## 1. Frege and Russell: Existence is not a Property of Individuals



There are two sets of reasons for denying that existence is a property
of individuals. The first is Hume and Kant's puzzlement over
what existence would add to an object. What is the difference between
a red apple and a red existing apple? To be red (or even to be an
apple) it must already exist, as only existing things instantiate
properties. (This principle--that existence is conceptually prior
to predication--is rejected by Meinongians.) Saying it is red and
an apple and furthermore exists is to say one thing too many. The
thought seems to be that instantiating any property whatsoever
presupposes existence and so existence is not a further property over
and above a thing's genuine properties. The thought is not
merely that everything that instantiates any property exists, as the
same is true of being self-identical, being either human or not
human--assuming the law of excluded middle--and being such
that 2+2=4, all of which seem to be unproblematic properties of
individuals even if that status is denied of existence. Instead the
thought is that instantiating any property whatsoever *conceptually
presupposes* the existence of a subject in a way that makes it
incoherent to then think of existence as a further property of that
thing. The thing's existence is prior to any predication to it
and so it is incoherent to think of existence as a property had by the
thing. This thought is behind Aristotle's thesis that existence
is not a further feature of a thing beyond its essence.



The second consideration favoring the thesis that existence is not a
property of individuals concerns the puzzle of negative singular
existentials. Suppose that existence is a property of the designation
of the subject term in a singular existential sentence. Then
'Ronald McDonald does not exist' predicates nonexistence
of the designation of the subject term, in which case reality includes
an entity--the designation of the singular term and subject of
predication--that has the property of not existing. That, Russell
complained, runs contrary to a robust sense of reality, according to
which everything exists. (See [Russell 1905a].) So, we should reject the claim that existence
is a property of the designation of subject terms in existential
sentences.



To appreciate Russell's alternative account, consider first
general nonexistence claims. To say that foxes exist is to say that
there are some things that are foxes; that is, the property of being a
fox is instantiated. This is reflected in the standard regimentation
of the sentences 'Foxes exist' and 'There are
foxes' in first-order quantificational logic as
[?]*xFx*, where *Fx* is the translation for the
predicate '*x* is a fox'. General kind terms do
not, then, designate individuals, which we then (redundantly) say
exist when using the predicate 'exists' or (paradoxically)
say are not when using the predicate 'does not
exist'. Instead, kind terms designate properties and simple
seeming subject-predicate sentences like 'Foxes are
carnivores' are claimed to possess a more complicated logical
form, [?]*x*(*Fx*- *Cx*),
where *Cx* translates the predicate '*x* is a
carnivore'. (This ignores the difficult question whether
generics are really quantifiers at all, made more troubling by the
fact that some generics seem to admit of exceptions--'Birds
fly' is true, even though penguins are birds and don't
fly; 'Cats have four legs' is true, even though there is a
three-legged cat wandering the planet. See the
entry generics.) Given this analysis,
general nonexistence claims are unproblematic. The sentence
'Dragons do not exist' says, on this analysis, that the
property of being a dragon is not instantiated. Take the most
inclusive class of what there is; nothing in that class has the
property of being a dragon. That is what ![?]*xDx*
says, letting *Dx* translate the predicate '*x* is
a dragon'. This is significant because it does not require
identifying some entity to then predicate of that thing the property
of nonexistence.



The Frege-Russell view that existence is a second-order property is
based on the idea that seemingly singular existential and negative
existential sentence like 'Bill Gates exists' and
'Ronald McDonald does not exist' are, in their deeper
logical form, general existential and negative existential claims. Let
us focus on Russell's version of the view.



Russell claimed that ordinary proper names like 'Bill
Gates' are disguised definite descriptions, something like
'the richest man in the world'. And definite descriptions,
given Russell's view of definite descriptions, are not genuine
referring terms but are instead quantificational expressions. The
sentence 'The richest man in the world lives in
Washington' has, as its logical form, a quantificational
structure and not a subject-predicate structure, equivalent to
something like the following: There is a unique richest person who
lives in Washington. Individuals do not enter directly into the
proposition expressed by the sentence and are not part of the
sentence's truth conditions.



These features of Russell's account of definite descriptions are
significant for the treatment of seemingly singular existential and
negative existentials as they remove the need for entities to serve as
the designation of the singular terms for the meaningfulness and truth
of negative existentials. Seemingly singular existentials like
'Bill Gates exists' are assimilated to general
existentials like 'Foxes exist'. Assuming the proper name
'Bill Gates' is analyzed as the definite description
'the richest person alive', the sentence 'Bill Gates
exists' has a logical form that can be more accurately expressed
as *There is someone that is uniquely richer than anyone else
alive*. This is neither redundant nor uninformative, as we can
grasp in thought properties while coherently and rationally wondering
whether or not they are instantiated. Russell's account
similarly dissolves the problems generated by seemingly singular
negative existentials like 'Ronald McDonald does not
exist'. The truth of this sentence does not require a
designation for the term of which nonexistence is then predicated.
'Ronald McDonald' is short for a definite description,
say, 'the happy hamburger clown'. The sentence
'Ronald McDonald does not exist' expresses a proposition
of the form *It is not the case that there is a unique happy
hamburger clown*. This proposition is true even if absolutely
everything there is exists. The proposition concerns the property of
being a happy hamburger clown and says of that property that it is not
uniquely instantiated. As the property--the true subject of
predication--exists, however, we are not forced to countenance
the reality of entities that do not exist in order to recognize this
sentence as saying something true.



Russell's strategy depends on two claims. The first is that the
negation in a negative existential takes wide scope, applying to the
whole sub-sentence and not just the predicate. So, 'Ronald
McDonald does not exist' does not involve ascribing the
predicate 'is nonexistent' to the subject 'Ronald
McDonald'. Instead, it is more faithfully represented as
'It is not the case that [Ronald McDonald exists]'. The
second is that 'Ronald McDonald' is not a genuine
referring expression and the predicate 'exists' really
means something like *is instantiated*. Notice that the first
in solitude is not sufficient to overcome the problems generated by
seemingly true singular negative existentials. Even if the deep form of
'Ronald McDonald does not exist' is  'It is not
the case that [Ronald McDonald exists]', assuming that
'Ronald McDonald' is a genuine singular term, the problem
remains of finding in reality some entity to serve as the designation
of 'Ronald McDonald'. That entity is then part of reality
and so, assuming that Meinongianism is false, is existent. In that
case, the sub-proposition *Ronald McDonald exists* is true and
so its negation false. The problem of true singular negative
existentials does not rest on the supposition that they involve
ascribing the property of nonexistence. So, it is the second of the
above claims that carries the weight of Russell's solution to
the problem of singular negative existentials.



The second component of the Russellian solution--the claim that
ordinary proper names like 'Bill Gates' are disguised
definite descriptions--faces a number of objections. One is the
semantic argument. (See [Kripke 1972].) Suppose that the descriptive
equivalent of the name 'Bill Gates' is 'the richest
living person in the world'. An adequate semantic understanding
of the sentence 'Bill Gates is richer than everyone else
alive' would then be sufficient for recognition of its truth.
(More precisely, the sentence, 'If anyone is richer than
everyone else alive, then Bill Gates is richer than everyone else
alive' has this feature.) But that seems implausible. Surely we
must collect empirical data to determine its truth. One who wonders
whether someone, say, Warren Buffett, is wealthier than Bill Gates
does not display irrationality or semantic ignorance, comparable to
one who wonders whether a fortnight is longer than 14 nights.



Perhaps these considerations should motivate the descriptivist to
abandon "great deeds" descriptions in favor of
metalinguistic descriptions like 'the person named 'Bill
Gates'' or causal descriptions like 'the person that
stands at the origin of this chain of uses of the name 'Bill
Gates''. (For discussion, see [Bach 1981, 2002], [Kroon
1987], and [Lewis 1984].) It is plausible that semantic competence
suffices to know that the sentence 'Bill Gates is named
'Bill Gates'' is true and, while perhaps importing
extra-semantic facts about language use, it is plausible that any
reflective speaker of English knows that any token of 'Bill
Gates is the person that stands at the origin of this chain of uses of
the name 'Bill Gates'' is true. So these
descriptions seem to survive the semantic argument presented in the
previous paragraph. But they face another objection, also facing
simpler versions of descriptivism: Namely, the modal objection
([Kripke 1972]). While it is absolutely impossible that Bill Gates is
not Bill Gates, it is, it seems, metaphysically possible that Bill
Gates is not the richest person alive, instead being a middle
American, and it seems metaphysically possible that he is not named
'Bill Gates' and does not stand at the causal origin of
any particular chain of uses of the name 'Bill Gates',
unless the chain is individuated in part in terms of the actual
individual that grounds it. This suggests that ordinary proper names
and their alleged descriptive equivalents considered above are not, in
fact, semantically equivalent, as they embed differently under modals
like 'it is necessary that'. [See the entry on
 names
 for further discussion of these problems.]



In response to the modal argument, the descriptivist might avail
herself of individual essence descriptions like 'the person
identical to Bill Gates', 'the person that
Bill-Gatizes', or rigidifications of the above descriptions,
'the person actually named 'Bill Gates'' and
'the person that actually stands at the origin of this chain of
uses of the name 'Bill Gates'', all of which
designate the same person in every possible world in which they
designate anything. It is plausible that semantic competence suffices
for recognition of the truth of the sentence 'Bill Gates is the
person identical to Bill Gates' and that that sentence expresses
a necessary truth. So these versions of descriptivism seem to escape
the problems discussed in the previous paragraphs. The first two
candidates, however, do not hold much promise for solving the problem
of apparently true singular negative existentials. We know what the
property of being identical to Bill Gates is, but only because we know
the result of plugging up one of the relata in the two-place relation
*is identical to* with the individual Bill Gates.
Insofar as we think that reality does not include any entity identical
to Ronald McDonald, however, we are then left to wonder what the
property of being identical to Ronald McDonald is. Because the
contents of these properties are derivative from the individuals that
serve as the referents of their names, they are poor candidate
descriptive equivalences for a robust version of descriptivism and
unlikely to shed light on the truth of seemingly singular negative
existentials like 'Ronald McDonald does not exist'.
Similar considerations apply to the predicating view. 



The last candidates, rigidified metalinguistic and causal
descriptions, are the most promising for a robust form of descriptivism. But some have claimed to discern
important differences in the functioning of a name and its alleged
semantically equivalent rigidified description, of any flavor. First,
some have claimed that the name 'Bill Gates' designates
Bill Gates with respect to every possible world, including worlds at
which Bill Gates does not exist; otherwise the sentence 'Bill
Gates does not exist' would not be true with respect to those
worlds. But the rigidified description 'the person actually
named 'Bill Gates'', for example, does not designate
anything with respect to such a world, as nothing in the domain of
that world satisfies the condition being named 'Bill
Gates' at the actual world. That is because it is only Bill
Gates that satisfies that condition and he is not a member of the
domain of the possible world in question. So, differences in how a
name and a rigidified description embed under modal operators can
still be discerned. (See [Salmon 1981] for further discussion.) This
objection assumes that the domain of quantification varies from world
to world and that individuals that serve as the designation of
ordinary names are genuine contingent existents, theses that can be denied.
The objection also assumes that the range of the description is the
domain of the world with respect to which the description is being
evaluated, the actuality operator rigidifying only the condition of
the description, which may also be denied. The second objection to
rigidified descriptivism concerns the differences some have claimed
between how names and rigidified descriptions embed under
propositional attitude verbs. Intuitively, Jones would have still
believed that Bill Gates is wealthy even if things had been ever so
slightly different than they actually are--say, I bought a poppy
bagel instead of a sesame bagel this morning. But if the content of
Jones's belief concerns the actual world, as rigidified
descriptivism dictates, then, to retain his actual belief in that
counterfactual situation, he would have to believe something about
another possible world--the actual world. But it is implausible
that Jones would have a belief about another possible world. So, the
content of Jones's belief does not concern the actual world and
so one can believe what is expressed by 'Bill Gates is
wealthy' without believing what is expressed by 'The
person that actually stands at the origin of this chain of uses of the
name 'Bill Gates' is wealthy'. (See [Soames
1998].) 



This section examined the thesis that seemingly singular
existential and negative existential sentences are really general
existentials, which are then treated as ascribing the property of
being instantiated or not instantiated to some property. The need to
grant being to entities that do not exist in order to account for the
truth of sentences like 'Ronald McDonald does not exist'
is then avoided, which is no small victory. The success of that
proposal, however, was seen to rest on the claim that ordinary proper
names have descriptive equivalences, which many philosophers of
language reject. (For more on the question of whether or not
'exists' is a genuine first-order predicate in deep
logical form, see, in addition to the earlier references in this
section: [Crane 2012], [Dancy 1986], [Geach 1954.1986], [Haaparanta
1986], [Hintikka 1984,1986], [Kneale 1936], [Mackie 1976], [McGinn
2000], [Miller 1975,1986] [Moltmamnn 2013], [Moore 1936], [Owen 1965],
[Pears 1967], [Quine 1948], [van Inwagen 2008], [Vilkko and Hintikka
2006], [Wiggins 1995], [Williams 1981], and [Williams 1995].


## 2. Meinongianism



In part on the basis of the above discussed problems, many
philosophers reject descriptivism and accept that ordinary proper
names are devices of direct reference, that there are true genuinely
singular negative existentials, and so that there are nonexistent
objects. 'Ronald McDonald' seems like a referring term,
open to existential generalization, in the sense that a sentence like
'Ronald McDonald does not exist' entails 'There is
something that does not exist', and 'exists' seems
like a predicate that applies or fails to apply to the designation of
subject-place terms, on a par with a predicate like
'sits'. The Meinongian embraces these appearances and
concludes that reality includes referents for empty names and those
referents do not exist. The Meinongian trades logical and semantic
simplicity for metaphysical abundance.



Meinongianism is the thesis that there are objects that do not exist
and so included in the most unrestricted domain of quantification and
discourse are nonexistent entities. One immediate challenge for the
Meinongian is to offer individuating conditions for nonexistents. The
most straightforward comprehension principle is the naive principle
that, for any condition on objects, there is a unique object
satisfying exactly that condition. For our purposes, we can conceive
of a condition as determining a set of properties; crudely, the
properties expressed by the predicates composing the condition. In
that case, condition *C* is the same condition as
*C*' when they determine the same set of properties. It
follows that corresponding to any set of properties, there is exactly
one object with exactly those properties. The naive comprehension
principle faces several problems. In what remains of this section, we
shall present these problems and distinguish different versions of
Meinongianism in terms of the devices employed to develop a restricted
comprehension principle for objects that avoids those problems. (All
of these problems are developed in Russell's discussion of Meinong,
see [Russell 1905a, 1907]. For a discussion of the debate between
Russell and Meinong, see [Smith 1985].)



The first is the problem of incomplete objects. Conditions need not be
total; that is, we do not require that the set of properties a
condition determines is such that, for every property, either it or
its complement is a member of that set. So, by the naive comprehension
principle, the condition of being a singer defines an object with
exactly that property--being a singer--and no other
properties. A set with other properties as well is a distinct set of
properties and so corresponds to a different condition and hence a
different object. Some find incomplete objects problematic in
themselves, as they are counterexamples to bivalence: Our singer, for
example, has neither the property of wearing a dress nor the property
of not wearing a dress. But they also lead to more general threats of
paradox. Our singer is an object with exactly one property: That of
being a singer. This is its sole defining characteristic. So having a
exactly one property is also a property of our singer and that
property is distinct from the property of being a singer, which our
singer also has. So, the singer has two properties. Contradiction. One
simple solution is to restrict the comprehension principle to total
conditions. The resulting proposal, however, leads to a questionable
application of Meinongian metaphysics to problems of fictional truth,
as many want to claim that there is simply no fact of the matter as to
whether or not Sherlock Holmes has a mole on his left shoulder, as
that is left underdetermined by the Holmes stories and there are no
deeper grounds for either predication. The promise of employing
nonexistent objects in explaining apparent truths about fiction is one
of the theory's main virtues. Relatedly, this solution
undermines a primary motivation for Meinongianism--namely, the
idea that there is a subject of predication corresponding to any
object of thought, as we certainly do not think only of complete
objects. So, the simple solution is too simple and the Meinongian is
better to find another, more complex solution to the problems of
incompleteness.



The second is the problem of contradiction. A naive comprehension
principle generates objects that violate the principle of
noncontradiction. Consider the condition of being taller than
everything. By the naive comprehension principle, this condition
determines an object and so there is an object that has exactly the
property of being taller than everything. But then it is taller than
itself, which is a contradiction given the irreflexivity of the taller
than relation. The irreflexivity of the taller than relation is
nonlogical. But not so with the identity relation, as = is typically
taken to be a logical predicate. It is a logical truth that everything
is self-identical; i.e., the sentence [?]*x x=x* is true
under every interpretation. But consider the property of being
self-distinct. By the naive comprehension principle this condition
determines an object and that object is self-distinct. But then that
object does not satisfy the condition *x=x*. So our logically
true sentence has a counterinstance. Contradiction.



A third problem, one of Russell's objections to Meinongianism
(see [Russell 1905a, 1907]), turns on the fact that existence is, on
Meinongianism, a property and hence figures into the base of the naive
comprehension principle. So, consider the condition of being winged,
being a horse, and existing. By the naive comprehension principle,
there is an object with exactly these features. But then this object
exists, as existing is one of its characterizing features.
Intuitively, however, there is no existent winged horse. An existent
object cannot so easily be thought into being. Indeed, for every
intuitively nonexistent object that motivates
Meinongianism--Zeus, Pegasus, Santa Clause, and Ronald
McDonald--there is, by the naive abstraction principle, an object
just like it but with the additional property of existing. But then
there is an existing Zeus, an existing Pegasus, etc.. This is
overpopulation not of being but of existence as well.



The naive comprehension principle, then, must be rejected and a
restricted principle connecting sets of properties with objects be put
in its place. The principle should generate enough objects to serve
the Meinongian purpose of ensuring a corresponding object for every
thought while avoiding the problems discussed above. We can
distinguish two strategies, both suggested by Meinong's student
Ernst Mally [Mally 1912]. The first distinguishes two kinds of
properties, what, following Terence Parsons [Parsons 1978, 1980], we
shall call nuclear and extra-nuclear properties. While the distinction
remains ultimately unclear, the key idea is that nuclear properties
are part of a thing's nature, broadly construed, and
extra-nuclear properties are external to a thing's nature; more
precisely, nuclear properties, but not extra-nuclear properties, are
part of the characterization of what the object is. The comprehension
principle is then restricted to conditions involving only nuclear
predicates. Problematic properties, like existing, etc., are deemed
extra-nuclear and beyond the scope of the comprehension principle, not
determining the objects that there are. Nuclear, not extra-nuclear,
properties individuate objects. The second Meinongian camp
distinguishes two modes of predication: What Mally called determining
and satisfying, Hector-Neri Castaneda [Castaneda 1974,
1975,1978, 1980, 1986, 1989, 1990] called internal and external
predication, William Rapaport [Rapaport 1978] called constituency and
exemplification, Kit Fine [Fine 1982] called implicit and explicit,
and Edward Zalta [Zalta 1983, 1988] called encoding and
exemplifying. There is, on this view, a single class of properties
that the comprehension principle ranges over, but the principle
determines the properties encoded not exemplified (to follow
Zalta's terminology) by the object characterized. For every
condition, there is a unique object that encodes just those
properties. An object may or may not exemplify the properties it
encodes. Sherlock Holmes encodes the properties of being a detective
and living at 221B Baker Street, etc., but he does not exemplify those
properties. He exemplifies (but does not encode) the properties of
being a fictional character and being the hero of Arthur Conan
Doyle's Holmes stories. The properties an object exemplify are
not, on this view, a matter of mere stipulation.



How do these distinctions solve the problems raised above for the
naive comprehension principle? Let us begin with Parsons's view.
Parsons focuses on the problems of contradiction and of the existent
winged horse. Following Russell's discussion of Meinong, in
[Russell 1905a, 1907], Parsons considers the threat of contradiction
generated by impossible objects like the round square. Meinong claimed
that there is a round square, but that, complained Russell, leads to
violations of the principle of noncontradiction, as that entity is
then both round and not round, in light of the fact that it is square,
which entails that it is not round. Parsons's response (see
[Parsons 1980], 38-42) seems to be to deny that being square
entails not being round, in which case it is simply false that the
round square is not round. He thinks that that implication holds only
for "real" objects. He claims that there are
counterexamples to the claim that all square objects are not round;
after all, the round square is a square object that is round! This
solution, however, does not seem to solve the more general threat of
contradiction, as discussed above. Indeed, Parsons himself recognizes
the limited success of his response (see [Parsons, 1980, 42n8]). He
allows that being non-squared is a nuclear property. But then his
comprehension principle entails that there is an object corresponding
to the condition of being a non-squared square, where that object
instantiates the incompatible properties of being a square and being a
non-square. The threat of contradiction has not been silenced.



Let's turn to Parsons's response to the existence problem.
The naive comprehension principle faced the problem of generating an
existent winged horse. Because existence is an extra-nuclear property,
however, Parsons's version of the comprehension principle, which
correlates sets of only nuclear properties to objects, avoids this
problem. The condition of being an existent winged horse is not
composed solely of nuclear properties and so Parsons's principle
does not correlate it to an object. Parsons's distinction
between nuclear and extra-nuclear properties similarly promises to
solve the problem of incomplete objects. Recall our singer from above.
That object does not have exactly one property; instead, it has
exactly one nuclear property. As having exactly one nuclear property
is itself an extra-nuclear property, much as being a complete object
is on Parsons's view, the threat of contradiction is
avoided. 



The distinction between nuclear and extra-nuclear properties remains
unclear. Parsons introduced the distinction with lists of nuclear
predicates ('is blue', 'is tall',
'kicked Socrates', 'is a mountain') and
extra-nuclear predicates ('exists', 'is thought
about by Meinong', 'is complete'). He then tells us
that the extra-nuclear are those that do not stand for properties of
individuals ([Parsons 1980, 24]). And, of course, it is nuclear and
not extra-nuclear properties by which objects are individuated.
Parsons's individuation principle for objects is the following:
"(1) No two objects (real *or* unreal) have exactly the
same nuclear properties; and (2) For any set of nuclear properties,
some object has all the properties in that set and no other nuclear
properties" ([Parsons 1980, 19]). But it is not clear what
status individual identity properties--properties like
*being identical to A*, where *A* is an
individual substance like, say, Parsons himself--have with
respect to this distinction. He sometimes claims that they are
extra-nuclear properties ([Parsons 1980, 28]). In that case, however,
Parsons is committed to the problematic thesis of the identity of
indiscernibles and so the impossibility of two primitively distinct
but qualitatively identical objects. (For further discussion, see the
entry on
 the identity of indiscernibles.)
Many contemporary philosophers agree that objects are not individuated
qualitatively, their identity and diversity being primitive. Max
Black's two qualitatively indiscernible spheres are primitively
distinct, in virtue of which one has the property of being that very
thing and the other lacking that property (see [Black 1953]). For
Parsons to accept this, he needs to include individual identity
properties among the nuclear properties. Furthermore, it is hard to
see why identity properties are not properties of
individuals. Suppose, then, that we count individual identity
properties like *being identical to A* as nuclear properties,
those properties entering the range of Parsons's restricted
comprehension principle. Then the nuclear negations of those
properties are also nuclear. But then we can take the set of all
objects, construct the individual identity property for each,
construct the nuclear negation of each of those properties, and then
construct a condition from those properties that, by Parsons's
comprehension principle, corresponds to an object. Then there is an
object that is distinct from every object that there is, which is a
contradiction. It is unclear, then, that the distinction between
nuclear and extra-nuclear properties and the restriction of the
comprehension principle to nuclear properties solves the problems
facing the naive comprehension principle. (For further discussion of
Parsons's view, see [Fine 1982, 1984] and [Zalta 1992].)



Earlier we distinguished between two versions of sophisticated
Meinongianism. The first, based on the distinction between nuclear
and extra-nuclear properties, was found lacking. We turn now to the
second, based on the distinction between encoding and exemplifying a
property, focusing on Zalta's version of the view, which is the
most fully developed in the literature. Whereas Parsons distinguished
different kinds of properties, restricting the comprehension principle
to only nuclear properties in the hope of thereby avoiding the
problems plaguing the naive comprehension principle, Zalta
distinguishes two different modes of having a property for the same
effect. Exemplifying a property is the familiar way in which an
individual has a property; it is roughly what most metaphysicians have
in mind when the speak of instantiating a property. Obama exemplifies
humanity, my chair exemplifies being comfortable, and the fig tree in
my backyard exemplifies needing water. What the comprehension
principle does is say not what properties object exemplify, in this
sense, but rather what properties they encode. So, for any
condition *C* on properties, there is an object that encodes
exactly those properties, which leaves open whether or not those
objects also exemplify those properties.



How does this distinction solve the problems facing Meinongianism
presented earlier in this section? By the comprehension principle, the
condition of being a singer determines an object with exactly that
property. But the comprehension principle does not imply that that
object exemplifies the property of being a singer but rather that it
encodes that property. Exemplifying the property of being a singer
requires exemplifying other properties like having a spatial location,
having a voice box, etc., all properties our singer neither encodes
nor exemplifies. But the object can encode the property of being a
singer without encoding these further properties. The singer does
exemplify some properties, such as the property of being abstract. The
singer *encodes* the property of being a singer, does not
encode the property of being abstract, and *exemplifies*
multiple properties, including the property of being abstract, being
the topic of this paragraph, and not being a singer. This is not
contradictory given the fundamental difference between encoding and
exemplifying. More generally, Zalta's comprehension principle
correlates sets of properties with objects that encode, not
(necessarily) exemplify, those properties. Insofar as the set of
properties characterizing an object are not complete, the resulting
object will be incomplete with respect to the properties it
encodes. But it need not be incomplete with respect to the properties
it exemplifies. While our singer encodes neither the property of
wearing blue shoes nor the property of not wearing blue shoes, we can
say that it exemplifies the property of not wearing blue
shoes. Bi-valence is saved, at least with respect to
exemplification.



Restricting the comprehension principle to the properties encoded and
rejecting an easy transfer between properties encoded and properties
exemplified also promises to avoid the other threats of contradiction
presented above. Recall the logically impossible condition of being
self-distinct. The principle of noncontradiction concerns the
properties objects exemplify, not the properties objects encode
(assuming our Meinongian is going to account for impossible
objects). Because an object can encode inconsistent properties without
exemplifying them, impossible objects do not violate the principle of
noncontradiction. Finally, Russell's worry that a Meinongian
comprehension principle generates existent winged horses can be
answered. There is an object correlated to the condition of being an
existent winged horse, but that object encodes and does not exemplify
the property of existing. Being existent can characterize an object
without that object exemplifying existence. So we do not need to worry
about an overpopulation of existent beings, as existent beings
exemplify existence, which the existent winged horse does
not. 



A view based on the distinction between encoding and exemplifying
avoids the standard objections to Meinongianism while promising to
deliver that view's many benefits. The semantics and logic is
straightforward and simple and surface forms of the natural language
sentences of interest in this article match their deep logical forms.
But the ontological costs are evident. There is semantic and logical
simplicity at a metaphysical price. (For more on Meingianism, in
addition to the references earlier in this section, see the following:
[Barz 2016], [Berto 2012], [Berto and Priest 2014], [Findlay 1963],
[Griffin 1985], [Jacquette 1989, 1996], [Lambert 1983], [Landini
1990], [Lewis 1990],[Priest 2005],[Rapaport 1976, 1978,,1981],
[Routley 1966, 1979, 1980], [Voltolini 1995, 2006], [Zalta 1983,
1985,1988,1992].) 


## 3. An Anti-Meinongian First-Order View



The previous two sections discussed views that deny that existence is
a property of individuals and views that deny that existence is a
universal property. This section considers views according to which
existence is a universal property of individuals, in the hope of
reaping the benefits of both the earlier views. It then explores the
interaction between quantifiers, tense operators, modal operators, and
a universal, first-order existence predicate in an attempt to expose
some difficulties such a view faces.



For both the Meinongian and the proponent of the proposal under
consideration, proper names are directly referential and simple
sentences in which they occur express singular propositions. However,
unlike the Meinongian, a proponent of the view to be developed in this
section insists that absolutely everything exists. In that case, a
sentence like 'Ronald McDonald does not exist' either
expresses a fully articulate singular proposition and so is false, as
in that case there is a referent of the subject-place singular term
which exists, or does not express a truth evaluative proposition at
all, as the singular term lacks a semantic content. In neither case is
the sentence true. Avoiding that consequence was a primary motivation
behind all of the alternative accounts discussed in the previous two
sections. The first challenge facing a proponent of such a view, then,
is to explain how sentences like 'Ronald McDonald does not
exist' are both meaningful and sometimes apparently true without
abandoning the theses that absolutely everything exists and that all
names are devices of direct reference.



One important suggestion, adopted by Saul Kripke (1973 [2013]), Peter
Inwagen (1977, 1983, 2000, 2003), Nathan Salmon (1998), David Braun
(1993, 2005), and Amie Thomasson (1999, 2003, 2009), among others, is
that seemingly empty names like 'Ronald McDonald' refer to
existent, albeit abstract, fictional characters. Fictional characters
have both being and existence. (For a powerful critique of this form
of fictional realism, see Hofweber 2000.) As we don't run into
them on the street, see them on the bus, or feel them in our beds,
given their lack of spatiotemporal location, it is plausible that what
a speaker *means* when she utters the sentence 'Ronald
McDonald does not exist' is not the false proposition that that
sentence expresses but instead the true proposition that (the
fictional character) Ronald McDonald is not a real person or is not
concrete. Indeed, this is suggested by the natural amendment,
''Ronald McDonald does not exist; he's a creation of
advertisement!'' On this view, then, there are no
genuinely true singular negative existentials. All meaningful singular
existentials are true and their negations false. We mistakenly take
some singular negative existentials to be true because we conflate or
do not sharply distinguish existing from being concrete. The benefit
of this account is the simple semantics of proper names and the sparse
metaphysics. The cost is revisionism regarding what we mean when we
use apparently true singular negative existentials.



We conclude this section by briefly discussing issues that arise with
the interaction between quantifiers, tense and modal operators, and a
universal, first-order existence predicate, as this interaction is the
source of another important cost of the account of existence being
outlined in this section. There are two sets of intuitions that seem
to pull in opposite directions. The first concerns the transience and
contingency of existence. Things seem to come in and go out of
existence through time. While Plato and Descartes used to exist, they
no longer do; when Plato existed, Descartes did not yet exist; and
right now the first child to be born in 2150 does not exist, but that
individual will. So, it seems, different things exist at different
times. Likewise, of the things that in fact exist, it seems that some
of them might not have existed at all and different
things--things that in fact do not exist--might have existed
instead or in addition. So, it seems, different things exist at
different worlds. These intuitions are quite robust. The second set of
intuitions concern the ontological status of nonactual and nonpresent
objects. Many philosophers are drawn to the thesis of actualism: The
thesis that absolutely everything is actual and how an object is
*simpliciter* is how it actually is, unactualized possibilities
for an object being in some sense hypothetical ways of being for that
object. While less popular, many philosophers accept the temporal
analog of actualism, the thesis of presentism, according to which
absolutely everything is present and how an object is
*simpliciter* is how it presently is, how an object was and
will be are in some sense hypothetical ways of being for that object.
These two sets of intuitions combined with the view of existence under
consideration in this section lead to difficulties.



Let's begin with the modal problem. There could have been an
object distinct from all actually existing objects. For example, I
could have had a brother and, given origin essentialism, if I had a
brother, he would have been distinct from every actually existing
objects, as no actually existing thing could have been my brother. Our
intuitions concerning how things might have been lead us to accept
this claim as true. But, by the thesis of actualism, absolutely
everything is actual and, by our view of existence, exists and so
actually exists. So, it seems that actualism and our view of existence
are incompatible with the intuitive possibility of there being an
object distinct from all existing objects and the intuition that I
might have had a brother.



We can regiment the contingency of existence intuition as followings,
letting A be the actuality operator,
where Aph is true with respect to a
world **w** under an interpretation **I**
just in case ph is true with respect to the distinguished world of
**I**: 
*[?]*x*!A[?]*y*(*y*=*x*).
Call this
sentence *Alien*. The worry is that the truth of Alien carries
ontological commitment to merely possible individuals and so the
falsity of the thesis of actualism. One way to substantiate this worry
is to invoke the Barcan Formula, or one of the mixing axioms proposed
for modal operators and quantifiers in Ruth Barcan Marcus's
groundbreaking work in quantified modal logic [Marcus 1946], according
to which all instances of the sentence
*[?]*x*ph(*x*)
-[?]*x**ph(*x*) are logical true. (In the
foregoing formulas, ph(*x*) stands for any formula in which
the variable *x* may or may not be free.) We can then transpose
the modal and quantifier in Alien to derive
[?]*x**!A[?]*y*(*y*=*x*).
The truth
of this second sentence evidently requires that there is something
that is not actual, contrary to the dictates of actualism. The Barcan
Formula, and in part for this very reason, is controversial and
rejected by those that subscribe to a varying domains possible worlds
semantics for modal discourse. So this line of argument is not likely
to convince everyone that our modal intuitions lead to problems. 



The Barcan Formula is controversial. There is, however, a second line
of argument that does not rest on the validity of the Barcan Formula,
relying instead on combining standard truth definitions for quantified
and modal sentences in the most straightforward way. Alien is true
under an interpretation
**I** just in case there is a world **w**
accessible from the distinguished world of **I** with an
object in its domain that is not in the domain of the distinguished
world of **I**. This is because its truth requires that
[?]*x*!A[?]*y*(*y*=*x*)
is true
with respect to **w** and so, it is tempting to conclude,
that there is a witness that satisfies the condition !A[?]*y*(*y*=*x*)
at
**w**. But that is the rub. If actualism is true, then
there is no such witness, even if there could have been. If we are
realistic about possible worlds semantics, the model theory for modal
talk itself does not contain primitive modality, instead containing
worlds as points of evaluation and the notion of truth at a world, in
which case 'there is' in the above truth recursion does
not occur inside the scope of a possibility operator. So, if Alien is
true, there is some object **o** and accessible possible
world **w** such that **o** satisfies
!A[?]*y*(*y*=*x*)
at **w**, which seems to run contrary to the thesis of
actualism, as that witness does not actually exist. (For further
discussion of this problem and some of the solutions considered below,
see the entry on the
 possibilism-actualism debate.)



One solution is to abandon actualism and accept that there are merely
possible objects. According to this possibilist position, merely
possible objects are among the most unrestricted domain of
quantification, being constituents of fundamental reality. While this
position deserves serious consideration, let us set it aside and
explore only actualist solutions. (The position is structurally
similar to the Meinongian position, as the most inclusive domain of
quantification, where there is in the most inclusive and unrestricted
of senses, includes entities that do not actually exist, even if they
exist simplicter.) A second solution rests on the Meinongian
distinction between being, in the sense of being a member of the most
inclusive domain of quantification and discourse, and existing and the
claim that there are objects that do not exist. Armed with a
Meinongian metaphysics, we can reject Alien as capturing the intuition
that *existence* is contingent, opting instead for the
following sentence as doing that, where *E*!*x* is the
Meinongian logically primitive existence predicate:
[?]*x*(!*E*!*x* [?] **E*!*x*).
The Meinongian can then deny Alien and appeal to the truth of this
sentence to explain our intuitions concerning the contingency of
existence. Everything is actual, on this view, although some of those
actual things do not exist but could have, even though they all have
being and the domain of being is fixed across all possible
worlds. This solution to our problems, however, is unavailable to a
proponent of the view that existence is a universal property of
individuals.



Bernard Linsky and Edward Zalta [Linsky and Zalta 1994] present a
novel solution to this problem that promises to be consistent with the
tenets of the view of existence under consideration in this section.
(A similar account is defended by Timothy Williamson [Williamson 1998,
1999a [2000], 1999b, 2000, 2002, 2013]. For a very interesting
discussion of Williamson, see [Goodman 2016].) Consider the intuitive
possibility that I have a brother. An entity that encodes the property
of being my brother actually exists, but as a nonconcrete object. That
object is only contingently nonconcrete; it could have been concrete,
and had it been concrete, it would have exemplified the property of
being my brother (along with the other properties that it encodes and
the necessary consequences thereof). On this view, my possible brother
(as well as any alleged merely possible object) actually exists, but
as a nonconcrete individual that could have been concrete. The view is
both actualist, as absolutely everything is actual, and
anti-Meinongian, as absolutely everything exists. Note, however, that
Alien, the sentence two paragraphs above purported to capture our
intuitions concerning the contingency of existence, is false on this
view, as every individual is a necessary existent. Instead, our
intuition that what there is is contingent is to be explained in terms
of the contingency of what is concrete and nonconcrete. So,
where *C*!*x* is a logically primitive predicate of
concreteness, it is the truth of the following sentence, not Alien,
that explains those intuitions: [?]*x*(!*C*!*x*
[?] **C*!*x*). While the explanation of the
contingency of existence bears a structural similarity to the
Meinongian explanation discussed in the previous paragraph, the
metaphysics is importantly different and so the two views should not
be collapsed. Linsky and Zalta describe a non-Meinongian, actualist
view that treats existence as a universal property of individuals.



Linsky and Zalta's view entails that concreteness is an
accidental property, in the sense that the self-same individual that
is in fact nonconcrete (my possible brother, for example) could have
been concrete and the self-same individual that is in fact concrete
(both you and me, for example) could have been nonconcrete. Many
metaphysicians will reject this on the grounds that concreteness is
categorical and an individual does not migrate through categorical
properties across modal space. But now consider the temporal analog of
the modal issues with existence and concreteness that we have been
exploring: The problem of temporary existents. While one's
accounts of the two problems do not need to swing together (Linsky and
Zalta, for example, do not offer the temporal analog of their account
of contingent existents), as there are differences between alethic
modality and temporality, it is useful to consider them as a pair for
our purposes. Intuitively things come in and go out of existence;
what exists at one time does not exist at another. The temporal analog
of Linsky and Zalta's view of contingent existents entails that
everything always exists. What there is and what exists at one time is
the same as what is and what exists at any other time; the domain of
quantification is fixed across all times. What varies from time to
time is instead which of those individuals are concrete. Socrates
still exists now, although as a nonconcrete individual, who was
concrete in 450 BCE, and similarly for the first child to be born in
2150. This view requires that a thing can survive the change from
being nonconcrete to concrete, which is the explanation of what the
ancients would call generation, and the change from being concrete to
nonconcrete, which is the explanation of what the ancients would call
destruction. On this view, then, seeming substantial changes are
really forms of qualitative change: A change in the quality of
concreteness. This runs contrary to the common conception that
concreteness is necessary and eternal to any object that instantiates
it, the divide between concrete and nonconcrete individuals marking a
divide between categories of being. Many metaphysicians insist that,
just as one and the same thing cannot go from being an individual to
being a property, so too one and the same thing cannot go from being
nonconcrete to being concrete.



What are the prospects of a theory according to which existence is a
universal, genuinely contingent and transient property of individuals?
Such a view requires that the domain of quantification varies from
world to world and time to time, as everything that is exists but
different individuals exist at different possible worlds and at
different times, in which case the domain of quantification varies
from world to world and time to time. In that case, Alien from above
is true. So fault must be found with the earlier argument that the
truth of Alien is inconsistent with the thesis of actualism. One
response found in the literature rejects the last step, insisting that
there are general claims that could have been true, and so are true at
some accessible possible world, without there being specific instances
of those claims that are true at those accessible worlds. In nonmodal
environments, the quantified sentence [?]*x*ph(*x*)
is true just in case there is some witness **o** that
satisfies the condition ph(*x*). That condition fails,
however, for quantified sentences true at a merely possible world. The
model theory for a model language--with its space of possible
worlds and individuals populating the domains of possible
worlds--contains, like everything else if actualism is true, only
actually existing entities. Still, sentences like Alien are true and
so there are merely possible worlds at which
[?]*x*!A[?]*y*(*y*=*x*)
is true. There is no individual of which
!A[?]*y*(*y*=*x*)
is true in virtue of which the quantified sentence is true, although
there would have been had that merely possible world been actual. This
is perhaps more clear when we turn from sentences being true with
respect to merely possible worlds to propositions being true at merely
possible worlds. There is a world **w** at which the
existential proposition [there is something such that there is no
actual thing identical to it] is true but there is no singular
proposition [there is no actual thing identical to **o**]
true at **w** as there is no such
entity **o**. Had
**w** been actual, however, then there would have been
such an entity and it is this fact that grounds the truth of the
existential proposition at **w**. (The classic source for
this distinction is [Adams 1981]. See also [Fine 1985] and [Fitch
1996].) This suggestion, then, runs contrary to the standard
semantics for quantificational sentences, which reduces the truth or
falsity of existential and universal sentences to the truth or falsity
of their instances, when extending that semantics to truth at a
world. The suggestion also requires a distinction between truth at a
world, in terms of which the model theory for modal operators is
given, and truth in a world, which involves the notion of considering
what would have been had a nonactual world been actual. (For more on
this distinction and the problem of the contingency of existence more
generally, see the entry on the
on possibilism-actualism debate.)


## 4. Conclusion



This entry began by noting that existence raises a number of deep and
important problems in metaphysics, philosophy of language, and
philosophical logic. The entry has examined some of those problems and
surveyed a number of different accounts of existence. None of the
theories surveyed is wholly satisfying and without cost. The first
view proposed by Frege and Russell treats existence as a second-order
property and assimilates seemingly singular existentials to general
existentials. The proposal requires descriptivism, the thesis that
ordinary proper names have descriptive equivalences, which many find
to be a problematic thesis. The second Meinongian view requires
countenancing individuals that do not exist. We have seen the view
face challenges in giving coherent and yet informative and compelling
individuation principles for nonexistent individuals and all versions
of the view suffer from the problem of metaphysical
overpopulation. Finally, the naive view that existence is a universal
property of individuals was presented. That view faced the problem of
having to reject the truth of highly intuitively true singular
negative existential sentences like 'Ronald McDonald does not
exist'. The view also faces difficulties in properly accounting
for the interaction of quantifiers and modal and tense
operators. Existence remains, then, itself a serious problem in
philosophy of language, metaphysics, and logic and one connected to
some of the deepest and most important problems in those areas.