## 1. The Concept of a Nonexistent Object



The very concept of a "nonexistent object" has an air of
paradox about it, at least for those philosophers whose thinking is
rooted in the Humean tradition. For Hume suggested that to think of an
object is always and necessarily to think of an *existent*
object, or to put it differently, that to think of an object and to
think of the same object as existing are just one and the same thing.
Immanuel Kant took up Hume's idea and claimed that existence is
not a "real predicate", a claim that is often interpreted
as an anticipation of Gottlob Frege's famous doctrine that
existence is not a predicate of individuals. (See Hume 2000, Book 1,
Part 2, Sect. 6; Kant 2003, B 627; Frege 1966, pp. 37f.) Kant's
motivation for rejecting the view that existence is a "real
predicate" was the so-called "ontological proof" of
God's existence, which says, roughly, that God's
perfection entails God's existence, since a being that would
have all of God's perfections except existence (i.e.,
omniscience, omnipotence, benevolence) would be less perfect than a
being with the same perfections plus existence. For centuries,
philosophers have felt that there is something wrong with this proof,
but Kant was the first one who was able to point out a possible error:
he argued that the mistake of the "ontological argument"
lies in the treatment of existence as a "real
predicate".



If Hume is right, then the concept of an object includes the concept
of existence, and the concept of a nonexistent object would be as
self-contradictory as the concept of a round square. If existence is
not a predicate of individuals, then one might suppose that neither is
nonexistence. Therefore, if Frege is right, to say of an object that
it is nonexistent is a kind of nonsense that arises from a violation
of logical grammar. (For Frege and those who follow him, a claim like
"God exists/does not exist" is to be understood as a claim
about the concept *God*, or about the property of being God. On
this view, the logical form of "God exists" is not
*Exists (God)*--where *Exists* is a predicate of
individuals, but rather: *The concept God applies to
something*, or *Something possesses the property of being
God.*)



Thus, in order to take the idea of nonexistent objects seriously, one
has to give up views held by important philosophers about the nature
of existence and adopt the view that existence is some kind of
predicate of individuals. This view entails, among other things, that
to say, for instance, that some white elephants exist is to say that
some white elephants have the property of existence (or, to put it the
other way around, that not all white elephants are
nonexistent)--a consequence that might strike some as
strange.



Furthermore, in order to assert "there are nonexistent
objects" without implying "nonexistent objects
exist", one has to suppose that sentences of the form
"There are \(F\)s" mean something different from
sentences of the form "\(F\)s
 exist".[1]
 Some philosophers reject a distinction between "there is"
and "exists" (see, for instance, Lewis 1990, Priest 2005,
Quine 1953), some philosophers (e.g., Meinong 1960, Parsons 1980,
Zalta 1988) think that there are good reasons for making this
distinction. Some of the latter think that the distinction between
"there is" and "exists" is rooted in ordinary
language, but others deny this firmly (see, for instance, Geach 1971).
Obviously, although there might be a tendency among competent English
speakers to use "there is" and "exists" in
different contexts, ordinary language use is too wavering and
non-uniform in this respect to be a stable ground for a philosophical
theory. Of course, this does not rule out that there are
*theoretical* reasons for a distinction between "there
is" and "exists", some of which are discussed
below.


### 1.1 The Logics of Nonexistent Objects



In those logics that stand in the Frege-Quine tradition, both
"there is" and "exists" are expressed by means
of the "existential quantifier" ("\(\exists\)"),
which is, consequently, interpreted as having "ontological
import". Thus, in these formal systems, there is no means to
distinguish between "there is" and "exists".
However, it has been shown that the distinction between the two can be
coherently regimented in various ways. In the systems of Terence
Parsons, Edward N. Zalta and Dale Jacquette, for instance,
"there is an \(x\) such that \(\ldots x\ldots\)" is expressed by
"\(\exists x(\ldots x\ldots)\)", whereas
"there exists an \(x\) such that \(\ldots x\ldots\)" is expressed by
"\(\exists x\rE !x \amp \ldots x\ldots)\)", where "E!" is the
existence predicate (Parsons 1980, Zalta 1983, Zalta 1988, Jacquette
1996). "Some things do not exist" could thus be rendered
in logical notation as follows:
"\(\exists x(\neg\rE !x)\)"; "Pegasus
does not exist" as "\(\neg\rE !p\)"; and so
forth.



Graham Priest (2005) has proposed a theory of nonexistent objects that
treats "there is" and "exists" as synonyms. He
interprets quantification as utterly ontologically neutral. The
quantifier should express neither "there is" nor
"there exists". Rather, quantifier expressions should be
read "For some \(x, \ldots x\ldots\)",
where "For some \(x, \ldots x\ldots\)"
does not imply that "there is (or exists) an \(x\) such
that \(\ldots x\ldots\)".



Thus, Priest belongs to those philosophers who distinguish between
"quantifier commitment" and "ontological
commitment" (see Azzouni 2004), claiming that to
"quantifier over" objects of a certain kind does not
entail an ontological commitment to objects of this
 kind.[2]



The various logics of nonexistent objects cannot be described and
discussed here in detail. However, it is now clear that there is no
*formal* obstacle to a theory of nonexistent objects. The only
questions are philosophical: can the concepts that such theories aim
to formalize be explained, and do we have good reason to accept a
theory formulated in these terms? In the following two sections, the
main motivations for believing in nonexistent objects are
delineated.


## 2. Historical Roots: Alexius Meinong and the Problem of Intentionality



Philosophical writings on nonexistent objects in the 20th and 21st
century usually take as their starting point the so-called
"theory of objects" of the Austrian philosopher Alexius
Meinong (1853-1920). Therefore, it is appropriate to give an
outline of the basic principles of and motives behind this theory.
(For a detailed presentation see the entry on
 Meinong.)



Meinong was concerned about the problem of intentional states which
are not directed at anything existent. The starting point of this
problem is the so-called "principle of intentionality",
which says that mental phenomena are characterized by an
"intentional directedness" towards an object. For
instance, to love is always to love something, to imagine is always to
imagine something, and so forth. In other words, every intentional act
is "about" something. The problem is that sometimes people
imagine, desire or fear things that do not exist. Some people fear the
devil, although the devil doesn't exist. Many people hope for
peace in the Middle East. But there is no peace in the Middle East.
Ponce the Leon searched for the fountain of youth, even though it
doesn't exist. It is easy to imagine a golden mountain, even if
no such thing exists.



Cases like these seem to be clear counterexamples to the principle of
intentionality. However, many philosophers found this principle too
appealing to be given up completely. While some came to the conclusion
that intentionality is not a real relation and therefore does not
require the existence of an object (see, for instance, Brentano 1874,
Prior 1971, Searle 1983, Crane 2013), Meinong offered another
solution: there is indeed an object for every mental state
whatsoever--if not an existent object then at least a nonexistent
 one.[3]



The problem of intentionality may still count as one of the most
important motivations for thinking there are nonexistent
 objects.[4]
 But there are other motivations as well.


## 3. Further Motivations for Belief in Nonexistent Objects


### 3.1 The Problem of Negative Singular Existence Statements



Very briefly, the problem can be stated as follows: it seems that in
order to deny the existence of a given individual, one must assume the
existence of that very individual. Thus, it seems that it is
impossible to deny the existence of an individual without getting
involved in a contradiction.



However, this conclusion seems hard to accept. In fact, there are many
negative existence statements that we take not only to be sensible but
also to be true (or at least not to be necessarily false). Consider,
for instance:


* Pegasus does not exist.
* Yugoslavia does not exist anymore.
* The perpetual motion machine does not exist and never will exist.



From the common sense point of view, negative singular existence
statements are ubiquitous, comprehensible and sometimes true. So why
is it that many philosophers are so puzzled about them? In particular,
why think one has to assume the existence of an individual in order to
deny its existence?



One traditional reason that has been given is based on the following
assumptions:


1. Only meaningful sentences can be true.
2. In a meaningful sentence, every constituent of the sentence must
be meaningful.
3. If a singular term is meaningful, then it denotes something.
4. If a singular term "\(b\)" denotes something,
then "\(b\) does not exist" is false.



Let's see how these assumptions lead to a problem in light of
the negative singular existence sentence "Pegasus does not
exist". If "Pegasus does not exist" is true, then it
must be meaningful (by (1) above). If it is meaningful, all of its
constituents must be meaningful, including the singular term
"Pegasus" (by (2) above). If "Pegasus" is
meaningful, then "Pegasus" denotes something (by (3)
above). If "Pegasus" denotes something, then
"Pegasus does not exist" is false (by (4) above). Thus,
the assumption that "Pegasus does not exist" is true leads
to the conclusion that this same sentence is false. So if the above
premises are correct, it is impossible that "Pegasus does not
exist" is true: either "Pegasus" denotes something,
in which case "Pegasus does not exist" is false; or
"Pegasus" does not denote anything, in which case
"Pegasus does not exist" is not even meaningful, let alone
true.



There are several ways to resolve this problem, i.e., to account for
meaningful and true negative singular existence sentences. One
solution that became very prominent in the 20th century consists in
the strategy of "analyzing away" the proper names and
definite descriptions appearing in negative singular existential
claims. This strategy consists of two steps:


* Ordinary proper names are interpreted as disguised definite
descriptions. For instance, "Pegasus" is to be analyzed as
short for "the flying horse from Greek mythology". This is
often called *the description theory of proper names*. Thus to
say "Pegasus exists" is simply to say "the flying
horse of Greek mythology exists".
* Definite descriptions are to be analyzed along the lines of
Bertrand Russell's theory of definite descriptions. On
Russell's theory, to say "the flying horse of Greek
mythology exists" is to say "there is exactly one
\(x\) which is a flying horse of Greek mythology".



Thus, combining these two steps, it follows that:


* To say "Pegasus doesn't exist" is to say
"it is not the case that there is exactly one \(x\) which
is a flying horse of Greek
 mythology".[5]



If "Vulcan" is short for "the planet between Mercury
and the sun", then:


* To say "Vulcan doesn't exist" is to say
"it is not the case that there is exactly one \(x\) which
is such that \(x\) is a planet between Mercury and the
sun".



The point of these paraphrases is to show that the original sentences
can be analyzed in terms of sentences in which the singular terms
("Pegasus", "Vulcan", "the flying horse
of Greek mythology" and "the planet between Mercury and
the sun") have all disappeared. The paraphrases involve the
general terms "flying horse from Greek mythology" and
"planet between Mercury and the sun", along with the
existential quantifier ("there is") and a uniqueness
condition ("exactly one"). (Let's ignore the fact
that the singular terms "Mercury" and "Le
Verrier" appear within the general terms; of course, this means
that the procedure isn't complete, but, in principle, it can be
completed.) The problem of negative singular existentials is thereby
resolved because sentences containing names which appear to be about
nonexistent objects are paraphrased in terms of sentences involving
general terms, quantifiers and uniqueness conditions. These latter
sentences are meaningful independently of whether the general terms
apply to anything.



However, both the description theory of proper names and
Russell's theory of definite descriptions have been subject to
serious criticisms. One might object that they fail to do full justice
to our actual use of proper names and definite descriptions. Often we
use proper names--successfully--without having any definite
description in mind. Sometimes we don't need a definite
description in order to refer to a particular object, because we
individuate the respective object by means of perception or perceptual
memories. Sometimes we simply do not know of a definite description
that individuates the object we wish to refer to. Most of us know
about Cicero just that he was a famous Roman orator; but the Romans
had more than one famous orator. Nevertheless, we can use the name
"Cicero" successfully to refer to a *particular*
famous Roman orator. Moreover, even when we do have something like the
mental correlate of a definite description in mind when we use a
proper name, we do not usually treat the description as a
*definition* of the proper name (as the Russellian picture
suggests). Suppose what I have in mind when I use the name
"Socrates" corresponds to the description "the
ancient Greek philosopher who died from drinking hemlock".
Suppose furthermore that the famous story about Socrates' death
is actually a myth and that Socrates in fact died peacefully of old
age. Do I then simply fail to refer to Socrates whenever I use the
name "Socrates"? It does not seem so. When I eventually
come to know that Socrates did not die from drinking hemlock, I will
take this as a piece of information *about* Socrates, the
person I referred to all the time by using the name
"Socrates". (See Kripke 1980.)



As to the theory of definite descriptions, two kinds of problem arise.
First, some philosophers simply deny that the paraphrases properly
capture the meaning of sentences with definite descriptions, simply on
the grounds that the meaning of a proper name like
"Pegasus" is just less specific than the meaning of the
definite description "the flying horse of Greek
mythology". Second, some philosophers have objected that the
theory of definite descriptions sometimes yields the wrong results.
Consider, for instance: "The ancient Greeks worshipped
Zeus." *Prima facie*, this sentence expresses a real
relation between the ancient Greeks and Zeus; and it is surely a
historical fact that the ancient Greeks worshipped Zeus. Yet on
Russell's analysis, proper names like "Zeus" have to
be replaced by definite descriptions, even in contexts other than
existence claims. So "Zeus" would get replaced by a
definite description like "the Greek god who lived on Mt.
Olympus and who ...". Thus, the above true sentence would
get analyzed in terms of the following *false* one:
"There exists one and only one Greek god who lived on Mt.
Olympus and who ... and who was such that the ancient Greeks
worshipped him." There are numerous other true sentences like
this, such as "Sherlock Holmes is more famous than any real
detective", etc., all of which appear to involve real relations
between existent objects and nonexistent ones, but whose Russellian
paraphrases are false. Third, the use of the anaphoric pronoun
"it" in "Teams of scientists have searched for the
Loch Ness monster, but since it doesn't exist, no one will ever
find it" seems problematic. The pronoun in both of its
occurrences in this sentence seems to pick up its meaning/denotation
from the definite description "the Loch Ness
monster"--which is not easy to explain given
Russell's theory of definite descriptions.



There might be ways to defend the theory of definite descriptions, but
they will not be pursued here. In the context of this article, the
relevant point is that Russell's theory does not provide a
generally accepted solution to the problem of negative existence
sentences. The appeal to nonexistent objects, on the other hand,
provides a very simple solution to this problem. It consists in
rejecting the premise


4. If a singular term "\(b\)" denotes something,
then "\(b\) does not exist" is false.



If there are nonexistent objects, then "\(b\)" may
denote an object that does not exist.



The idea here is that whereas the quantifiers "there is"
and "something" range over everything whatsoever, the
objects that exist constitute only a portion of that domain.
Therefore, it would be fallacious to derive from
"'\(b\)' denotes *something*" that
"\(b\)" denotes *something that exists*.
According to this picture, "Pegasus does not exist" simply
expresses that Pegasus is a nonexistent object. Premises 1-3
from above can be accepted without restriction. "Pegasus"
denotes a nonexistent flying horse and thus is meaningful. Thus, the
whole sentence "Pegasus does not exist" is meaningful as
well. Since it is true that Pegasus does not belong to the class of
existent objects, "Pegasus does not exist" is true. Of
course, this solution can be generalized to all negative singular
existence statements. The appeal to nonexistent objects thus supplies
an elegant solution to the problem of negative singular
existentials.



Naturally, there are alternative solutions to the problem of negative
singular existence statements. Among other things, it is possible to
reject premise 4 without committing oneself to an ontology of
nonexistent objects. One might simply accept a positive Free Logic,
i.e., the conjunction of the following two principles: 1. Singular
terms do not need to denote anything in order to be meaningful. 2.
Sentences containing non-denoting singular terms can be true. (This
strategy is to be found, for instance, in Crane 2013.) One of the
difficulties of this solution, however, is to give an account of what
makes such sentences true, i.e., of what their truthhmakers are (given
the principle that, for every true sentence, there is something in the
world that makes it true, i.e., something that is the sentence's
truthmaker). For the special case of negative singular existence
sentences, one might claim that that their truthmaker is just the
entire world (see, e.g., Crane 2013, Section 3.5; for more about
Crane's position see Section 5.1 below). However, this answer to
the truthmaker question is not available for the problem of fictional
discourse, which provides another important motivation for a
commitment to nonexistent objects.


### 3.2 The Problem of Fictional Discourse



By "fictional discourse" we mean here and in what follows
*discourse about fictitious objects*. Sometimes, the term
"fictitious object" is used as synonymous with
"nonexistent object". Here, the term is used in a
different sense, namely for objects (characters, things, events etc.)
which occur in fictions, i.e., in myths or fairy tales, in fictional
novels, movies, operas etc. Pegasus is a fictitious object in this
sense (as are Sherlock Holmes and Hamlet) but Vulcan (the hypothetical
planet sought by Le Verrier) is not.



Consider, for instance, the sentence



(1)
Pegasus is a flying horse.


Like many other sentences of fictional discourse, it appears to
fulfill the following three conditions:


1. It has the grammatical structure of a predication, i.e., the
structure that is rendered in logical notation by
"\(Fb\)" (where "\(F\)" stands for a
predicate expression--here: "is a flying
horse"--and "\(b\)" stands for a singular
term--here: "Pegasus").
2. The singular term in subject position is a name for a fictitious
object.
3. It is commonly, and with good reason, taken to be true.



The problem of fictional discourse is closely connected to two logical
principles. The first one is well known as "the principle of
existential generalization":



**Existential Generalization** \((\mathbf{EG})\):
  

\(Fb \rightarrow \exists x(Fx)\), i.e.,
  

If \(b\) is \(F\), then there is something that is
 \(F\).[6]




The second principle is less prominent, rather seldom explicitly
stated, but often tacitly assumed. We call it "the predication
principle":



**Predication Principle** \((\mathbf{PP})\):
  

\(Fb \rightarrow \exists x(x = b)\).[7]




(PP) may be read in two ways:



(PPa)
If \(b\) is \(F\), then there is something that is
identical with \(b\).
(PPb)
If \(b\) is \(F\), then \(b\) exists.


Both principles are *prima facie* extremely plausible: If it is
true of some individual that the predicate "\(F\)"
applies to *it*, then the predicate "\(F\)"
applies to *something*. If some predicate
"\(F\)" applies to an individual, then the individual
has to exist (for if it were otherwise, how could the predicate apply
to *it*?).



Yet, when applied to fictional discourse, these two principles lead to
consequences that seem to contradict hard empirical facts on the one
hand and trivial truths about the ontological status of fictitious
objects on the other. According to (EG), the sentence



(1)
Pegasus is a flying horse.


implies



(2)
There are flying horses.


Yet, as we all know, there are no flying horses.



According to (PP),



(1)
Pegasus is a flying horse.


implies



(3)
Pegasus exists.


But Pegasus is a fictitious object; and it seems that to call an
object fictitious is just to say that it does not exist.



The problem is that obviously true sentences of fictional discourse
seem to lead into outright contradictions. Of course, there are
several ways to avoid the contradictions. One of them consists in
rejecting the principles (EG) and (PP). By this move, one blocks the
inference from "Pegasus is a flying horse" to "There
are flying horses" and "Pegasus exists". Indeed,
some logicians, notably proponents of Free Logics, take this path.
(See Crane 2013, Hintikka 1959, Lambert 1983 and 1991, Leonard
 1956.)[8]
 Again (as with the case of negative singular existence statements)
this raises the question of what the truthmakers of such sentences
are. There are attempts to answer this question in a
"reductionist" fashion, i.e., to claim that sentences
about fictitious objects are made true not by fictitious objects but
by something else, e.g., by literary works, myths, stories or facts
about these,
 respectively.[9]



Another way to avoid the contradictions would be simply to reject the
sentence "Pegasus is a flying horse" (and, in general, all
alleged predications about fictitious objects) as false or untrue.
This radical solution, however, fails to do justice to the widespread
intuition that there is a difference in truth-value between
"Pegasus is a flying horse" and, say, "Pegasus is a
flying dog".



A third attempt to resolve the problem is what may be called
"the story-operator strategy". According to the
story-operator strategy, we have to interpret sentences of fictional
discourse as incomplete. A complete rendition of, for instance,



(1)
Pegasus is a flying horse.


would be as follows:



(1')
According to the story \(S\) (where
"\(S\)" here and in what follows stands for the story
of Greek mythology): Pegasus is a flying horse.


The expression "according to the story \(S\)" is the
so-called "story
 operator",[10]
 which is a *sentence* operator (that is, it is the sentence as
a whole that is in its scope, not just a part of the sentence, for
instance the predicate). While the sentence within the scope of the
story operator (here: "Pegasus is a flying horse") may be
false when taken in isolation, the complete sentence may be true.
(This strategy is developed in detail in Kunne 1990.)



Sentence (1') does *not* imply that there are flying
horses; neither does it imply that Pegasus exists. Thus, the
contradictions are
 avoided.[11]
 This looks like an elegant solution, at least as long as we confine
ourselves to a particular kind of example. Unfortunately, however, it
does not work equally well for all kinds of sentences of fictional
discourse. Consider, for instance:



(4)
Pegasus is a character from Greek mythology.


This sentence seems to be straightforwardly true; but if we put a
story operator in front of it, we get a straightforward falsehood:



(4')
According to the story \(S\): Pegasus is a character
from Greek mythology.


It is not true that according to the relevant story, Pegasus is a
character. Rather, according to this story, Pegasus is a living being
of flesh and blood.



One may call sentences like "Pegasus is a flying horse" or
"Hamlet hates his stepfather" "*internal*
sentences of fictional discourse", in distinction from
*external* sentences of fictional discourse, like
"Pegasus is a character from Greek mythology" or
"Hamlet has fascinated many psychoanalysts". The story
operator strategy can be applied to internal sentences only and thus
fails as a general solution to the problem of fictional
 discourse.[12]



The claim that there are nonexistent objects provides a solution that
can be applied uniformly both to internal and external sentences of
fictional discourse. It allows us to admit that fictitious objects do
not *exist* but at the same time to acknowledge that *there
are* fictitious objects. According to this position, fictitious
objects are just a species of nonexistent objects.



In order to see how this assumption is supposed to avoid the
contradictions spelled out above, consider:



(1)
Pegasus is a flying
 horse.[13]
(2)
There are flying horses. (1, EG)
(3)
There are no flying horses.


According to the Meinongian solution, premise 3 has to be rejected as
false. The Meinongian grants that flying horses do not *exist*,
but this does not imply that *there are* no flying horses.
According to the Meinongian, there are flying horses, and they belong
to the class of nonexistent objects, and Pegasus is one of them.
Premise 3 may be replaced by



(3')
Flying horses do not exist.


But this does not contradict



(2)
There are flying horses.


Thus, the problem is
 solved.[14]



Consider next:



(1)
Pegasus is a flying horse.
(2)
Pegasus exists. (1, PP)
(3)
Pegasus is a fictitious object.
(4)
Fictitious objects do not exist.
(5)
Pegasus doesn't exist. (3, 4)


In this case, the Meinongian solution consists in rejecting premise 2.
The Meinongian cannot accept 2, since Pegasus is supposed to be a
*nonexistent* object.



What, then, about the predication principle? Does the Meinongian have
to reject it?--Not necessarily. Remember that (PP) can be read in
(at least) two ways:



(PPa)
If \(b\) is \(F\), then there is something that is
identical with \(b\).
(PPb)
If \(b\) is \(F\), then \(b\) exists.


Within the Meinongian framework, these two readings are not
equivalent. According to the Meinongian, certainly there is something
that is identical with Pegasus, although Pegasus does not exist. Thus,
the Meinongian must reject the reading (PPb), but she can (and does)
accept the reading
 (PPa).[15]



Since the Meinongian accepts only the weaker version (PPa) of the
predication principle, the inference from premise 1 ("Pegasus is
a flying horse") to "Pegasus exists" is blocked. All
that can be derived from premise 1 is the weaker claim



(2')
There is something that is identical with Pegasus.


But this is not in conflict with "Pegasus does not exist".
Thus, the problem is resolved.



Alternatively, one may abstain from the Meinongian distinction between
being and existence and hold that fictitious objects are existent
abstract objects. According to this position, "Pegasus does not
exist" has to be rejected as false, and thus, again, the
contradiction is avoided. This position (it might be called
"abstractionism with respect to fictitious objects") comes
in two varieties. The first one might be characterized, in a somewhat
simplified fashion, as follows: To every set of properties, there
is/exists a corresponding abstract object. These abstract objects
exist necessarily. Some of them occur in fictional stories, and these
are what we call "fictitious objects". Thus, fictitious
objects are necessarily existent objects that have been somehow
"discovered" or "selected" by the authors of
fictional stories. (For this position, see, for instance, Parsons
1975, Zalta 1983 and 1988, Jacquette 1996, Berto 2008 and Priest 2011.
Actually, this is one of the applications of contemporary versions of
Meinongianism. See Sections 5.4 and 5.5 below.) According to the other
variety of abstractionism, fictitious objects are abstract artefacts,
i.e., they are not discovered or selected but *created* by the
authors of fictional
 stories.[16]



The latter view (today often referred to as "creationism")
fits well into a general ontology of abstract artefacts (like, for
instance, literary and other works of fiction as well as non-fictional
cultural entities) and does justice to the intuition that fictitious
objects as well as the works in which they occur are literally brought
into being through human acts of creation. However, it is objected
against creationism that the creation of an abstract object is
something deeply mysterious.


### 3.3 The Problem of Discourse about the Past and the Future



The structure of the problem of discourse about the past and the
future is very similar to the structure of the problem of fictional
discourse. Consider the following sentences:



(1)
Socrates was a philosopher.
(2)
The first female pope will be black.


Given that the sentences (1) and (2) have the logical structure of
predications, i.e., the structure "\(Fb\)", and given
that (PP) is valid, (1) implies that Socrates exists and (2) implies
that the first female pope exists.



Indeed, the sentences (1) and (2) look like predications.
Grammatically speaking, they consist of a subject term
("Socrates", "the first female pope") and a
predicate term ("was a philosopher", "will be
black".) But while it is certainly true *now* (in the
third millennium C.E.) that Socrates was a philosopher, it is also
certainly true now that Socrates does not exist anymore.



Second, let's assume, for the sake of argument, that indeed
there will be a female pope (and exactly one first female pope) at
some time in the far future and that she will be black and that she
has not even been fathered yet. Given these assumptions, it is
certainly true now that the first female pope does not yet exist.



Again, there are several attempts to resolve this problem. One
possible strategy is to deny that sentences like (1) and (2) really
have the logical structure of predications. One might suggest the
following alternative interpretations, using "\(P\)"
(read: "It has been the case") and
"\(F\)" (read: "It will be the case") as
"tense operators":



(1')
\(P\)(Socrates is a philosopher).
(2')
\(F\)(The first female pope is black).


Note that the tense operators "\(P\)" and
"\(F\)" are sentence operators, like the story
operator from above. Just as the story operator blocks the inference
to existence claims about fictitious objects, the tense operators
block the inference from (1') to



(3)
Socrates exists.


and from (2') to



(4)
The first female pope exists. (For a tense operator strategy see
Prior 1968.)


There is a lot to be said in favor of this logical interpretation of
tenses. Yet, it leaves some problems unresolved. One of them is the
problem of *tensed plural quantifiers*. Consider, for
instance:



(5)
There have been two kings named Charles.


The standard tense operator interpretation of (5) yields:



(5')
\(P\)(There are two kings named Charles).


However, while (5) is true, (5') is false, since at no time in
the past there have been two kings named Charles
*simultaneously*. (See Lewis 2004.) Thus, the standard tense
operator strategy seems to fail in cases like this one.



Another problem that the tense operator strategy leaves unresolved is
the problem of *relations between present and non-present
objects*. Given the principle that a real (two-place) relation can
obtain only if both terms of the relation exist, and given that past
and future objects do not (now) exist, relations between present and
past or future objects are impossible. Yet it seems that there are
plenty of relations between present and past (or future) objects. For
instance, I stand in the relation of *being one of six
granddaughters of* to my grandmother. Likewise, perhaps I stand in
the relation of *being the grandmother of* to a future
child.



Here is a Meinongian solution: Suppose objects pop in and out of
*existence* but thereby do not gain or lose their
*being*. (For a Meinongian, all existent objects have being but
not all being objects exist.) According to this picture,
"Socrates" now denotes the nonexistent Socrates and
"the first female pope" now denotes the nonexistent first
female pope. Accordingly, although we cannot allow for the inference
from



(1)
Socrates was a philosopher.


and



(2)
The first female pope will be black.


to



(3)
Socrates exists.


and



(4)
The first female pope exists.


we can allow for the inference from (1) and (2) to



(3')
There is something that is identical with Socrates.


and



(4')
There is something that is identical with the first female
 pope.[17]


This result does justice to two otherwise incompatible intuitions,
namely (i) the intuition that neither Socrates nor the first female
pope exist right now, and (ii) the intuition that it is nevertheless
possible to refer to Socrates and to the first female pope (or, to put
it another way: the intuition that the name "Socrates" and
the description "the first female pope" are not
empty).



Tensed plural quantifiers do not pose a problem for a Meinongian.
Tensed quantifiers in general may be interpreted as
*restricted* quantifiers that range over a particular subdomain
of nonexistent objects: "there was" may be interpreted as
a quantifier that ranges over the subdomain of past objects (i.e.,
objects that have existed but do not exist anymore); analogously,
"there will be" may be interpreted as a quantifier that
ranges over the subdomain of future objects (i.e., objects that will
exist but do not exist
 yet).[18]



Furthermore, from a Meinongian point of view, relations between
existent and nonexistent objects are ubiquitous. Remember the
Meinongian solution to the problem of intentionality: people fear,
admire, dream of, hope for, or imagine nonexistent objects. Thus,
relations between present and non-present objects do not pose a
particular problem for a Meinongian.


### 3.4 The Problem of Alleged Analytic Truths Like "The round square is square"



Sentences like



(1)
The round square is round and a square. 


seem to be logically true (at least according to the intuitions of
some logicians--see Lambert 1983). Furthermore, they seem to have
the logical structure of predications. According to (PP) and (EG), (1)
implies



(2)
There is something that is identical with the round square.


and



(3)
There is something that is both round and a square.


If "there is" means the same as "exist", these
are, of course, unacceptable consequences.



There are two obvious ways out: (i) One could simply reject (1) as
false (or truth-valueless). (ii) One could try to find an adequate
paraphrase for (1) which accounts for the intuition that (1) is
"in some sense" true. Such a paraphrase might be



(1')
If there were such a thing as the round square, it would be
round and a square.


But according to the Meinongian picture, (2) and (3) are acceptable
consequences, since they do not entail the *existence* of
something that is both round and square. Something that is both round
and square is an *impossible object*, according to Meinong,
which means that it cannot *exist*, but this does not entail
that *there is no* such thing. Therefore, the Meinongian can
accept (1) as true, without resorting to any kind of paraphrase.



We have seen that there are alternative solutions for every single one
of the abovementioned problems. But, for all we know, the assertion
that there are nonexistent objects is the only way to resolve all
these diverse problems in a uniform way.


### 3.5 Nonexistent Objects in Practical Philosophy



There is a debate in practical philosophy as to whether nonexistent
persons are morally relevant. The basic question is this: do
nonexistent people have interests that we ought to take into account
in our decisions? Obviously, some of our decisions affect not only
existent but also future (i.e., not yet existent) persons; matters of
climate change or the disposal of radioactive waste are relevant cases
in point. Intuitively, we ought to act in such a way as to prevent
disasters for future generations. It is a matter of controversy,
though, whether, in order to take into account this moral intuition,
we have to commit ourselves to an ontology of not yet existent beings.
Some, however, go still a step further and argue that not only future
persons are morally relevant but even persons who will never exist
(and never existed). In particular, this debate concerns questions of
procreative ethics and population
 policies.[19]


## 4. Problems with Belief in Nonexistent Objects



The foregoing considerations suggested that the claim that there are
nonexistent objects has considerable explanatory force. Why, then, is
this claim not generally accepted but, rather to the contrary, so
controversial? Is the reason just, as Meinong has put it, "a
prejudice in favor of the actual"? -- Although ontological
prejudices may play a role, there are also some good reasons for
reservations (to put it very carefully).



Even in Meinong's own writings, there are (roughly) two versions
of the theory, the original one and a later, revised one. In what
follows, we will refer to the *original* Meinongian object
theory by means of the abbreviation "MOT\(^o\)".



Perhaps the most basic principle of MOT\(^o\) is the so-called
"*principle of independence*", which says,
literally: *So-being is independent from being* (see Meinong
1959). Ignoring, for the sake of simplicity, Meinong's
particular use of the term "being", we can paraphrase this
principle as: *So-being is independent from existence*.



The "so-being" of an object is the totality of the
object's properties apart from the object's existence or
non-existence. The principle of independence says, thus, that an
object may have any properties whatsoever, independently of whether
the object exists or not. For instance, the (nonexistent) golden
mountain literally *is* golden and a mountain; the round square
literally *is* round and a square.



To every single property and to every set of properties, there is a
corresponding object, either an existent or a nonexistent one. Thus,
there is, for instance, an object that has the property of being round
as its sole property; one might call it "the object
*round*", or simply "*round*". There
is also an object that has the property of being blue as its sole
property (the object *blue*, or *blue*, for short).
Furthermore, there is an object that has the property of being round
and the property of being blue, and no other properties (the object
*round and blue*); and so forth.



In the notation of classical logic extended with definite descriptions
of the form \(\iota x\phi(x)\), the object that has the
property of being blue as its sole property may be represented by
"\(\iota x\forall F(Fx \equiv F = B)\)"[20]
 (where "\(B\)" stands for "is blue"),
the object that has the property of being blue and the property of
being round as its sole properties by
"\(\iota x\forall F(Fx \equiv F = B \vee F = R)\)" (where
"\(R\)" stands for "is round"), and so
forth.



The object *blue* is *not* identical with the
*property* of being blue; neither is it identical with the
*set* that contains the property of being blue as its sole
member. Neither is the object *round and blue* identical with
the set of the property of being blue and the property of being round.
The property of being blue is not itself blue, the property of being
round is not itself round. Analogous considerations hold for sets of
properties: sets have neither colors nor shapes. But the object
*blue* is blue, and the object *round* is round, and so
forth.



One might wish to ask: Isn't it impossible that there exists an
object that has the property of being blue as its *sole*
property? Isn't it necessarily the case that every colored
object also has some particular shape, some particular size, is made
of some particular material, and so forth?



The Meinongian answer to this question is as follows: It is indeed
impossible that such an object *exists*! Therefore, the object
*blue* is not only nonexistent but even *necessarily*
nonexistent. Of course, the same holds for the object *round*,
the object *red and round*, and infinitely many other objects
as well. Every existing object has *infinitely many*
properties. Every existing object is a *completely determined*
(or, in short: a *complete*) object. Objects like *blue*
and *round and blue* are *incompletely determined* (or,
in short: *incomplete*)
 objects.[21]



Incomplete objects are necessarily nonexistent. They are, in this
sense, *impossible* objects (even though their properties may
not be contradictory). It should be noted, however, that not every
complete object exists. Consider, for instance, the object that looks
exactly like me except that it has green eyes instead of blue ones.
Let's assume that this object (my nonexistent green-eyed
counterpart) has all the properties that I have except for those that
are entailed by the difference in eye color, given the actual laws of
nature. My nonexistent green-eyed counterpart is completely determined
and nevertheless does not exist. But, in contrast to *blue*,
this counterpart *could* exist, i.e., it is a *possible*
nonexistent
 object.[22]



Unfortunately, however, MOT\(^o\) has a number of paradoxical
consequences. Bertrand Russell, Meinong's most famous critic,
put forward two objections against
 MOT\(^o\).[23]
 The first objection goes as follows: According to MOT\(^o\),
there is an object that is both round and square, but such an object
is "apt to infringe the law of contradiction", since it
would be both round and not round (Russell 1973c, 107).



Meinong perhaps could have replied to this objection that the object
called "the round square" has the properties of being
round and being square, but not the property of being not round, and
thus the round square does not infringe the law of contradiction (but
only the geometrical law that everything that is square is not round).
Such a reply, however, would have been a bit beside the point, since
it is clear that, according to the principles of MOT\(^o\),
there is an object that is both round and not round (and evidently the
object that Russell had in mind was of this sort). Indeed, Meinong did
not deny that the round square infringes the law of contradiction.
Instead, he replied to Russell's first objection that the law of
contradiction holds for existent objects only. Objects that are both
round and not round, however, are necessarily nonexistent.



Russell accepted this reply but forged a second objection that could
not be dismissed in the same vein. Russell argues that since it is a
principle of MOT\(^o\) that to *every* set of properties
there is a corresponding object and since existence is treated as a
property within MOT\(^o\), there must be an object that has
exactly the following three properties: being golden, being a
mountain, and being existent. If "\(G\)" stands for
"is golden", "\(M\)" stands for "is
a mountain" and "\(\rE!\)" stands for "is
existent", this object is denoted by
"\(\iota x\forall F(Fx \equiv F = G \vee F = M \vee F = \rE!)\)". Thus, it follows from the principles of
MOT\(^o\) that there is an *existent* object that is
golden and a mountain. But it is an empirical fact that no golden
mountain exists. Given the (apparently trivial) assumption that
"\(b\) is existent" is equivalent with
"\(b\) exists", this is a contradiction.



A further paradox seems to arise from the incompleteness of many
Meinongian objects:


1. The object *blue* (i.e.,
\(\iota x\forall F(Fx \equiv F = B)\), according to MOT\(^o)\) has the property of being
blue as its sole property. (Theorem of MOT\(^o)\)
2. The object *blue* has exactly one property. (1)
3. The object *blue* has the property of having exactly one
property. (2)
4. The property of being blue is not identical with the property of
having exactly one property.
5. Thus, *blue* has (at least) two properties, namely the
property of being blue and the property of having exactly one
property. (1, 3, 4)
6. Thus, *blue* has exactly one property and *blue* has
(at least) two properties. (2, 5)



Furthermore, it seems that many Meinongian objects do not only
infringe laws of logic and geometry, but also intuitively plausible
principles like "If something is round, it occupies some region
in space" and "If something is a mountain, it is
accessible to the senses". It seems that having a particular
shape entails occupying a region in space and that being a mountain
entails accessibility to the senses (in principle). According to
MOT\(^o\), the round square is round and the golden mountain is
a mountain, but obviously neither the round square nor the golden
mountain occupies any region in space and neither of them is
accessible to the senses.



Another strange consequence of MOT\(^o\) is the following: If an
object comes into existence, all that happens is that the object turns
from a nonexistent into an existent one. Analogously, if an object
goes out of existence, all that happens is that the object turns from
an existent again into a nonexistent one. Apart from this, neither the
object in question nor the world as a whole changes in any way. For
instance, when I cease to exist, all that happens is that I will again
be nonexistent (as it was from the beginning of time to 1966). In all
other respects, I will stay just the same. Maybe such a thought is
potentially comforting for those who love me, but it is surely at odds
with our normal understanding of coming into existence and passing
away.


## 5. Contemporary Theories of Nonexistent Objects: From Nonexistence to Abstractness



There is a diversity of contemporary theories of nonexistent objects,
where "theory of nonexistent objects" is meant to include
any theory that attempts to make sense of (alleged) talk about
nonexistent objects and/or (seeming) intentional directedness to
nonexistent objects. Some of them, like the de-ontologization strategy
and fictionalism, take a reductionist route. The de-ontologization
strategy claims that there can be true sentences about nonexistent
objects, although there are no nonexistent objects. Fictionalism
claims that talk about nonexistent objects is not to be taken
literally but as a sort of "pretense". The other worlds
strategy makes use of the assumption of merely possible (and even
impossible) worlds. Other contemporary theories of nonexistent
objects, however, are closer to Meinong's original theory but
have amended MOT\(^o\) in such a way as to avoid at least some
of the abovementioned paradoxes. Those are often called
"neo-Meinongian theories". Usually, they adopt either the
nuclear-extranuclear strategy or the dual copula strategy in order to
free Meinongian object theory from inconsistencies and
counterintuitive consequences.


### 5.1 The De-ontologization Strategy



Tim Crane (see Crane 2012 and 2013) holds that all of the following
claims are true:


1. We can think and talk about nonexistent objects.
2. Nonexistent objects do not have any kind of being whatsoever.
3. The sentence "There are nonexistent objects" is
true.
4. Some predications with non-referring singular terms in subject
positions are true, e.g.: "Vulcan was a planet postulated by Le
Verrier"; "Sherlock Holmes is more famous than any living
detective"; "Pegasus is a mythical horse".
5. Contrary to what Meinongians think, nonexistent objects do not
have all of the properties they are characterized as having. For
instance, Pegasus is a not a horse; thus, "Pegasus is a
horse" is not true (although "Pegasus is a mythical
horse" is). Neither is the round square round.



Crane can hold the conjunction of 1 and 2 because he interprets
*aboutness* in a non-relational way. He can hold the
conjunction of 2 and 3 because he denies that "there are"
and its cognates (both in natural and formal languages) are
ontologically committing in any way. (For this reason, I call this the
de-ontologization strategy.) He can hold the conjunction of 4 and 5
because he endorses a positive free logic, i.e., the view that there
may be true as well as false sentences of the form \(Fb\), where
"\(b\)" stands for a non-referring singular term.



By denying that Pegasus is a horse and the round square is round Crane
circumvents some of the above-mentioned problems of Meinongianism.
However, his view raises another problem: Why is "Pegasus is a
mythical horse" true, while "Pegasus is a horse" is
not? In general, why is it that certain predications with
non-referring singular terms are true and others are not? For,
according to the de-ontologization strategy, neither "Pegasus is
a mythical horse" nor "Pegasus is a horse" can be
made true by the referent of "Pegasus", because there is
no such thing.

 Crane (2013) offers what he calls a
"reductionist" solution to this problem. That is,
according to Crane, sentences "about" nonexistent objects
are made true by something else, i.e., by something existent. For
instance, the sentence "Vulcan was a planet postulated by Le
Verrier in 1859 to explain the perturbations in the orbit of
Mercury" is made true by certain events in 1859, namely by
postulation events; the sentence "Sherlock Holmes is more famous
than Sir Ian Blair" is made true by the fact that more people
have heard about Sherlock Holmes than about Sir Ian Blair (where to
have heard about Holmes is to have heard about the respective
stories); the sentence "Pegasus is a mythical winged horse that
sprung into being from the blood of Medusa" is made true by a
myth which represents Pegasus as being such-and-such; the sentence
"Siegfried is one of the most unappealing heroes in all dramatic
works" is made true by certain facts about the last two parts of
Wagner's *Ring*. As these examples already show, Crane
does not give a uniform, systematic account of the truth of sentences
about fictitious objects, as he himself concedes. (See Crane 2013,
Section 5.5.)


For another example of a reductionist solution, Frank Jackson holds
that one can assent to "Mr. Pickwick is Dickens' most
famous character" without an ontological commitment to
fictitious characters in general and Mr. Pickwick in particular. For,
according to Jackson's de-ontologization strategy, object
language sentences are ontologically neutral. Ontological commitment
comes in only at the meta-language level, for instance, if we would
claim that the name "Mr. Pickwick" denotes Dickens's
most famous character or that the predicate "a character in
Dickens" applies to something. (See Jackson 1980.)



A de-ontologization strategy with respect to fictitious characters is
also to be found in Crittenden 1973 and in Azzouni 2010.


### 5.2 Fictionalism and Indifferentism



In recent years, something close to the de-ontologization
strategy--or rather a bundle of more or less similar
strategies--became prominent, known under the heading
"fictionalism". The basic idea of fictionalism is, roughly
put, that utterances belonging to a certain region of discourse are
not to be taken literally, that speakers producing such utterances
have a fictional attitude towards them and are engaged in a sort of
pretense or make-believe. (For an overview of the diverse versions of
fictionalism as well as a succinct presentation of its most important
pros and cons see the entry on
 fictionalism.)



Fictionalism differs from the de-ontologization strategy since
fictionalists do not claim that the relevant utterances are literally
true; to the contrary, according to fictionalism, certain kinds of
discourse consist of utterances that are false (if taken literally),
but nevertheless it may be useful in some respects to stick to that
sorts of discourse.



A general assessment of fictionalism is difficult since the positions
included under this heading differ considerably from each other. Much
depends on how exactly the "fictional attitude" is spelled
out. Many versions of fictionalism are prone to the
"phenomenological objection": external talk about
fictitious objects--to mention one of the applications of the
fictionalist strategy that is particularly relevant in the context of
the present entry--does not feel like "make-believe";
introspection does not reveal that we are engaged in any kind of
pretense when we say things like "Sherlock Holmes is one of the
most famous characters of popular literature" and the like.



A position inspired by and in important respects similar to
fictionalism that, however, avoids the phenomenological objection is
Eklund's "indifferentism". Indifferentism is the
view that speakers outside the "philosophy room" are often
simply indifferent with regards of the ontological implications of
their utterances and thus are not committed to the existence of those
entities whose existence is implied by their utterances. As Eklund
emphasizes, however, indifferentism does not say anything about which
entities one *should* accept in one's ontology; it is, in
this sense, not an ontological thesis. (See Eklund 2005.)


### 5.3 The Other Worlds Strategy



The other worlds strategy has been proposed by Graham Priest (2005)
and Francesco Berto (2008). Priest calls his theory *noneism*;
Berto names it *modal Meinongianism*. The term
"noneism" has been coined by Richard Routley, and Priest
not only takes over the name but also essential features of
Routley's theory (among other things the assumption that basic
principles of standard logics, like the principle of contradiction, do
not hold without restriction--without, of course, accepting that
everything is true).



Proponents of the other worlds strategy reject both the
nuclear-extranuclear strategy and the dual copula strategy. Instead,
they assume merely possible and even impossible worlds. All worlds
(possible as well as impossible ones) share the same domain of
discourse. But not all objects of the domain exist in all worlds.
Thus, Pegasus does not exist in the actual world, but it exists in a
variety of merely possible worlds (namely in those which are such as
represented by the Greek mythology).



According to the other worlds strategy, nonexistent objects literally
*have* the properties through which they are
"characterized"--but they have these properties not
in the actual world but only in those worlds "which realize the
way the objects are represented as being in the appropriate cognitive
state [...]." (Priest 2011b, 249, footnote 35) Suppose you
imagine a winged horse. In this case, in your imagination, you have an
intentional object that is represented as being winged and a horse.
Thus, the intentional object of your present intentional state is a
nonexistent winged horse, which is, however, in the actual world
neither winged nor a horse. In some worlds, however, this object
\(is\) winged and a horse - namely in those worlds which
realize the way the object is represented in your
 imagination.[24]



The other worlds strategy provides the following solution to the
paradox of contradiction: The round square exists only in impossible
worlds. In impossible worlds, however, the principle of contradiction
does not hold. Therefore, the round square's being both round
and not round does not infringe the laws of logic which hold in those
worlds in which the round square exists.



In the actual world, however, the round square is neither round nor
square, since roundness and squareness are "existence-entailing
properties", i.e., "\(b\) is round/square"
entails "\(b\) exists". Therefore, even if in the
actual world (and in all other possible worlds) the law of
contradiction holds, the round square does not infringe this law,
since in these worlds the round square is neither round nor not
round.



In the light of this theory, it is easy to explain why nobody has ever
seen the round square or a golden mountain and why the round square is
obviously not located in space: since the round square is neither
round nor square in the actual world, there is no reason to assume
that it occupies space or is accessible to the senses. Similar
considerations hold for the golden mountain.



It is worth noting that the postulation of existence-entailing
properties is an implicit rejection of Meinong's principle of
independence, which is one of the cornerstones of Meinongian object
theory.



Proponents of the other worlds strategy reject the
nuclear-extranuclear distinction because they find it "difficult
to avoid the feeling that the class [of nuclear predicates] has been
gerrymandered simply to avoid problems" (Priest 2005, 83).



But Priest's proposal has difficulties of its
 own.[25]
 To mention some of them: First, Priest does not give a principled
characterization of which properties are existence-entailing and which
are not (which looks quite similar to the problem with the
nuclear-extranuclear distinction which Priest points out in the above
quotation). Second, it remains unclear which properties nonexistent
objects have in the actual world (apart from logical properties like
being self-identical and intentional properties like being thought of
by
 Priest).[26]
 Furthermore, Priest's noneism raises difficult questions about
cross-world identity and the ontological status of non-actual worlds.
The ontological status of non-actual worlds is far from obvious: they
may be taken to be concrete objects (structured sets of physical
objects) or abstract objects (sets of sentences, propositions, or
states of affairs). (For an elaborate survey of various conceptions of
non-actual worlds see the entry on
 possible worlds, i.e., Menzel
 2014.)[27]
 Apart from this, it is doubtful whether Priest's theory
provides an adequate account of fictitious objects. Among other
things, it does not do justice to the widespread intuition that
fictitious objects are *created* by the authors of the stories
to which they
 belong.[28]


### 5.4 Nuclear and Extranuclear Properties



According to the nuclear-extranuclear strategy, there are two kinds of
properties: nuclear and extranuclear ones. (Meinong 1972,
 SS25)[29]
 An object's nuclear properties are supposed to constitute the
object's "nature", while its extranuclear properties
are supposed to be external to the object's nature. Nuclear
properties are, for instance: being blue, being tall, kicking
Socrates, having been kicked by Socrates, kicking somebody, being
golden, being a mountain (Parsons 1980, 23).



Which properties are extranuclear? Terence Parsons distinguishes four
categories of "extranuclear predicates" (i.e., predicates
that stand for extranuclear properties): ontological
("exists", "is mythical", "is
fictional"), modal ("is possible", "is
impossible"), intentional ("is thought about by
Meinong", "is worshipped by someone"), technical
("is complete") (Parsons 1980,
 23).[30]



Nuclear properties are either *constitutive* or
*consecutive*, in Meinong's terms (Meinong 1972, 176). An
object's constitutive properties are those properties that are
mentioned explicitly in a description that is used to pick out the
object. Thus, the constitutive properties of the golden mountain are
being golden and being a mountain. An object's consecutive
properties are those properties that are somehow included or implied
by the object's constitutive properties. Thus, among the
consecutive properties of the golden mountain are probably the
properties of being a material thing and of being extended.



According to MOT\(^o\), the object called "the golden
mountain" was \(\iota x\forall F(Fx \equiv F = G \vee F = M)\), i.e.,
the object that has the property of being golden and the property of
being a mountain (and no other properties). According to the revised
version of object theory, the object called "the golden
mountain" is the object that has all the nuclear properties that
are implied by the nuclear property of being golden and the nuclear
property of being a mountain, i.e.,
\(\iota x\forall F^n (F^n x \equiv G^n \Rightarrow F^n \vee
M^n \Rightarrow F^n)\).[31]



How does the nuclear-extranuclear distinction help to avoid the
paradoxes mentioned in the section above? -- Consider again the
paradox from incompleteness: According to MOT\(^o\), there is an
object that has the property of being blue as its sole property
(we've called it "the object *blue*", for
short), in logical notation:
\(\iota x\forall F(Fx \equiv F = B)\). It seems to be true of the object *blue*, *by
definition*, that it has exactly one property. Yet, the property
of having exactly one property is clearly distinct from the property
of being blue. Thus, it seems that the object *blue* has at
least two properties.



According to the revised version of object theory with the
nuclear-extranuclear distinction (MOT\(^{ne}\), for short), this
paradox is avoided in the following way: The property of being blue is
a nuclear (constitutive) property, the property of having exactly one
property, however, is an *extranuclear* property. There
aren't any objects that have exactly one property. There are
only objects that have exactly one *constitutive* (nuclear)
property. Objects that have only a limited number of constitutive
properties may (and necessarily do) have additional extranuclear
properties--like the property of having exactly \(n\)
constitutive properties or the property of being incomplete. The
object called "*blue*" is
\(\iota x\forall F^n(F^n x \equiv B^n \Rightarrow F^n\)), i.e.,
the object that has the property of being blue as its sole
constitutive property. This does not rule out that the object
*blue* may have additional *extranuclear* properties.
Thus, the paradox from incompleteness does not arise in
 MOT\(^{ne}\).[32]



To Russell's objection that the existent golden mountain
infringes the law of contradiction (since it is both existent and
nonexistent), advocates of MOT\(^{ne}\) may reply as follows:
Existence is an extranuclear property, but only nuclear properties can
be constitutive properties of an object. Therefore, according to
MOT\(^{ne}\), there simply is no such object as
\(\iota x\forall F(Fx \equiv F = G \vee F = M \vee F = \rE!)\)
(i.e., the existent golden mountain). (This route is taken by Dale
Jacquette and Richard Routley. See Jacquette 1996, 81 and Routley
1980, 496.)



This solution, however, imposes quite a heavy restriction on the
theory of objects. Probably this was the reason why Meinong himself
did not even mention it as a possible solution. Instead, he introduced
in addition to the nuclear-extranuclear distinction the *doctrine
of watered-down extranuclear properties*: at least some
extranuclear properties (existence, possibility) have nuclear
counterparts, i.e., "watered-down" versions of
extranuclear properties (Meinong 1972,
 SS37).[33]



If the extranuclear property of existence has a watered-down nuclear
counterpart, the following answer to Russell's objection is
available: "The existent golden mountain exists" is
ambiguous. It may be read as "The existent golden mountain
exemplifies extranuclear existence" (which is false), or it may
be read as "The existent golden mountain exemplifies nuclear
existence" (which is true). There is no contradiction between
"The existent golden mountain exemplifies nuclear
existence" and "The existent golden mountain does not
exist" (in the proper, extranuclear sense).



Do other extranuclear properties (besides existence) also have nuclear
counterparts? Do perhaps *all* extranuclear properties have
nuclear counterparts? Meinong himself is not explicit about this
point, but it seems very natural to extend the theory in this way.
Terence Parsons has adopted this extension (Parsons 1980, 68), while
Dale Jacquette rejects the doctrine of watered-down extranuclear
properties altogether, even for existence and possibility (Jacquette
1996, 85-87).



There are several paradoxes for which MOT\(^{ne}\) does not supply
a solution (even if it is supplemented with the doctrine of
watered-down extranuclear properties). It still seems that the round
square infringes the law of contradiction; one still may wonder why it
is impossible to discover round squares and golden mountains; and one
still may be baffled by the doctrine that nonexistent objects differ
from existent ones only in that the former lack
 existence.[34]


### 5.5 The Dual Copula Strategy



According to the dual copula strategy, there are two kinds of
relations between properties and
 individuals.[35]
 Different advocates of this strategy use different terminologies for
it. Here are some of them:


* The golden mountain *is determined by* the property of
being golden and by the property of being a mountain.
  

The golden mountain *satisfies* the property of being
incompletely determined. (Mally 1912)
* The golden mountain *has* the property of being golden and
the property of being a mountain *assigned to it.*
  

The golden mountain *immanently contains* the property of
being incompletely determined. (Ingarden 1931 [1973], SS20, p.
122)
* The golden mountain *is consociated with* the property of
being golden and the property of being a mountain.  

The golden mountain *is consubstantiated with* the
property of being incompletely determined. (Castaneda
1972)
* The property of being golden and the property of being a
mountain *are ascribed to* the golden mountain.
  

The golden mountain *has* the property of being
incompletely determined. (van Inwagen
 1977)[36]
* The golden mountain *is constituted by* the properties of
being golden and being a mountain.
  

The golden mountain *exemplifies* the property of being
incompletely determined. (Rapaport 1978)
* The golden mountain *encodes* the property of being golden
and the property of being a mountain.  

The golden mountain *exemplifies* the property of being
incompletely determined. (Zalta 1983)



The various versions of the dual copula strategy share the assumption
that the copula "is" is ambiguous. In what follows, we
will use the exemplification-encoding terminology. In addition, we
will borrow from Zalta the following notational convention:
"\(Fb\)" stands for "\(b\)
*exemplifies* the property of being \(F\)".
"\(bF\)" stands for "\(b\)
*encodes* the property of being \(F\)". Furthermore,
we will use MOT\(^{dc}\) as an abbreviation for "the revised
version of Meinongian object theory which makes use of a dual copula
distinction".



According to MOT\(^{dc}\), the object called "the round
square" is the object that encodes the property of being round
and the property of being square (and all of the properties that are
implied by these properties) and no other properties. Thus, according
to MOT\(^{dc}\), the object called "the round square"
is \(\iota x\forall F(xF \equiv R \Rightarrow F \vee S \Rightarrow F)\).



Thus, according to MOT\(^{dc}\), the object called "the
round square" encodes exactly two constitutive properties (being
round and being square). However, over and above this, there are many
(indeed *infinitely many*) properties that are
*exemplified* by this object, for instance: the property of not
being red, the property of not encoding the property of being red, the
property of not being determined with respect to its side length, the
property of having thought of by Bertrand Russell, the property of
encoding exactly two constitutive properties, the property of being
incompletely determined.



To mention another popular example, consider Pegasus: Among other
things, Pegasus encodes the properties of being a horse, of having
wings, of having been tamed by Bellerophon. But there are also
infinitely many properties that Pegasus exemplifies, for instance, the
property of not being determined with respect to the number of hairs
in its tail, the property of being a character of Greek mythology, the
property of being a fictitious object.



It must be emphasized that something that encodes the property of
being a horse *is not* a horse (in the usual predicative sense
of "is"). Analogously, something that encodes the
properties of being round and square is neither round nor square. That
is to say, something that encodes the property of being a horse does
not belong to the class of horses, and something that encodes the
properties of being round and square does neither belong to the class
of round things nor to the class of square things. Rather, things that
encode the properties of being a horse or being a square or being a
Danish prince are *abstract objects*--abstract in the
sense that they are neither mental nor spatio-temporal things. In
general, everything which encodes at least one property is an abstract
object in this
 sense.[37]



Let's see how MOT\(^{dc}\) avoids the alleged paradoxes
mentioned in section 4. The first objection was that objects like the
round square infringe the law of contradiction, since such objects
would be both round and not round. According to MOT\(^{dc}\),
however, the object called "the round
square"--\(\iota x\forall F(xF \equiv R \Rightarrow F \vee S \Rightarrow F)\)--is not round (i.e., does not exemplify the property
of being round). Thus, no contradiction arises.



The second objection was that the existent golden mountain would
infringe the law of contradiction, since, if there were such an
object, it would be both existent and nonexistent. According to
MOT\(^{dc}\), one could answer to this objection as follows: The
object called "the existent golden mountain" is
\(\iota x\forall F(xF \equiv G \Rightarrow F \vee M \Rightarrow F \vee \rE! \Rightarrow F)\). This object *encodes* the property of being
existent, but it does not *exemplify* it. Since
"\(b\) encodes \(F\)" does not imply
"\(b\) exemplifies \(F\)", there is no
contradiction involved here.



According to MOT\(^{dc}\), the object *blue* is
\(\iota x\forall F(xF \equiv B \Rightarrow F)\), i.e., the object that encodes exclusively the
properties that are implied by being blue. Thus, the object
*blue* *exemplifies* the property of encoding only the
properties that are implied by being blue. It is not the case that the
object *blue* has exactly one property and at the same time has
at least two properties, at least not, if "has" is used in
the same sense in both occurrences. In this way, the apparent
contradiction disappears.



Furthermore, according to MOT\(^{dc}\), the object called
"the round square", i.e.,
\(\iota x\forall F(xF \equiv R \Rightarrow F \vee S \Rightarrow F)\), does not occupy
any region in space. More exactly, it does not exemplify the property
of occupying some region in space (though, perhaps it encodes this
property, if being round implies occupying some region in space).
Analogously, according to MOT\(^{dc}\), the object called
"the golden mountain", i.e.,
\(\iota x\forall F(xF \equiv G \Rightarrow F \vee M \Rightarrow F)\), does not
exemplify the property of being accessible to the senses (at best, it
encodes this property). Therefore, there is nothing paradoxical in the
fact that nobody has ever seen a golden mountain and that it is
impossible to determine the location of the round square.



Finally, MOT\(^{dc}\) does not have the counterintuitive
consequence that the only difference between existent and nonexistent
objects is that the latter lack the property of being existent, such
that if an object goes out of existence, the vast majority of its
properties (like being human, loving pancakes, being violent-tempered,
and so forth) stay exactly the same. Consider again my nonexistent
green-eyed counterpart. According to MOT\(^{dc}\), this object
*encodes* being human, being female, being a philosopher, and
so forth, but does not *exemplify* these properties; therefore,
it does not belong to the class of female philosophers, not even to
the class of humans or to the class of living beings. Thus, it is
clear that my green-eyed counterpart's nonexistence is by far
not the only difference between it and myself. In general, nonexistent
objects are a particular kind of objects, according to
MOT\(^{dc}\)--very different from ordinary existent objects.
In what follows, we'll call them "Meinongian
objects".


### 5.6 Nonexistence Does Not Hold the Key



MOT\(^{dc}\) is very remote from MOT\(^o\). Recall that,
according to MOT\(^o\), the object called "the golden
mountain" is not an abstract object but something as concrete as
every existent mountain in the world. Secondly, and related to this,
the idea that some objects do not exist is one of the cornerstones of
MOT\(^o\)--but it is not an essential feature of
MOT\(^{dc}\), i.e., it doesn't play an essential role within
MOT\(^{dc}\). Within MOT\(^{dc}\), Meinongian objects are
defined as a particular kind of abstract objects (namely abstract
objects to which two kinds of predicates apply). Of course, one can
decide to say that these objects are "nonexistent"; but
nothing hinges upon this decision. According to MOT\(^o\), the
only difference between Meinongian objects and normal objects consists
in the alleged nonexistence of the former. However, in
MOT\(^{dc}\), Meinongian objects are distinct from normal objects
because only the former are abstract objects which encode properties.
This suffices to distinguish Meinongian objects from normal objects.
Thus, there is no need to assume that existence is a property of
individuals and that there is a difference between "There are
objects that are such-and-such" and "Objects that are
such-and-such exist".



If MOT\(^{dc}\) is essentially different from MOT\(^o\), the
question arises to what extent MOT\(^{dc}\) can fulfill the tasks
MOT\(^o\) was supposed to fulfill. It seems that
MOT\(^{dc}\) cannot do *everything* MOT\(^o\) was
supposed to do. First, consider the problem of intentionality: if
somebody fears the devil, does he fear an abstract object? --
This seems to be psychologically impossible, for an abstract object
cannot do any harm to
 anybody.[38]
 Second, recall the problem of negative singular existence sentences:
Astronomers claim that Vulcan does not exist. Do they thereby intend
to deny the existence of an abstract object that only encodes being
such-and-such a planet? -- Probably not. They rather deny the
existence of something that *is* a planet, i.e., a concrete
material thing. Finally, consider the problem of discourse about the
past and the future: when a teacher in a history of philosophy class
talks about Socrates, does she then intend to talk about an abstract
object that only encodes all of the properties that Socrates (the
"real" one) once exemplified? -- Presumably not. If
there is an object which she is intentionally directed at, then it is
probably the "real" Socrates, not its abstract
counterpart.



It may be that proponents of MOT\(^{dc}\) find ways to meet these
objections such that their theories provide solutions for the problem
of intentionality, the problem of singular existence sentences, and
the problem of reference to past and future objects. But even if they
don't, it is beyound doubt that Neo-Meinongian theories can be
and indeed are fruitful in many ways. In particular, they provide the
basis for a consistent realist ontology of fictitious objects. (For a
variety of further applications see in particular the writings of
Jacquette, Parsons, and Zalta.)


## 6. Themes for Further Investigation



There are several ways in which Meinongian object theory can be
developed further. Here are some of
 them:[39]



1. Both MOT\(^{ne}\) and MOT\(^{dc}\) could perhaps benefit
from a clarification of their basic distinctions, namely the
nuclear-extranuclear distinction and the dual copula distinction,
respectively.



2. One feature of Meinong's mature object theory not mentioned
so far is the "doctrine of implexion". Implexion is a
relation between incomplete and complete objects which seems to be
very close to what is often called "instantiation", i.e.,
a relation between universals and particulars. Incomplete objects are
"implected" in complete ones. (See Meinong 1972,
SS29.) Meinong himself eventually came to interpret incomplete
objects as universals (see Meinong 1972, 739f). Meinongian object
theory may thus be interpreted as a sophisticated theory of
universals, in particular as a theory of *types* (as opposed to
properties), which might open further fields of application.



3. Throughout this entry, we have presupposed realism with respect to
properties. However, it is doubtful whether a theory of Meinongian
objects is *necessarily* ontologically committed to properties.
An ontologically neutral quantifier and the use of non-objectual
variables for predicates (not for *names* of predicates or
properties) may help to avoid this commitment and thus could make
Meinongian object theory much more parsimonious.