## 1. What They Are



Possible objects--*possibilia* (sing.
*possibile*)--are objects that are possible. What it is to
be an object--which is a basic and universal metaphysical
category--will not be discussed but will be simply assumed as
understood. What it is to be possible is the focus. Possibility of an
object 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 controversial
relation between the two notions is expressed as follows: (ii) not
every possible object is an actual object, that is, some possible
object is a non-actual object.



There is a wide-spread conservative view on objects, which says that
any object is an actual object. In other words, the adjective
'actual' is redundant, for it excludes no object. From
this it follows that non-actual possible objects are not objects, that
is, they are nothing. Thus on this view, the adjective
'possible' is equivalent to 'actual' when
applied to objects and (ii) is false. This makes the notion of a
possible object, or equivalently the notion of an actual object,
uninteresting. The notion of an object is the basic notion and does
all the work. There is another conservative view on objects, which
does not deal in actuality or possibility directly. It deals in
existence instead. It is the view that any object is an existing
object. On this view, the following analog of (ii) is false: not every
object is an existing object, that is, some object is a non-existing
object. This view makes the notion of an existing object equivalent to
that of an object; existence adds nothing to objecthood. If we combine
talk of actuality and talk of existence, we obtain five alternative
conservative views with varying degrees of conservatism:




(1) Any object is an actual existing object;



(2) Any object is an actual object, that is, it is either an actual
existing object or an actual non-existing object;



(3) Any object is an existing object, that is, it is either an actual
existing object or a non-actual existing object;



(4) Any object that is actual is an existing object;



(5) Any object that exists is an actual object.




(1) is a stronger claim than the other four. (2) and (3) are stronger
than (5) and (4), respectively. (1)-(3) give characterizations of all
objects, whereas (4) and (5) are more limited in scope. When the verb
'exists' is understood with the most comprehensive domain
of discourse (assuming the availability of such a domain), (5) is
known as *actualism*. If the domain of discourse for
'exists' is stipulated to consist only of actual objects,
(5) is trivial and compatible with *possibilism*, the position
which says that some object is outside the domain consisting of all
actual objects; *cf*. (ii). Most of those who advertise their
positions as actualist hold not only (5) with the most comprehensive
domain of discourse in mind but also (1), and therefore (2)-(4) as
well. 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 maintaining
that some object is a non-existing object. Such a view is one version
of Meinongianism. But let us start with actualism and possibilism.



We shall first examine possibilism. It is superficially the most
commonsensical position. It is superficially commonsensical to hold
that some objects are not actual: e.g., Santa Claus, the Fountain of
Youth. If we understand this view in terms of existence, that is, as
the claim that there are--that is, there exist--some objects
that 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 but
also non-actual possible objects as genuine objects. To flesh out the
idea of such a domain as proposed by the best-known version of
possibilism, it is necessary to start with the idea of a possible
world. After we articulate and examine possibilism as couched in the
possible-worlds framework, we shall discuss versions of actualism also
couched in the possible-worlds framework. We shall then examine other
theories outside the possible-worlds framework.


## 2. Possible Worlds



According to the framework of possible worlds, all alethic modal
statements involving possibility are existential quantifications over
possible worlds and all alethic modal statements involving actuality
are singular statements about a particular possible world, namely, the
actual world (Kripke 1959, 1963a, 1963b). For example, to say that
Julius Caesar was possibly not assassinated is to say that Julius
Caesar was not assassinated at some possible world, and to say that
Julius Caesar was actually assassinated is to say that Julius Caesar
was assassinated at the actual world. Likewise with existence: to say
that Julius Caesar possibly existed is to say that Julius Caesar
existed at some possible world, and to say that Julius Caesar actually
existed is to say that Julius Caesar existed at the actual world.
Assuming that the actual world is a possible world, it follows that if
Julius Caesar actually existed, he possibly existed.



In general, any object that actually exists possibly exists. Assuming
that actuality (of an object) is nothing but actual existence and
possibility (of an object) is nothing but possible existence, this
grounds the plausible conceptual connection between actuality and
possibility noted earlier: (i) every actual object is a possible
object. The overall philosophical merit of the possible-worlds
framework cannot be judged without close scrutiny of its metaphysical
foundations. Specifically, the two key questions which need to be
asked are: "What are possible worlds in general?" and
"What is the actual world in particular?" Metaphysical
theorizing about possible worlds goes back at least to Leibniz, but
the 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 par
with that of actual objects. When possibilist realists assert,
"Non-actual possible objects exist", their word
'exist' has the same linguistic meaning as when actualists
assert, "Actual objects exist". Possibilist realists
believe that some domains of discourse with respect to which
'exist' may be understood include more than actual
objects, whereas actualists deny it. Thus according to possibilist
realism, to call an object non-actually possibly existent is merely to
deny its inclusion in a particular realm--call it
'actuality'--and affirm its inclusion in some other
realm. That other realm is no less a realm of existence than actuality
is a realm of existence. All realms of existence are metaphysically on
a par with one another. Every token use of the existence predicate is
to be understood with respect to some realm of existence, either
explicitly or implicitly.



What distinguishes actuality from all other realms? The leading answer
is due to David Lewis, who is the proponent of the best-known version
of possibilist realism, namely, modal counterpart theory.
Lewis's view on actuality is known as the indexical theory of
actuality (Lewis 1970). The basic idea is that actuality for us is the
realm which includes us, and more generally, actuality for *x*
is the realm which includes *x*. But there are many different
realms which include us: this room, this building, this town, this
continent, this planet, this galaxy, this minute, this hour, this day,
this month, this year, this century, etc. So, to fix our actuality as
a unique realm which includes us, Lewis takes the largest
spatiotemporal whole which includes us. More precisely, actuality for
us is the maximal spatiotemporally related whole of which we are
(mereological) part. In general, actuality for *x* is the
maximal spatiotemporally related whole of which *x* is part.
For anything to exist non-actually-for-*x* but possibly is for
it to be part of some realm outside actuality for *x*, that is,
to be part of some maximal spatiotemporally related whole of which
*x* is not part. Note that this is a reductionist view of
existence, both actual and non-actual possible. Existence is first
relativized to a maximal spatiotemporally related whole, and then
existence in such a whole is defined reductively in terms of
(mereological) parthood. Lewis characterizes possible worlds as
maximal spatiotemporally related wholes. Actuality is the actual
world, and all other maximal spatiotemporally related wholes are
non-actual possible worlds.



A possible object is simply a part of a maximal spatiotemporally
related whole (Lewis 1986). (Strictly speaking Lewis prefers to say
"analogically spatiotemporal" instead of
"spatiotemporal" but we shall let that pass.) By most
criteria, Lewis's possible worlds, hence also his possible
objects, fall under the label 'concrete' rather than
'abstract'. Every non-actual possible object (apart from
pure Cartesian egos, perhaps) is a spatiotemporal object and bears no
spatiotemporal relation to any actual object, or to any possible
object exiting at any possible world at which it does not exist. This
makes non-actual possible objects as real as non-actual possible
worlds. It is worth while to remind ourselves that this does not make
it automatically true to say that non-actual possible objects exist,
even if we accept non-actual possible worlds. Whether it is true to
say so depends on the domain of discourse with respect to which the
existence predicate is to be understood.


#### 2.1.1 Modal Counterpart Theory



On Lewis's modal counterpart theory, every possible object is
confined to one possible world. Indeed, Lewis defines a possible
object as an object all of whose parts exist at some single possible
world (Lewis 1986: 211). This conception of a possible object forces
Lewis to resort to his counterpart theoretic account of modality
*de re* (Lewis 1968). According to any possible-worlds theory
of modality, to say that you could have been the leader of a religious
cult is to say that at some possible world you are the leader of a
religious cult. According to Lewis, to say that at a possible world
you are the leader of a religious cult is to say that at that possible
world there is a counterpart of you, that is, someone who resembles
you to sufficient degrees in relevant respects, who is the leader of a
religious cult. The counterpart relation is a similarity relation in
most cases (but arguably not in all cases). As such, it is not an
equivalence relation. This affords Lewis ample theoretical
maneuverability but at the same time causes him some theoretical
trouble. For example, as Lewis himself admits, his counterpart
theoretic account of modality either yields the consequence that every
actual object necessarily exists or yields the consequence that some
actual object is not identical to itself (Lewis 1983: 32). There is
also a famous complaint voiced by Saul Kripke (Kripke 1972:
344-45, note 13). It in effect says that whether someone other
than you is the leader of a religious cult at some possible world is
irrelevant to whether you could have been the leader of a religious
cult. Lewis's reply to this is that the *de re* character
of the possibility is preserved by the stipulation that the person who
is the cult leader is the counterpart of you, rather than the
counterpart of someone else, at an appropriate possible world. For an
attempt to avoid counterparts and still retain a broadly Lewisian
realistic framework, see McDaniel 2004.



A significantly different counterpart theory is proposed by Delia
Graff Fara (Fara 2008, 2012). Fara analyzes modality *de re* in
terms of sortal sameness rather than similarity. She clearly
distinguishes sortal sameness (e.g., "is the same boat
as") from identity ("is identical with"), and this
qualifies her analysis as a version of counterpart theory: a given
boat is F at a world if and only if at that world something that is
the same boat as--rather than identical with--that given boat is F.
This also somewhat alleviates Kripke's famous complaint against
counterpart theory. Suppose that a boat *B* is actually made up
of a hunk of wood *W* and a small plank *P* is a proper
part of *W*. It is intuitively sensible to hold that *B*
is identical with *W*, that *B* could have lacked
*P* as a part, and that *W* could not have lacked
*P* as a part. But this intuitive view appears internally
incoherent. If *B* is identical with *W* and *W*
could not have lacked *P* as a part, then it appears that
*B* also could not have lacked *P* as a part; in other
words, *B* without *P* appears to be an impossible
object. On Fara's analysis, *B* could have lacked
*P* if and only if at some possible world, some *x* is
such that *x* is the same boat as *B* and *x*
lacks *P*, and *W* could have lacked *P* if and
only if at some possible world, some *y* is such that
*y* is the same hunk of wood as *W* and *y* lacks
*P*. Since *y* may not be the same boat as *x*
(e.g., *y* may not be a boat at all), there is not even an
appearance of inconsistency with the latter lacking (a counterpart of)
*P* and the former not lacking it. Thus, even if *B* is
identical with *W* and *W* could not have lacked
*P*, *B* could have lacked *P*, i.e., *B*
without *P* is a possible object even though *W* without
*P* is not. Whereas Lewis invokes similarity, which is relative
to contextually shifting respects, Fara invokes sortal sameness, which
is less shifty. Fara's counterpart theory also interestingly
avoids denying the necessity of identity.



Independently of his counterpart theory, Lewis's definition of a
possible object has some peculiar consequences, given that existence
in general is understood as bearing of the part-of relation to the
whole that constitutes the domain of discourse. Take any two possible
worlds *w*1 and *w*2. Lewis wants
to assert that both *w*1 and *w*2
exist in some sense. So for the assertion to be true, it must be true
relative to a domain of discourse which contains as a sub-domain some
whole of which both *w*1 and *w*2
are 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 of *w*1 and *w*2. So, some
domain *D* containing such a sum as a sub-domain must count as
an acceptable domain of discourse for the evaluation of an existence
claim. Consider a proper part *p1* of
*w*1 and a proper part *p2* of
*w*2. Let Gerry be the sum of *p1*
and *p2*. Then it is true to say that Gerry exists
when the domain of discourse is *D*. So, there is a sense in
which Gerry exists. In fact it is the same sense in which
*w*1 and *w*2 exist. But Gerry is
not a possible object, according to Lewis's conception, for
Gerry does not have all of its parts at a single possible world. This
is peculiar. Gerry is an object which exists in the same sense in
which possible worlds exist but Gerry is not a possible object.
Since--as sanctioned by the universality of mereological
summation, which Lewis accepts--Gerry is an object, Gerry is an
impossible object. But there is nothing impossible about Gerry any
more than there is about the sum of *w*1 and
*w*2. Perhaps the sum of *w*1 and
*w*2 is an impossible object, too. But this idea
flouts the initially plausible principle of recombination for
possibility of objects, which says that if *x* is a possible
object and *y* is a possible object independent of *x*,
then the totality consisting exactly of *x* and *y* is a
possible object. Defenders of Lewis's theory may take this to
mean that the principle of recombination, despite its initial
plausibility, is to be rejected. There is another unexpected
consequence of Lewis's theory. If the sum of
*w*1 and *w*2 is an impossible
object, then the sum of all possible worlds is an impossible object,
for the former is part of the latter and no impossible object is part
of a possible object. But this makes the domain in which all possible
worlds reside, or "logical space", an impossible object.
This appears unwelcome. Lewis does consider an alternative conception
of a possible object, which says that a possible object is an object
every part of which exists at some possible world or other (Lewis
1986: 211). This allows a possible object to have parts at different
possible worlds. Lewis, who accepts the universality of mereological
summation, does not deny that possible objects in this sense are as
real as possible objects in his preferred sense. He however dismisses
them as unimportant on the ground that we do not normally name them,
speak of them, or quantify over them. But given that sets of possible
worlds and sets of possible objects figure in important philosophical
discussions concerning the identity of propositions and properties,
these sets seem important. If the sum of the members of an important
set is important, then Lewis's dismissal appears hasty. Again,
defenders of Lewis may stand this line of reasoning on its head and
conclude that the sum of the members of an important set is not always
important.



A useful overview of various issues concerning Lewis's
possibilist realism, as well as actualist representationism, is found
in Divers 2002, which is the first systematic attempt to defend parts
of Lewis's theory since Lewis 1986. Cameron 2012 presents a
defense of Lewis's reductive analysis of modality. Loux 1979 is
the standard anthology of classical writings in modal metaphysics in
1963-79.


#### 2.1.2 Modal-Dimensionalism



Lewis's is the most developed version of possibilist realism
based on possible worlds. As a result, discussion of possibilist
realism almost always focuses exclusively on Lewis's version.
There are, however, other versions of possible-worlds-based
possibilist realism, and one of them deserves a brief mention. Assume
that the universe is spread out in three-dimensional space and
persists through one-dimensional time. The non-Lewisian version of
possibilist realism in question may then be called
'modal-dimensionalism'. It says that in addition to
the four physical (spatiotemporal) dimensions, the universe has modal
dimensions. Possible worlds are points in modal space as defined by
the modal axes just as physical spatiotemporal points are points in
physical spacetime as defined by the four physical spatiotemporal
axes, and possible objects "persist" through possible
worlds. A version of modal-dimensionalism is what W. V. Quine
argued against when he took himself to be arguing against a typical
possibilist realism (Quine 1976), and it is arguably the view many
possible-worlds theorists adumbrated, however vaguely and inchoately,
as the representative possibilist realist theory before Lewis
forcefully articulated his own version.



Modal-dimensionalism differs from Lewis's theory in a
number of important respects but the most striking is the absence of
counterpart theory. Modal-dimensionalism eschews counterparts
and proposes that to say that you are the leader of a religious cult
at a possible world is to say that you yourself exist at that world
and are the leader of a religious cult at that world. Another
difference between modal-dimensionalism and Lewis's theory
is that unlike the latter, the former avoids the mereological
conception of the existence of a possible object at a possible world.
According to modal-dimensionalism, just as a temporally or
spatially persisting object is (arguably) not part of the temporal or
spatial points or regions at which it exists, a modally persisting
object is not part of the possible worlds at which it exists.
Modal-dimensionalism also differs from Lewis's theory in
not being a thoroughly reductionist theory. It does not analyze the
notion of a possible world in mereological terms but leaves it as
largely primitive (Yagisawa 2002, 2010, 2017). This enables
modal-dimensionalists to allow the possibility of there being no
concrete object, whereas on Lewis' theory, if there is no
concrete object, there is no possible world. For a different attempt
to reconcile possibilist realism with the possibility of the
non-existence of anything concrete, see Rodriguez-Pereyra 2004.



Though free from some difficulties inherent in Lewis's
theoretical machinery, modal-dimensionalism has its own
obstacles to overcome, not the least of which is to make substantive
sense of the idea of an object's persisting not just in physical
space and time but in modal space. One idea is to mimic the
"endurantist" approach to temporal persistence and say
that a possible object persists through many possible worlds by having
all of its parts existing at each of those worlds. Another idea is to
mimic the "perdurantist" approach to temporal persistence
and say that a possible object persists through many possible worlds
by having different parts (world stages) at different possible worlds
and being the modal-dimensional "worm" consisting of those
world stages. Note that this does not make the object mereological
part of a possible world at which it exists. It only makes each of the
object's world stages part of the object. Lewis, in contrast,
has it that a possible object has all of its parts at a single
possible world (where they are mereological part of that world) and
therefore does not persist through different worlds at all. Despite
these differences, Lewis, speaking of the "perdurantist"
version of modal-dimensionalism, says that it is but a
notational variant of his own theory. He then proceeds to criticize it
(Lewis 1968: 40-2). Lewis formulates his opposition to
modal-dimensionalism more carefully in Lewis 1986: 213-20.
Achille Varzi derives Lewis's theory from a theory similar to
modal-dimensionalism (Varzi 2001). Unlike
modal-dimensionalism, the theory he uses follows Lewis and
defines the existence of a possible object at a possible world in
terms of the object being mereological part of the world. Varzi notes
some differences between this theory and Lewis's. Vacek 2017
defends modal-dimensionalism from some objections.


#### 2.1.3 Specificity Problem



It is well known that Quine fiercely objects against the ontology of
non-actual possible objects. Referring to an unoccupied doorway, he
asks whether the possible fat man in the doorway and the possible bald
man in the doorway are one possible man or two possible men (Quine,
1948). The point of this rhetorical question is that there is no
serious issue here because we have no non-trivial criterion of
identity for non-actual possible objects. No respectable ontology
should embrace objects for which we have no non-trivial criterion of
identity. Quine encapsulates this in his famous slogan: "No
entity without identity". Actual ordinary mid-sized objects have
vague boundaries, so the *sorites* argument may be used to show
that we have no coherent non-trivial criterion of identity for them.
Quine's slogan then appears to apply to such objects. Some take
this to be good reason against the ontology of actual ordinary
mid-sized objects, whereas others take this to be good reason against
Quine's slogan. Whatever the ultimate fate of Quine's
slogan may be, there is an objection against possibilist realism
which, while not explicitly invoking Quine's slogan, is at least
Quinean in spirit. It goes as follows:



Lewis's possibilist realism faces the problem of specifying
non-actual possible objects. Take Vulcan, the innermost planet between
Sun and Mercury erroneously believed to exist by some astronomers in
the nineteenth century, when the universe was assumed to be Newtonian.
Vulcan is not actually between Sun and Mercury or actually anywhere at
all. Vulcan also does not actually have any mass, shape, or chemical
composition. Still it is possible that Vulcan be a unique planet
between Sun and Mercury and have a particular mass *m*, a
particular shape *s*, and a particular chemical composition
*c*. Or so it seems. It is also possible, it seems, that Vulcan
be a unique planet between Sun and Mercury and have a slightly
different particular mass *m'*, a slightly different
particular shape *s'*, and a slightly different
particular chemical composition *c'*, where the slight
differences in question lie within the range of deviations the
original astronomers would have tolerated. So at some possible world
*w* Vulcan is a unique planet between Sun and Mercury and has
*m*, *s*, and *c*, and at some possible world
*w'* Vulcan is a unique planet between Sun and Mercury
and has *m'*, *s'*, and *c'*.
Clearly *w* and *w'* are different worlds. On
Lewis's theory, every possible object exists at only one world.
So either the planet in question at *w* is not Vulcan or the
planet at *w'* is not Vulcan. Whichever planet that is
not Vulcan is Vulcan's counterpart at best. Is either planet
Vulcan? If so, which one? If neither is, where is Vulcan? What
possible world hosts Vulcan? There seems to be no non-arbitrary way to
answer these questions within Lewis's theory.



The modal-dimensionalist version of possibilist realism is capable of
offering the ready answer, "The planet at *w* and the
planet at *w'* are both (world stages of) Vulcan",
but faces an only slightly different challenge of its own. It seems
intuitive to say that there is a possible world at which Vulcan exists
between Sun and Mercury and some remote heavenly body distinct from
Vulcan but qualitatively identical with it in relevant respects (such
as mass, shape, size, chemical composition, etc.) also exists. Let
*w*1 be such a world and call Vulcan's double
at *w*1 'Nacluv'. Thus at
*w*1, Vulcan and Nacluv exist, Vulcan is between Sun
and Mercury, and Nacluv is somewhere far away. It is possible for
Vulcan and Nacluv to switch positions. So there is a possible world,
*w*2, which is exactly like *w*1
except that at *w*2 Nacluv is between Sun and
Mercury and Vulcan is far away. Since Vulcan and Nacluv are two
distinct objects, *w*1 and *w*2
are two distinct worlds. But this difference seems empty. Given that
*w*1 and *w*2 are exact
qualitative duplicates of each other, on what ground can we say that
the object between Sun and Mercury at *w*1 and far
away at *w*2 is Vulcan and the object far away at
*w*1 and between Sun and Mercury at
*w*2 is Nacluv, rather than the other way around? It
is unhelpful to say that Vulcan and Nacluv are distinguished by the
fact that Vulcan possesses Vulcan's haecceity and Nacluv does
not. An object's haecceity is the property of being that very
object (Kaplan 1975, Adams 1979, Lewis 1986: 220-48). Since what
is at issue is the question of which object is Vulcan, it does not
help to be told that Vulcan is the object possessing the property of
being that very object, unless the property of being that very object
is clarified independently. To say that it is the property of being
that very object which is Vulcan is clearly uninformative. It is not
obvious that there is any way to clarify it independently.



Alternatively, one might choose to insist that if anything at any
possible world is Vulcan, it has to possess at that world the
properties relevant to the introduction of the name
'Vulcan', such as being the heavenly body with
such-and-such mass and orbit and other astrophysical characteristics
and being between Sun and Mercury in a Newtonian universe. This is
supported by descriptionism concerning the semantics of proper names,
according to which 'Vulcan' is a proper name which is
semantically equivalent to a definite description ('the heavenly
body with such-and-such mass and ...'). But forceful criticisms
of descriptionism for proper names were launched in the early 1970s
(Donnellan 1972, Kripke 1972). Kripke's criticism has been
especially influential. The kernel of Kripke's criticism rests
on the intuitive idea that a sentence containing a referring proper
name expresses a singular proposition about the referent independently
of any qualitative characterization of the referent but that a
corresponding sentence containing a description does not so express a
singular proposition. If Kripke's criticism applies to
'Vulcan', it is difficult to defend descriptionism for
'Vulcan'. But 'Vulcan' and other apparent
proper names of non-actual possible objects may not be as readily
amenable to the Kripkean considerations as proper names of actual
objects are. The so-called "problem of empty names" is the
problem of providing a semantic theory for "empty names"
like 'Vulcan' as non-descriptional designators. For some
recent contributions to the project of solving this problem, see Braun
1993, 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 under
Lewis's tendentious label *ersatzism*, a possible world
is an actual maximally consistent representation of how the universe
could possibly have been, and the actual world is the representation
of how the universe actually is. A representation *r* is
maximally consistent if and only if *r* is consistent and for
any representation *r'*, either *r* &
not-*r'* is not consistent or *r* &
*r'* is not consistent (assuming the appropriate
conceptions of the negation and conjunction of representations).
Different actualist representationists employ different actual items
to play the role of the maximally consistent representations, such as
sentences, propositions, states of affairs, properties, etc. (Adams
1974, 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 the
notion of consistency of a representation is not ultimately eliminated
in actualist representationism. Most actualist representationists
accept consistency as a modal notion, for they doubt it can be reduced
to a non-modal notion, such as a proof-theoretic notion or a
model-theoretic notion. If those actualist representationists are
right and consistency is indeed a modal notion, then actualist
representationism is not a reductionist theory of modality. This,
however, should not automatically be taken to be a serious challenge
to actualist representationism, for a thoroughly reductionist theory
of modality may or may not be feasible. Not even every possibilist
realist believes in thorough reduction; *cf*.
modal-dimensionalists.



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



In actualist representationism, existence is conceptually prior to
actual existence. This is in concert with the priority of the truth of
any proposition *P* over the actual truth of *P*.
*P* is actually true if and only if *P* is true at the
actual world, which in turn is so if and only if the actual world
represents *P* as true. And by definition, the actual world is
the possible world which represents *P* as true if and only if
*P* is true. Likewise, for an object to exist at the actual
world is for the actual world to represent it as existing; the actual
world represents an object as existing if and only if the object
exists. Actual existence is thus reducible to existence
*simpliciter*.



Non-actual possible existence is defined as existence at some possible
world other than the actual world, which in turn is defined in terms
of existence *simpliciter* as follows: *x* exists at a
possible world *w* not identical with the actual world if and
only if *x* would exist if *w* were actual, that is, if
the universe were as *w* represents it to be. According to this
picture, non-actual possible existence is not a special mode of
existence completely separate from actual existence. It is not
existence *simpliciter*, but instead "would-be"
existence *simpliciter* on a counterfactual supposition. There
is no room for non-actual possible objects in this picture. Many
representations which are possible worlds other than the actual world
include representations of the existence of non-actual possible
objects, but non-actual possible objects are not mereological part of
those possible worlds. Neither are they set-theoretic members, or
constituents in any other sense, of those possible worlds. For them to
exist at those possible worlds is for the worlds to say (represent)
that they exist; nothing more, nothing less. This is a non-realist
picture of the existence of the non-actual. Non-actual possible
objects are thus nothing at all. This is the conservative view
(1).



Let us examine how actualist representationists handle apparent modal
truths asserting the possibility of non-actual objects. There are two
types of such truth and the first type is easy to handle. It is
possible that Julius Caesar (congenitally) had a sixth finger on his
right hand (whereas, we assume, he actually had only five fingers).
This possibility only calls for a possible world to represent Julius
Caesar as having had a sixth finger on his right hand, which may
easily 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 never
burnt but which could have been burnt. This involves a nested
possibility, which is troublesome to actualist representationism
(McMichael 1983). To reveal the nesting clearly, let us articulate the
possibility in question in a more pedantic and rigorous way. The
following is possible: Julius Caesar had a sixth right finger such
that (a) it was never burnt, and (b) the following is possible: it was
burnt. The trouble for actualist representationism is that there is no
obvious way to make sense of the pronoun 'it' in (b). The
possibility of Julius Caesar having had a sixth right finger which was
never burnt is, as before, easily representable by, say, the sentence,
'Julius Caesar had a sixth right finger which was never
burnt'. This means that the pronoun 'it' in (a) is
unproblematic; it is replaceable by 'Julius Caesar's sixth
right finger'. How about the pronoun 'it' in (b)? It
should designate the sixth right finger Julius Caesar is said to have
had within the scope of the first possibility operator. It should
therefore be bound by the appropriate existential quantifier, just
like the pronoun 'it' in (a). But unlike the pronoun
'it' in (a), the pronoun 'it' in (b) occurs
separated from the quantifier by the intervening second possibility
operator, 'the following is possible'. This
"quantifying in" from outside the possibility operator
forces the sentence representing the possibility specified in (b) to
retain 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 the
possibility in question. But no part of the representation that is the
possible world in question, or any other possible world, may serve as
the object which the pronoun 'it' in (b) designates, as
the pronoun needs to designate something that is said to be a human
finger but no part of any such representation is said to be a human
finger. Notice that Lewis has no corresponding difficulty here. On his
theory, the modal statement in question is true if and only if at some
possible world there is a counterpart of Julius Caesar who had a sixth
right finger *f* such that *f* was never burnt and at
some possible world there is a counterpart of *f* which was
burnt. Julius Caesar, his counterpart, and the counterpart's
sixth finger *f* are all real objects, and the pronoun
'it' in (b) designates *f*. (Note that the pronoun
'it' in (b) does not designate the counterpart of
*f* any more than 'it' in (a) does.)



One way to handle this without postulating a non-actual possible
object is to say that there was an actual finger belonging to someone
else and that it could have belonged to Julius Caesar's right
hand as his extra finger (congenitally). If this sounds biologically
too bizarre, actualist representationists may say instead that there
are actual elementary particles none of which was part of Julius
Caesar's body but which collectively could have constituted his
sixth right finger. This is along the lines of David Kaplan's
possible automobile (Kaplan 1973: 517, note 19) and Nathan
Salmon's Noman (Salmon 1981: 39, footnote 41). Kaplan imagines a
complete set of automobile parts laid out on a factory floor ready for
assembly. If the parts are assembled, a particular automobile will be
created; if not, not. Suppose that the parts are destroyed before they
are assembled. Then the particular automobile which would have been
created if the parts had been assembled is in fact not created. It is
a non-actual possible automobile. Salmon, taking a cue from
Kripke's suggestion of the necessity of origin (Kripke 1972),
imagines a particular human egg and a particular human sperm which
could merge into a particular human zygote and develop into a
particular human being. Suppose that the egg and the sperm in fact
fail to merge, hence fail to develop into a human being. The
particular human being, Noman, who would have been created if the egg
and the sperm had merged and developed normally is in fact not
created. Noman is a non-actual possible human being. These lines of
thought afford actualist representationists a powerful means to
accommodate many apparently recalcitrant modal truths about non-actual
possible objects, provided that these non-actual possible objects can
be individuated uniquely by means of actually existing potential parts
or origin. In fact, it may even be taken further to afford actualist
representationists a way to maintain that Kaplan's automobile is
not only possible but is an actual object after all. This can be done
by not only individuating Kaplan's automobile uniquely by means
of the collection of the automobile parts but also identifying it with
the collection. Call Kaplan's automobile
'*k*'. Suppose that *k* is identical with
the collection. Then there exists an actual object, namely *k*,
which actually is not an automobile but is a collection of automobile
parts and which is possibly an automobile. That is, *k* is
represented as an unassembled collection of automobile parts by the
actual world and is represented as an automobile by some possible
world. Similarly, actualist representationists may identify Noman with
the collection of the egg and the sperm. Noman is an actual object
which actually is not a human being but is a collection of an egg and
a sperm and which is possibly a human being. The case of Julius
Caesar's sixth finger can be handled likewise. There exists an
actual object which actually is not a finger but is a (widely
scattered) collection of particles and which is possibly Julius
Caesar's sixth right finger.



But now consider the planet Vulcan. There is no collection of actual
particles which were supposed to constitute Vulcan. So, if Vulcan is a
non-actual possible object, which it apparently is, it seems possible
for Vulcan to exist and not be constituted by any actual particles
differently located and arranged. Likewise, it seems perfectly
possible that Julius Caesar had a sixth finger which was not
constituted by any actually existing particles and satisfied (a) and
(b). Despite initial plausibility, actualist representationists may
choose to deny such a possibility. To do so is, in effect, to commit
oneself to the position that the universe, as it actually is, already
contains maximally possible constituents of any possible state of the
universe, that is, it is impossible for the universe to contain even a
single constituent object not already in the universe as it actually
is. To make this plausible is not an easy task. If, on the other hand,
actualist representationists choose not to deny the possibility in
question, they appear to have to say that Julius Caesar's
entirely new sixth finger is not an object but is possibly an object.
But then the problem is to make sense of the finger's being
nothing yet possibly something. How can there be a true predication of
any kind, including "is possibly an object", of nothing?
(Oliver & Smiley 2013 offers the beginning of a partial answer to
this question.)


#### 2.2.2 Essence Solution



Alvin Plantinga is responsible for a widely-discussed actualist
representationist response to this problem. He invokes unactualized
individual essences (Plantinga 1974, 2003). Every object is said to
have an individual essence. An individual essence of a given object is
a property which that object necessarily has and everything else
necessarily lacks. Moreover, and this is crucial to the solution of
the problem at hand, individual essences are independent of the
objects which have them, whether the objects are actual or non-actual.
That is, an individual essence can exist without being an individual
essence of any existing object. The problematic pronoun
'it' in (b) is then said to designate such an individual
essence, and the rest of the characterization of the possibility in
question is appropriately and systematically reinterpreted. For
example, 'it was burnt' in (b) is reinterpreted to mean
that the individual essence in question is an individual essence of
something that was burnt.



One difficulty with this view is the failure to produce a single
plausible example of such an essence. We saw that possibilist realism
faces the problem of specifying non-actual possible objects.
Plantinga's version of actualist representationism faces its own
version of the Quinean challenge, namely, the problem of specifying
the individual essences which are supposed to replace non-actual
possible objects. What individual essence did Julius Caesar have? What
readily comes to mind is the property of being Julius Caesar. As Ruth
Barcan Marcus and Kripke have forcefully argued (Barcan 1947, Marcus
1961, Kripke 1972), identity is necessary; that is, if an object
*x* is identical with an object *y*, it is necessarily
the case that *x* is identical with *y*. Given this, it
is easy to see that Julius Caesar necessarily had the property of
being Julius Caesar and everything other than Julius Caesar
necessarily lacks it. However, it is implausible to suggest that this
property is independent of Julius Caesar. Our canonical specification
of it by means of the noun phrase 'the property of being Julius
Caesar' certainly is not independent of our canonical
specification of Julius Caesar by means of the name 'Julius
Caesar', and this does not seem to be an accidental fact merely
indicative of the paucity of our language devoid of deep metaphysical
underpinnings. Kaplan's automobile and Salmon's Noman
merely push the dependence of the individual essence to the level of
the constituent parts or origin of the object of which it is an
individual essence. This difficulty is magnified when we ask for a
specification of an individual essence of Vulcan or Julius
Caesar'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 regard
different non-actual possible worlds as achieving their representation
more or less independently of one another. Instead, we should regard
all possible worlds as representations which are given all at once in
concert with one another so that cross references to non-actual
possible objects by different possible worlds are guaranteed from the
outset.



Reina Hayaki proposes yet another solution (Hayaki 2003). When we say
that Julius Caesar had an unburnt sixth right finger at some possible
world *w*1, we take *w*1 to
represent Julius Caesar as having an unburnt sixth right finger. When
we say further that that finger at *w*1 was burnt at
a different possible world *w*2, we should likewise
take *w*2 to represent that finger as having been
burnt. According to Hayaki, this requires a hierarchical arrangement
of possible worlds in which the representation of the finger by
*w*2 is parasitic on the representation by
*w*1.



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


## 3. Without Possible Worlds



Some important theories concerning possible objects and related issues
do not invoke possible worlds as a theoretical cornerstone. Most
prominent among them are so-called Meinongian theories. But before
turning to them, let us briefly take note of two non-Meinongian
approaches outside the framework of possible worlds: Kit Fine's
and Michael Jubien's.



Like Plantinga, Fine takes individual essences seriously but he
regards the notion of necessity as prior to the notion of a possible
world, and the notion of an individual essence as prior to the notion
of necessity (Fine 1994, 1995a, 1995b, 2000). Fine's modal
theory is based on the broadly Aristotelian idea that alethic modality
stems from natures of things. Understanding of actual or non-actual
possible objects should therefore be firmly grounded on understanding
of natures of things. Fine believes that 'There is a possible
object *x*' is reducible to 'Possibly there is an
object *x*' (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 having
had an entirely new sixth right finger satisfying (a) and (b) is
analyzed roughly as follows: the property of being a particular sixth
finger on Julius Caesar's right hand is simultaneously
compatible with the properties of existing, being composed of
non-actual stuff, and being never burnt, and also simultaneously
compatible with the properties of existing, being composed of
non-actual stuff, and being burnt. The underlying idea is to start
with the ontology of stuff and use properties and relations, including
modal properties and relations, as the fundamental metaphysical items
to account for all statements about objects, including all modal
statements about possible objects. It specifically avoids talk of
non-actual possible objects. It, however, does not avoid talk of
non-actual possible stuff. So it does embrace the ontology of the
non-actual possible in a broad sense.


### 3.1 Subsistence vs. Existence



Alexius Meinong's theory of objects has had much influence on
some 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 (Meinong
1904). So the subject term in the sentence, 'The sixth right
finger of Julius Caesar is a finger', stands for an object,
assuming that the sentence is true. (Such an assumption is strongly
disputed in Salmon 1987.) Even though the exact respects in which
contemporary Meinongian proposals are Meinongian and the extent of
their Meinongianism differ from one proposal to another, all of them
inherit this claim by Meinong in some form. They are thus united in
resisting Bertrand Russell's criticism of Meinong, which
mandates analyzing sentences containing a definite description, like
the one above concerning the sixth right finger of Julius Caesar, as
general statements rather than singular statements (Russell 1905); see
3.1.2 for a particularly famous piece of Russell's criticism and
how two leading Meinongian theories handle it.



Meinong distinguishes two ontological notions: subsistence and
existence. Subsistence is a broad ontological category, encompassing
both concrete objects and abstract objects. Concrete objects are said
to exist and subsist. Abstract objects are said not to exist but to
subsist. The talk of abstract objects may be vaguely reminiscent of
actualist representationism, which employs representations, which are
actual abstract objects. At the same time, for Meinong, the nature of
an object does not depend on its being actual. This seems to give
objects reality that is independent of actuality. Another interesting
feature of Meinong's theory is that it sanctions the postulation
not only of non-actual possible objects but also of impossible
objects, for it says that 'The round square is round' is a
true sentence and therefore its subject term stands for an object.
This aspect of Meinong's theory has been widely pointed out, but
non-trivial treatment of impossibility is not confined to
Meinongianism (Lycan & Shapiro 1986). For more on Meinong's
theory, see Chisholm 1960, Findlay 1963, Grossmann 1974, Lambert 1983,
Zalta 1988: sec.8. For some pioneering work in contemporary
Meinongianism, see Castaneda 1974, Rapaport 1978, Routley 1980.
We shall examine the theories of two leading Meinongians: Terence
Parsons and Edward Zalta. We shall take note of some other Meinongians
later in the section on fictional objects, as their focus is primarily
on fiction. Parsons and Zalta not only propose accounts of fictional
objects but offer comprehensive Meinongian theories of objects in
general.


#### 3.1.1 Theory of Non-Existent Objects



Quine thought it curious that the ontological problem was so simple as
to be put in three monosyllables: "What is there?" He
famously answered this simple question equally simply:
"Everything" (Quine 1948). Parsons rejects Quine's
claim that every object exists, and asserts that some objects do not
exist. Parsons proposes a theory of all objects, both existent and
non-existent (Parsons 1980). He uses the word 'actual' as
a synonym for 'existent', so he rejects (1), (2), and (3),
but accepts (4) and (5) as trivialities. It would be a mistake to
classify him as an actualist simply because he accepts (5). On the
contrary, he has much in common with possibilists in claiming that
some objects are not actual, that is, in denying (2). He, however,
admits only one sense of existence and claims that some objects do not
exist in that sense. If this sole sense of existence corresponds to
the possibilist conception of existence relativized to any domain of
discourse smaller than the largest available domain, then Parsons is
in agreement with possibilists. But if it corresponds to the
possibilist conception of existence relativized to the largest
available domain, then Parsons' ontology goes beyond that of
possibilists. There is good evidence that the latter is the case, for
Parsons' ontology, as a typically Meinongian ontology, includes
the round square and other impossible objects, which the possibilist
ontology does not include. Lewis's discussion (Lewis 1990) of
how the non-Meinongian should understand "noneism", which
is 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', see
Parsons 1983. A sympathizer of Routley, Graham Priest, uses
dialetheism (the thesis that some contradictions are true) and
paraconsistent logic, along with the (possible- and impossible-)
worlds framework, to bolster noneism (Priest 2005, 2016).



Parsons' theory is based on the Meinongian distinction between
nuclear and extra-nuclear properties. Nuclear properties include all
ordinary properties, such as being blue, being tall, being kicked by
Socrates, being a mountain, and so on. Extra-nuclear properties
include ontological properties such as existence and being fictional,
modal properties such as being possible, intentional properties such
as being thought of by Socrates, and technical properties such as
being complete. See Parsons 1980: 24-27, 166-74 for more
on nuclear and extra-nuclear properties and a test for distinguishing
between them. Parsons' theory can be encapsulated in the
following two principles:




(P1) No two objects have exactly the same nuclear properties;



(P2) For any set of nuclear properties, some object has all the
nuclear properties in the set and no other nuclear properties.




Take the set of nuclear properties, {being golden, being a mountain}.
By (P1) and (P2), some unique object has exactly the two nuclear
properties in the set. That object is the golden mountain. Take
another set of nuclear properties, {being square, being round}, and
the two principles give us the round square. Both of these objects are
radically incomplete; they have no weight, height, shape, or size, for
example. The need for distinguishing nuclear properties from
extra-nuclear properties is readily seen by considering the set,
{being golden, being a mountain, being existent}. If (P2) is to apply
to such a set, it should yield an object having the three properties
in the set. Such an object is golden, a mountain, and existent, that
is, it is a golden mountain which exists. So it should be true that a
golden mountain exists, but it is in fact not true. Parsons defines a
possible object as an object such that it is possible that there exist
an object having all of its nuclear properties. On this conception,
all existing objects are possible objects, some golden mountains are
possible objects, and the round square is not a possible object. It is
worth noting that in Parsons' theory, negation needs to be
handled delicately (Parsons 1980: 19-20, 105-06, Zalta
1988: 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 the
case that *x* is round, then we should be entitled to say that
*x* is round and it is not the case that *x* is round,
which is a contradiction. Thus, we should not be allowed to infer
'It is not the case that *x* 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 best
candidate appears to be a non-existent incomplete object corresponding
to the set of properties, {being a finger, belonging to Julius
Caesar's right hand, being never burnt}. This set includes
neither the property of being constituted by particles which do not
(actually) exist nor the property of being possibly burnt. Both of
these properties are extra-nuclear properties, hence ineligible to be
included in a set to which (P2) applies. So (P2) does not confer them
on the object corresponding to the set. How then does the object come
to have the properties? It is not obvious how this question should be
answered (Parsons 1980: 21, note 4, where Parsons says, "The
present theory is very neutral about *de re*
modalities"), but we should at least note that on
Parsons's theory, objects are allowed to have properties not
included in their corresponding sets of nuclear properties: e.g., the
round square, whose corresponding set only includes roundness and
squareness, has the property of being non-existent and the property of
being incomplete. Also, Parsons allows nuclear properties which are
"watered-down" versions of extra-nuclear properties. So
the set may include the "watered-down" versions of the two
extra-nuclear properties in question and that may be enough. For more
on 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 by
Meinong's student, Ernst Mally, between two kinds of
predication: exemplification and encoding (Mally 1912, Zalta 1983,
1988). The idea is to maintain the Meinongian claim that the round
square is a genuine object while avoiding contradicting oneself.
Russell argues that since the round square is round and square, and
since if an object is square it is not the case that it is round, it
follows that the round square is such that both it is round and it is
not the case that it is round, which is a contradiction. Parsons
avoids the contradiction by refusing the inference from
'*x* is square' to 'it is not the case that
*x* is round', where '*x*' ranges over
all objects. In contrast, Zalta accepts the inference for all objects
and avoids the contradiction by refusing to interpret the predication,
'is round and square', of the round square as
exemplification. He instead interprets it as encoding; the round
square encodes roundness and squareness. Encoding squareness is not
incompatible with encoding roundness, even though exemplifying
squareness is incompatible with exemplifying roundness. Predication as
understood as encoding follows a different logic from predication as
understood as exemplification. The crux of Zalta's theory is
encapsulated in the following two principles:




(Z1) Objects which could sometimes have a spatial location do not, and
cannot, encode properties;



(Z2) For any condition on properties, some object that could never
have a spatial location encodes exactly those properties which satisfy
the condition.




Some object is the round square, for, by (Z2), among objects which
could never have a spatial location is an object which encodes
roundness and squareness. The noun phrase, 'the round
square', unambiguously denotes such a necessarily non-spatial
object. Other noun phrases of the same kind include those which denote
numbers, sets, Platonic forms, and so on. There are, however, many
noun phrases which are ambiguous. They allow an interpretation under
which they denote an object that is necessarily non-spatial, and also
allow an interpretation under which they denote an object that is
possibly spatial and possibly non-spatial. The phrase, 'the
golden mountain', is an example. The golden mountain in one
sense is an object which is necessarily non-spatial and which encodes
goldenness and mountainhood. The golden mountain in the other sense is
an object which actually is non-spatial but could be spatial. When we
say that the golden mountain in the second sense is golden, it means
that necessarily if the golden mountain is spatial, it is golden.
Since, by (Z1), such an object cannot encode properties, all
predications in the preceding sentence have to be understood as
exemplification. Similarly with Julius Caesar's entirely new
finger satisfying (a) and (b).



Zalta endorses the claim that some objects are non-actual possible
objects, so he appears to side with possibilists. But he defines a
non-actual possible object as an object which could have a spatial
location but does not (Zalta 1988: 67). So the claim means for Zalta
that some objects could have a spatial location but do not. This is
compatible with actualism, provided that all such objects are actual
in the sense of actually existing (Linsky & Zalta 1994, also
Williamson 1998, 2002, 2013; it is noteworthy that Timothy Williamson
independently argues for what he calls *necessitism*, which
says [in a nutshell] that every possible object is a necessary
object). If we understand Zalta's theory this way, we have the
following actualist picture: all objects are actual and existing, some
objects are necessarily non-spatial, and other objects are possibly
spatial and possibly non-spatial. (For an alternative interpretation
of Zalta's formal theory, according to which some objects do not
exist, see Zalta 1983: 50-52, 1988: 102-04, Linsky &
Zalta 1996: note 8.) Among the latter type of objects are those which
are actually spatial but possibly not, like you and me, and those
which are possibly spatial but actually not, like the golden mountain
in the appropriate sense. The distinction between the golden mountain
in 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 view
is not actualist, and Nelson & Zalta 2009 for a response. Hayaki
2006 critiques both Linsky-Zalta and Williamson.



If we confine our attention to necessarily non-spatial objects, a
definition of a possible object which corresponds to Parsons'
definition is easily available to Zalta: a possible (necessarily
non-spatial) object is a (necessarily non-spatial) object such that
some object could exemplify exactly the properties it encodes. In this
sense, some object which encodes goldenness and mountainhood, among
other properties, is a possible object but the object which encodes
squareness and roundness is not. Julius Caesar's entirely new
finger satisfying (a) and (b) can be treated in the same way as the
golden mountain. Complications similar to those which arise for
Parsons' theory do not arise for Zalta's theory, for all
properties are equally subject to encoding, including those properties
Parsons regards as extra-nuclear. For a comparison of the
two-kinds-of-property approach and the two-kinds-of-predication
approach, see Rapaport 1985.


## 4. Unicorns



If anything is a non-actual possible object, a unicorn is. Or so it
appears. But Kripke vigorously argues against such a view in the 1980
version of Kripke 1972: 24, 156-58. His argument starts with the
assumption that the unicorn is (intended to be) an animal species if
anything. This excludes the possibility that a horse with a horn
artificially attached to its forehead is a unicorn. Kripke assumes
obviously that there are actually no unicorns and that unicorns are
purely mythical creatures. Also assumed is the absence in the relevant
myth of any specification of the genetic structure, evolutionary
history, or other potentially defining essential features of the
unicorn. (Possession of a horn is not a defining essential feature of
the unicorn any more than having tawny stripes is a defining feature
of the tiger.) The myth describes the unicorn only in stereotypical
terms: looking like a horse, having a horn protruding from its
forehead, etc. Suppose that there are objects with all such
stereotypical features of the unicorn. This seems perfectly possible
and Kripke accepts such a possibility. But he rejects its sufficiency
for establishing the possibility of unicorns. Suppose that among the
objects with the stereotypical unicorn features, some have a genetic
makeup, an evolutionary history, or some other potentially defining
essential unicorn characteristic which is radically different from the
corresponding characteristic had by the others with the same
stereotypical unicorn features. Which ones among those with the
stereotypical unicorn features would then be real unicorns and which
ones fool's unicorns (*a la* fool's gold)?
There is no fact of the matter. Given that the unicorn is an animal
species, not everything that looks and behaves like a unicorn is
guaranteed to be a unicorn. To be a unicorn, an object has to possess
the defining essential characteristics of the unicorn. But there are
no defining characteristics of the unicorn; the myth does not specify
them, and the universe does not instantiate them. This surprising
argument has convinced many philosophers of the impossibility of
unicorns, but others have raised doubt by arguing that the notion of a
biological kind, such as a species, is far more malleable than Kripke
assumes (Dupre 1993).



The line of argument Kripke uses, if successful, is applicable to all
non-actual natural kinds and their analogs (except for natural-kind
analogs of Kaplan's automobile or Salmon's Noman). It is
unclear that it or something like it is successfully applicable to
individuals like Vulcan, but if it is, then we must say that such
individuals are impossible objects. Some theorists liken Vulcan to
fictional objects, as we will see in the next section, and some
theorists argue that fictional objects are impossible objects (Kaplan
1973, 1980 version of Kripke 1972: 157-58, Fine 1984:
126-28, Yagisawa 2010: 271-77). If Vulcan is an impossible
object, the problem of uniquely specifying Vulcan, as opposed to
Nacluv, becomes less urgent, for it is not evident that we should be
able to specify an impossible object uniquely and non-trivially.


## 5. Fictional Objects



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



There are two main problems with the claim that fictional objects are
possible objects. One is the problem of impossible fictional objects.
Some fictional objects are ascribed incompatible properties in their
home fiction by their original author (usually inadvertently). This
seems to be sufficient for them to have those properties according to
their home fiction, for what the author says in the fiction
(inadvertently or not) seems to hold the highest authority on truth in
that fiction. On the assumption that a fictional object has a given
property if it has that property according to its home fiction, those
fictional objects are impossible objects, for no possible object has
incompatible properties. The other problem is the failure of
uniqueness. It may be viewed as the problem of meeting the Quinean
demand for clear identity conditions. Holmes is a particular fictional
object. So if we are to identify Holmes with a possible object, we
should identify Holmes with a particular possible object. But there
are many particular possible objects that are equally suited for the
identification with Holmes. One of them has *n*-many hairs,
whereas another has (*n*+1)-many hairs. No fictional story
about a particular fictional object written or told by a human being
is detailed enough to exclude all possible objects but one to be
identified with that fictional object, unless it is a fiction about an
actual object or a non-actual possible object analogous to
Kaplan's automobile or Salmon's Noman.



Strangely enough, there is also a problem with the claim that
fictional objects are non-actual objects. That is, there is some
plausible consideration in support of the claim that fictional objects
are actual objects. We make various assertions about fictional objects
outside the stories in which they occur and some of them are true: for
example, that Sherlock Holmes is admired by many readers of the Holmes
stories. The simplest and most systematic explanation appears to be to
postulate Holmes as an actual object possessing the properties such
true assertions ascribe to him. Fictional objects may then be said to
be theoretical objects of literary criticism as much as electrons are
theoretical objects of physics. This type of view enjoys surprisingly
wide acceptance. (Searle 1974, van Inwagen 1977, 1983, Fine 1982,
Salmon 1998, Thomasson 1999). The theorists in this camp, except van
Inwagen (van Inwagen 2003: 153-55), also think that fictional
objects are brought into existence by their authors as actual objects.
Even if this type of view is to be followed, it must still be denied
that Holmes is actually a detective, for if we enumerate all
individuals who are actually detectives, Holmes will not be among
them. By the same token, Holmes is not actually a resident of Baker
Street or even a human being. Though actual, Holmes is actually hardly
any of those things Conan Doyle's stories describe him as being.
Holmes must not be a concrete object at all but instead an abstract
object which has the property of being a detective according to
Doyle's stories, the property of being a resident of Baker
Street according to Doyle's stories, and so on.



Meinongian theories overcome the problems of impossibility and
non-uniqueness in a straightforward way. According to Parsons'
theory, a fictional object *x* which originates in a certain
story is the object that has exactly the nuclear properties *F*
such that according to the story, *Fx* (Parsons 1980:
49-60, 228-23). A fictional object to which the story
ascribes incompatible properties is simply an impossible object, but
such an object is harmless because it does not exist. As for the
problem of non-uniqueness, Sherlock Holmes is not identified as a
complete object. Instead Holmes is said to be the object having just
the nuclear properties Holmes has according to the stories. There is
no number *n* such that Holmes has exactly *n*-many
hairs according to the stories. So Parsons' Holmes does not have
*n*-many hairs, for any *n*. It is an incomplete
object.



Zalta offers a similar picture of fictional objects which is subsumed
under his general theory of encoding. According to him, a fictional
object *x* which originates in a certain story is the object
that encodes exactly the properties *F* such that according to
the story, *Fx* (Zalta 1988: 123-29). Zalta's
treatment of the problem of impossibility is similar to
Parsons'. A fictional object to which the story ascribes
incompatible properties is an object which encodes those properties,
among others. Such an object is harmless because it does not exemplify
the incompatible properties. Zalta's solution to the problem of
non-uniqueness is equally similar to Parsons'. Sherlock Holmes,
for Zalta, is simply an incomplete object which does not encode the
property of having exactly *n*-many hairs, for any
*n*.



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



For another Meinongian approach to fictional objects, see
Castaneda 1979. Charles Crittenden offers a view in a
Meinongian spirit but with a later-Wittgensteinian twist (Crittenden
1991). Like Parsons, Crittenden maintains that some objects do not
exist and that fictional objects are such objects. Following later
Wittgenstein, however, he sees no need to go beyond describing the
"language game" we play in our fictional discourse and
dismisses all metaphysical theorizing. Robert Howell criticizes
Parsons' theory, among others, and recommends an approach which
construes 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 that
fictional objects are kinds (Wolterstorff 1980). For criticism of this
view, see Walton 1983. Van Inwagen 2003 contains useful compact
discussions of some Meinongian and non-Meinongian theories of
fictional objects.



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



Kendall Walton urges that we should take seriously the element of
make-believe, or pretense, inherent in the telling of a fictional
story by the author and the listening to it by the audience (Walton
1990, also Evans 1982: 353-68, Kripke 2013). According to this
pretense theory, the pretense involved in the language game of
fictional discourse shields the whole language game from a separate
language game aimed at non-fictional reality, and it is in the latter
language game that we seek theories of objects of various kinds as
real objects. If this is right, any search for the real ontological
status of fictional objects appears to be misguided. For the view that
the pretense theory is compatible with a theory of fictional objects
as real objects, see Zalta 2000.


## 6. Quantified Modal Logic



One important theoretical use of non-actual possible objects is to
bolster the most straightforward quantified modal logic (Scott 1970,
Parsons 1995). If we add a modal sentential operator meaning "it
is possible that" or "it is necessary that" to
classical first-order quantificational logic, along with appropriate
axioms and an appropriate rule of inference catering to the added
operator, the resulting system yields a sentence meaning the following
as a theorem:



If it is possible that something is *F*, then something is such
that it is possible that it is *F*.



The formal logical sentence with this meaning is known as the
*Barcan Formula*, after Ruth C. Barcan, who published the first
systematic treatment of quantified modal logic, in which she
postulated the formula as an axiom (Barcan 1946), and who has
published under the name 'Ruth Barcan Marcus' since 1950.
If we read '*F*' as meaning "non-identical
with every actual object", the Barcan Formula says that if it is
possible that something is non-identical with every actual object,
then something *x* is such that it is possible that *x*
is non-identical with every actual object. The antecedent is plausibly
true, for there could have been more objects than the actual ones. But
if so, the consequent is true as well, assuming the truth of the
Barcan Formula. But no actual object is non-identical with every
actual object, for every actual object is identical with itself, an
actual object. Assuming the necessity of identity, if an object
*y* is identical with an object *z*, it is not possible
that *y* is non-identical with *z*. So, no actual object
is such that it is possible that it is non-identical with every actual
object. Therefore, any object *x* such that it is possible that
*x* is non-identical with every actual object must be a
non-actual possible object.



The converse of the Barcan Formula is also a theorem along with the
Barcan Formula in classical logic augmented with a possibility or
necessity operator, and is as interesting. The *Converse Barcan
Formula*, as it is known, says the following:



If something is such that it is possible that it is *F*, then
it is possible that something is *F*.



The ontology of non-actual possible objects is an integral part of the
possibilist view that quantifiers in quantified modal logic range over
all possible objects, non-actual as well as actual. This possibilist
view validates the Converse Barcan Formula. If we read
'*F*' as meaning "does not exist", the
Converse Barcan Formula says that if something *x* is such that
it is possible that *x* does not exist, then it is possible
that something does not exist. The antecedent is plausibly true, for
any one of us, actual people, could have failed to exist. But if so,
the consequent is true as well, assuming the truth of the Converse
Barcan Formula. But on actualist representationism, no possible world
contains 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 true
on actualist representationism, 'something' should not
mean "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 free
range independently of the possibility operator in whose scope it
occurs, which is hard to fathom on actualist representationism but
which the possibilist view allows. The consequent does not even appear
to be threatened with contradiction if we assume the possibilist view
and let the existential quantifier range over all possible objects,
including non-actual ones.



In classical logic, the domain for quantification is assumed to be
non-empty and every individual constant is assumed to refer to
something in the domain. In *free logic*, neither of these
assumptions is made. Thus free logic appears to be particularly suited
to theorizing about non-existent objects; see Lambert 1991, Jacquette
1996. For a criticism of the free-logical approach to fictional
discourse, see Woods 1974: 68-91. Interestingly, the Barcan
Formula and the Converse Barcan Formula are not derivable in free
logic.



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



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



Williamson 2013 also proposes that we should replace the
possibilism-actualism distinction in favor of the distinction between
necessitism (necessarily everything is necessarily something) and
contingentism, which is the negation of necessitism. Necessitism
entails that everything necessarily exists. Possibilism holds that
some things are contingent existents, like you and me. Intuitively
contingentism seems correct; it seems that you and I fail to exist at
some possible worlds. But according to necessitism, such worlds are
worlds where you and I do not exist as concrete objects but do exist
as abstract objects. Williamson defends his proposal by arguing that
the possibilism-actualism distinction is a distinction between a
logical falsity and a logical triviality and that it neglects
impossibilia. Menzel 2020 gives a critical examination of
Williamson's proposal. Also see Cameron 2016.