Nonexistent Objects

First published Tue Aug 22, 2006; substantive revision Wed Dec 7, 2022

Are there nonexistent objects, i.e., objects that do not exist? Someexamples often cited are: Zeus, Pegasus, Sherlock Holmes, Vulcan (thehypothetical planet postulated by the 19th century astronomer LeVerrier), the perpetual motion machine, the golden mountain, thefountain of youth, the round square, etc. Some important philosophershave thought that the very concept of a nonexistent object iscontradictory (Hume) or logically ill-formed (Kant, Frege), whileothers (Leibniz, Meinong, the Russell ofPrinciples ofMathematics) have embraced it wholeheartedly.

One of the reasons why there are doubts about the concept of anonexistent object is this: to be able to say truly of an object thatit doesn’t exist, it seems that one has to presuppose that itexists, for doesn’t a thing have to exist if we are to make atrue claim about it? In the face of this puzzling situation, one hasto be very careful when accepting or formulating the idea that thereare nonexistent objects. It turns out that Kant’s view that“exists” is not a “real” predicate andFrege’s view, that “exists” is not a predicate ofindividuals (i.e., a predicate that yields a well-formed sentence ifone puts a singular term in front of it), has to be abandoned if oneis to accept the claim that there are nonexistent objects.

This entry is an examination of the many questions which arise inconnection with the view that there are nonexistent objects. Thefollowing are particularly salient: What reasons are there (if any)for thinking that there are nonexistent objects? If there arenonexistent objects, then what kind of objects are they? How can theybe characterized? Is it possible to provide a consistent theory ofnonexistent objects? What is the explanatory force of a consistenttheory of nonexistent objects (if such a thing is possible)?

1. The Concept of a Nonexistent Object

The very concept of a “nonexistent object” has an air ofparadox about it, at least for those philosophers whose thinking isrooted in the Humean tradition. For Hume suggested that to think of anobject is always and necessarily to think of anexistentobject, or to put it differently, that to think of an object and tothink of the same object as existing are just one and the same thing.Immanuel Kant took up Hume’s idea and claimed that existence isnot a “real predicate”, a claim that is often interpretedas an anticipation of Gottlob Frege’s famous doctrine thatexistence is not a predicate of individuals. (See Hume 2000, Book 1,Part 2, Sect. 6; Kant 2003, B 627; Frege 1966, pp. 37f.) Kant’smotivation for rejecting the view that existence is a “realpredicate” was the so-called “ontological proof” ofGod’s existence, which says, roughly, that God’sperfection entails God’s existence, since a being that wouldhave all of God’s perfections except existence (i.e.,omniscience, omnipotence, benevolence) would be less perfect than abeing 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 “realpredicate”.

If Hume is right, then the concept of an object includes the conceptof existence, and the concept of a nonexistent object would be asself-contradictory as the concept of a round square. If existence isnot a predicate of individuals, then one might suppose that neither isnonexistence. Therefore, if Frege is right, to say of an object thatit is nonexistent is a kind of nonsense that arises from a violationof logical grammar. (For Frege and those who follow him, a claim like“God exists/does not exist” is to be understood as a claimabout the conceptGod, or about the property of being God. Onthis view, the logical form of “God exists” is notExists (God)—whereExists is a predicate ofindividuals, but rather:The concept God applies tosomething, orSomething possesses the property of beingGod.)

Thus, in order to take the idea of nonexistent objects seriously, onehas to give up views held by important philosophers about the natureof existence and adopt the view that existence is some kind ofpredicate of individuals. This view entails, among other things, thatto say, for instance, that some white elephants exist is to say thatsome white elephants have the property of existence (or, to put it theother way around, that not all white elephants arenonexistent)—a consequence that might strike some asstrange.

Furthermore, in order to assert “there are nonexistentobjects” without implying “nonexistent objectsexist”, one has to suppose that sentences of the form“There are \(F\)s” mean something different fromsentences 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 thisdistinction. Some of the latter think that the distinction between“there is” and “exists” is rooted in ordinarylanguage, but others deny this firmly (see, for instance, Geach 1971).Obviously, although there might be a tendency among competent Englishspeakers to use “there is” and “exists” indifferent contexts, ordinary language use is too wavering andnon-uniform in this respect to be a stable ground for a philosophicaltheory. Of course, this does not rule out that there aretheoretical reasons for a distinction between “thereis” and “exists”, some of which are discussedbelow.

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 meansof the “existential quantifier” (“\(\exists\)”),which is, consequently, interpreted as having “ontologicalimport”. Thus, in these formal systems, there is no means todistinguish between “there is” and “exists”.However, it has been shown that the distinction between the two can becoherently regimented in various ways. In the systems of TerenceParsons, 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 theexistence predicate (Parsons 1980, Zalta 1983, Zalta 1988, Jacquette1996). “Some things do not exist” could thus be renderedin logical notation as follows:“\(\exists x(\neg\rE !x)\)”; “Pegasusdoes not exist” as “\(\neg\rE !p\)”; and soforth.

Graham Priest (2005) has proposed a theory of nonexistent objects thattreats “there is” and “exists” as synonyms. Heinterprets quantification as utterly ontologically neutral. Thequantifier should express neither “there is” nor“there exists”. Rather, quantifier expressions should beread “For some \(x, \ldots x\ldots\)”,where “For some \(x, \ldots x\ldots\)”does not imply that “there is (or exists) an \(x\) suchthat \(\ldots x\ldots\)”.

Thus, Priest belongs to those philosophers who distinguish between“quantifier commitment” and “ontologicalcommitment” (see Azzouni 2004), claiming that to“quantifier over” objects of a certain kind does notentail an ontological commitment to objects of this kind.^[2]

The various logics of nonexistent objects cannot be described anddiscussed here in detail. However, it is now clear that there is noformal obstacle to a theory of nonexistent objects. The onlyquestions are philosophical: can the concepts that such theories aimto formalize be explained, and do we have good reason to accept atheory formulated in these terms? In the following two sections, themain motivations for believing in nonexistent objects aredelineated.

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

Philosophical writings on nonexistent objects in the 20th and 21stcentury usually take as their starting point the so-called“theory of objects” of the Austrian philosopher AlexiusMeinong (1853–1920). Therefore, it is appropriate to give anoutline of the basic principles of and motives behind this theory.(For a detailed presentation see the entry onMeinong.)

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

Cases like these seem to be clear counterexamples to the principle ofintentionality. However, many philosophers found this principle tooappealing to be given up completely. While some came to the conclusionthat intentionality is not a real relation and therefore does notrequire the existence of an object (see, for instance, Brentano 1874,Prior 1971, Searle 1983, Crane 2013), Meinong offered anothersolution: there is indeed an object for every mental statewhatsoever—if not an existent object then at least a nonexistent one.^[3]

The problem of intentionality may still count as one of the mostimportant 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 inorder to deny the existence of a given individual, one must assume theexistence of that very individual. Thus, it seems that it isimpossible to deny the existence of an individual without gettinginvolved in a contradiction.

However, this conclusion seems hard to accept. In fact, there are manynegative existence statements that we take not only to be sensible butalso 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 existencestatements are ubiquitous, comprehensible and sometimes true. So whyis it that many philosophers are so puzzled about them? In particular,why think one has to assume the existence of an individual in order todeny its existence?

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

Only meaningful sentences can be true.
In a meaningful sentence, every constituent of the sentence mustbe meaningful.
If a singular term is meaningful, then it denotes something.
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 ofthe negative singular existence sentence “Pegasus does notexist”. If “Pegasus does not exist” is true, then itmust be meaningful (by (1) above). If it is meaningful, all of itsconstituents must be meaningful, including the singular term“Pegasus” (by (2) above). If “Pegasus” ismeaningful, 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 leadsto the conclusion that this same sentence is false. So if the abovepremises are correct, it is impossible that “Pegasus does notexist” 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 alonetrue.

There are several ways to resolve this problem, i.e., to account formeaningful and true negative singular existence sentences. Onesolution that became very prominent in the 20th century consists inthe strategy of “analyzing away” the proper names anddefinite descriptions appearing in negative singular existentialclaims. This strategy consists of two steps:

Ordinary proper names are interpreted as disguised definitedescriptions. For instance, “Pegasus” is to be analyzed asshort for “the flying horse from Greek mythology”. This isoften calledthe description theory of proper names. Thus tosay “Pegasus exists” is simply to say “the flyinghorse of Greek mythology exists”.
Definite descriptions are to be analyzed along the lines ofBertrand Russell’s theory of definite descriptions. OnRussell’s theory, to say “the flying horse of Greekmythology 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 \(x\) whichis a flying horse of Greek mythology”.^[5]

If “Vulcan” is short for “the planet between Mercuryand the sun”, then:

To say “Vulcan doesn’t exist” is to say“it is not the case that there is exactly one \(x\) whichis such that \(x\) is a planet between Mercury and thesun”.

The point of these paraphrases is to show that the original sentencescan be analyzed in terms of sentences in which the singular terms(“Pegasus”, “Vulcan”, “the flying horseof Greek mythology” and “the planet between Mercury andthe sun”) have all disappeared. The paraphrases involve thegeneral terms “flying horse from Greek mythology” and“planet between Mercury and the sun”, along with theexistential quantifier (“there is”) and a uniquenesscondition (“exactly one”). (Let’s ignore the factthat the singular terms “Mercury” and “LeVerrier” appear within the general terms; of course, this meansthat the procedure isn’t complete, but, in principle, it can becompleted.) The problem of negative singular existentials is therebyresolved because sentences containing names which appear to be aboutnonexistent objects are paraphrased in terms of sentences involvinggeneral terms, quantifiers and uniqueness conditions. These lattersentences are meaningful independently of whether the general termsapply to anything.

However, both the description theory of proper names andRussell’s theory of definite descriptions have been subject toserious criticisms. One might object that they fail to do full justiceto our actual use of proper names and definite descriptions. Often weuse proper names—successfully—without having any definitedescription in mind. Sometimes we don’t need a definitedescription in order to refer to a particular object, because weindividuate the respective object by means of perception or perceptualmemories. Sometimes we simply do not know of a definite descriptionthat individuates the object we wish to refer to. Most of us knowabout Cicero just that he was a famous Roman orator; but the Romanshad more than one famous orator. Nevertheless, we can use the name“Cicero” successfully to refer to aparticularfamous Roman orator. Moreover, even when we do have something like themental correlate of a definite description in mind when we use aproper name, we do not usually treat the description as adefinition of the proper name (as the Russellian picturesuggests). Suppose what I have in mind when I use the name“Socrates” corresponds to the description “theancient Greek philosopher who died from drinking hemlock”.Suppose furthermore that the famous story about Socrates’ deathis actually a myth and that Socrates in fact died peacefully of oldage. Do I then simply fail to refer to Socrates whenever I use thename “Socrates”? It does not seem so. When I eventuallycome to know that Socrates did not die from drinking hemlock, I willtake this as a piece of informationabout Socrates, theperson 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 properlycapture the meaning of sentences with definite descriptions, simply onthe grounds that the meaning of a proper name like“Pegasus” is just less specific than the meaning of thedefinite description “the flying horse of Greekmythology”. Second, some philosophers have objected that thetheory of definite descriptions sometimes yields the wrong results.Consider, for instance: “The ancient Greeks worshippedZeus.”Prima facie, this sentence expresses a realrelation between the ancient Greeks and Zeus; and it is surely ahistorical fact that the ancient Greeks worshipped Zeus. Yet onRussell’s analysis, proper names like “Zeus” have tobe replaced by definite descriptions, even in contexts other thanexistence claims. So “Zeus” would get replaced by adefinite description like “the Greek god who lived on Mt.Olympus and who …”. Thus, the above true sentence wouldget analyzed in terms of the followingfalse one:“There exists one and only one Greek god who lived on Mt.Olympus and who … and who was such that the ancient Greeksworshipped him.” There are numerous other true sentences likethis, such as “Sherlock Holmes is more famous than any realdetective”, etc., all of which appear to involve real relationsbetween existent objects and nonexistent ones, but whose Russellianparaphrases are false. Third, the use of the anaphoric pronoun“it” in “Teams of scientists have searched for theLoch Ness monster, but since it doesn’t exist, no one will everfind it” seems problematic. The pronoun in both of itsoccurrences in this sentence seems to pick up its meaning/denotationfrom the definite description “the Loch Nessmonster”—which is not easy to explain givenRussell’s theory of definite descriptions.

There might be ways to defend the theory of definite descriptions, butthey will not be pursued here. In the context of this article, therelevant point is that Russell’s theory does not provide agenerally accepted solution to the problem of negative existencesentences. The appeal to nonexistent objects, on the other hand,provides a very simple solution to this problem. It consists inrejecting the premise

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

If there are nonexistent objects, then “\(b\)” maydenote an object that does not exist.

The idea here is that whereas the quantifiers “there is”and “something” range over everything whatsoever, theobjects that exist constitute only a portion of that domain.Therefore, it would be fallacious to derive from“‘\(b\)’ denotessomething” that“\(b\)” denotessomething that exists.According to this picture, “Pegasus does not exist” simplyexpresses that Pegasus is a nonexistent object. Premises 1–3from above can be accepted without restriction. “Pegasus”denotes a nonexistent flying horse and thus is meaningful. Thus, thewhole sentence “Pegasus does not exist” is meaningful aswell. Since it is true that Pegasus does not belong to the class ofexistent objects, “Pegasus does not exist” is true. Ofcourse, this solution can be generalized to all negative singularexistence statements. The appeal to nonexistent objects thus suppliesan elegant solution to the problem of negative singularexistentials.

Naturally, there are alternative solutions to the problem of negativesingular existence statements. Among other things, it is possible toreject premise 4 without committing oneself to an ontology ofnonexistent objects. One might simply accept a positive Free Logic,i.e., the conjunction of the following two principles: 1. Singularterms do not need to denote anything in order to be meaningful. 2.Sentences containing non-denoting singular terms can be true. (Thisstrategy is to be found, for instance, in Crane 2013.) One of thedifficulties of this solution, however, is to give an account of whatmakes such sentences true, i.e., of what their truthhmakers are (giventhe principle that, for every true sentence, there is something in theworld that makes it true, i.e., something that is the sentence’struthmaker). For the special case of negative singular existencesentences, one might claim that that their truthmaker is just theentire world (see, e.g., Crane 2013, Section 3.5; for more aboutCrane’s position see Section 5.1 below). However, this answer tothe truthmaker question is not available for the problem of fictionaldiscourse, which provides another important motivation for acommitment to nonexistent objects.

3.2 The Problem of Fictional Discourse

By “fictional discourse” we mean here and in what followsdiscourse about fictitious objects. Sometimes, the term“fictitious object” is used as synonymous with“nonexistent object”. Here, the term is used in adifferent sense, namely for objects (characters, things, events etc.)which occur in fictions, i.e., in myths or fairy tales, in fictionalnovels, movies, operas etc. Pegasus is a fictitious object in thissense (as are Sherlock Holmes and Hamlet) but Vulcan (the hypotheticalplanet 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 tofulfill the following three conditions:

It has the grammatical structure of a predication, i.e., thestructure that is rendered in logical notation by“\(Fb\)” (where “\(F\)” stands for apredicate expression—here: “is a flyinghorse”—and “\(b\)” stands for a singularterm—here: “Pegasus”).
The singular term in subject position is a name for a fictitiousobject.
It is commonly, and with good reason, taken to be true.

The problem of fictional discourse is closely connected to two logicalprinciples. The first one is well known as “the principle ofexistential 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 explicitlystated, but often tacitly assumed. We call it “the predicationprinciple”:

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 isidentical with \(b\).
(PPb): If \(b\) is \(F\), then \(b\) exists.

Both principles areprima facie extremely plausible: If it istrue of some individual that the predicate “\(F\)”applies toit, then the predicate “\(F\)”applies tosomething. If some predicate“\(F\)” applies to an individual, then the individualhas to exist (for if it were otherwise, how could the predicate applytoit?).

Yet, when applied to fictional discourse, these two principles lead toconsequences that seem to contradict hard empirical facts on the onehand and trivial truths about the ontological status of fictitiousobjects 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 anobject fictitious is just to say that it does not exist.

The problem is that obviously true sentences of fictional discourseseem to lead into outright contradictions. Of course, there areseveral ways to avoid the contradictions. One of them consists inrejecting the principles (EG) and (PP). By this move, one blocks theinference from “Pegasus is a flying horse” to “Thereare 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 sentencesare. There are attempts to answer this question in a“reductionist” fashion, i.e., to claim that sentencesabout fictitious objects are made true not by fictitious objects butby something else, e.g., by literary works, myths, stories or factsabout these, respectively.^[9]

Another way to avoid the contradictions would be simply to reject thesentence “Pegasus is a flying horse” (and, in general, allalleged predications about fictitious objects) as false or untrue.This radical solution, however, fails to do justice to the widespreadintuition that there is a difference in truth-value between“Pegasus is a flying horse” and, say, “Pegasus is aflying dog”.

A third attempt to resolve the problem is what may be called“the story-operator strategy”. According to thestory-operator strategy, we have to interpret sentences of fictionaldiscourse 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 storyof Greek mythology): Pegasus is a flying horse.

The expression “according to the story \(S\)” is theso-called “story operator”,^[10] which is asentence operator (that is, it is the sentence asa whole that is in its scope, not just a part of the sentence, forinstance the predicate). While the sentence within the scope of thestory operator (here: “Pegasus is a flying horse”) may befalse when taken in isolation, the complete sentence may be true.(This strategy is developed in detail in Künne 1990.)

Sentence (1′) doesnot imply that there are flyinghorses; neither does it imply that Pegasus exists. Thus, thecontradictions are avoided.^[11] This looks like an elegant solution, at least as long as we confineourselves to a particular kind of example. Unfortunately, however, itdoes not work equally well for all kinds of sentences of fictionaldiscourse. Consider, for instance:

(4): Pegasus is a character from Greek mythology.

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

(4′): According to the story \(S\): Pegasus is a characterfrom Greek mythology.

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

One may call sentences like “Pegasus is a flying horse” or“Hamlet hates his stepfather” “internalsentences of fictional discourse”, in distinction fromexternal sentences of fictional discourse, like“Pegasus is a character from Greek mythology” or“Hamlet has fascinated many psychoanalysts”. The storyoperator strategy can be applied to internal sentences only and thusfails as a general solution to the problem of fictional discourse.^[12]

The claim that there are nonexistent objects provides a solution thatcan be applied uniformly both to internal and external sentences offictional discourse. It allows us to admit that fictitious objects donotexist but at the same time to acknowledge thatthereare fictitious objects. According to this position, fictitiousobjects are just a species of nonexistent objects.

In order to see how this assumption is supposed to avoid thecontradictions 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 asfalse. The Meinongian grants that flying horses do notexist,but this does not imply thatthere are no flying horses.According to the Meinongian, there are flying horses, and they belongto 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 anonexistent object.

What, then, about the predication principle? Does the Meinongian haveto 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 isidentical with \(b\).
(PPb): If \(b\) is \(F\), then \(b\) exists.

Within the Meinongian framework, these two readings are notequivalent. According to the Meinongian, certainly there is somethingthat 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 thepredication principle, the inference from premise 1 (“Pegasus isa flying horse”) to “Pegasus exists” is blocked. Allthat 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 betweenbeing and existence and hold that fictitious objects are existentabstract objects. According to this position, “Pegasus does notexist” has to be rejected as false, and thus, again, thecontradiction is avoided. This position (it might be called“abstractionism with respect to fictitious objects”) comesin two varieties. The first one might be characterized, in a somewhatsimplified fashion, as follows: To every set of properties, thereis/exists a corresponding abstract object. These abstract objectsexist necessarily. Some of them occur in fictional stories, and theseare what we call “fictitious objects”. Thus, fictitiousobjects are necessarily existent objects that have been somehow“discovered” or “selected” by the authors offictional stories. (For this position, see, for instance, Parsons1975, Zalta 1983 and 1988, Jacquette 1996, Berto 2008 and Priest 2011.Actually, this is one of the applications of contemporary versions ofMeinongianism. See Sections 5.4 and 5.5 below.) According to the othervariety of abstractionism, fictitious objects are abstract artefacts,i.e., they are not discovered or selected butcreated by theauthors of fictional stories.^[16]

The latter view (today often referred to as “creationism”)fits well into a general ontology of abstract artefacts (like, forinstance, literary and other works of fiction as well as non-fictionalcultural entities) and does justice to the intuition that fictitiousobjects as well as the works in which they occur are literally broughtinto being through human acts of creation. However, it is objectedagainst creationism that the creation of an abstract object issomething 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 thefuture is very similar to the structure of the problem of fictionaldiscourse. 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 ofpredications, i.e., the structure “\(Fb\)”, and giventhat (PP) is valid, (1) implies that Socrates exists and (2) impliesthat 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 apredicate term (“was a philosopher”, “will beblack”.) But while it is certainly truenow (in thethird millennium C.E.) that Socrates was a philosopher, it is alsocertainly true now that Socrates does not exist anymore.

Second, let’s assume, for the sake of argument, that indeedthere will be a female pope (and exactly one first female pope) atsome time in the far future and that she will be black and that shehas not even been fathered yet. Given these assumptions, it iscertainly true now that the first female pope does not yet exist.

Again, there are several attempts to resolve this problem. Onepossible strategy is to deny that sentences like (1) and (2) reallyhave the logical structure of predications. One might suggest thefollowing 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 storyoperator from above. Just as the story operator blocks the inferenceto existence claims about fictitious objects, the tense operatorsblock the inference from (1′) to

(3): Socrates exists.

and from (2′) to

(4): The first female pope exists. (For a tense operator strategy seePrior 1968.)

There is a lot to be said in favor of this logical interpretation oftenses. Yet, it leaves some problems unresolved. One of them is theproblem oftensed plural quantifiers. Consider, forinstance:

(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 inthe past there have been two kings named Charlessimultaneously. (See Lewis 2004.) Thus, the standard tenseoperator strategy seems to fail in cases like this one.

Another problem that the tense operator strategy leaves unresolved isthe problem ofrelations between present and non-presentobjects. Given the principle that a real (two-place) relation canobtain only if both terms of the relation exist, and given that pastand future objects do not (now) exist, relations between present andpast or future objects are impossible. Yet it seems that there areplenty of relations between present and past (or future) objects. Forinstance, I stand in the relation ofbeing one of sixgranddaughters of to my grandmother. Likewise, perhaps I stand inthe relation ofbeing the grandmother of to a futurechild.

Here is a Meinongian solution: Suppose objects pop in and out ofexistence but thereby do not gain or lose theirbeing. (For a Meinongian, all existent objects have being butnot all being objects exist.) According to this picture,“Socrates” now denotes the nonexistent Socrates and“the first female pope” now denotes the nonexistent firstfemale pope. Accordingly, although we cannot allow for the inferencefrom

(1): Socrates was a philosopher.

and

(2): The first female pope will be black.

(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 femalepope exist right now, and (ii) the intuition that it is neverthelesspossible to refer to Socrates and to the first female pope (or, to putit another way: the intuition that the name “Socrates” andthe description “the first female pope” are notempty).

Tensed plural quantifiers do not pose a problem for a Meinongian.Tensed quantifiers in general may be interpreted asrestricted quantifiers that range over a particular subdomainof nonexistent objects: “there was” may be interpreted asa 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 thatranges over the subdomain of future objects (i.e., objects that willexist but do not exist yet).^[18]

Furthermore, from a Meinongian point of view, relations betweenexistent and nonexistent objects are ubiquitous. Remember theMeinongian 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 aparticular 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 ofsome logicians—see Lambert 1983). Furthermore, they seem to havethe 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”, theseare, of course, unacceptable consequences.

There are two obvious ways out: (i) One could simply reject (1) asfalse (or truth-valueless). (ii) One could try to find an adequateparaphrase 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 beround and a square.

But according to the Meinongian picture, (2) and (3) are acceptableconsequences, since they do not entail theexistence ofsomething that is both round and square. Something that is both roundand square is animpossible object, according to Meinong,which means that it cannotexist, but this does not entailthatthere is no such thing. Therefore, the Meinongian canaccept (1) as true, without resorting to any kind of paraphrase.

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

3.5 Nonexistent Objects in Practical Philosophy

There is a debate in practical philosophy as to whether nonexistentpersons are morally relevant. The basic question is this: dononexistent people have interests that we ought to take into accountin our decisions? Obviously, some of our decisions affect not onlyexistent but also future (i.e., not yet existent) persons; matters ofclimate change or the disposal of radioactive waste are relevant casesin point. Intuitively, we ought to act in such a way as to preventdisasters 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 futurepersons are morally relevant but even persons who will never exist(and never existed). In particular, this debate concerns questions ofprocreative ethics and population policies.^[19]

4. Problems with Belief in Nonexistent Objects

The foregoing considerations suggested that the claim that there arenonexistent objects has considerable explanatory force. Why, then, isthis claim not generally accepted but, rather to the contrary, socontroversial? Is the reason just, as Meinong has put it, “aprejudice in favor of the actual”? — Although ontologicalprejudices may play a role, there are also some good reasons forreservations (to put it very carefully).

Even in Meinong’s own writings, there are (roughly) two versionsof the theory, the original one and a later, revised one. In whatfollows, we will refer to theoriginal Meinongian objecttheory 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 Meinong1959). Ignoring, for the sake of simplicity, Meinong’sparticular use of the term “being”, we can paraphrase thisprinciple as:So-being is independent from existence.

The “so-being” of an object is the totality of theobject’s properties apart from the object’s existence ornon-existence. The principle of independence says, thus, that anobject may have any properties whatsoever, independently of whetherthe object exists or not. For instance, the (nonexistent) goldenmountain literallyis golden and a mountain; the round squareliterallyis round and a square.

To every single property and to every set of properties, there is acorresponding object, either an existent or a nonexistent one. Thus,there is, for instance, an object that has the property of being roundas its sole property; one might call it “the objectround”, or simply “round”. Thereis also an object that has the property of being blue as its soleproperty (the objectblue, orblue, for short).Furthermore, there is an object that has the property of being roundand the property of being blue, and no other properties (the objectround and blue); and so forth.

In the notation of classical logic extended with definite descriptionsof the form \(\iota x\phi(x)\), the object that has theproperty 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 ofbeing round as its sole properties by“\(\iota x\forall F(Fx \equiv F = B \vee F = R)\)” (where“\(R\)” stands for “is round”), and soforth.

The objectblue isnot identical with theproperty of being blue; neither is it identical with theset that contains the property of being blue as its solemember. Neither is the objectround and blue identical withthe 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 beinground is not itself round. Analogous considerations hold for sets ofproperties: sets have neither colors nor shapes. But the objectblue is blue, and the objectround is round, and soforth.

One might wish to ask: Isn’t it impossible that there exists anobject that has the property of being blue as itssoleproperty? Isn’t it necessarily the case that every coloredobject also has some particular shape, some particular size, is madeof some particular material, and so forth?

The Meinongian answer to this question is as follows: It is indeedimpossible that such an objectexists! Therefore, the objectblue is not only nonexistent but evennecessarilynonexistent. Of course, the same holds for the objectround,the objectred and round, and infinitely many other objectsas well. Every existing object hasinfinitely manyproperties. Every existing object is acompletely determined(or, in short: acomplete) object. Objects likeblueandround and blue areincompletely determined (or,in short:incomplete) objects.^[21]

Incomplete objects are necessarily nonexistent. They are, in thissense,impossible objects (even though their properties maynot be contradictory). It should be noted, however, that not everycomplete object exists. Consider, for instance, the object that looksexactly like me except that it has green eyes instead of blue ones.Let’s assume that this object (my nonexistent green-eyedcounterpart) has all the properties that I have except for those thatare entailed by the difference in eye color, given the actual laws ofnature. My nonexistent green-eyed counterpart is completely determinedand nevertheless does not exist. But, in contrast toblue,this counterpartcould exist, i.e., it is apossiblenonexistent object.^[22]

Unfortunately, however, MOT\(^o\) has a number of paradoxicalconsequences. 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 objectis “apt to infringe the law of contradiction”, since itwould be both round and not round (Russell 1973c, 107).

Meinong perhaps could have replied to this objection that the objectcalled “the round square” has the properties of beinground and being square, but not the property of being not round, andthus the round square does not infringe the law of contradiction (butonly the geometrical law that everything that is square is not round).Such a reply, however, would have been a bit beside the point, sinceit is clear that, according to the principles of MOT\(^o\),there is an object that is both round and not round (and evidently theobject that Russell had in mind was of this sort). Indeed, Meinong didnot deny that the round square infringes the law of contradiction.Instead, he replied to Russell’s first objection that the law ofcontradiction holds for existent objects only. Objects that are bothround and not round, however, are necessarily nonexistent.

Russell accepted this reply but forged a second objection that couldnot be dismissed in the same vein. Russell argues that since it is aprinciple of MOT\(^o\) that toevery set of propertiesthere is a corresponding object and since existence is treated as aproperty within MOT\(^o\), there must be an object that hasexactly the following three properties: being golden, being amountain, and being existent. If “\(G\)” stands for“is golden”, “\(M\)” stands for “isa mountain” and “\(\rE!\)” stands for “isexistent”, 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 ofMOT\(^o\) that there is anexistent object that isgolden and a mountain. But it is an empirical fact that no goldenmountain 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 manyMeinongian objects:

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

Furthermore, it seems that many Meinongian objects do not onlyinfringe laws of logic and geometry, but also intuitively plausibleprinciples like “If something is round, it occupies some regionin space” and “If something is a mountain, it isaccessible to the senses”. It seems that having a particularshape entails occupying a region in space and that being a mountainentails accessibility to the senses (in principle). According toMOT\(^o\), the round square is round and the golden mountain isa mountain, but obviously neither the round square nor the goldenmountain occupies any region in space and neither of them isaccessible to the senses.

Another strange consequence of MOT\(^o\) is the following: If anobject comes into existence, all that happens is that the object turnsfrom a nonexistent into an existent one. Analogously, if an objectgoes out of existence, all that happens is that the object turns froman existent again into a nonexistent one. Apart from this, neither theobject in question nor the world as a whole changes in any way. Forinstance, when I cease to exist, all that happens is that I will againbe nonexistent (as it was from the beginning of time to 1966). In allother respects, I will stay just the same. Maybe such a thought ispotentially comforting for those who love me, but it is surely at oddswith our normal understanding of coming into existence and passingaway.

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 includeany theory that attempts to make sense of (alleged) talk aboutnonexistent objects and/or (seeming) intentional directedness tononexistent objects. Some of them, like the de-ontologization strategyand fictionalism, take a reductionist route. The de-ontologizationstrategy claims that there can be true sentences about nonexistentobjects, although there are no nonexistent objects. Fictionalismclaims that talk about nonexistent objects is not to be takenliterally but as a sort of “pretense”. The other worldsstrategy makes use of the assumption of merely possible (and evenimpossible) worlds. Other contemporary theories of nonexistentobjects, however, are closer to Meinong’s original theory buthave amended MOT\(^o\) in such a way as to avoid at least someof the abovementioned paradoxes. Those are often called“neo-Meinongian theories”. Usually, they adopt either thenuclear-extranuclear strategy or the dual copula strategy in order tofree Meinongian object theory from inconsistencies andcounterintuitive consequences.

5.1 The De-ontologization Strategy

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

We can think and talk about nonexistent objects.
Nonexistent objects do not have any kind of being whatsoever.
The sentence “There are nonexistent objects” istrue.
Some predications with non-referring singular terms in subjectpositions are true, e.g.: “Vulcan was a planet postulated by LeVerrier”; “Sherlock Holmes is more famous than any livingdetective”; “Pegasus is a mythical horse”.
Contrary to what Meinongians think, nonexistent objects do nothave all of the properties they are characterized as having. Forinstance, Pegasus is a not a horse; thus, “Pegasus is ahorse” is not true (although “Pegasus is a mythicalhorse” is). Neither is the round square round.

Crane can hold the conjunction of 1 and 2 because he interpretsaboutness in a non-relational way. He can hold theconjunction of 2 and 3 because he denies that “there are”and its cognates (both in natural and formal languages) areontologically committing in any way. (For this reason, I call this thede-ontologization strategy.) He can hold the conjunction of 4 and 5because he endorses a positive free logic, i.e., the view that theremay 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 Cranecircumvents some of the above-mentioned problems of Meinongianism.However, his view raises another problem: Why is “Pegasus is amythical horse” true, while “Pegasus is a horse” isnot? In general, why is it that certain predications withnon-referring singular terms are true and others are not? For,according to the de-ontologization strategy, neither “Pegasus isa mythical horse” nor “Pegasus is a horse” can bemade true by the referent of “Pegasus”, because there isno such thing.

Crane (2013) offers what he calls a“reductionist” solution to this problem. That is,according to Crane, sentences “about” nonexistent objectsare made true by something else, i.e., by something existent. Forinstance, the sentence “Vulcan was a planet postulated by LeVerrier in 1859 to explain the perturbations in the orbit ofMercury” is made true by certain events in 1859, namely bypostulation events; the sentence “Sherlock Holmes is more famousthan Sir Ian Blair” is made true by the fact that more peoplehave heard about Sherlock Holmes than about Sir Ian Blair (where tohave heard about Holmes is to have heard about the respectivestories); the sentence “Pegasus is a mythical winged horse thatsprung into being from the blood of Medusa” is made true by amyth which represents Pegasus as being such-and-such; the sentence“Siegfried is one of the most unappealing heroes in all dramaticworks” is made true by certain facts about the last two parts ofWagner’sRing. As these examples already show, Cranedoes not give a uniform, systematic account of the truth of sentencesabout fictitious objects, as he himself concedes. (See Crane 2013,Section 5.5.)

For another example of a reductionist solution, Frank Jackson holdsthat one can assent to “Mr. Pickwick is Dickens’ mostfamous character” without an ontological commitment tofictitious characters in general and Mr. Pickwick in particular. For,according to Jackson’s de-ontologization strategy, objectlanguage sentences are ontologically neutral. Ontological commitmentcomes in only at the meta-language level, for instance, if we wouldclaim that the name “Mr. Pickwick” denotes Dickens’smost famous character or that the predicate “a character inDickens” applies to something. (See Jackson 1980.)

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

5.2 Fictionalism and Indifferentism

In recent years, something close to the de-ontologizationstrategy—or rather a bundle of more or less similarstrategies—became prominent, known under the heading“fictionalism”. The basic idea of fictionalism is, roughlyput, that utterances belonging to a certain region of discourse arenot to be taken literally, that speakers producing such utteranceshave a fictional attitude towards them and are engaged in a sort ofpretense or make-believe. (For an overview of the diverse versions offictionalism as well as a succinct presentation of its most importantpros and cons see the entry onfictionalism.)

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

A general assessment of fictionalism is difficult since the positionsincluded under this heading differ considerably from each other. Muchdepends on how exactly the “fictional attitude” is spelledout. Many versions of fictionalism are prone to the“phenomenological objection”: external talk aboutfictitious objects—to mention one of the applications of thefictionalist strategy that is particularly relevant in the context ofthe present entry—does not feel like “make-believe”;introspection does not reveal that we are engaged in any kind ofpretense when we say things like “Sherlock Holmes is one of themost famous characters of popular literature” and the like.

A position inspired by and in important respects similar tofictionalism that, however, avoids the phenomenological objection isEklund’s “indifferentism”. Indifferentism is theview that speakers outside the “philosophy room” are oftensimply indifferent with regards of the ontological implications oftheir utterances and thus are not committed to the existence of thoseentities whose existence is implied by their utterances. As Eklundemphasizes, however, indifferentism does not say anything about whichentities oneshould accept in one’s ontology; it is, inthis 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 theorynoneism;Berto names itmodal Meinongianism. The term“noneism” has been coined by Richard Routley, and Priestnot only takes over the name but also essential features ofRoutley’s theory (among other things the assumption that basicprinciples of standard logics, like the principle of contradiction, donot hold without restriction—without, of course, accepting thateverything is true).

Proponents of the other worlds strategy reject both thenuclear-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 ofdiscourse. But not all objects of the domain exist in all worlds.Thus, Pegasus does not exist in the actual world, but it exists in avariety of merely possible worlds (namely in those which are such asrepresented by the Greek mythology).

According to the other worlds strategy, nonexistent objects literallyhave the properties through which they are“characterized”—but they have these properties notin the actual world but only in those worlds “which realize theway the objects are represented as being in the appropriate cognitivestate […].” (Priest 2011b, 249, footnote 35) Suppose youimagine a winged horse. In this case, in your imagination, you have anintentional object that is represented as being winged and a horse.Thus, the intentional object of your present intentional state is anonexistent winged horse, which is, however, in the actual worldneither winged nor a horse. In some worlds, however, this object\(is\) winged and a horse – namely in those worlds whichrealize the way the object is represented in your imagination.^[24]

The other worlds strategy provides the following solution to theparadox of contradiction: The round square exists only in impossibleworlds. In impossible worlds, however, the principle of contradictiondoes not hold. Therefore, the round square’s being both roundand not round does not infringe the laws of logic which hold in thoseworlds in which the round square exists.

In the actual world, however, the round square is neither round norsquare, since roundness and squareness are “existence-entailingproperties”, i.e., “\(b\) is round/square”entails “\(b\) exists”. Therefore, even if in theactual world (and in all other possible worlds) the law ofcontradiction holds, the round square does not infringe this law,since in these worlds the round square is neither round nor notround.

In the light of this theory, it is easy to explain why nobody has everseen the round square or a golden mountain and why the round square isobviously not located in space: since the round square is neitherround nor square in the actual world, there is no reason to assumethat it occupies space or is accessible to the senses. Similarconsiderations hold for the golden mountain.

It is worth noting that the postulation of existence-entailingproperties is an implicit rejection of Meinong’s principle ofindependence, which is one of the cornerstones of Meinongian objecttheory.

Proponents of the other worlds strategy reject thenuclear-extranuclear distinction because they find it “difficultto avoid the feeling that the class [of nuclear predicates] has beengerrymandered 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 principledcharacterization of which properties are existence-entailing and whichare not (which looks quite similar to the problem with thenuclear-extranuclear distinction which Priest points out in the abovequotation). Second, it remains unclear which properties nonexistentobjects have in the actual world (apart from logical properties likebeing self-identical and intentional properties like being thought ofby Priest).^[26] Furthermore, Priest’s noneism raises difficult questions aboutcross-world identity and the ontological status of non-actual worlds.The ontological status of non-actual worlds is far from obvious: theymay be taken to be concrete objects (structured sets of physicalobjects) or abstract objects (sets of sentences, propositions, orstates of affairs). (For an elaborate survey of various conceptions ofnon-actual worlds see the entry onpossible worlds, i.e., Menzel 2014.)^[27] Apart from this, it is doubtful whether Priest’s theoryprovides an adequate account of fictitious objects. Among otherthings, it does not do justice to the widespread intuition thatfictitious objects arecreated by the authors of the storiesto which they belong.^[28]

5.4 Nuclear and Extranuclear Properties

According to the nuclear-extranuclear strategy, there are two kinds ofproperties: nuclear and extranuclear ones. (Meinong 1972, §25)^[29] An object’s nuclear properties are supposed to constitute theobject’s “nature”, while its extranuclear propertiesare supposed to be external to the object’s nature. Nuclearproperties are, for instance: being blue, being tall, kickingSocrates, having been kicked by Socrates, kicking somebody, beinggolden, being a mountain (Parsons 1980, 23).

Which properties are extranuclear? Terence Parsons distinguishes fourcategories of “extranuclear predicates” (i.e., predicatesthat stand for extranuclear properties): ontological(“exists”, “is mythical”, “isfictional”), modal (“is possible”, “isimpossible”), intentional (“is thought about byMeinong”, “is worshipped by someone”), technical(“is complete”) (Parsons 1980, 23).^[30]

Nuclear properties are eitherconstitutive orconsecutive, in Meinong’s terms (Meinong 1972, 176). Anobject’s constitutive properties are those properties that arementioned explicitly in a description that is used to pick out theobject. Thus, the constitutive properties of the golden mountain arebeing golden and being a mountain. An object’s consecutiveproperties are those properties that are somehow included or impliedby the object’s constitutive properties. Thus, among theconsecutive properties of the golden mountain are probably theproperties of being a material thing and of being extended.

According to MOT\(^o\), the object called “the goldenmountain” 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 ofbeing a mountain (and no other properties). According to the revisedversion of object theory, the object called “the goldenmountain” is the object that has all the nuclear properties thatare implied by the nuclear property of being golden and the nuclearproperty of being a mountain, i.e.,\(\iota x\forall F^n (F^n x \equiv G^n \Rightarrow F^n \veeM^n \Rightarrow F^n)\).^[31]

How does the nuclear-extranuclear distinction help to avoid theparadoxes mentioned in the section above? — Consider again theparadox from incompleteness: According to MOT\(^o\), there is anobject that has the property of being blue as its sole property(we’ve called it “the objectblue”, forshort), in logical notation:\(\iota x\forall F(Fx \equiv F = B)\). It seems to be true of the objectblue,bydefinition, that it has exactly one property. Yet, the propertyof having exactly one property is clearly distinct from the propertyof being blue. Thus, it seems that the objectblue has atleast two properties.

According to the revised version of object theory with thenuclear-extranuclear distinction (MOT\(^{ne}\), for short), thisparadox is avoided in the following way: The property of being blue isa nuclear (constitutive) property, the property of having exactly oneproperty, however, is anextranuclear property. Therearen’t any objects that have exactly one property. There areonly objects that have exactly oneconstitutive (nuclear)property. Objects that have only a limited number of constitutiveproperties may (and necessarily do) have additional extranuclearproperties—like the property of having exactly \(n\)constitutive properties or the property of being incomplete. Theobject 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 soleconstitutive property. This does not rule out that the objectblue may have additionalextranuclear properties.Thus, the paradox from incompleteness does not arise in MOT\(^{ne}\).^[32]

To Russell’s objection that the existent golden mountaininfringes the law of contradiction (since it is both existent andnonexistent), advocates of MOT\(^{ne}\) may reply as follows:Existence is an extranuclear property, but only nuclear properties canbe constitutive properties of an object. Therefore, according toMOT\(^{ne}\), 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 DaleJacquette and Richard Routley. See Jacquette 1996, 81 and Routley1980, 496.)

This solution, however, imposes quite a heavy restriction on thetheory of objects. Probably this was the reason why Meinong himselfdid not even mention it as a possible solution. Instead, he introducedin addition to the nuclear-extranuclear distinction thedoctrineof watered-down extranuclear properties: at least someextranuclear properties (existence, possibility) have nuclearcounterparts, i.e., “watered-down” versions ofextranuclear properties (Meinong 1972, §37).^[33]

If the extranuclear property of existence has a watered-down nuclearcounterpart, the following answer to Russell’s objection isavailable: “The existent golden mountain exists” isambiguous. It may be read as “The existent golden mountainexemplifies extranuclear existence” (which is false), or it maybe read as “The existent golden mountain exemplifies nuclearexistence” (which is true). There is no contradiction between“The existent golden mountain exemplifies nuclearexistence” and “The existent golden mountain does notexist” (in the proper, extranuclear sense).

Do other extranuclear properties (besides existence) also have nuclearcounterparts? Do perhapsall extranuclear properties havenuclear counterparts? Meinong himself is not explicit about thispoint, but it seems very natural to extend the theory in this way.Terence Parsons has adopted this extension (Parsons 1980, 68), whileDale Jacquette rejects the doctrine of watered-down extranuclearproperties altogether, even for existence and possibility (Jacquette1996, 85–87).

There are several paradoxes for which MOT\(^{ne}\) does not supplya solution (even if it is supplemented with the doctrine ofwatered-down extranuclear properties). It still seems that the roundsquare infringes the law of contradiction; one still may wonder why itis impossible to discover round squares and golden mountains; and onestill may be baffled by the doctrine that nonexistent objects differfrom 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 ofrelations between properties and individuals.^[35] Different advocates of this strategy use different terminologies forit. Here are some of them:

The golden mountainis determined by the property ofbeing golden and by the property of being a mountain.
The golden mountainsatisfies the property of beingincompletely determined. (Mally 1912)
The golden mountainhas the property of being golden andthe property of being a mountainassigned to it.
The golden mountainimmanently contains the property ofbeing incompletely determined. (Ingarden 1931 [1973], §20, p.122)
The golden mountainis consociated with the property ofbeing golden and the property of being a mountain.
The golden mountainis consubstantiated with theproperty of being incompletely determined. (Castañeda1972)
The property of being golden and the property of being amountainare ascribed to the golden mountain.
The golden mountainhas the property of beingincompletely determined. (van Inwagen 1977)^[36]
The golden mountainis constituted by the properties ofbeing golden and being a mountain.
The golden mountainexemplifies the property of beingincompletely determined. (Rapaport 1978)
The golden mountainencodes the property of being goldenand the property of being a mountain.
The golden mountainexemplifies the property of beingincompletely determined. (Zalta 1983)

The various versions of the dual copula strategy share the assumptionthat the copula “is” is ambiguous. In what follows, wewill use the exemplification-encoding terminology. In addition, wewill 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 revisedversion of Meinongian object theory which makes use of a dual copuladistinction”.

According to MOT\(^{dc}\), the object called “the roundsquare” is the object that encodes the property of being roundand the property of being square (and all of the properties that areimplied by these properties) and no other properties. Thus, accordingto 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 “theround square” encodes exactly two constitutive properties (beinground and being square). However, over and above this, there are many(indeedinfinitely many) properties that areexemplified by this object, for instance: the property of notbeing red, the property of not encoding the property of being red, theproperty of not being determined with respect to its side length, theproperty of having thought of by Bertrand Russell, the property ofencoding exactly two constitutive properties, the property of beingincompletely determined.

To mention another popular example, consider Pegasus: Among otherthings, Pegasus encodes the properties of being a horse, of havingwings, of having been tamed by Bellerophon. But there are alsoinfinitely many properties that Pegasus exemplifies, for instance, theproperty of not being determined with respect to the number of hairsin its tail, the property of being a character of Greek mythology, theproperty of being a fictitious object.

It must be emphasized that something that encodes the property ofbeing a horseis not a horse (in the usual predicative senseof “is”). Analogously, something that encodes theproperties of being round and square is neither round nor square. Thatis to say, something that encodes the property of being a horse doesnot belong to the class of horses, and something that encodes theproperties of being round and square does neither belong to the classof round things nor to the class of square things. Rather, things thatencode the properties of being a horse or being a square or being aDanish prince areabstract objects—abstract in thesense that they are neither mental nor spatio-temporal things. Ingeneral, everything which encodes at least one property is an abstractobject in this sense.^[37]

Let’s see how MOT\(^{dc}\) avoids the alleged paradoxesmentioned in section 4. The first objection was that objects like theround square infringe the law of contradiction, since such objectswould be both round and not round. According to MOT\(^{dc}\),however, the object called “the roundsquare”—\(\iota x\forall F(xF \equiv R \Rightarrow F \vee S \Rightarrow F)\)—is not round (i.e., does not exemplify the propertyof being round). Thus, no contradiction arises.

The second objection was that the existent golden mountain wouldinfringe the law of contradiction, since, if there were such anobject, it would be both existent and nonexistent. According toMOT\(^{dc}\), one could answer to this objection as follows: Theobject called “the existent golden mountain” is\(\iota x\forall F(xF \equiv G \Rightarrow F \vee M \Rightarrow F \vee \rE! \Rightarrow F)\). This objectencodes the property of beingexistent, but it does notexemplify it. Since“\(b\) encodes \(F\)” does not imply“\(b\) exemplifies \(F\)”, there is nocontradiction involved here.

According to MOT\(^{dc}\), the objectblue is\(\iota x\forall F(xF \equiv B \Rightarrow F)\), i.e., the object that encodes exclusively theproperties that are implied by being blue. Thus, the objectblueexemplifies the property of encoding only theproperties that are implied by being blue. It is not the case that theobjectblue has exactly one property and at the same time hasat least two properties, at least not, if “has” is used inthe same sense in both occurrences. In this way, the apparentcontradiction 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 occupyany region in space. More exactly, it does not exemplify the propertyof occupying some region in space (though, perhaps it encodes thisproperty, 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 notexemplify the property of being accessible to the senses (at best, itencodes this property). Therefore, there is nothing paradoxical in thefact that nobody has ever seen a golden mountain and that it isimpossible to determine the location of the round square.

Finally, MOT\(^{dc}\) does not have the counterintuitiveconsequence that the only difference between existent and nonexistentobjects is that the latter lack the property of being existent, suchthat if an object goes out of existence, the vast majority of itsproperties (like being human, loving pancakes, being violent-tempered,and so forth) stay exactly the same. Consider again my nonexistentgreen-eyed counterpart. According to MOT\(^{dc}\), this objectencodes being human, being female, being a philosopher, andso forth, but does notexemplify these properties; therefore,it does not belong to the class of female philosophers, not even tothe class of humans or to the class of living beings. Thus, it isclear that my green-eyed counterpart’s nonexistence is by farnot the only difference between it and myself. In general, nonexistentobjects are a particular kind of objects, according toMOT\(^{dc}\)—very different from ordinary existent objects.In what follows, we’ll call them “Meinongianobjects”.

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 goldenmountain” is not an abstract object but something as concrete asevery existent mountain in the world. Secondly, and related to this,the idea that some objects do not exist is one of the cornerstones ofMOT\(^o\)—but it is not an essential feature ofMOT\(^{dc}\), i.e., it doesn’t play an essential role withinMOT\(^{dc}\). Within MOT\(^{dc}\), Meinongian objects aredefined as a particular kind of abstract objects (namely abstractobjects to which two kinds of predicates apply). Of course, one candecide to say that these objects are “nonexistent”; butnothing hinges upon this decision. According to MOT\(^o\), theonly difference between Meinongian objects and normal objects consistsin the alleged nonexistence of the former. However, inMOT\(^{dc}\), Meinongian objects are distinct from normal objectsbecause 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 ofindividuals and that there is a difference between “There areobjects that are such-and-such” and “Objects that aresuch-and-such exist”.

If MOT\(^{dc}\) is essentially different from MOT\(^o\), thequestion arises to what extent MOT\(^{dc}\) can fulfill the tasksMOT\(^o\) was supposed to fulfill. It seems thatMOT\(^{dc}\) cannot doeverything MOT\(^o\) wassupposed to do. First, consider the problem of intentionality: ifsomebody fears the devil, does he fear an abstract object? —This seems to be psychologically impossible, for an abstract objectcannot 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 intendto deny the existence of an abstract object that only encodes beingsuch-and-such a planet? — Probably not. They rather deny theexistence of something thatis a planet, i.e., a concretematerial thing. Finally, consider the problem of discourse about thepast and the future: when a teacher in a history of philosophy classtalks about Socrates, does she then intend to talk about an abstractobject that only encodes all of the properties that Socrates (the“real” one) once exemplified? — Presumably not. Ifthere is an object which she is intentionally directed at, then it isprobably the “real” Socrates, not its abstractcounterpart.

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

6. Themes for Further Investigation

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

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

2. One feature of Meinong’s mature object theory not mentionedso far is the “doctrine of implexion”. Implexion is arelation between incomplete and complete objects which seems to bevery 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,§29.) Meinong himself eventually came to interpret incompleteobjects as universals (see Meinong 1972, 739f). Meinongian objecttheory may thus be interpreted as a sophisticated theory ofuniversals, in particular as a theory oftypes (as opposed toproperties), which might open further fields of application.

3. Throughout this entry, we have presupposed realism with respect toproperties. However, it is doubtful whether a theory of Meinongianobjects isnecessarily ontologically committed to properties.An ontologically neutral quantifier and the use of non-objectualvariables for predicates (not fornames of predicates orproperties) may help to avoid this commitment and thus could makeMeinongian object theory much more parsimonious.

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Acknowledgments

This article is an outcome of the project “Philosophie ethistoire de la logique. Les concepts formels” at the Universityof Geneva, in which I was involved from January to September 2004. Iam indebted to the University of Geneva for financial support. I alsowish to thank Gideon Rosen and Edward N. Zalta for constructivecriticism and helpful advice.

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