CHAPTER 4

The Ontological Arguments

Graham Oppy
Professor of Philosophy
Monash University, Melbourne, Australia

Typically, when Australasian philosophers get together to sing, one of their first choices—to
the tune of the unofficial Australian national anthem, “Waltzing Matilda”—is “The Ballad
of St. Anselm”:
Once a jolly friar got himself an argument
And couldn’t get it out of his mind.
He thought he could prove the existence of the Deity
Because of the way that the words are defined.

Thus spake St. Anselm, thus spake St. Anselm,

Thus spake St. Anselm, who now is long dead,
And we’re awed as we read his proof so ontological;
Who can deny a word that he said?
If that than which nothing greater can be conceived
Can be conceived not to exist,
Then ’tis not that than which nothing greater can be conceived:
This is unquestionable, I insist.

For in that case a being greater can be conceived,

Whose major traits we can easily list:
Namely, that than which nothing greater can be conceived
And which cannot be conceived not to exist.

For if that than which nothing greater can be conceived

Has no existence outside of man’s mind,
Then ’tis not that than which nothing greater can be conceived,
Due to the way that the words are defined.

For in that case a greater can be conceived

(This is of course analytically true);
Namely, that than which nothing greater can be conceived
And which exists in reality too!
Thus spake St. Anselm, thus spake St. Anselm,
Thus spake St. Anselm with weighty intent,

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Chapter 4: The Ontological Arguments

And we’re awed as we read his proof so ontological

Would that we could understand just what it meant.

It is unlikely that any performance of this song—let alone any performance of it by

Australasian philosophers—will top the charts. This is only in part because the lyrics are not
entirely faithful to the ontological argument that St. Anselm devised.

WHAT ARE ONTOLOGICAL ARGUMENTS?

Ontological arguments are arguments for the existence of God. There are many different
kinds of ontological arguments, all of which have a conclusion that is taken to evidently and
immediately entail that God exists. In many cases the conclusion of an ontological argument is
just the claim that God exists. The logical rules that are supposed to justify the derivational
steps in ontological arguments—and the logical systems to which those logical rules belong—
are many and varied. Although the logical rules required for some ontological arguments are
relatively uncontroversial, there is serious dispute about the justification of the derivational
steps in other ontological arguments. The premises of ontological arguments—and the key
concepts or vocabulary employed in the framing of these premises—are also many and varied.
In almost all ontological arguments, at least one of the premises is highly controversial.
A traditional characterization of ontological arguments says that what these arguments
have in common is that they purport to be a priori demonstrations of the existence of God.
They are said to be a priori arguments because it is said that all of their premises can be
known to be true independently of experience and empirical evidence; they are said to be
demonstrations because it is said that their conclusions are logical consequences of their
premises. Some say that ontological arguments appeal only to definitions of God; others say
that ontological arguments appeal only to the concept or idea of God. Although it is
doubtful that much of the traditional characterization of ontological arguments is exactly
right, it will do for the purposes of this discussion.
Significant defenders of ontological arguments include: Saint Anselm (c. 1033–1109),
René Descartes (1596–1650), Gottfried Wilhelm Leibniz (1646–1716), Georg Wilhelm
Friedrich Hegel (1770–1831), Kurt Gödel (1906–1978), Charles Hartshorne (1897–
2000), and Alvin Plantinga (1932–). Important critics of ontological arguments include:
Gaunilo (fl. eleventh century), Thomas Aquinas (1225–1274), Immanuel Kant (1724–
1804), Gottlob Frege (1848–1925), Alexius Meinong (1853–1920), John Niemeyer
Findlay (1903–1987), J. L. Mackie (1917–1981), and Jordan Howard Sobel (1929–2010).
In this chaper, we shall examine: (1) Anselm’s ontological argument and its criticism by
Gaunilo; (2) Plantinga’s ontological argument and its criticism by Mackie and Sobel; and (3) a
simplified version of Gödel’s ontological argument. We shall also look carefully at (4) Kant’s
attempt to show that it is impossible for there to be a successful ontological argument. (For
more extensive survey and discussion of ontological arguments, see Oppy 1995, 2006.)

ANSELM’S ARGUMENT AND GAUNILO’S OBJECTION

Anselm of Canterbury, a Benedictine monk and Catholic theologian, set out his ontological
argument in Proslogion II. Here is one well-regarded translation of the text from the original
medieval Latin:

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Even the Fool, then, is forced to agree that something than which nothing greater
can be thought exists in the mind, since he understands this when he hears it, and
whatever is understood is in the mind. And surely that than which a greater cannot be
thought cannot exist in the mind alone. For if it exists solely in the mind even, it can
be thought to exist in reality also, which is greater. If then that than which a greater
cannot be thought exists in the mind alone, this same that than which a greater cannot
be thought is that than which a greater can be thought. But this is obviously
impossible. Therefore there is absolutely no doubt that something than which a greater
cannot be thought exists both in the mind and in reality. (1965, 117)
Although there are many challenges to the interpretation of the argument contained in this
text—and, indeed, many different arguments that have been read into this text—it is
plausible to reconstruct the argument along the following lines:
1. When the words “that than which no greater can be conceived” are heard, they are
understood. (Premise)
2. Whatever is understood exists in the understanding. (Premise)
3. (Therefore) That than which no greater can be conceived exists in the understanding.
(From 1, 2)
4. If that than which no greater can be conceived exists in the understanding alone, it can
be conceived to exist in reality. (Premise)
5. That than which no greater can be conceived is greater if it exists in reality than if it
exists in the understanding alone. (Premise)
6. (Therefore) If that than which no greater can be conceived exists in the understanding
alone, it is something than which a greater can be conceived. (From 4, 5)
7. It is impossible to conceive of something greater than that than which no greater can be
conceived. (Premise)
8. (Therefore) That than which no greater can be conceived does not exist in the
understanding alone. (From 6, 7)
9. (Therefore) That than which no greater can be conceived exists in reality. (From 3, 8)
The key vocabulary that is used in framing this argument raises many questions. What is it
for one thing to be “greater” than another? What is required for it to be true that
something “can be conceived”? What is meant by “the understanding”? What is it for
something to “exist in the understanding”? How is “existence in the understanding”
related to being something that “can be conceived”? Can the very same thing “exist in the
understanding” and “exist in reality”? If so, does it have the very same properties “in the
understanding” and “in reality”? Since we certainly appear to understand the expression
“the really existent tallest inhabitant of the planet Mars,” does Anselm think that the really
existent tallest inhabitant of the planet Mars exists in the understanding? If so, does he
think that, in the understanding, the really existent tallest inhabitant of the planet Mars
has the property of really existing? If so, does he think that it follows that the really
existent tallest inhabitant of the planet Mars has the property of really existing? Would
Anselm be uncomfortable with a priori commitment to the existence of Martians? Would
he deny that we understand the expression “the really existent tallest inhabitant of the
planet Mars”? Would he say that, even though, in the understanding, the really existent
tallest inhabitant of the planet Mars has the property of really existing, nonetheless it does
not follow that the really existent tallest inhabitant of the planet Mars has the property of
really existing?

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Some philosophers have thought that we do not need to answer all of these questions
before we come to the conclusion that Anselm’s ontological argument is unsuccessful. In
particular, some philosophers have thought that Anselm’s contemporary and fellow monk,
Gaunilo of Marmoutiers, provided a method for showing that there must be something wrong
with Anselm’s argument. Gaunilo’s strategy is to provide a parallel argument with premises
that are no less acceptable than the premises of Anselm’s original argument, but with the
absurd conclusion that there exists an island than which no greater island can be conceived:
1. When the words “that island than which no greater island can be conceived” are heard,
they are understood. (Premise)
2. Whatever is understood exists in the understanding. (Premise)
3. (Therefore) That island than which no greater island can be conceived exists in the
understanding. (From 1, 2)
4. If that island than which no greater island can be conceived exists in the understanding
alone, it can be conceived to exist in reality. (Premise)
5. That island than which no greater island can be conceived is greater if it exists in reality
than if it exists in the understanding alone. (Premise)
6. (Therefore) If that island than which no greater island can be conceived exists in the
understanding alone, it is an island than which a greater island can be conceived. (From 4, 5)
7. It is impossible to conceive of an island greater than that island than which no greater
island can be conceived. (Premise)
8. (Therefore) That island than which no greater island can be conceived does not exist in
the understanding alone. (From 6, 7)
9. (Therefore) That island than which no greater island can be conceived exists in reality.
(From 3, 8)
Because everyone agrees that the conclusion of Gaunilo’s argument is absurd, and because it
is obvious that the derivational moves in the two arguments are exactly the same, it is clear
that we can only defend Anselm’s original argument by defending the claim that, while one
of the premises in Anselm’s original argument is acceptable, the corresponding premise in
Gaunilo’s argument is not acceptable. Which premise might that be?
It seems obvious that the expressions “being than which no greater being can be
conceived” and “island than which no greater island can be conceived” are on a par: we can
be credited with understanding the one if and only if we can be credited with understanding
the other.
It seems obvious that the claim that if that being than which no greater being can be
conceived exists in the understanding alone it can be conceived to exist in reality stands or falls
with the claim that if that island than which no greater island can be conceived exists in the
understanding alone it can be conceived to exist in reality.
It seems no less obvious that that being than which no greater being can be conceived is
greater if it exists in reality than if it exists in the understanding alone if and only if that
island than which no greater island can be conceived is greater if it exists in reality than if it
exists in the understanding alone.
It seems equally obvious that it is impossible to conceive of a being greater than a being
than which no greater being can be conceived if and only if it is impossible to conceive of an
island greater than an island than which no greater island can be conceived.

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The only remaining premise—that whatever is understood exists in the understand-

ing—is shared in common between the two arguments. In this case, we can be absolutely
certain that the premise in Anselm’s argument is acceptable if and only if the corresponding
premise in Gaunilo’s argument is acceptable.
Given that there is no premise in Anselm’s original argument that is more acceptable
than the corresponding premise in Gaunilo’s argument, it seems that we are drawn to the
conclusion that there is something wrong with Anselm’s argument.
It is sometimes said that Gaunilo’s objection fails because there is—and can be—no
such thing as an island than which no greater island can be conceived. For example,
Plantinga says:
The idea of an island than which it is not possible that there be a greater is like the
idea of a natural number than which it is not possible that there be a greater, or the
idea of a line than which none more crooked is possible. There neither is nor could
be a greatest possible number, indeed, there isn’t a greatest actual number. And the
same goes for islands. No matter how great an island is, no matter how many Nubian
maidens and dancing girls adorn it, there could always be a greater—one with twice
as many, for example. The qualities that make for greatness in islands—number of
palm trees, amount and quality of coconuts, for example—have no intrinsic
maximum. That is, there is no degree of productivity or number of palm trees (or of
dancing girls) such that it is impossible that an island display more of that quality. So
the idea of a greatest possible island is an inconsistent or incoherent idea; it’s not
possible that there is such a being. (1974a, 90–91)
Note, however, that it is supposed to be uncontroversial that the words “that than which no
greater can be conceived” are understood. If we are going to enter into (controversial)
philosophical arguments about whether words are, in some technical sense, “coherent”—for
example, whether they refer to something that could possibly exist—then it is controversial
whether the words “that than which no greater can be conceived” are understood. There are
plenty of (controversial) philosophical arguments for the conclusion that the words “that
than which no greater can be conceived” are incoherent in relevant technical senses. It is, for
example, highly controversial whether the words “that than which no greater can be
conceived” refer to something that could possibly exist.
It is also worth noting that it is controversial whether considerations about an “intrinsic
maximum” suggest that there is a more serious worry about the “coherence” of the words
“that island than which no greater island can be conceived” than there is about the
“coherence” of the words “that being than which no greater being can be conceived.”
On one hand, greatness for islands involves trading off a whole lot of considerations,
including size, ecodiversity, population, and so forth. An island than which no greater can
be conceived will not be too large, nor too crowded with palm trees, nor too crowded with
people. That there is no intrinsic maximum to size, or number of palm trees, or population
provides no reason to suppose that we cannot coherently speculate about islands than which
no greater islands can be conceived.
On the other hand, if that than which no greater can be conceived is to hit intrinsic
maxima for every attribute that it has, then those intrinsic maxima must be possibly jointly
co-instantiated. But, for example, there is a serious question as to whether something can be
both maximally merciful and maximally just. Moreover, there are attributes that do not hit
intrinsic maxima that at least some philosophers want to ascribe to that than which no
greater can be conceived: for example, that it consists of three persons.

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It is perhaps also worth observing that, in an everyday sense, we do understand the

words “the greatest possible number”: we must first understand the words in order to be
able to see that there can be no such thing. Indeed, in this everyday sense, Anselm’s
argument requires that we understand the words “something greater than that than which
nothing greater can be conceived.” But, on that everyday understanding, it seems to follow
that premise 7 is just false, given premise 2: if we understand the words “something greater
than that than which nothing greater can be conceived,” it follows that there is in the
understanding “something greater than that than which nothing greater can be conceived.”
Although this seems to rule out the everyday sense of “understanding,” it also leaves
completely unclear how “understanding” and “conceivability” are to be understood in
Anselm’s argument.
As we have already observed, even if you are persuaded by Gaunilo’s objection, you
may well be uncertain exactly why Anselm’s argument fails. Is it because the argument is
invalid? Is it because the argument is question-begging? Is it because at least one of the
premises is plainly unacceptable (at least to neutral parties and those who already reject the
conclusion of the argument)? It is part of the lasting fascination of Anselm’s argument that
there is no agreed answer to these questions even among those who think that Gaunilo’s
objection shows that the argument is plainly unsuccessful.

PLANTINGA’S ARGUMENT

Plantinga’s (modal) ontological argument may be set out as follows:

Say that a being is unsurpassably great if and only if it is both necessarily existent and
necessarily maximally excellent (hence, in particular, necessarily omnipotent, necessarily
omniscient, and necessarily perfectly good). It follows from this definition of unsurpassable
greatness that there is a being that is unsurpassably great if and only if it is necessary that
there is a being that is unsurpassably great. We then argue as follows:
1. It is possible that there is a being that is unsurpassably great. (Premise)
2. (Therefore) It is possible that it is necessary that there is a being that is unsurpassably
great. (From 1)
3. (Therefore) It is necessary that there is a being that is unsurpassably great. (From 2)
4. (Therefore) There is a being that is unsurpassably great. (From 3)
The moves in this argument depend on some principles of modal logic, which is the study
of the logic of possibility and necessity. The move from (2) to (3) relies on the principle that
possibly necessarily p entails necessarily p. The move from (3) to (4) relies on the principle
that necessarily p entails p. And the move from (1) to (2) is justified by the observation that
there is a being that is unsurpassably great if and only if it is necessary that there is a being
that is unsurpassably great.
The principle that necessarily p entails p is obvious: if it must be the case that p, then, in
particular it is the case that p. The principle that possibly necessarily p entails necessarily p is
not so obvious; indeed, it is denied by some philosophers. Suppose that there is a domain of
possible worlds. Suppose that the claim that it is possible that p is true in a given world just
in case there is some possible world accessible from the given world in which it is true that p;
suppose that the claim that it is necessary that p is true in a given world just in case it is true

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that p in all worlds accessible from the given world; and suppose that every world is
accessible from every world (including from itself). If, in some world, it is true that it is
possible that it is necessary that p, then there is an accessible world in which it is necessary
that p. Because every world is accessible from the world in which it is necessary that p, it
follows that it is true that p in every world. Hence, it follows that it is true that it is necessary
that p in every world. So, in particular, in the world at which we started, it is necessary that
p. If it is possible that it is necessary that p, then it is necessary that p.
Perhaps the most obvious objection to Plantinga’s argument is motivated by
consideration of another argument. Note that it follows from the definition of an
unsurpassably great being that, if it is not the case that there is an unsurpassably great being,
then it is necessary that it is not the case that there is an unsurpassably great being.
1. It is possible that it is not the case that there is an unsurpassably great being. (Premise)
2. (Therefore) It is possible that it is necessary that it is not the case that there is an
unsurpassably great being. (From 1)
3. (Therefore) It is necessary that it is not the case that there is an unsurpassably great
being (From 2)
4. (Therefore) It is not the case that there is an unsurpassably great being. (From 3)
Note that the inferential moves in this argument are justified if and only if the
corresponding inferential moves in Plantinga’s are justified: we appeal to exactly the same
principle in each case.
If you accept the principles of modal logic that support the inferential moves in the
argument, and you agree with Plantinga that there is an unsurpassably great being, then you
will think that the first argument is sound; but if you accept the principles of modal logic
that support the inferential moves in the argument and you agree with those who deny that
there is an unsurpassably great being, then you will think that the second argument is
sound. Once we have both arguments before us, it is obvious that neither of these
arguments provides anyone with any reason to change their views about whether there is an
unsurpassably great being.
Plantinga agrees with this verdict. He acknowledges that, granted the modal logical
principles that are used to justify the inferential steps, judgments about the soundness of
these two arguments simply track prior judgments about the truth of the conclusions of
these two arguments. Nonetheless, Plantinga claims that the first argument is “victorious.”
In his view, the first argument establishes that it is reasonable to believe the claim that there
is an unsurpassably great being.
Suppose that you think that it is not reasonable to believe that there is an unsurpassably
great being. Given minimal rationality, and taking for granted the modal logical principles
that justify the inferential moves in the two arguments, when you consider the claim that it
is possible that there is an unsurpassably great being, you will recognize that, if it is not
reasonable to believe that there is an unsurpassably great being, then it is also not reasonable
to believe that it is possible that there is an unsurpassably great being. So, if you think that it
is not reasonable to believe that there is an unsurpassably great being, then, given minimal
rationality on your part, Plantinga’s “victorious” argument will give you no reason to revise
your belief that it is not reasonable to believe that there is an unsurpassably great being.
Suppose, instead, that you are undecided about whether it is reasonable to believe that
there is an unsurpassably great being. Given minimal rationality, and taking for granted the

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modal logical principles that justify the inferential moves in the two arguments, when you
consider the claim that it is possible that there is an unsurpassably great being, you will
recognize that, so long as you are undecided about whether it is reasonable to believe that
there is an unsurpassably great being, you ought also to be undecided about whether it is
reasonable to believe that it is possible that there is an unsurpassably great being. So, if you
are undecided about whether it is reasonable to believe that there is an unsurpassably great
being, then, given minimal rationality on your part, Plantinga’s “victorious” argument gives
you no reason to move away from your indecision about whether it is reasonable to believe
that there is an unsurpassably great being.
Perhaps you might think that, if you are initially confused—holding inconsistent beliefs
about the reasonableness of believing that there is an unsurpassably great being—then
Plantinga’s “victorious” argument gives you a reason to accept the claim that it is reasonable
to believe that there is an unsurpassably great being. But how could that be? Consider the
following set of arguments (from which intermediate steps of reasoning are omitted):
1.1 It is reasonable to believe that it is possible that there is an unsurpassably great being.
(Premise)
1.2 (Therefore) It is reasonable to believe that there is an unsurpassably great being. (From 1.1)
2.1 It is reasonable to believe that it is possible that there is no unsurpassably great being.
(Premise)
2.2 (Therefore) It is reasonable to believe that there is no unsurpassably great being. (From 2.1)
3.1 It is not reasonable to believe that it is possible that there is an unsurpassably great
being. (Premise)
3.2 (Therefore) It is not reasonable to believe that there is an unsurpassably great being.
(From 3.1)
4.1 It is not reasonable to believe that it is possible that there is no unsurpassably great
being. (Premise)
4.2 (Therefore) It is not reasonable to believe that there is no unsurpassably great being.
(From 4.1)
There is nothing in the six arguments that we now have before us that tells us how to resolve
inconsistency in our beliefs about whether it is reasonable to believe that there is an
unsurpassably great being. In particular, Plantinga’s “victorious” argument gives you no
guidance at all about how you should resolve the inconsistency in your beliefs about
whether it is reasonable to believe that there is an unsurpassably great being. Whichever way
you revise your beliefs, some of these arguments will come out sound, and others will come
out unsound. In themselves, these arguments simply give you no guidance at all about how
to revise your beliefs.

A SIMPLE HIGHER-ORDER ARGUMENT

Gödel’s ontological argument develops some ideas originally due to Leibniz. In what
follows, I present a simplified version of Gödel’s argument. Although it is simplified, it is
still quite challenging. I begin with some definitions.
An object has a property essentially if and only if it is impossible for that object to exist
and yet to lack that property. (I could lose all of my hair. So the property of being hairy is

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not one of my essential properties. On the other hand, I could not exist and yet be
something other than human. So the property of being human is one of my essential
properties.)
A collection of properties entails a further property if and only if, necessarily, anything that
has all of the properties in the collection also has the further property. (Necessarily, anything that
has the following four properties—being a plane figure, being closed, having three rectilinear
sides, and having equal internal angles—has the further property of being an equilateral triangle.
So the collection of properties—being a plane figure, being closed, having three rectilinear sides,
having equal internal angles—entails the property of being an equilateral triangle.)
A collection of properties is closed under entailment if and only if any property that is
entailed by a subset of the properties in the set of properties also belongs to the set of
properties. (For any existing object, the set of its essential properties is closed under
entailment. Suppose that a property P is entailed by an object’s essential properties. Because
the property P is entailed by the object’s essential properties, it is impossible for the object to
exist without having the property P. But that’s just to say that the property P is one of the
object’s essential properties.)
A property P is a God-property if and only if P is one of the properties that God has
essentially if God exists. (That is, a property P is a God-property if and only if, necessarily, if
God exists, God has property P.)
The core of our simple higher-order ontological argument is the following:
1. There are properties that are not God-properties. (Premise)
2. The God-properties are closed under entailment. (Premise)
3. (Therefore) It is possible that there is something that has all of the God-properties.
(From 1, 2)
In order to argue that (3) follows from (1) and (2), we rely on the principle that, for any p and q,
the claim necessarily, if p then q is true if it is impossible that p. This principle is one of the
“paradoxes” of classical logic. In classical logic, a sentence of the form if p then q is only false if p is
true and q is false; otherwise, it is true. So, if it is impossible for p to be true, then it is impossible for
if p then q to be false. Which is just to say that it is necessary that if p then q is true.
We then argue that (3) follows from (1) and (2) as follows. Suppose (for reductio) that it
is not possible that there is something that has all of the God-properties. By our first
premise, there are properties that are not God-properties. Arbitrarily select one of them: the
property P. Because it is not possible that there is something that has all of the God-
properties, it follows by the principle noted above that, necessarily, anything that has all of
the God-properties has property P. But that is just to say that the God-properties entail
property P. So, by our second premise, property P is one of the God-properties. But that
means that property P both is and is not one of the God-properties. Contradiction! We
conclude (by reductio) that our initial supposition is false: it is possible that there is
something that has all of the God-properties.
It seems plausible to suppose that there are properties that are not God-properties.
Consider the property of being ignorant about almost everything. Surely, if God exists, that
is not one of God’s properties.
It seems plausible that the God-properties are closed under entailment. After all, as we
noted earlier, for any existing object, the collection of its essential properties is closed under

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entailment. Clearly, if God exists, the God-properties—those properties that God has
essentially if God exists—are closed under entailment.
So, it seems we have very good reason to accept that it is possible that there is
something that has all of the God-properties. But now let’s ask, what properties number
among the God-properties, that is, among the properties that God has essentially if God
exists? Many theists say that the properties that God has essentially if God exists include
necessary existence. Suppose that those theists are right. Then we can argue as follows:
1. It is possible that there is something that has all of the God-properties.
2. The God-properties include necessary existence.
3. (Therefore) There is something that has all of the God-properties. (From 1, 2)
4. (Therefore) God exists. (From 3)
To justify the move from (1) and (2) to (3), we observe that, given (2), (1) says that it is
possible that there is something that is necessarily existent. Because it is possible that there is
this necessarily existent thing, it follows—by the modal principles that we introduced in our
discussion of Plantinga’s modal ontological argument—that this thing actually exists. The
justification of the move from (3) to (4) is straightforward: the thing that we have just been
discussing has every one of the properties that God has essentially if God exists; so, of
course, it is God.
How might one object to this simplified higher-order ontological argument?
If we are supposing that, were God to exist, God would be necessarily existent, then, of
course, those who deny that God exists also deny that it is possible that God exists. So, by the
lights of those who deny that God exists, it follows that every sentence of the form necessarily, if
God exists, God has property P is (trivially) true. But that’s just the denial of the claim that there
are properties that are not God-properties. Holding fixed the claims that the God-properties are
closed under entailment and that necessary existence is one of the God-properties, there are
properties that are not God-properties, if and only if it is possible that God exists.
Perhaps proponents of the argument might think to reply that we ought to understand
the conditional that occurs in the definition of God-property in a way that means that it is
not trivialized if the antecedent of that conditional is impossible. After all, there are ways of
understanding conditionals on which claims of the form if God exists, God has property P
essentially do not come out trivially true if it is impossible that God exists. So why not adopt
one of those ways of understanding conditionals?
Short answer: because, as we noted way back, the derivation at the core of our simple
higher-order ontological argument depends on the claim that conditionals with impossible
antecedents are trivially true. In order to derive the claim that it is possible that there is
something that has all of the God-properties from the claim that there are properties that are
not God-properties and the claim that the God-properties are closed under entailment, we
need to suppose that conditionals with impossible antecedents are trivially true. Given that
we make this supposition, we are obliged to accept that conditionals of the form if God
exists, God has property P essentially are trivially true if it is impossible that God exists.
The upshot of our examination of our simple higher-order ontological argument is
clear. Those who suppose that God necessarily exists will suppose that the argument is
sound; but those who deny that it is possible that God exists will suppose that the argument
is unsound. Moreover, holding fixed commitment to the claim that the God-properties are
closed under entailment, those who suppose that God necessarily exists will suppose that

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there are properties that are not God-properties, while those who deny that it is possible that
God exists will suppose that all properties are God-properties. Because the argument
contains as a premise the claim that there are properties that are not God-properties, the
argument is powerless to decide between that claim and its denial. Consequently, the
argument provides no assistance in deciding between worldviews according to which God
necessarily exists and worldviews according to which it is not possible that God exists.

KANT’S ARGUMENT

In the Critique of Pure Reason (in the Transcendental Doctrine of Elements, Second Division,
Book II, Chapter II, Section IV), Kant argues for the impossibility of an ontological proof of
the existence of God. The only ontological argument that Kant actually mentions is that
of Descartes, but there is no textual citation. So it is not entirely clear which version of
Descartes’s argument—Discourse, Meditations, or Replies—Kant has in mind. As the
discussion in the Discourse is a good fit, we will run with that.
In the Discourse, Descartes writes as follows: “Existence is comprised in the idea [of a perfect
being] in the same way that the equality of the three angles of a triangle to two right angles is
comprised in the idea of a triangle.… Consequently, it is at least as certain that God … exists as
any geometric demonstration can be” (1985, 57). In what looks like a direct response to this
passage, Kant writes:
To posit a triangle, and yet to reject its three angles, is self-contradictory; but there is
no contradiction in rejecting the triangle together with its three angles. The same
holds true of the concept of an absolutely necessary being. If the existence is rejected,
we reject the thing itself with all its predicates; and no question of contradiction can
then arise. (1998, 502)
The relevant geometrical proposition is that, in all triangles, the internal angles sum to 180
degrees. The necessary truth of this proposition does not require the existence of even one
triangle. By analogy, the relevant theological proposition is that all perfect beings exist. The
necessary truth of this proposition does not require the existence of even one perfect being.
If it is said that God is a perfect being—and so exists—then the obvious question to ask
is whether those who deny that there are any perfect beings should accept the claim that
God is a perfect being. If we agree that the claim that God is a perfect being entails the claim
that there are perfect beings, then it is clear that those who deny that there are any perfect
beings should deny that God is a perfect being. By their lights, the most that is true is that,
according to some theists, God is a perfect being. But there is no legitimate way to move
from the premise that, according to some theists, God is a perfect being, to the conclusion
that God is a perfect being (and still less to the conclusion that God exists).
Consider the claim that Santa Claus lives at the North Pole. Is that true? Surely not. If Santa
Claus lives at the North Pole, then there is someone who lives at the North Pole. But we all know
that there is not anyone living at the North Pole. The most that is true is that, according to the
well-known story, Santa Claus lives at the North Pole. And, plainly enough, there is no legitimate
way to move from the premise that, according to the well-known story, Santa Claus lives at the
North Pole, to the conclusion that there is someone who lives at the North Pole.
If you have a residual urge to insist that it is true that Santa Claus lives at the North
Pole, consider the following case. The idea of existence is comprised in the idea of an

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existent Martian. I introduce the name “Rod” for the

oldest existent Martian. Now, consider the claim that
Rod is an oldest existent Martian. Is this claim true?
Surely not. If Rod is an oldest existent Martian, then
there are existent Martians, that is, there really
are Martians. But it is not true that there really are
Martians. Even if you do suppose that there
are Martians, you should surely deny that you can
prove that there are Martians by consideration of the
claim that Rod is an oldest existent Martian.
In response to this kind of objection, Descartes
says that the concept of an existent Martian differs
from the concept of a perfect being because the former
concept is artificial whereas the latter concept is
natural. But this consideration is irrelevant. That all
existent Martians exist is no less a necessary truth than
that all perfect beings exist. If it is fine to infer that
God exists from the claim that God is a perfect being,
then it is fine to infer that Rod exists from the claim
that Rod is an oldest existent Martian.
Kant’s ambition extends much further than
criticism of Descartes’s arguments. He aims to show
that it is impossible for there to be a successful
ontological argument. Famously, he writes: “‘Being’ is
Immanuel Kant (1724–1804). SPUTNIK/ALAMY STOCK obviously not a real predicate, that is, it is not a concept
PHOTO. of something which could be added to the concept of a
thing.… If … we … say ‘God is’ or ‘There is a God,’ …
we … merely posit the subject [God] … as being an
object that stands in relation to my concept” (1998, 567). According to Kant, ontological
arguments all fail because they depend on the false assumption that “being” is a real predicate.
One obvious question to ask Kant is, If we say “Santa Claus is not” or “There is no Santa
Claus,” what are we doing? We need to be able to mark the salient ontological distinction
between Barack Obama and Santa Claus: Barack Obama exists whereas Santa Claus does not.
If my saying that Barack Obama exists is merely my positing Barack Obama as an object that
stands in relation to my concept, then what is my saying that Santa Claus does not exist?
Clearly, I am not positing the subject (Santa Claus) as an object that fails to stand in relation
to my concept: I am not saying that there is a Santa Claus that fails to be suitably related to my
concept of him. Equally clearly, I am not merely failing to posit the subject Santa Claus as an
object that stands in relation to my concept: in saying that Santa Claus does not exist, there is
something that I am doing, not merely something that I am failing to do. So what are we
doing when we say that Santa Claus does not exist?
Kant can hardly deny that we have a Santa Claus concept. When we compare our Santa
Claus concept with our Barack Obama concept, it seems entirely natural to say that one
difference between them is that only the Barack Obama concept contains existence. Of
course, because the Santa Claus story does not say that Santa Claus is a nonexistent object that
lives at the North Pole, there is a part or aspect of our Santa Claus concept—reflecting the

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content of the story—that does “contain existence”; but there is another part or aspect of
our Santa Claus concept—reflecting the ontological reality about Santa Claus—that
“contains nonexistence.” It seems to be part of our Santa Claus concept that there is no
Santa Claus: your understanding of Santa Claus is seriously incomplete if you do not
understand that the Santa Claus story is just a story.
While there is much more to say about Kant’s claim that “being” is not a real predicate, I do
not think that he manages to make out the case. But, if he does not make out the case that “being”
is not a real predicate, then it cannot be true that he has shown that ontological arguments fail
because “being” is not a real predicate. Moreover, even if he had managed to show that “being” is
not a real predicate, it is not clear that that would provide us with a forceful objection to the
ontological arguments that we considered earlier: where, exactly, would this critique strike against
the arguments of Anselm, Plantinga and Gödel? And, in any case, who is to say what other—
hitherto unconsidered—forms of ontological arguments might emerge in the future?

Summary
Although philosophers have been discussing ontological arguments for nearly 1,000 years,
there is no expert agreement on the general standing of ontological arguments. Throughout
that history, some of the best and smartest philosophers have supposed that particular
ontological arguments successfully prove the existence of God, while others have maintained
that it is obvious that no ontological arguments can be successful.
In this discussion, I have charted a middle path. On one hand, I have urged that none
of the ontological arguments considered here—Anselm’s Proslogion II argument, Plantinga’s
“victorious” modal argument, and our simplified version of Gödel’s argument—is
successful. On the other hand, I have emphasized (a) that we have only examined some
among the many extant ontological arguments; (b) that it is very likely that there will be
new and challenging ontological arguments devised in the future; and (c) that extant
arguments for the claim that there could not be a successful ontological argument are no
more successful than the ontological arguments that we have examined here.
My discussion of the arguments of Anselm, Plantinga, and (simplified) Gödel illustrates
some of the main strategies taken up by critics of ontological arguments. Against Anselm, it
was suggested that there are parallel arguments with absurd conclusions whose credentials
are on a par with those of the Proslogion II argument. Against Plantinga, it was observed that
there are parallel arguments with exactly opposed conclusions whose credentials are on a par
with those of the “victorious” modal argument. Against (simplified) Gödel, it was claimed
that the core of the argument depends on a principle whose acceptance provides a defeater
for the first premise of the argument. In the face of an ontological argument, it is often
illuminating to think about parallel arguments with absurd conclusions, parallel arguments
with exactly opposed conclusions, and possible ways in which the argument might be self-
defeating. Of course, there are ontological arguments that are obviously invalid, and there
are ontological arguments that are obviously unsound. But interesting ontological
arguments—including those considered in this chapter—typically do not have readily
pinpointed features in virtue of which they are invalid or unsound.
My discussion of Kant illustrates some of the main strategies taken up by critics of those
who purport to be able to prove that there cannot be a successful ontological argument. In

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the face of such a purported demonstration, it is often illuminating to consider the

implications of that demonstration for what we can say about fictional objects and things
that we agree do not exist. If a purported demonstration that there cannot be a successful
ontological argument has the consequence that it is unproblematically and straightforwardly
true that Santa Claus lives at the North Pole, then there is good reason to doubt that the
purported demonstration succeeds.
Ontological arguments have challenged and entertained philosophers for centuries.
Even if you have not been awed as you have read about these “proofs so ontological,” I hope
that you have gained some understanding of just what they mean.

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