theory from a theory similar tomodal–dimensionalism (Varzi 2001). Unlikemodal–dimensionalism, the theory he uses follows Lewis anddefines the existence of a possible object at a possible world interms of the object being mereological part of the world. Varzi notessome differences between this theory and Lewis’s. Vacek 2017defends modal-dimensionalism from some objections.

2.1.3 Specificity Problem

It is well known that Quine fiercely objects against the ontology ofnon-actual possible objects. Referring to an unoccupied doorway, heasks whether the possible fat man in the doorway and the possible baldman in the doorway are one possible man or two possible men (Quine,1948). The point of this rhetorical question is that there is noserious issue here because we have no non-trivial criterion ofidentity for non-actual possible objects. No respectable ontologyshould embrace objects for which we have no non-trivial criterion ofidentity. Quine encapsulates this in his famous slogan: “Noentity without identity”. Actual ordinary mid-sized objects havevague boundaries, so thesorites argument may be used to showthat we have no coherent non-trivial criterion of identity for them.Quine’s slogan then appears to apply to such objects. Some takethis to be good reason against the ontology of actual ordinarymid-sized objects, whereas others take this to be good reason againstQuine’s slogan. Whatever the ultimate fate of Quine’sslogan may be, there is an objection against possibilist realismwhich, while not explicitly invoking Quine’s slogan, is at leastQuinean in spirit. It goes as follows:

Lewis’s possibilist realism faces the problem of specifyingnon-actual possible objects. Take Vulcan, the innermost planet betweenSun and Mercury erroneously believed to exist by some astronomers inthe nineteenth century, when the universe was assumed to be Newtonian.Vulcan is not actually between Sun and Mercury or actually anywhere atall. Vulcan also does not actually have any mass, shape, or chemicalcomposition. Still it is possible that Vulcan be a unique planetbetween Sun and Mercury and have a particular massm, aparticular shapes, and a particular chemical compositionc. Or so it seems. It is also possible, it seems, that Vulcanbe a unique planet between Sun and Mercury and have a slightlydifferent particular massm′, a slightly differentparticular shapes′, and a slightly differentparticular chemical compositionc′, where the slightdifferences in question lie within the range of deviations theoriginal astronomers would have tolerated. So at some possible worldw Vulcan is a unique planet between Sun and Mercury and hasm,s, andc, and at some possible worldw′ Vulcan is a unique planet between Sun and Mercuryand hasm′,s′, andc′.Clearlyw andw′ are different worlds. OnLewis’s theory, every possible object exists at only one world.So either the planet in question atw is not Vulcan or theplanet atw′ is not Vulcan. Whichever planet that isnot Vulcan is Vulcan’s counterpart at best. Is either planetVulcan? If so, which one? If neither is, where is Vulcan? Whatpossible world hosts Vulcan? There seems to be no non-arbitrary way toanswer these questions within Lewis’s theory.

The modal-dimensionalist version of possibilist realism is capable ofoffering the ready answer, “The planet atw and theplanet atw′ are both (world stages of) Vulcan”,but faces an only slightly different challenge of its own. It seemsintuitive to say that there is a possible world at which Vulcan existsbetween Sun and Mercury and some remote heavenly body distinct fromVulcan but qualitatively identical with it in relevant respects (suchas mass, shape, size, chemical composition, etc.) also exists. Letw₁ be such a world and call Vulcan’s doubleatw₁ ‘Nacluv’. Thus atw₁, Vulcan and Nacluv exist, Vulcan is between Sunand Mercury, and Nacluv is somewhere far away. It is possible forVulcan and Nacluv to switch positions. So there is a possible world,w₂, which is exactly likew₁except that atw₂ Nacluv is between Sun andMercury and Vulcan is far away. Since Vulcan and Nacluv are twodistinct objects,w₁ andw₂are two distinct worlds. But this difference seems empty. Given thatw₁ andw₂ are exactqualitative duplicates of each other, on what ground can we say thatthe object between Sun and Mercury atw₁ and faraway atw₂ is Vulcan and the object far away atw₁ and between Sun and Mercury atw₂ is Nacluv, rather than the other way around? Itis unhelpful to say that Vulcan and Nacluv are distinguished by thefact that Vulcan possesses Vulcan’s haecceity and Nacluv doesnot. An object’s haecceity is the property of being that veryobject (Kaplan 1975, Adams 1979, Lewis 1986: 220–48). Since whatis at issue is the question of which object is Vulcan, it does nothelp to be told that Vulcan is the object possessing the property ofbeing that very object, unless the property of being that very objectis clarified independently. To say that it is the property of beingthat very object which is Vulcan is clearly uninformative. It is notobvious that there is any way to clarify it independently.

Alternatively, one might choose to insist that if anything at anypossible world is Vulcan, it has to possess at that world theproperties relevant to the introduction of the name‘Vulcan’, such as being the heavenly body withsuch-and-such mass and orbit and other astrophysical characteristicsand being between Sun and Mercury in a Newtonian universe. This issupported by descriptionism concerning the semantics of proper names,according to which ‘Vulcan’ is a proper name which issemantically equivalent to a definite description (‘the heavenlybody with such-and-such mass and ...’). But forceful criticismsof descriptionism for proper names were launched in the early 1970s(Donnellan 1972, Kripke 1972). Kripke’s criticism has beenespecially influential. The kernel of Kripke’s criticism restson the intuitive idea that a sentence containing a referring propername expresses a singular proposition about the referent independentlyof any qualitative characterization of the referent but that acorresponding sentence containing a description does not so express asingular proposition. If Kripke’s criticism applies to‘Vulcan’, it is difficult to defend descriptionism for‘Vulcan’. But ‘Vulcan’ and other apparentproper names of non-actual possible objects may not be as readilyamenable to the Kripkean considerations as proper names of actualobjects are. The so-called “problem of empty names” is theproblem of providing a semantic theory for “empty names”like ‘Vulcan’ as non-descriptional designators. For somerecent contributions to the project of solving this problem, see Braun1993, 2005, Everett & Hofweber 2000, Brock 2004, Piccinini &Scott 2010, Cullison & Caplan 2011, Kripke 2013.

2.2 Actualist Representationism

According to actualist representationism, which is also known underLewis’s tendentious labelersatzism, a possible worldis an actual maximally consistent representation of how the universecould possibly have been, and the actual world is the representationof how the universe actually is. A representationr ismaximally consistent if and only ifr is consistent and forany representationr′, eitherr &not-r′ is not consistent orr &r′ is not consistent (assuming the appropriateconceptions of the negation and conjunction of representations).Different actualist representationists employ different actual itemsto play the role of the maximally consistent representations, such assentences, propositions, states of affairs, properties, etc. (Adams1974, Armstrong 1989, Bigelow and Pargetter 1990, Carnap 1947,Cresswell 1972, Forrest 1986, Hintikka 1962, Jeffrey 1965, Lycan 1979,Lycan & Shapiro 1986, Plantinga 1974, 1987, Prior & Fine 1977,Quine 1968, Roper 1982, Skyrms 1981, Stalnaker 1976). Note that thenotion of consistency of a representation is not ultimately eliminatedin actualist representationism. Most actualist representationistsaccept consistency as a modal notion, for they doubt it can be reducedto a non-modal notion, such as a proof-theoretic notion or amodel-theoretic notion. If those actualist representationists areright and consistency is indeed a modal notion, then actualistrepresentationism is not a reductionist theory of modality. This,however, should not automatically be taken to be a serious challengeto actualist representationism, for a thoroughly reductionist theoryof modality may or may not be feasible. Not even every possibilistrealist believes in thorough reduction;cf.modal–dimensionalists.

It is important to note that according to most versions of actualistrepresentationism, the universe, as it (actually) is, is not theactual world. Since the actual world is a possible world and everypossible world is a representation, the actual world is arepresentation. The universe, as it (actually) is, is not arepresentation but includes all representations, along with everythingelse. But it does not include non-actual possible objects. Theuniverse includes all and only those objects which exist.

In actualist representationism, existence is conceptually prior toactual existence. This is in concert with the priority of the truth ofany propositionP over the actual truth ofP.P is actually true if and only ifP is true at theactual world, which in turn is so if and only if the actual worldrepresentsP as true. And by definition, the actual world isthe possible world which representsP as true if and only ifP is true. Likewise, for an object to exist at the actualworld is for the actual world to represent it as existing; the actualworld represents an object as existing if and only if the objectexists. Actual existence is thus reducible to existencesimpliciter.

Non-actual possible existence is defined as existence at some possibleworld other than the actual world, which in turn is defined in termsof existencesimpliciter as follows:x exists at apossible worldw not identical with the actual world if andonly ifx would exist ifw were actual, that is, ifthe universe were asw represents it to be. According to thispicture, non-actual possible existence is not a special mode ofexistence completely separate from actual existence. It is notexistencesimpliciter, but instead “would-be”existencesimpliciter on a counterfactual supposition. Thereis no room for non-actual possible objects in this picture. Manyrepresentations which are possible worlds other than the actual worldinclude representations of the existence of non-actual possibleobjects, but non-actual possible objects are not mereological part ofthose possible worlds. Neither are they set-theoretic members, orconstituents in any other sense, of those possible worlds. For them toexist at those possible worlds is for the worlds to say (represent)that they exist; nothing more, nothing less. This is a non-realistpicture of the existence of the non-actual. Non-actual possibleobjects are thus nothing at all. This is the conservative view(1).

Let us examine how actualist representationists handle apparent modaltruths asserting the possibility of non-actual objects. There are twotypes of such truth and the first type is easy to handle. It ispossible that Julius Caesar (congenitally) had a sixth finger on hisright hand (whereas, we assume, he actually had only five fingers).This possibility only calls for a possible world to represent JuliusCaesar as having had a sixth finger on his right hand, which mayeasily be done by means of, say, the (interpreted English) sentence,‘Julius Caesar had a sixth finger on his right hand’.

2.2.1 Nesting Problem

The second type of apparent modal truth, however, is more challenging.Julius Caesar could have had a sixth right finger which was neverburnt but which could have been burnt. This involves a nestedpossibility, which is troublesome to actualist representationism(McMichael 1983). To reveal the nesting clearly, let us articulate thepossibility in question in a more pedantic and rigorous way. Thefollowing is possible: Julius Caesar had a sixth right finger suchthat (a) it was never burnt, and (b) the following is possible: it wasburnt. The trouble for actualist representationism is that there is noobvious way to make sense of the pronoun ‘it’ in (b). Thepossibility of Julius Caesar having had a sixth right finger which wasnever burnt is, as before, easily representable by, say, the sentence,‘Julius Caesar had a sixth right finger which was neverburnt’. This means that the pronoun ‘it’ in (a) isunproblematic; it is replaceable by ‘Julius Caesar’s sixthright finger’. How about the pronoun ‘it’ in (b)? Itshould designate the sixth right finger Julius Caesar is said to havehad within the scope of the first possibility operator. It shouldtherefore be bound by the appropriate existential quantifier, justlike the pronoun ‘it’ in (a). But unlike the pronoun‘it’ in (a), the pronoun ‘it’ in (b) occursseparated from the quantifier by the intervening second possibilityoperator, ‘the following is possible’. This“quantifying in” from outside the possibility operatorforces the sentence representing the possibility specified in (b) toretain the pronoun ‘it’: ‘it was burnt’. Thus,unlike the pronoun ‘it’ in (a), the pronoun‘it’ in (b) is not eliminable in the representation of thepossibility in question. But no part of the representation that is thepossible world in question, or any other possible world, may serve asthe object which the pronoun ‘it’ in (b) designates, asthe pronoun needs to designate something that is said to be a humanfinger but no part of any such representation is said to be a humanfinger. Notice that Lewis has no corresponding difficulty here. On histheory, the modal statement in question is true if and only if at somepossible world there is a counterpart of Julius Caesar who had a sixthright fingerf such thatf was never burnt and atsome possible world there is a counterpart off which wasburnt. Julius Caesar, his counterpart, and the counterpart’ssixth fingerf are all real objects, and the pronoun‘it’ in (b) designatesf. (Note that the pronoun‘it’ in (b) does not designate the counterpart off any more than ‘it’ in (a) does.)

One way to handle this without postulating a non-actual possibleobject is to say that there was an actual finger belonging to someoneelse and that it could have belonged to Julius Caesar’s righthand as his extra finger (congenitally). If this sounds biologicallytoo bizarre, actualist representationists may say instead that thereare actual elementary particles none of which was part of JuliusCaesar’s body but which collectively could have constituted hissixth right finger. This is along the lines of David Kaplan’spossible automobile (Kaplan 1973: 517, note 19) and NathanSalmon’s Noman (Salmon 1981: 39, footnote 41). Kaplan imagines acomplete set of automobile parts laid out on a factory floor ready forassembly. If the parts are assembled, a particular automobile will becreated; if not, not. Suppose that the parts are destroyed before theyare assembled. Then the particular automobile which would have beencreated if the parts had been assembled is in fact not created. It isa non-actual possible automobile. Salmon, taking a cue fromKripke’s suggestion of the necessity of origin (Kripke 1972),imagines a particular human egg and a particular human sperm whichcould merge into a particular human zygote and develop into aparticular human being. Suppose that the egg and the sperm in factfail to merge, hence fail to develop into a human being. Theparticular human being, Noman, who would have been created if the eggand the sperm had merged and developed normally is in fact notcreated. Noman is a non-actual possible human being. These lines ofthought afford actualist representationists a powerful means toaccommodate many apparently recalcitrant modal truths about non-actualpossible objects, provided that these non-actual possible objects canbe individuated uniquely by means of actually existing potential partsor origin. In fact, it may even be taken further to afford actualistrepresentationists a way to maintain that Kaplan’s automobile isnot only possible but is an actual object after all. This can be doneby not only individuating Kaplan’s automobile uniquely by meansof the collection of the automobile parts but also identifying it withthe collection. Call Kaplan’s automobile‘k’. Suppose thatk is identical withthe collection. Then there exists an actual object, namelyk,which actually is not an automobile but is a collection of automobileparts and which is possibly an automobile. That is,k isrepresented as an unassembled collection of automobile parts by theactual world and is represented as an automobile by some possibleworld. Similarly, actualist representationists may identify Noman withthe collection of the egg and the sperm. Noman is an actual objectwhich actually is not a human being but is a collection of an egg anda sperm and which is possibly a human being. The case of JuliusCaesar’s sixth finger can be handled likewise. There exists anactual object which actually is not a finger but is a (widelyscattered) collection of particles and which is possibly JuliusCaesar’s sixth right finger.

But now consider the planet Vulcan. There is no collection of actualparticles which were supposed to constitute Vulcan. So, if Vulcan is anon-actual possible object, which it apparently is, it seems possiblefor Vulcan to exist and not be constituted by any actual particlesdifferently located and arranged. Likewise, it seems perfectlypossible that Julius Caesar had a sixth finger which was notconstituted by any actually existing particles and satisfied (a) and(b). Despite initial plausibility, actualist representationists maychoose to deny such a possibility. To do so is, in effect, to commitoneself to the position that the universe, as it actually is, alreadycontains maximally possible constituents of any possible state of theuniverse, that is, it is impossible for the universe to contain even asingle constituent object not already in the universe as it actuallyis. To make this plausible is not an easy task. If, on the other hand,actualist representationists choose not to deny the possibility inquestion, they appear to have to say that Julius Caesar’sentirely new sixth finger is not an object but is possibly an object.But then the problem is to make sense of the finger’s beingnothing yet possibly something. How can there be a true predication ofany kind, including “is possibly an object”, of nothing?(Oliver & Smiley 2013 offers the beginning of a partial answer tothis question.)

2.2.2 Essence Solution

Alvin Plantinga is responsible for a widely-discussed actualistrepresentationist response to this problem. He invokes unactualizedindividual essences (Plantinga 1974, 2003). Every object is said tohave an individual essence. An individual essence of a given object isa property which that object necessarily has and everything elsenecessarily lacks. Moreover, and this is crucial to the solution ofthe problem at hand, individual essences are independent of theobjects which have them, whether the objects are actual or non-actual.That is, an individual essence can exist without being an individualessence of any existing object. The problematic pronoun‘it’ in (b) is then said to designate such an individualessence, and the rest of the characterization of the possibility inquestion is appropriately and systematically reinterpreted. Forexample, ‘it was burnt’ in (b) is reinterpreted to meanthat the individual essence in question is an individual essence ofsomething that was burnt.

One difficulty with this view is the failure to produce a singleplausible example of such an essence. We saw that possibilist realismfaces the problem of specifying non-actual possible objects.Plantinga’s version of actualist representationism faces its ownversion of the Quinean challenge, namely, the problem of specifyingthe individual essences which are supposed to replace non-actualpossible objects. What individual essence did Julius Caesar have? Whatreadily comes to mind is the property of being Julius Caesar. As RuthBarcan Marcus and Kripke have forcefully argued (Barcan 1947, Marcus1961, Kripke 1972), identity is necessary; that is, if an objectx is identical with an objecty, it is necessarilythe case thatx is identical withy. Given this, itis easy to see that Julius Caesar necessarily had the property ofbeing Julius Caesar and everything other than Julius Caesarnecessarily lacks it. However, it is implausible to suggest that thisproperty is independent of Julius Caesar. Our canonical specificationof it by means of the noun phrase ‘the property of being JuliusCaesar’ certainly is not independent of our canonicalspecification of Julius Caesar by means of the name ‘JuliusCaesar’, and this does not seem to be an accidental fact merelyindicative of the paucity of our language devoid of deep metaphysicalunderpinnings. Kaplan’s automobile and Salmon’s Nomanmerely push the dependence of the individual essence to the level ofthe constituent parts or origin of the object of which it is anindividual essence. This difficulty is magnified when we ask for aspecification of an individual essence of Vulcan or JuliusCaesar’s entirely new finger. For more on individual essence,see Adams 1981, McMichael 1983, Fine 1985, Menzel 1990, Lycan 1994,Linsky & Zalta 1994, Plantinga 2003.

2.2.3 Other Solutions

Theodore Sider proposes a different solution to the nesting problem(Sider 2002). According to his proposal, we should not regarddifferent non-actual possible worlds as achieving their representationmore or less independently of one another. Instead, we should regardall possible worlds as representations which are given all at once inconcert with one another so that cross references to non-actualpossible objects by different possible worlds are guaranteed from theoutset.

Reina Hayaki proposes yet another solution (Hayaki 2003). When we saythat Julius Caesar had an unburnt sixth right finger at some possibleworldw₁, we takew₁ torepresent Julius Caesar as having an unburnt sixth right finger. Whenwe say further that that finger atw₁ was burnt ata different possible worldw₂, we should likewisetakew₂ to represent that finger as having beenburnt. According to Hayaki, this requires a hierarchical arrangementof possible worlds in which the representation of the finger byw₂ is parasitic on the representation byw₁.

Other solutions to the nesting problem include the claim that despitestrong appearance to the contrary, there are no modal statements aboutobjects which do not actually exist; see Adams 1981, Fitch 1996.

3. Without Possible Worlds

Some important theories concerning possible objects and related issuesdo not invoke possible worlds as a theoretical cornerstone. Mostprominent among them are so-called Meinongian theories. But beforeturning to them, let us briefly take note of two non-Meinongianapproaches outside the framework of possible worlds: Kit Fine’sand Michael Jubien’s.

Like Plantinga, Fine takes individual essences seriously but heregards the notion of necessity as prior to the notion of a possibleworld, and the notion of an individual essence as prior to the notionof necessity (Fine 1994, 1995a, 1995b, 2000). Fine’s modaltheory is based on the broadly Aristotelian idea that alethic modalitystems from natures of things. Understanding of actual or non-actualpossible objects should therefore be firmly grounded on understandingof natures of things. Fine believes that ‘There is a possibleobjectx’ is reducible to ‘Possibly there is anobjectx’ (Prior and Fine 1977: 130–9, Fine 1979,1981, 2003). For a similar reductive proposal, see Peacocke 1978,2002. For some difficulties with such a project, see Hazen 1976.

Jubien builds his modal theory out of properties and their relations(Jubien 1996, 2009). The possibility of Julius Caesar’s havinghad an entirely new sixth right finger satisfying (a) and (b) isanalyzed roughly as follows: the property of being a particular sixthfinger on Julius Caesar’s right hand is simultaneouslycompatible with the properties of existing, being composed ofnon-actual stuff, and being never burnt, and also simultaneouslycompatible with the properties of existing, being composed ofnon-actual stuff, and being burnt. The underlying idea is to startwith the ontology of stuff and use properties and relations, includingmodal properties and relations, as the fundamental metaphysical itemsto account for all statements about objects, including all modalstatements about possible objects. It specifically avoids talk ofnon-actual possible objects. It, however, does not avoid talk ofnon-actual possible stuff. So it does embrace the ontology of thenon-actual possible in a broad sense.

3.1 Subsistence vs. Existence

Alexius Meinong’s theory of objects has had much influence onsome contemporary theorists, resulting in a variety of proposals.These proposals are known broadly as Meinongian. According to Meinong,a subject term in any true sentence stands for an object (Meinong1904). So the subject term in the sentence, ‘The sixth rightfinger of Julius Caesar is a finger’, stands for an object,assuming that the sentence is true. (Such an assumption is stronglydisputed in Salmon 1987.) Even though the exact respects in whichcontemporary Meinongian proposals are Meinongian and the extent oftheir Meinongianism differ from one proposal to another, all of theminherit this claim by Meinong in some form. They are thus united inresisting Bertrand Russell’s criticism of Meinong, whichmandates analyzing sentences containing a definite description, likethe one above concerning the sixth right finger of Julius Caesar, asgeneral statements rather than singular statements (Russell 1905); see3.1.2 for a particularly famous piece of Russell’s criticism andhow two leading Meinongian theories handle it.

Meinong distinguishes two ontological notions: subsistence andexistence. Subsistence is a broad ontological category, encompassingboth concrete objects and abstract objects. Concrete objects are saidto exist and subsist. Abstract objects are said not to exist but tosubsist. The talk of abstract objects may be vaguely reminiscent ofactualist representationism, which employs representations, which areactual abstract objects. At the same time, for Meinong, the nature ofan object does not depend on its being actual. This seems to giveobjects reality that is independent of actuality. Another interestingfeature of Meinong’s theory is that it sanctions the postulationnot only of non-actual possible objects but also of impossibleobjects, for it says that ‘The round square is round’ is atrue sentence and therefore its subject term stands for an object.This aspect of Meinong’s theory has been widely pointed out, butnon-trivial treatment of impossibility is not confined toMeinongianism (Lycan & Shapiro 1986). For more on Meinong’stheory, see Chisholm 1960, Findlay 1963, Grossmann 1974, Lambert 1983,Zalta 1988: sec.8. For some pioneering work in contemporaryMeinongianism, see Castañeda 1974, Rapaport 1978, Routley 1980.We shall examine the theories of two leading Meinongians: TerenceParsons and Edward Zalta. We shall take note of some other Meinongianslater in the section on fictional objects, as their focus is primarilyon fiction. Parsons and Zalta not only propose accounts of fictionalobjects but offer comprehensive Meinongian theories of objects ingeneral.

3.1.1 Theory of Non-Existent Objects

Quine thought it curious that the ontological problem was so simple asto be put in three monosyllables: “What is there?” Hefamously answered this simple question equally simply:“Everything” (Quine 1948). Parsons rejects Quine’sclaim that every object exists, and asserts that some objects do notexist. Parsons proposes a theory of all objects, both existent andnon-existent (Parsons 1980). He uses the word ‘actual’ asa synonym for ‘existent’, so he rejects (1), (2), and (3),but accepts (4) and (5) as trivialities. It would be a mistake toclassify him as an actualist simply because he accepts (5). On thecontrary, he has much in common with possibilists in claiming thatsome objects are not actual, that is, in denying (2). He, however,admits only one sense of existence and claims that some objects do notexist in that sense. If this sole sense of existence corresponds tothe possibilist conception of existence relativized to any domain ofdiscourse smaller than the largest available domain, then Parsons isin agreement with possibilists. But if it corresponds to thepossibilist conception of existence relativized to the largestavailable domain, then Parsons’ ontology goes beyond that ofpossibilists. There is good evidence that the latter is the case, forParsons’ ontology, as a typically Meinongian ontology, includesthe round square and other impossible objects, which the possibilistontology does not include. Lewis’s discussion (Lewis 1990) ofhow the non-Meinongian should understand “noneism”, whichis the view that some things do not exist, held by another Meinongian,Richard Routley (later Richard Sylvan), is helpful in this connection.For differences between Routley’s theory and Parsons’, seeParsons 1983. A sympathizer of Routley, Graham Priest, usesdialetheism (the thesis that some contradictions are true) andparaconsistent logic, along with the (possible- and impossible-)worlds framework, to bolster noneism (Priest 2005, 2016).

Parsons’ theory is based on the Meinongian distinction betweennuclear and extra-nuclear properties. Nuclear properties include allordinary properties, such as being blue, being tall, being kicked bySocrates, being a mountain, and so on. Extra-nuclear propertiesinclude ontological properties such as existence and being fictional,modal properties such as being possible, intentional properties suchas being thought of by Socrates, and technical properties such asbeing complete. See Parsons 1980: 24–27, 166–74 for moreon nuclear and extra-nuclear properties and a test for distinguishingbetween them. Parsons’ theory can be encapsulated in thefollowing two principles:

Take the set of nuclear properties, {being golden, being a mountain}.By (P1) and (P2), some unique object has exactly the two nuclearproperties in the set. That object is the golden mountain. Takeanother set of nuclear properties, {being square, being round}, andthe two principles give us the round square. Both of these objects areradically incomplete; they have no weight, height, shape, or size, forexample. The need for distinguishing nuclear properties fromextra-nuclear properties is readily seen by considering the set,{being golden, being a mountain, being existent}. If (P2) is to applyto such a set, it should yield an object having the three propertiesin the set. Such an object is golden, a mountain, and existent, thatis, it is a golden mountain which exists. So it should be true that agolden mountain exists, but it is in fact not true. Parsons defines apossible object as an object such that it is possible that there existan object having all of its nuclear properties. On this conception,all existing objects are possible objects, some golden mountains arepossible objects, and the round square is not a possible object. It isworth noting that in Parsons’ theory, negation needs to behandled delicately (Parsons 1980: 19–20, 105–06, Zalta1988: 131–34). Take the set, {being round, being non-round}. By(P2), we have an object,x, which is round and non-round. So,x is non-round. If we can infer from this that it is not thecase thatx is round, then we should be entitled to say thatx is round and it is not the case thatx is round,which is a contradiction. Thus, we should not be allowed to infer‘It is not the case thatx is round’ from‘x is non-round’.

If Julius Caesar’s entirely new right finger satisfying (a) and(b) is to be a Meinongian object of Parsons’ theory, the bestcandidate appears to be a non-existent incomplete object correspondingto the set of properties, {being a finger, belonging to JuliusCaesar’s right hand, being never burnt}. This set includesneither the property of being constituted by particles which do not(actually) exist nor the property of being possibly burnt. Both ofthese properties are extra-nuclear properties, hence ineligible to beincluded in a set to which (P2) applies. So (P2) does not confer themon the object corresponding to the set. How then does the object cometo have the properties? It is not obvious how this question should beanswered (Parsons 1980: 21, note 4, where Parsons says, “Thepresent theory is very neutral aboutde remodalities”), but we should at least note that onParsons’s theory, objects are allowed to have properties notincluded in their corresponding sets of nuclear properties: e.g., theround square, whose corresponding set only includes roundness andsquareness, has the property of being non-existent and the property ofbeing incomplete. Also, Parsons allows nuclear properties which are“watered-down” versions of extra-nuclear properties. Sothe set may include the “watered-down” versions of the twoextra-nuclear properties in question and that may be enough. For moreon these and related issues in Parsons’ theory, see Howell 1983,Fine 1984.

3.1.2 Theory of Encoding

Zalta’s theory is based on the distinction made byMeinong’s student, Ernst Mally, between two kinds ofpredication: exemplification and encoding (Mally 1912, Zalta 1983,1988). The idea is to maintain the Meinongian claim that the roundsquare is a genuine object while avoiding contradicting oneself.Russell argues that since the round square is round and square, andsince if an object is square it is not the case that it is round, itfollows that the round square is such that both it is round and it isnot the case that it is round, which is a contradiction. Parsonsavoids the contradiction by refusing the inference from‘x is square’ to ‘it is not the case thatx is round’, where ‘x’ ranges overall objects. In contrast, Zalta accepts the inference for all objectsand avoids the contradiction by refusing to interpret the predication,‘is round and square’, of the round square asexemplification. He instead interprets it as encoding; the roundsquare encodes roundness and squareness. Encoding squareness is notincompatible with encoding roundness, even though exemplifyingsquareness is incompatible with exemplifying roundness. Predication asunderstood as encoding follows a different logic from predication asunderstood as exemplification. The crux of Zalta’s theory isencapsulated in the following two principles:

Some object is the round square, for, by (Z2), among objects whichcould never have a spatial location is an object which encodesroundness and squareness. The noun phrase, ‘the roundsquare’, unambiguously denotes such a necessarily non-spatialobject. Other noun phrases of the same kind include those which denotenumbers, sets, Platonic forms, and so on. There are, however, manynoun phrases which are ambiguous. They allow an interpretation underwhich they denote an object that is necessarily non-spatial, and alsoallow an interpretation under which they denote an object that ispossibly spatial and possibly non-spatial. The phrase, ‘thegolden mountain’, is an example. The golden mountain in onesense is an object which is necessarily non-spatial and which encodesgoldenness and mountainhood. The golden mountain in the other sense isan object which actually is non-spatial but could be spatial. When wesay that the golden mountain in the second sense is golden, it meansthat necessarily if the golden mountain is spatial, it is golden.Since, by (Z1), such an object cannot encode properties, allpredications in the preceding sentence have to be understood asexemplification. Similarly with Julius Caesar’s entirely newfinger satisfying (a) and (b).

Zalta endorses the claim that some objects are non-actual possibleobjects, so he appears to side with possibilists. But he defines anon-actual possible object as an object which could have a spatiallocation but does not (Zalta 1988: 67). So the claim means for Zaltathat some objects could have a spatial location but do not. This iscompatible with actualism, provided that all such objects are actualin the sense of actually existing (Linsky & Zalta 1994, alsoWilliamson 1998, 2002, 2013; it is noteworthy that Timothy Williamsonindependently argues for what he callsnecessitism, whichsays [in a nutshell] that every possible object is a necessaryobject). If we understand Zalta’s theory this way, we have thefollowing actualist picture: all objects are actual and existing, someobjects are necessarily non-spatial, and other objects are possiblyspatial and possibly non-spatial. (For an alternative interpretationof Zalta’s formal theory, according to which some objects do notexist, see Zalta 1983: 50–52, 1988: 102–04, Linsky &Zalta 1996: note 8.) Among the latter type of objects are those whichare actually spatial but possibly not, like you and me, and thosewhich are possibly spatial but actually not, like the golden mountainin the appropriate sense. The distinction between the golden mountainin this (exemplification) sense and the golden mountain in the other(encoding) sense is key to overcoming some objections (Linsky &Zalta 1996). See Bennett 2006 for the claim that the Linsky-Zalta viewis not actualist, and Nelson & Zalta 2009 for a response. Hayaki2006 critiques both Linsky-Zalta and Williamson.

If we confine our attention to necessarily non-spatial objects, adefinition of a possible object which corresponds to Parsons’definition is easily available to Zalta: a possible (necessarilynon-spatial) object is a (necessarily non-spatial) object such thatsome object could exemplify exactly the properties it encodes. In thissense, some object which encodes goldenness and mountainhood, amongother properties, is a possible object but the object which encodessquareness and roundness is not. Julius Caesar’s entirely newfinger satisfying (a) and (b) can be treated in the same way as thegolden mountain. Complications similar to those which arise forParsons’ theory do not arise for Zalta’s theory, for allproperties are equally subject to encoding, including those propertiesParsons regards as extra-nuclear. For a comparison of thetwo-kinds-of-property approach and the two-kinds-of-predicationapproach, see Rapaport 1985.

4. Unicorns

If anything is a non-actual possible object, a unicorn is. Or so itappears. But Kripke vigorously argues against such a view in the 1980version of Kripke 1972: 24, 156–58. His argument starts with theassumption that the unicorn is (intended to be) an animal species ifanything. This excludes the possibility that a horse with a hornartificially attached to its forehead is a unicorn. Kripke assumesobviously that there are actually no unicorns and that unicorns arepurely mythical creatures. Also assumed is the absence in the relevantmyth of any specification of the genetic structure, evolutionaryhistory, or other potentially defining essential features of theunicorn. (Possession of a horn is not a defining essential feature ofthe unicorn any more than having tawny stripes is a defining featureof the tiger.) The myth describes the unicorn only in stereotypicalterms: looking like a horse, having a horn protruding from itsforehead, etc. Suppose that there are objects with all suchstereotypical features of the unicorn. This seems perfectly possibleand Kripke accepts such a possibility. But he rejects its sufficiencyfor establishing the possibility of unicorns. Suppose that among theobjects with the stereotypical unicorn features, some have a geneticmakeup, an evolutionary history, or some other potentially definingessential unicorn characteristic which is radically different from thecorresponding characteristic had by the others with the samestereotypical unicorn features. Which ones among those with thestereotypical unicorn features would then be real unicorns and whichones fool’s unicorns (à la fool’s gold)?There is no fact of the matter. Given that the unicorn is an animalspecies, not everything that looks and behaves like a unicorn isguaranteed to be a unicorn. To be a unicorn, an object has to possessthe defining essential characteristics of the unicorn. But there areno defining characteristics of the unicorn; the myth does not specifythem, and the universe does not instantiate them. This surprisingargument has convinced many philosophers of the impossibility ofunicorns, but others have raised doubt by arguing that the notion of abiological kind, such as a species, is far more malleable than Kripkeassumes (Dupré 1993).

The line of argument Kripke uses, if successful, is applicable to allnon-actual natural kinds and their analogs (except for natural-kindanalogs of Kaplan’s automobile or Salmon’s Noman). It isunclear that it or something like it is successfully applicable toindividuals like Vulcan, but if it is, then we must say that suchindividuals are impossible objects. Some theorists liken Vulcan tofictional objects, as we will see in the next section, and sometheorists argue that fictional objects are impossible objects (Kaplan1973, 1980 version of Kripke 1972: 157–58, Fine 1984:126–28, Yagisawa 2010: 271–77). If Vulcan is an impossibleobject, the problem of uniquely specifying Vulcan, as opposed toNacluv, becomes less urgent, for it is not evident that we should beable to specify an impossible object uniquely and non-trivially.

5. Fictional Objects

Let us shift our attention from mythological creatures to fictionalobjects. Fictional objects include fictional characters but not allfictional objects are fictional characters. Sherlock Holmes is afictional object and a fictional character. His liver is a fictionalobject but not a fictional character. It may be tempting to think thatfictional objects are non-actual possible objects, even though it isobvious that not all non-actual possible objects are fictionalobjects.

There are two main problems with the claim that fictional objects arepossible objects. One is the problem of impossible fictional objects.Some fictional objects are ascribed incompatible properties in theirhome fiction by their original author (usually inadvertently). Thisseems to be sufficient for them to have those properties according totheir home fiction, for what the author says in the fiction(inadvertently or not) seems to hold the highest authority on truth inthat fiction. On the assumption that a fictional object has a givenproperty if it has that property according to its home fiction, thosefictional objects are impossible objects, for no possible object hasincompatible properties. The other problem is the failure ofuniqueness. It may be viewed as the problem of meeting the Quineandemand for clear identity conditions. Holmes is a particular fictionalobject. So if we are to identify Holmes with a possible object, weshould identify Holmes with a particular possible object. But thereare many particular possible objects that are equally suited for theidentification with Holmes. One of them hasn-many hairs,whereas another has (n+1)-many hairs. No fictional storyabout a particular fictional object written or told by a human beingis detailed enough to exclude all possible objects but one to beidentified with that fictional object, unless it is a fiction about anactual object or a non-actual possible object analogous toKaplan’s automobile or Salmon’s Noman.

Strangely enough, there is also a problem with the claim thatfictional objects are non-actual objects. That is, there is someplausible consideration in support of the claim that fictional objectsare actual objects. We make various assertions about fictional objectsoutside the stories in which they occur and some of them are true: forexample, that Sherlock Holmes is admired by many readers of the Holmesstories. The simplest and most systematic explanation appears to be topostulate Holmes as an actual object possessing the properties suchtrue assertions ascribe to him. Fictional objects may then be said tobe theoretical objects of literary criticism as much as electrons aretheoretical objects of physics. This type of view enjoys surprisinglywide acceptance. (Searle 1974, van Inwagen 1977, 1983, Fine 1982,Salmon 1998, Thomasson 1999). The theorists in this camp, except vanInwagen (van Inwagen 2003: 153–55), also think that fictionalobjects are brought into existence by their authors as actual objects.Even if this type of view is to be followed, it must still be deniedthat Holmes is actually a detective, for if we enumerate allindividuals who are actually detectives, Holmes will not be amongthem. By the same token, Holmes is not actually a resident of BakerStreet or even a human being. Though actual, Holmes is actually hardlyany of those things Conan Doyle’s stories describe him as being.Holmes must not be a concrete object at all but instead an abstractobject which has the property of being a detective according toDoyle’s stories, the property of being a resident of BakerStreet according to Doyle’s stories, and so on.

Meinongian theories overcome the problems of impossibility andnon-uniqueness in a straightforward way. According to Parsons’theory, a fictional objectx which originates in a certainstory is the object that has exactly the nuclear propertiesFsuch that according to the story,Fx (Parsons 1980:49–60, 228–23). A fictional object to which the storyascribes incompatible properties is simply an impossible object, butsuch an object is harmless because it does not exist. As for theproblem of non-uniqueness, Sherlock Holmes is not identified as acomplete object. Instead Holmes is said to be the object having justthe nuclear properties Holmes has according to the stories. There isno numbern such that Holmes has exactlyn-manyhairs according to the stories. So Parsons’ Holmes does not haven-many hairs, for anyn. It is an incompleteobject.

Zalta offers a similar picture of fictional objects which is subsumedunder his general theory of encoding. According to him, a fictionalobjectx which originates in a certain story is the objectthat encodes exactly the propertiesF such that according tothe story,Fx (Zalta 1988: 123–29). Zalta’streatment of the problem of impossibility is similar toParsons’. A fictional object to which the story ascribesincompatible properties is an object which encodes those properties,among others. Such an object is harmless because it does not exemplifythe incompatible properties. Zalta’s solution to the problem ofnon-uniqueness is equally similar to Parsons’. Sherlock Holmes,for Zalta, is simply an incomplete object which does not encode theproperty of having exactlyn-many hairs, for anyn.

Though not meant to be a fictional object, Vulcan may be given thesame treatment as explicitly fictional objects. According to Parsons,the word ‘Vulcan’ is ambiguous. In one sense, it is thename of a fictional object which originates in a false astronomicalstory. In the other sense, it does not refer to anything. Zalta doesnot recognize Parsons’ second sense and simply regards‘Vulcan’ as the name of a fictional object.

For another Meinongian approach to fictional objects, seeCastañeda 1979. Charles Crittenden offers a view in aMeinongian spirit but with a later-Wittgensteinian twist (Crittenden1991). Like Parsons, Crittenden maintains that some objects do notexist and that fictional objects are such objects. Following laterWittgenstein, however, he sees no need to go beyond describing the“language game” we play in our fictional discourse anddismisses all metaphysical theorizing. Robert Howell criticizesParsons’ theory, among others, and recommends an approach whichconstrues fictional objects as non-actual objects in fictional worlds,where fictional worlds include not just possible but impossible worlds(Howell 1979). Nicholas Wolterstorff argues for the view thatfictional objects are kinds (Wolterstorff 1980). For criticism of thisview, see Walton 1983. Van Inwagen 2003 contains useful compactdiscussions of some Meinongian and non-Meinongian theories offictional objects.

Gregory Currie denies that fictional names like ‘SherlockHolmes’ are proper names or even singular terms (Currie 1990).He claims that sentences of fiction in which ‘SherlockHolmes’ occurs should be regarded as jointly forming a longconjunction in which every occurrence of ‘Sherlock Holmes’is replaced with a variable bound by an initial existential quantifierin the way suggested by Frank Ramsey (Ramsey 1931).

Kendall Walton urges that we should take seriously the element ofmake-believe, or pretense, inherent in the telling of a fictionalstory by the author and the listening to it by the audience (Walton1990, also Evans 1982: 353–68, Kripke 2013). According to thispretense theory, the pretense involved in the language game offictional discourse shields the whole language game from a separatelanguage game aimed at non-fictional reality, and it is in the latterlanguage game that we seek theories of objects of various kinds asreal objects. If this is right, any search for the real ontologicalstatus of fictional objects appears to be misguided. For the view thatthe pretense theory is compatible with a theory of fictional objectsas real objects, see Zalta 2000.

6. Quantified Modal Logic

One important theoretical use of non-actual possible objects is tobolster the most straightforward quantified modal logic (Scott 1970,Parsons 1995). If we add a modal sentential operator meaning “itis possible that” or “it is necessary that” toclassical first-order quantificational logic, along with appropriateaxioms and an appropriate rule of inference catering to the addedoperator, the resulting system yields a sentence meaning the followingas a theorem:

If it is possible that something isF, then something is suchthat it is possible that it isF.

The formal logical sentence with this meaning is known as theBarcan Formula, after Ruth C. Barcan, who published the firstsystematic treatment of quantified modal logic, in which shepostulated the formula as an axiom (Barcan 1946), and who haspublished under the name ‘Ruth Barcan Marcus’ since 1950.If we read ‘F’ as meaning “non-identicalwith every actual object”, the Barcan Formula says that if it ispossible that something is non-identical with every actual object,then somethingx is such that it is possible thatxis non-identical with every actual object. The antecedent is plausiblytrue, for there could have been more objects than the actual ones. Butif so, the consequent is true as well, assuming the truth of theBarcan Formula. But no actual object is non-identical with everyactual object, for every actual object is identical with itself, anactual object. Assuming the necessity of identity, if an objecty is identical with an objectz, it is not possiblethaty is non-identical withz. So, no actual objectis such that it is possible that it is non-identical with every actualobject. Therefore, any objectx such that it is possible thatx is non-identical with every actual object must be anon-actual possible object.

The converse of the Barcan Formula is also a theorem along with theBarcan Formula in classical logic augmented with a possibility ornecessity operator, and is as interesting. TheConverse BarcanFormula, as it is known, says the following:

If something is such that it is possible that it isF, thenit is possible that something isF.

The ontology of non-actual possible objects is an integral part of thepossibilist view that quantifiers in quantified modal logic range overall possible objects, non-actual as well as actual. This possibilistview validates the Converse Barcan Formula. If we read‘F’ as meaning “does not exist”, theConverse Barcan Formula says that if somethingx is such thatit is possible thatx does not exist, then it is possiblethat something does not exist. The antecedent is plausibly true, forany one of us, actual people, could have failed to exist. But if so,the consequent is true as well, assuming the truth of the ConverseBarcan Formula. But on actualist representationism, no possible worldcontains a representation which says that something does not exist,for it is contradictory provided that ‘something’ means“some existing thing”. So if the consequent is to be trueon actualist representationism, ‘something’ should notmean “some existing thing” but rather should mean“some thing, irrespective of whether it exists”. That is,the existential quantifier in the consequent needs to have a freerange independently of the possibility operator in whose scope itoccurs, which is hard to fathom on actualist representationism butwhich the possibilist view allows. The consequent does not even appearto be threatened with contradiction if we assume the possibilist viewand let the existential quantifier range over all possible objects,including non-actual ones.

In classical logic, the domain for quantification is assumed to benon-empty and every individual constant is assumed to refer tosomething in the domain. Infree logic, neither of theseassumptions is made. Thus free logic appears to be particularly suitedto theorizing about non-existent objects; see Lambert 1991, Jacquette1996. For a criticism of the free-logical approach to fictionaldiscourse, see Woods 1974: 68–91. Interestingly, the BarcanFormula and the Converse Barcan Formula are not derivable in freelogic.

Marcus herself proposes the substitutional reading of quantificationto skirt the need for non-actual possible objects (Marcus 1976), andlater suggests combining it with objectual quantification over actualobjects (Marcus 1985/86).

Williamson 2013 contains a detailed and useful discussion of theBarcan Formula and the Converse Barcan Formula.

Williamson 2013 also proposes that we should replace thepossibilism-actualism distinction in favor of the distinction betweennecessitism (necessarily everything is necessarily something) andcontingentism, which is the negation of necessitism. Necessitismentails that everything necessarily exists. Possibilism holds thatsome things are contingent existents, like you and me. Intuitivelycontingentism seems correct; it seems that you and I fail to exist atsome possible worlds. But according to necessitism, such worlds areworlds where you and I do not exist as concrete objects but do existas abstract objects. Williamson defends his proposal by arguing thatthe possibilism-actualism distinction is a distinction between alogical falsity and a logical triviality and that it neglectsimpossibilia. Menzel 2020 gives a critical examination ofWilliamson’s proposal. Also see Cameron 2016.

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