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Difference Between the Existen-
tial Quantifier and the Existence
Predicate According to Mario
Bunge
Martín Orensanz1
Abstract—Most analytic philosophers believe that the existential quantifier, ∃, has
ontological import. Mario Bunge was one of the first thinkers to challenge this
view. He traces a distinction between the quantifier ∃ and a first-order existence
predicate. Furthermore, he acknowledges two kinds of existence: real and con-
ceptual. One of the reasons for accepting Bunge’s proposal is that it can do justice
to statements about fictional entities, which is something that rival proposals do
not seem to be capable of doing. Additionally, I will also discuss the issue of the
ontological argument, and the problem of material constitution.
Résumé — La plupart des philosophes analytiques croient que le quantificateur exis-
tentiel, ∃, a une portée ontologique. Mario Bunge a été l'un des premiers penseurs
à contester ce point de vue. Il fait une distinction entre le quantificateur ∃ et un
prédicat d'existence de premier ordre. De plus, il reconnaît deux types d'existence
: réelle et conceptuelle. L'une des raisons d'accepter la position de Bunge est
qu'elle peut rendre justice aux énoncées portant sur des entités fictives, ce que les
positions rivales ne semblent pas capables de faire. Je discuterai également de la
question de l'argument ontologique et du problème de la constitution matérielle.
Keywords— Existence; Existential quantifier; Existential predicate; Ontological argu-
ment; Material constitution.
1Martìn Orensanz is a Doctor en Filosofía from Argentina. His work focuses on
three main topics: Argentine philosophy, contemporary philosophy and philosophy
of science. He has published a book, as well as several articles in international
journals. He won two scholarships (doctoral and postdoctoral) from the National
Scientific and Technical Research Council of Argentina (CONICET). Together with
Guillermo Denegri, he is working on the philosophical, historical and theoretical
aspects of parasitology and helminthology.
2
Mεtascience n° 3-2024
unge claims that the quantifier ∃ doesn’t have ontological
import. He argues that ∃ only means “for some...”, just as ∀
only means “for all...”. For this reason, he suggest that ∃
should be called “the particularizing quantifier” instead of “the ex-
istential quantifier”, and that in order to talk about existence, we
need a first-order existence predicate.2 Furthermore, he indicates
that the standard view among philosophers leads to a problem if we
consider the case of fictional entities:
Surely most contemporary philosophers hold that ∃ formalizes both
the logical concept "some" and the ontological concept of existence.
I shall argue that this is a mistake. Consider the statement "Some
sirens are beautiful", which can be symbolized "(∃x)(Sx & Bx)". So
far so good. The trouble starts when the formula is read "There are
beautiful sirens". The existential interpretation is misleading be-
cause it suggests belief in the real existence of sirens, while all we
intended to say was "Some of the sirens existing in Greek mythology
are beautiful". (Bunge, 1977: 155)
I would like to propose a different example in defense of Bunge’s
idea. It relies on the use of individual constants. Recall that in pred-
icate logic, there are individual variables, which are usually sym-
bolized with the letters “x”, “y” and “z”, and there are also individual
constants, which are typically symbolized with other letters, like
“a”, “b”, and “c”. With this in mind, take a look at the following ar-
gument:
(1) ∀x(x = x) Principle of Identity.
(2) p = p From (1), by universal elimination.
(3) ∃x(x = p) From (2), by existential introduction.
The translation of that argument is this:
(1’) Everything is identical to itself.
(2’) So, Pegasus is identical to Pegasus.
(3’) So, Pegasus exists.
If the quantifier ∃ has ontological import, as most logicians be-
lieve, then the statement that Pegasus is identical to itself leads to
2 Some other philosophers also trace this distinction. Meinongians usually use the
symbol E! as the existence predicate, different from the quantifier ∃. See, for ex-
ample, Parsons (1980), Zalta (1983), Linksy & Zalta (1991), and Jacquette (1996).
B
3
Martín Orensanz Difference Between the Existential Quantifier and the Existence Predicate
the conclusion that Pegasus exists in the real world. This is a prob-
lem because we know that Pegasus doesn’t really exist.
But this is only a problem if we believe that ∃ has ontological
import. If we agree with Bunge that it doesn’t, then there is no prob-
lem. It’s true that (3) can be deduced from (2), but (3) should be read
as “Some x is identical to Pegasus”, instead of reading it as if it said
“There exists some x in the real world that is identical to Pegasus”.
On the other hand, if we say “Pegasus does not exist”, that state-
ment is also problematic. If we formalize it as ¬∃x(x = p), then it can
be shown that this formula leads to a contradiction. The following
argument indicates why this is the case:
(4) ¬∃x(x = p) Premise.
(5) ∀x¬(x = p) From (4), by change of quantifier.
(6) ¬(p = p) From (5), by universal elimination.
Informally, here’s what the argument says:
(4’) Pegasus does not exist.
(5’) So, nothing is identical to Pegasus.
(6’) So, Pegasus is not identical to Pegasus.
And we know that from a contradiction, anything follows. This is
the Principle of Explosion, also known as ex falso sequitur quodlibet,
or the rule of EFSQ for short. So, if we say that Pegasus does not
exist, we can end up saying that Pegasus does exist. In other words,
it can be shown that ¬(p = p) leads to ∃x(x = p), which is what we
were supposed to deny in the first place.
The upshot is that there are good reasons for rejecting the idea
that ∃ has ontological import. From a purely logical point of view,
the formula ∃x(x = p) can’t fail to be true, and its negation, ¬∃x(x =
p), must be false. In other words, we have arrived a the wrong re-
sult: that the statement “Pegasus exists” is true, while its negation,
“Pegasus does not exist”, is false. The result should be exactly the
opposite of this.
As we’ll see later, from a Bungean perspective there’s a simple
and elegant solution to this problem. But before we examine it, we
need to consider the possibility of avoiding individual constants.
4
Mεtascience n° 3-2024
1] Getting Rid of Individual Constants
Recall that the formulas ∃x(x = p) and ¬∃x(x = p) both use an
individual constant, a lower-case “p” that stands for Pegasus. If one
believes that this is the root of the problem, then it seems that the
solution would be to avoid using an individual constant in the first
place. This type of solution draws its support from the works of
Frege, Russell and Quine, though the details differ in each case.
From a Fregean point of view, the statement “Pegasus exists”
can be paraphrased as “The concept ‘Pegasus’ is instantiated”, and
it can be symbolized like this:
(7) ∃x(Cx)
Similarly, the statement “Pegasus does not exist” can be para-
phrased as “The concept ‘Pegasus’ is not instantiated”, and we can
formalize it like this:
(8) ¬∃x(Cx)
While (7) is false, (8) is true. What’s interesting about these for-
mulas is that they’re contingent. In other words, they are not nec-
essarily true nor necessarily false. Unlike ∃x(x = p), the formula
∃x(Cx) can’t be deduced from p = p. And the formula ¬∃x(Cx), unlike
¬∃x(x = p), does not lead to ¬(p = p). So, the Fregean proposal is
quite sound, at least from a purely formal point of view.
But the solution is not entirely free from problems of its own. In
particular, it does not seemed to be able to handle statements like
the following one: “The concept ‘Pegasus’ is not instantiated in Az-
tec mythology but it is instantiated in Greek mythology”, which can
be symbolized like this:
(9) ¬∃x(Cx ∧ Ax) ∧ ∃x(Cx ∧ Gx)
Is that statement true or false? From a Bungean point of view,
that statement is true. But Fregeans will have a hard time with this
example. Since they believe that ∃ has ontological import, they are
forced into the awkward position of having to say that the state-
ment in question is false. However, it seems reasonable to say that
Pegasus does not belong to Aztec mythology, but that it does belong
to Greek mythology.
Let’s take a look at the Russellian solution. It’s structurally sim-
ilar to the Fregean one. The only difference is that the name
5
Martín Orensanz Difference Between the Existential Quantifier and the Existence Predicate
“Pegasus” should be replaced by a definite description, like “the
winged horse”. In that case, the statement “Pegasus exists” can be
paraphrased as “There exists an x, such that x has the property of
being a winged horse”. Formally:
(10) ∃x(Wx)
Contrary to ∃x(x = p), which is necessarily true, ∃x(Wx) is false.
Likewise, the statement “Pegasus does not exist” can be para-
phrased as “There does not exist an x, such that x has the property
of being a winged horse”. Formally:
(11) ¬∃x(Wx)
The Russellian solution3 has the same advantages that the Fre-
gean one has. But it also has the same problems. If we want to say
that Pegasus is not among the list of fictional creatures of Aztec
mythology, but that it is one of the fictional creatures of Greek my-
thology, then we would have to paraphrase it like this: “There are
no winged horses in Aztec mythology but there is a winged horse in
Greek mythology”, which can be symbolized in the following way:
(12) ¬∃x(Wx ∧ Ax) ∧ ∃x(Wx ∧ Gx)
Russellians would have to claim that (12) is false. But, as I’ve
mentioned a few paragraphs back, one can argue that it’s true that
Pegasus is not part of Aztec mythology but that it is indeed part of
Greek mythology.
Lastly, there’s Quine’s solution, which is similar to the Fregean
and the Russellian ones in terms of its structure. From a Quinean
viewpoint, the statement “Pegasus does not exist” should instead be
paraphrased as “There is no individual that has the property of be-
ing Pegasus”, or more briefly, “Nothing pegasizes”.4
The idea is that, unlike the Russellian proposal, we don’t need to
know anything about Pegasus in order to say that nothing has
whatever properties that fictional creature might have. All that we
need to do is to turn a proper name, like “Pegasus”, into a predicate.
Symbolically, instead of a lower-case “p”, we use an uppercase “P”.
3 The formulas (10) and (11) are actually too simplistic. The former should be
∃x(Wx ∧ ∀y(Wy → (x = y))). Likewise, the latter should be ¬∃x(Wx ∧ ∀y(Wy → (x =
y))). I will simply ignore these complications here. Similar considerations apply to
the Fregean and Quinean formalizations.
4 See Quine (1948). For an early critique, see Hochberg (1957).
6
Mεtascience n° 3-2024
This being so, the statement “Nothing pegasizes” can be formalized
like this:
(13) ¬∃xPx
And the statement “Pegasus exists” should be paraphrased as
“Something pegasizes”, which can be formalized like this:
(14) ∃xPx
Predictively, I believe that Quine’s solution has the same ad-
vantages and the same drawbacks that its Fregean and Russellian
equivalents have. So, we can ask if the following statement is true:
“Nothing pegasizes in Aztec mythology, but something pegasizes in
Greek mythology”. Quineans would have to say that it’s false, even
though one can argue that the contrary is the case. In the next sec-
tion, we’ll examine the Bungean alternative to this problem.
2] Bunge and Pegasus
There are several things to note about Bunge’s proposal. Firstly,
unlike the ones we just saw, Bunge doesn’t believe that the individ-
ual constants of predicate logic should be avoided. It’s entirely le-
gitimate, and useful, to use a lower-case “p” that stands for Pegasus.
Secondly, as I’ve mentioned before, Bunge rejects the idea that the
quantifier ∃ has ontological import. This symbol does not refer to
existence in an ontological sense. All that it means is “for some…”,
just as the quantifier ∀ means “for all…”. Thirdly, in order to talk
about existence, Bunge says that we need a first-order existence
predicate. In his own words:
We need then an exact concept of existence different from ∃. Much
to the dismay of most logicians we shall introduce one in the sequel.
In fact we shall introduce an existence predicate, thus vindicating
the age-old intuition that existence is the most important property
anything can possess. (Bunge, 1977: 155)
This not only goes against Frege, Russell and Quine, it also goes
against Kant, who famously claimed that existence is not a predi-
cate. At this point, one may wonder if Bunge’s idea means that the
ontological argument should be accepted. The answer is negative.
But we’ll discuss this point later. For now, it’s necessary to indicate
that Bunge traces a distinction between two types of existence: real
and conceptual. Accordingly, he uses two types of existence
7
Martín Orensanz Difference Between the Existential Quantifier and the Existence Predicate
predicates: ER stands for real existence, while EC stands for concep-
tual existence. From this point of view, if the statement “Pegasus
exists” means “Pegasus really exists”, it can be formalized like this:
(15) ERp
(15) is false, because Pegasus doesn’t really exist. The negation
of that statement is “Pegasus does not really exist”, and it can be
symbolized like this:
(16) ¬ERp
(16) is true. Pegasus does not exist in the real world. Let’s take a
look now at conceptual existence. If we say “Pegasus exists in a con-
ceptual sense”, then this can be formalized in the following way:
(17) ECp
From a Bungean point of view, (17) is true. Pegasus does exist
conceptually, because it’s a fictional creature from Greek mythol-
ogy. The negation of (17) is this:
(18) ¬ECp
Which means “Pegasus does not exist conceptually”. This last
statement is false, at least from a Bungean perspective, because in
Greek mythology there is indeed a fictional creature called “Pega-
sus”.
With this in mind, the Bungean proposal manages to achieve
something that the Fregean, Russellian and Quinean ones don’t: it
can handle the statement “Pegasus does not exist conceptually in
Aztec mythology, but it does exist conceptually in Greek mythol-
ogy”. The three proposals that we saw before must claim that the
statement in question is false. By contrast, from a Bungean per-
spective, that statement is true, and it can be formalized like this:
(19) ¬EAp∧ EGp
As (19) shows, whenever we need to distinguish different concep-
tual contexts, like the difference between Aztec mythology and
Greek mythology, we can replace the subscript “C” in EC with an-
other letter. So, in (19), the subscript “A” in EA stands for “Aztec
mythology”, and the subscript “G” in EG stands for “Greek mythol-
ogy”.
8
Mεtascience n° 3-2024
The upshot is that the Bungean proposal is preferable to the Fre-
gean, Russellian and Quinean ones, if only because the former does
justice to fictional discourse in a way that the other three can’t. But
there’s an objection that can be raised against the Bungean account,
which we need to address.
3] An Objection and a Reply
Opponents of the existence predicate usually raise an objection
here. The objection is that the acceptance of an existence predicate
commits us to non-existing objects. More precisely, to claim that a
certain entity doesn’t exist entails, by existential introduction, that
there is some entity that does not exist. Here’s the argument:
(20) ¬ERp Premise.
(21) ∃x(¬ERx) From (20), by existential introduction.
Informally, (20) and (21) can be translated like this:
(20’) Pegasus does not really exist.
(21’) So, there is something that does not really exist.
This is an objection that is usually raised against Meinongians.
The charge is that the idea that there are non-existing entities is
not intelligible. Where are these entities located? They would seem
to float around in fantastical place, which is usually called
“Meinong’s jungle”, a sort of parallel dimension filled with unicorns,
square circles, and wooden iron. So, one could raise a similar objec-
tion against Bunge. If Pegasus doesn’t really exist, then -by the rule
of existential introduction-, there is a non-existing entity. Where is
it located? Presumably, it would be floating around in what could
be called “Bunge’s jungle”, the Bungean version of Meinong’s jungle.
Bungeans can meet this objection quite easily. Firstly, a state-
ment like (21) poses no problem to the Bungean, because that state-
ment simply says “Some particular x does not have the property
ER”. It doesn’t say “There exists an x such that x does not exist”,
because the quantifier ∃ does not have ontological import to begin
with. It’s true that there is some x, such that x doesn’t really exist,
and this claim is not contradictory. Secondly, fictional entities, like
Pegasus, are not located in some parallel dimension or otherworldly
jungle, instead they are brain processes. As he explains:
9
Martín Orensanz Difference Between the Existential Quantifier and the Existence Predicate
Ideas, then, do not exist by themselves any more than pleasures
and pains, memories and flashes of insight. All these are brain pro-
cesses. However, nothing prevents us from feigning that there are
ideas, that they are "there" up for grabs - which is what we do when
saying that someone "discovered" such and such an idea. We pre-
tend that there are infinitely many integers even though we can
think of only finitely many of them - and this because we assign the
set of all integers definite properties, such as that of being included
in the set of rational numbers. (Bunge, V4: 169)
Real existence is the property of being somewhere in the world.
Conceptual existence is the property of belonging to a conceptual
context, such as Greek mythology. For a Bungean, the statement
“Pegasus exists in the context of Greek mythology” is true, because
Pegasus does indeed belong to that context. Likewise, the statement
“Pegasus does not exist in reality” is also true, because Pegasus is
not a living creature located somewhere in the real world.
We turn now to the issue of the ontological argument, and how it
can be refuted even if one claims that existence can be conceptual-
ized as a first-order predicate.
4] The Refutation of the Ontological Argument
Kant famously claimed that existence is not a predicate. One of
the upsides of that idea is that it allows us to reject the ontological
argument. But here’s the question: if we claim, following Bunge,
that it makes sense to use an existence predicate, different from the
existential quantifier, does this mean that we should accept the on-
tological argument? In other words, does the ontological argument
prove that God exists?
Of course not. But the reason why the ontological argument fails
is not because existence is not a predicate, as Kant claims. Here’s
what Bunge has to say on this issue:
Let us now use the existential predicate introduced above to revisit
the most famous of all the arguments for God’s existence. Anselm
of Canterbury argued that God exists because He is perfect, and
existence is a property of perfection. Some mathematical logicians
have claimed that Anselm was wrong because existence is not a
predicate but the ∃ quantifier. I suggest that this objection is so-
phistic because in all the fields of knowledge we tacitly use an exis-
tential predicate that has nothing to do with the “existential”
10
Mεtascience n° 3-2024
quantifier, as when it is asserted or denied that there are living be-
ings in Mars or perpetual motion machines. (Bunge, 2012: 174-175)
One possible way to formulate the ontological argument using
Bunge’s real existence predicate, ER, is this:
(22) ∀x(Px → ERx) Premise.
(23) Pg Premise
(24) ERg From (22) and (23), by implication elimination.
Informally, here’s what the argument says:
(22’) For all x, if x is perfect, then x really exists.
(23’) God is perfect.
(24’) So, God really exists.
Of course, Bunge rejects that argument. After all, he was an
atheist. However, what he argues is that the argument shouldn't be
rejected in the way that Kant and some modern logicians do:
Hence the atheist will have to propose serious arguments against it
instead of the sophistry of the logical imperialist. An alternative is
to admit the existence of God for the sake of argument, and add the
ontological postulate that everything real is imperfect: that if some-
thing is perfect then it is ideal, like Pythagoras’ theorem or a Bee-
thoven sonata. But the conjunction of both postulates implies the
unreality of God. In short, Anselm was far less wrong than his mod-
ern critics would have it. (Bunge, 2012: 175)
In other words, Bunge rejects premise (22). It’s not true that if
something is perfect, then it must really exist. On the contrary, it’s
possible to say that if something is perfect, then it exists only in a
conceptual sense. In other words, one could say that God doesn't
exist in reality, but He, or She, or They, exist in the context of a
certain religion, just as Pegasus exists conceptually in the context
of Greek mythology. This being so, the ontological argument fails.
5] Existence and the Problem of Material Constitution
Bunge’s distinction between the existential quantifier and the
existence predicate is also useful for tackling some other philosoph-
ical topics, such as the problem of material constitution. Here’s the
gist of this problem. Imagine that on Monday, there exists a piece
of clay in Jane’s atelier. On Tuesday, she sculpts it, turning it into
a statue of the Greek goddess of wisdom. Intuitively, there seems to
11
Martín Orensanz Difference Between the Existential Quantifier and the Existence Predicate
be only one object where the sculpture is located. But a moment’s
reflection indicates that this claim is problematic, since the statue
has different properties from the piece of clay. For example, if the
statue is flattened, then it ceases to exist, but the piece of clay
doesn’t. The statue didn’t exist on Monday, but the piece of clay did.
The statue is Romanesque, but the piece of clay isn’t. And so forth.
So, contrary to our intuitions, we have to say that on Tuesday there
are two distinct material objects where there seems to be only one.
In other words, there are two numerically distinct objects that coin-
cide with each other. This is the problem of material constitution.
A popular solution to this problem is to claim that the piece of
clay exists, but that the statue doesn’t. There’s no such thing as a
statue, -the idea goes-, there’s only a piece of clay arranged statue-
wise. Korman provides one of the best reconstructions of this argu-
ment:
Here is an argument from material constitution for the elimination
of clay statues. Let Athena be a clay statue, and let Piece be the
piece of clay of which it’s made.
(MC1) Athena (if it exists) has different properties from Piece.
(MC2) If so, then Athena ≠ Piece.
(MC3) If so, then there exist distinct coincident objects.
(MC4) There cannot exist distinct coincident objects.
(MC5) So, Athena does not exist. (Korman, 2016: 9-10)
Korman believes that statues do exist. So, in order to reject the
preceding argument, at least one of the premises must be denied.
After reviewing the available options, he decides to reject MC4. As
he suggests, this solution is not optimal, but for anyone who accepts
a realist account of artifacts, the denial of MC4 is the least of the
available evils.
I won’t attempt to provide a solution to the problem of material
constitution here. I leave that for another article. This is an incred-
ibly difficult problem, which is why I think that any small step that
can be taken towards its resolution should be counted as a victory.
And I believe that the small step that can be taken here is the fol-
lowing one. Focus on the statements “Athena exists” (which is the
antecedent in MC1) and “Athena does not exist (which is what MC5
says). What would be the best way to formalize them? At first
glance, it might seem that we should translate them as ∃x(x = a)
and ¬∃x(x = a). But this can’t be the case. Because if it was, then
12
Mεtascience n° 3-2024
how could ∃x(x = a) fail to be true given that it can be deduced from
a = a, by the rule of existential introduction? It’s the same problem
that we saw at the beginning of the article in regards to Pegasus. If
we replace the name “Pegasus” with “Athena”, then the argument
looks like this:
(25) ∀x(x = x) Principle of Identity.
(26) a = a From (25), by universal elimination.
(27) ∃x(x = a) From (26), by existential introduction.
Which can be translated like this:
(25’) Everything is identical to itself.
(26’) So, Athena is identical to Athena.
(27’) So, Athena exists.
The only case in which ∃x(x = a) could be false is in the context
of some non-classical logic, such as free logic. So, if we want to for-
malize the statement “Athena exists” using classical predicate logic,
then ∃x(x = a) is not an option. Otherwise, the argument for the
elimination of clay statues has no bite.
Likewise, the statement “Athena does not exist”, which is what
MC5 says, shouldn’t be formalized as ¬∃x(x = a), because that for-
mula leads to ¬(a = a):
(28) ¬∃x(x = a) Premise.
(29) ∀x¬(x = a) From (28), by change of quantifier.
(30) ¬(a = a) From (29), by universal elimination.
Informally, the argument says this:
(28’) Athena does not exist.
(29’) So, nothing is identical to Athena.
(30’) So, Athena is not identical to Athena.
And, since anything follows from a contradiction, if we start with
¬∃x(x = a), then we could end up deducing ∃x(x = a). In other words,
if we say that Athena does not exist, we can conclude that Athena
does exist. Once again, if this is acceptable, then the argument for
the elimination of clay statues has no bite.
One possible option would be to avoid the use of the individual
constant “a”, and to formalize the statement “Athena exists” as
∃xAx. It’s open to debate what that formula means, exactly. From a
Fregean perspective, it means that the concept ‘Athena’ is
13
Martín Orensanz Difference Between the Existential Quantifier and the Existence Predicate
instantiated. From a Russellian point of view, it would mean “There
is an x, such that x is the statue created by Jane on Tuesday”. And
from a Quinean viewpoint, it would mean “Something has the prop-
erty of being Athena”, or “Something athenizes”. Similar consider-
ations apply to the statement “Athena does not exist”, which would
have to be formalized as ¬∃xAx. But I have argued that these view-
points are questionable. Even if they can account for real entities,
they can’t do justice to fictional discourse.
A second option is to simply refuse to formalize the argument for
the elimination of clay statues. The idea here is that the argument
doesn’t need to be translated into the language of predicate logic to
have bite. Granted, but it can be shown that itlacks bite if the state-
ments “Athena exists” and “Athena does not exist” are translated
respectively as ∃x(x = a) and ¬∃x(x = a).
The remaining option is to translate those statements using an
existence predicate, and to claim, as Bunge does, that the quantifier
∃ does not have ontological import. This being so, the statements
“Athena exists” and “Athena does not exist” can be formalized, re-
spectively, as ERa and ¬ERa.
There might be reasons for not accepting those Bungean formu-
las. But, in any case, I hope to have shown that the formulas ∃x(x =
a) and ¬∃x(x = a) should not be accepted either. And, when one deals
with an issue as difficult as the problem of material constitution, I
believe that what I have shown is no small victory.
6] Concluding Remarks
I have show that there are good reasons for accepting Bunge’s
idea that the existential quantifier should be distinguished from a
first-order existence predicate. This is because if ∃ has ontological
import, then existence claims about fictional entities, like Pegasus,
become problematic. Specifically, from the claim that Pegasus is
identical to Pegasus, we can conclude -by the rule of existential in-
troduction- that Pegasus exists. And the statement that Pegasus
does not exist, if it’s formalized as ¬∃x(x = p), leads to the contra-
dictory claim that Pegasus is not identical to Pegasus.
One possible solution would be to avoid individual constants,
such as “p”. In that case, the statements “Pegasus exists” and “Peg-
asus does not exist” can be formalized as ∃xPx and ¬∃xPx, respec-
tively. The philosophies of Frege, Russell and Quine support this
14
Mεtascience n° 3-2024
idea. However, those proposals don’t seem to do justice to fictional
discourse. In particular, they would have to claim that the following
statement is false: “Pegasus does not exist conceptually in Aztec
mythology but it does exist conceptually in Greek mythology”. By
contrast, from a Bungean point of view, that statement is true, and
it does not commit us to the claim that Pegasus exists in the real
world.
I have also answered a possible objection against the Bungean
proposal, which is the same objection that is usually raised against
Meinongians. The charge is that the use of an existence predicate
commits us to the claim that there are entities that do not exist.
Where are they located? In Meinong’s (or Bunge’s) jungle? I have
argued that Bungeans can meet this objection by arguing that fic-
tional objects exist conceptually, and that what this means is that
they are just brain processes. So, there is no otherworldly “jungle”
where fictional entities dwell.
Next, I addressed the problem of the ontological argument. The
acceptance of an existence predicate does not mean that the onto-
logical argument manages to prove that God exists. This argument
can be resisted by saying that God exists conceptually in the context
of some religions, in the same way that Pegasus exists conceptually
in the context of Greek mythology, but that neither of them exists
in the real world.
Lastly, I have indicated that the Bungean proposal is useful for
clarifying some aspects of the problem of material constitution. Spe-
cifically, the statements “Athena exists” and “Athena does not exist”
should not be formalized as ∃x(x = a) and ¬∃x(x = a), respectively.
This is because the former can’t fail to be true, while the latter leads
to a contradiction.
Acknowledgments
I would like to thank Daniel Z. Korman for his helpful comments on an
earlier version of this article.
References
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of the World. Dordrecht: D. Reidel Publishing.
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Martín Orensanz Difference Between the Existential Quantifier and the Existence Predicate
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Bunge, M. (2012). Evaluating Philosophies. Dordrecht: Springer.
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