all-perfect God is the ontological argument. While there are several
different versions of the argument, all purport to show that it is
self-contradictory to deny that there exists a greatest possible
being. Thus, on this general line of argument, it is a necessary truth
that such a being exists; and this being is the God of traditional
Western theism. This article explains and evaluates classic and
contemporary versions of the ontological argument.
1. Introduction: The Non-Empirical Nature of the Ontological Arguments
Most of the arguments for God's existence rely on at least one
empirical premise. For example, the "fine-tuning" version of the
design argument depends on empirical evidence of intelligent design;
in particular, it turns on the empirical claim that, as a nomological
matter, that is, as a matter of law, life could not have developed if
certain fundamental properties of the universe were to have differed
even slightly from what they are. Likewise, cosmological arguments
depend on certain empirical claims about the explanation for the
occurrence of empirical events.
In contrast, the ontological arguments are conceptual in roughly the
following sense: just as the propositions constituting the concept of
a bachelor imply that every bachelor is male, the propositions
constituting the concept of God, according to the ontological
argument, imply that God exists. There is, of course, this difference:
whereas the concept of a bachelor explicitly contains the proposition
that bachelors are unmarried, the concept of God does not explicitly
contain any proposition asserting the existence of such a being. Even
so, the basic idea is the same: ontological arguments attempt to show
that we can deduce God's existence from, so to speak, the very
definition of God.
It is worth reflecting for a moment on what a remarkable (and
beautiful!) undertaking this is. Normally, existential claims don't
follow from conceptual claims. If I want to prove that bachelors,
unicorns, or viruses exist, it is not enough just to reflect on the
concepts. I need to go out into the world and conduct some sort of
empirical investigation using my senses. Likewise, if I want to prove
that bachelors, unicorns, or viruses don't exist, I must do the same.
In general, positive and negative existential claims can be
established only by empirical methods.
There is, however, one class of exceptions. We can prove certain
negative existential claims merely by reflecting on the content of the
concept. Thus, for example, we can determine that there are no square
circles in the world without going out and looking under every rock to
see whether there is a square circle there. We can do so merely by
consulting the definition and seeing that it is self-contradictory.
Thus, the very concepts imply that there exist no entities that are
both square and circular.
The ontological argument, then, is unique among such arguments in that
it purports to establish the real (as opposed to abstract) existence
of some entity. Indeed, if the ontological arguments succeed, it is as
much a contradiction to suppose that God doesn't exist as it is to
suppose that there are square circles or female bachelors. In the
following sections, we will evaluate a number of different attempts to
develop this astonishing strategy.
2. The Classic Version of the Ontological Argument
a. The Argument Described
St. Anselm, Archbishop of Cantebury (1033-1109), is the originator of
the ontological argument, which he describes in the Proslogium as
follows:
[Even a] fool, when he hears of … a being than which nothing greater
can be conceived … understands what he hears, and what he understands
is in his understanding.… And assuredly that, than which nothing
greater can be conceived, cannot exist in the understanding alone. For
suppose it exists in the understanding alone: then it can be conceived
to exist in reality; which is greater.… Therefore, if that, than which
nothing greater can be conceived, exists in the understanding alone,
the very being, than which nothing greater can be conceived, is one,
than which a greater can be conceived. But obviously this is
impossible. Hence, there is no doubt that there exists a being, than
which nothing greater can be conceived, and it exists both in the
understanding and in reality.
The argument in this difficult passage can accurately be summarized in
standard form:
It is a conceptual truth (or, so to speak, true by definition) that
God is a being than which none greater can be imagined (that is, the
greatest possible being that can be imagined).
God exists as an idea in the mind.
A being that exists as an idea in the mind and in reality is, other
things being equal, greater than a being that exists only as an idea
in the mind.
Thus, if God exists only as an idea in the mind, then we can imagine
something that is greater than God (that is, a greatest possible being
that does exist).
But we cannot imagine something that is greater than God (for it is a
contradiction to suppose that we can imagine a being greater than the
greatest possible being that can be imagined.)
Therefore, God exists.
Intuitively, one can think of the argument as being powered by two
ideas. The first, expressed by Premise 2, is that we have a coherent
idea of a being that instantiates all of the perfections. Otherwise
put, Premise 2 asserts that we have a coherent idea of a being that
instantiates every property that makes a being greater, other things
being equal, than it would have been without that property (such
properties are also known as "great-making" properties). Premise 3
asserts that existence is a perfection or great-making property.
Accordingly, the very concept of a being that instantiates all the
perfections implies that it exists. Suppose B is a being that
instantiates all the perfections and suppose B doesn't exist (in
reality). Since Premise 3 asserts that existence is a perfection, it
follows that B lacks a perfection. But this contradicts the assumption
that B is a being that instantiates all the perfections. Thus,
according to this reasoning, it follows that B exists.
b. Gaunilo's Criticism
Gaunilo of Marmoutier, a monk and contemporary of Anselm's, is
responsible for one of the most important criticisms of Anselm's
argument. It is quite reasonable to worry that Anselm's argument
illegitimately moves from the existence of an idea to the existence of
a thing that corresponds to the idea. As the objection is sometimes
put, Anselm simply defines things into existence-and this cannot be
done.
Gaunilo shared this worry, believing that one could use Anselm's
argument to show the existence of all kinds of non-existent things:
Now if some one should tell me that there is … an island [than which
none greater can be conceived], I should easily understand his words,
in which there is no difficulty. But suppose that he went on to say,
as if by a logical inference: "You can no longer doubt that this
island which is more excellent than all lands exists somewhere, since
you have no doubt that it is in your understanding. And since it is
more excellent not to be in the understanding alone, but to exist both
in the understanding and in reality, for this reason it must exist.
For if it does not exist, any land which really exists will be more
excellent than it; and so the island understood by you to be more
excellent will not be more excellent."
Gaunilo's argument, thus, proceeds by attempting to use Anselm's
strategy to deduce the existence of a perfect island, which Gaunilo
rightly views as a counterexample to the argument form. The
counterexample can be expressed as follows:
It is a conceptual truth that a piland is an island than which none
greater can be imagined (that is, the greatest possible island that
can be imagined).
A piland exists as an idea in the mind.
A piland that exists as an idea in the mind and in reality is greater
than a piland that exists only as an idea in the mind.
Thus, if a piland exists only as an idea in the mind, then we can
imagine an island that is greater than a piland (that is, a greatest
possible island that does exist).
But we cannot imagine an island that is greater than a piland.
Therefore, a piland exists.
Notice, however, that premise 1 of Gaunilo's argument is incoherent.
The problem here is that the qualities that make an island great are
not the sort of qualities that admit of conceptually maximal
qualities. No matter how great any island is in some respect, it is
always possible to imagine an island greater than that island in that
very respect. For example, if one thinks that abundant fruit is a
great-making property for an island, then, no matter how great a
particular island might be, it will always be possible to imagine a
greater island because there is no intrinsic maximum for
fruit-abundance. For this reason, the very concept of a piland is
incoherent.
But this is not true of the concept of God as Anselm conceives it.
Properties like knowledge, power, and moral goodness, which comprise
the concept of a maximally great being, do have intrinsic maximums.
For example, perfect knowledge requires knowing all and only true
propositions; it is conceptually impossible to know more than this.
Likewise, perfect power means being able to do everything that it is
possible to do; it is conceptually impossible for a being to be able
to do more than this.
The general point here, then, is this: Anselm's argument works, if at
all, only for concepts that are entirely defined in terms of
properties that admit of some sort of intrinsic maximum. As C.D. Broad
puts this important point:
[The notion of a greatest possible being imaginable assumes that] each
positive property is to be present in the highest possible degree. Now
this will be meaningless verbiage unless there is some intrinsic
maximum or upper limit to the possible intensity of every positive
property which is capable of degrees. With some magnitudes this
condition is fulfilled. It is, e.g., logically impossible that any
proper fraction should exceed the ratio 1/1; and again, on a certain
definition of "angle," it is logically impossible for any angle to
exceed four right angles. But it seems quite clear that there are
other properties, such as length or temperature or pain, to which
there is no intrinsic maximum or upper limit of degree.
If any of the properties that are conceptually essential to the notion
of God do not admit of an intrinsic maximum, then Anselm's argument
strategy will not work because, like Guanilo's concept of a piland,
the relevant concept of God is incoherent. But insofar as the relevant
great-making properties are limited to omnipotence, omniscience, and
moral perfection (which do admit of intrinsic maximums), Anselm's
notion of a greatest possible being seems to avoid the worry expressed
by Broad and Guanilo.
c. Aquinas's Criticisms
While St. Thomas Aquinas (1224-1274) believed that God's existence is
self-evident, he rejected the idea that it can be deduced from claims
about the concept of God. Aquinas argued, plausibly enough, that "not
everyone who hears this word 'God' understands it to signify something
than which nothing greater can be thought, seeing that some have
believed God to be a body." The idea here is that, since different
people have different concepts of God, this argument works, if at all,
only to convince those who define the notion of God in the same way.
The problem with this criticism is that the ontological argument can
be restated without defining God. To see this, simply delete premise 1
and replace each instance of "God" with "A being than which none
greater can be conceived." The conclusion, then, will be that a being
than which none greater can be conceived exists – and it is, of
course, quite natural to name this being God.
Nevertheless, Aquinas had a second problem with the ontological
argument. On Aquinas's view, even if we assume that everyone shares
the same concept of God as a being than which none greater can be
imagined, "it does not therefore follow that he understands what the
word signifies exists actually, but only that it exists mentally."
One natural interpretation of this somewhat ambiguous passage is that
Aquinas is rejecting premise 2 of Anselm's argument on the ground
that, while we can rehearse the words "a being than which none greater
can be imagined" in our minds, we have no idea of what this sequence
of words really means. On this view, God is unlike any other reality
known to us; while we can easily understand concepts of finite things,
the concept of an infinitely great being dwarfs finite human
understanding. We can, of course, try to associate the phrase "a being
than which none greater can be imagined" with more familiar finite
concepts, but these finite concepts are so far from being an adequate
description of God, that it is fair to say they don't help us to get a
detailed idea of God.
Nevertheless, the success of the argument doesn't depend on our having
a complete understanding of the concept of a being than which none
greater can be conceived. Consider, for example, that, while we don't
have a complete understanding (whatever this means) of the concept of
a natural number than which none larger can be imagined, we understand
it well enough to see that there does not exist such a number. No more
complete understanding of the concept of a maximally great being than
this is required, on Anselm's view, to successfully make the argument.
If the concept is coherent, then even a minimal understanding of the
concept is sufficient to make the argument.
d. Kant's Criticism: Is Existence a Perfection?
Immanuel Kant (1724-1804) directs his famous objection at premise 3's
claim that a being that exists as an idea in the mind and in reality
is greater than a being that exists only as an idea in the mind.
According to premise 3, existence is what's known as a great-making
property or, as the matter is sometimes put, a perfection. Premise 3
thus entails that (1) existence is a property; and (2) instantiating
existence makes a thing better, other things being equal, than it
would have been otherwise.
Kant rejects premise 3 on the ground that, as a purely formal matter,
existence does not function as a predicate. As Kant puts the point:
Being is evidently not a real predicate, that is, a conception of
something which is added to the conception of some other thing. It is
merely the positing of a thing, or of certain determinations in it.
Logically, it is merely the copula of a judgement. The proposition,
God is omnipotent, contains two conceptions, which have a certain
object or content; the word is, is no additional predicate-it merely
indicates the relation of the predicate to the subject. Now if I take
the subject (God) with all its predicates (omnipotence being one), and
say, God is, or There is a God, I add no new predicate to the
conception of God, I merely posit or affirm the existence of the
subject with all its predicates – I posit the object in relation to my
conception.
Accordingly, what goes wrong with the first version of the ontological
argument is that the notion of existence is being treated as the wrong
logical type. Concepts, as a logical matter, are defined entirely in
terms of logical predicates. Since existence isn't a logical
predicate, it doesn't belong to the concept of God; it rather affirms
that the existence of something that satisfies the predicates defining
the concept of God.
While Kant's criticism is phrased (somewhat obscurely) in terms of the
logic of predicates and copulas, it also makes a plausible
metaphysical point. Existence is not a property (in, say, the way that
being red is a property of an apple). Rather it is a precondition for
the instantiation of properties in the following sense: it is not
possible for a non-existent thing to instantiate any properties
because there is nothing to which, so to speak, a property can stick.
Nothing has no qualities whatsoever. To say that x instantiates a
property P is hence to presuppose that x exists. Thus, on this line of
reasoning, existence isn't a great-making property because it is not a
property at all; it is rather a metaphysically necessary condition for
the instantiation of any properties.
But even if we concede that existence is a property, it does not seem
to be the sort of property that makes something better for having it.
Norman Malcolm expresses the argument as follows:
The doctrine that existence is a perfection is remarkably queer. It
makes sense and is true to say that my future house will be a better
one if it is insulated than if it is not insulated; but what could it
mean to say that it will be a better house if it exists than if it
does not? My future child will be a better man if he is honest than if
he is not; but who would understand the saying that he will be a
better man if he exists than if he does not? Or who understands the
saying that if God exists He is more perfect than if he does not
exist? One might say, with some intelligibility, that it would be
better (for oneself or for mankind) if God exists than if He does
not-but that is a different matter.
The idea here is that existence is very different from, say, the
property of lovingness. A being that is loving is, other things being
equal, better or greater than a being that is not. But it seems very
strange to think that a loving being that exists is, other things
being equal, better or greater than a loving being that doesn't exist.
But to the extent that existence doesn't add to the greatness of a
thing, the classic version of the ontological argument fails.
3. Anselm's Second Version of the Ontological Argument
As it turns out, there are two different versions of the ontological
argument in the Prosologium. The second version does not rely on the
highly problematic claim that existence is a property and hence avoids
many of the objections to the classic version. Here is the second
version of the ontological argument as Anselm states it:
God is that, than which nothing greater can be conceived.… And [God]
assuredly exists so truly, that it cannot be conceived not to exist.
For, it is possible to conceive of a being which cannot be conceived
not to exist; and this is greater than one which can be conceived not
to exist. Hence, if that, than which nothing greater can be conceived,
can be conceived not to exist, it is not that, than which nothing
greater can be conceived. But this is an irreconcilable contradiction.
There is, then, so truly a being than which nothing greater can be
conceived to exist, that it cannot even be conceived not to exist; and
this being thou art, O Lord, our God.
This version of the argument relies on two important claims. As
before, the argument includes a premise asserting that God is a being
than which a greater cannot be conceived. But this version of the
argument, unlike the first, does not rely on the claim that existence
is a perfection; instead it relies on the claim that necessary
existence is a perfection. This latter claim asserts that a being
whose existence is necessary is greater than a being whose existence
is not necessary. Otherwise put, then, the second key claim is that a
being whose non-existence is logically impossible is greater than a
being whose non-existence is logically possible.
More formally, the argument is this:
By definition, God is a being than which none greater can be imagined.
A being that necessarily exists in reality is greater than a being
that does not necessarily exist.
Thus, by definition, if God exists as an idea in the mind but does not
necessarily exist in reality, then we can imagine something that is
greater than God.
But we cannot imagine something that is greater than God.
Thus, if God exists in the mind as an idea, then God necessarily
exists in reality.
God exists in the mind as an idea.
Therefore, God necessarily exists in reality.
This second version appears to be less vulnerable to Kantian
criticisms than the first. To begin with, necessary existence, unlike
mere existence, seems clearly to be a property. Notice, for example,
that the claim that x necessarily exists entails a number of claims
that attribute particular properties to x. For example, if x
necessarily exists, then its existence does not depend on the
existence of any being (unlike contingent human beings whose existence
depends, at the very least, on the existence of their parents). And
this seems to entail that x has the reason for its existence in its
own nature. But these latter claims clearly attribute particular
properties to x.
And only a claim that attributes a particular property can entail
claims that attribute particular properties. While the claim that x
exists clearly entails that x has at least one property, this does not
help. We cannot soundly infer any claims that attribute particular
properties to x from either the claim that x exists or the claim that
x has at least one property; indeed, the claim that x has at least one
property no more expresses a particular property than the claim that x
exists. This distinguishes the claim that x exists from the claim that
x necessarily exists and hence seems to imply that the latter, and
only the latter, expresses a property.
Moreover, one can plausibly argue that necessary existence is a
great-making property. To say that a being necessarily exists is to
say that it exists eternally in every logically possible world; such a
being is not just, so to speak, indestructible in this world, but
indestructible in every logically possible world – and this does seem,
at first blush, to be a great-making property. As Malcolm puts the
point:
If a housewife has a set of extremely fragile dishes, then as dishes,
they are inferior to those of another set like them in all respects
except that they are not fragile. Those of the first set are dependent
for their continued existence on gentle handling; those of the second
set are not. There is a definite connection between the notions of
dependency and inferiority, and independence and superiority. To say
that something which was dependent on nothing whatever was superior to
anything that was dependent on any way upon anything is quite in
keeping with the everyday use of the terms superior and greater.
Nevertheless, the matter is not so clear as Malcolm believes. It might
be the case that, other things being equal, a set of dishes that is
indestructible in this world is greater than a set of dishes that is
not indestructible in this world. But it is very hard to see how
transworld indestructibility adds anything to the greatness of a set
of dishes that is indestructible in this world. From our perspective,
there is simply nothing to be gained by adding transworld
indestructibility to a set of dishes that is actually indestructible.
There is simply nothing that a set of dishes that is indestructible in
every possible world can do in this world that can't be done by a set
of dishes that is indestructible in this world but not in every other
world.
And the same seems to be true of God. Suppose that an omniscient,
omnipotent, omnibenevolent, eternal (and hence, so to speak,
indestructible), personal God exists in this world but not in some
other worlds. It is very hard to make sense of the claim that such a
God is deficient in some relevant respect. God's indestructibility in
this world means that God exists eternally in all logically possible
worlds that resemble this one in certain salient respects. It is
simply unclear how existence in these other worlds that bear no
resemblance to this one would make God greater and hence more worthy
of worship. From our perspective, necessary existence adds nothing in
value to eternal existence. If this is correct, then Anselm's second
version of the argument also fails.
4. Modal Versions of the Argument
Even if, however, we assume that Anselm's second version of the
argument can be defended against such objections, there is a further
problem: it isn't very convincing because it is so difficult to tell
whether the argument is sound. Thus, the most important contemporary
defender of the argument, Alvin Plantinga, complains "[a]t first
sight, Anselm's argument is remarkably unconvincing if not downright
irritating; it looks too much like a parlor puzzle or word magic." As
a result, despite its enduring importance, the ontological argument
has brought few people to theism.
There have been several attempts to render the persuasive force of the
ontological argument more transparent by recasting it using the
logical structures of contemporary modal logic. One influential
attempts to ground the ontological argument in the notion of God as an
unlimited being. As Malcolm describes this idea:
God is usually conceived of as an unlimited being. He is conceived of
as a being who could not be limited, that is, as an absolutely
unlimited being.… If God is conceived to be an absolutely unlimited
being He must be conceived to be unlimited in regard to His existence
as well as His operation. In this conception it will not make sense to
say that He depends on anything for coming into or continuing in
existence. Nor, as Spinoza observed, will it make sense to say that
something could prevent Him from existing. Lack of moisture can
prevent trees from existing in a certain region of the earth. But it
would be contrary to the concept of God as an unlimited being to
suppose that anything … could prevent Him from existing.
The unlimited character of God, then, entails that his existence is
different from ours in this respect: while our existence depends
causally on the existence of other beings (e.g., our parents), God's
existence does not depend causally on the existence of any other
being.
Further, on Malcolm's view, the existence of an unlimited being is
either logically necessary or logically impossible. Here is his
argument for this important claim. Either an unlimited being exists at
world W or it doesn't exist at world W; there are no other
possibilities. If an unlimited being does not exist in W, then its
nonexistence cannot be explained by reference to any causally
contingent feature of W; accordingly, there is no contingent feature
of W that explains why that being doesn't exist. Now suppose, per
reductio, an unlimited being exists in some other world W'. If so,
then it must be some contingent feature f of W' that explains why that
being exists in that world. But this entails that the nonexistence of
an unlimited being in W can be explained by the absence of f in W; and
this contradicts the claim that its nonexistence in W can't be
explained by reference to any causally contingent feature. Thus, if
God doesn't exist at W, then God doesn't exist in any logically
possible world.
A very similar argument can be given for the claim that an unlimited
being exists in every logically possible world if it exists in some
possible world W; the details are left for the interested reader.
Since there are only two possibilities with respect to W and one
entails the impossibility of an unlimited being and the other entails
the necessity of an unlimited being, it follows that the existence of
an unlimited being is either logically necessary or logically
impossible.
All that is left, then, to complete Malcolm's elegant version of the
proof is the premise that the existence of an unlimited being is not
logically impossible – and this seems plausible enough. The existence
of an unlimited being is logically impossible only if the concept of
an unlimited being is self-contradictory. Since we have no reason, on
Malcolm's view to think the existence of an unlimited being is
self-contradictory, it follows that an unlimited being, i.e., God,
exists. Here's the argument reduced to its basic elements:
God is, as a conceptual matter (that is, as a matter of definition) an
unlimited being.
The existence of an unlimited being is either logically necessary or
logically impossible.
The existence of an unlimited being is not logically impossible.
Therefore, the existence of God is logically necessary.
Notice that Malcolm's version of the argument does not turn on the
claim that necessary existence is a great-making property. Rather, as
we saw above, Malcolm attempts to argue that there are only two
possibilities with respect to the existence of an unlimited being:
either it is necessary or it is impossible. And notice that his
argument does not turn in any way on characterizing the property
necessary existence as making something that instantiates that
property better than it would be without it. Thus, Malcolm's version
of the argument is not vulnerable to the criticisms of Anselm's claim
that necessary existence is a perfection.
But while Malcolm's version of the argument is, moreover, considerably
easier to understand than Anselm's versions, it is also vulnerable to
objection. In particular, Premise 2 is not obviously correct. The
claim that an unlimited being B exists at some world W clearly entails
that B always exists at W (that is, that B's existence is eternal or
everlasting in W), but this doesn't clearly entail that B necessarily
exists (that is, that B exists at every logically possible world). To
defend this further claim, one needs to give an argument that the
notion of a contingent eternal being is self-contradictory.
Similarly, the claim that an unlimited being B does not exist at W
clearly entails that B never exists at W (that is, that it is always
true in W that B doesn't exist), but it doesn't clearly entail that B
necessarily doesn't exist (that is, B exists at no logically possible
world or B's existence is logically impossible. Indeed, there are
plenty of beings that will probably never exist in this world that
exist in other logically possible worlds, like unicorns. For this
reason, Premise 2 of Malcolm's version is questionable.
Perhaps the most influential of contemporary modal arguments is
Plantinga's version. Plantinga begins by defining two properties, the
property of maximal greatness and the property of maximal excellence,
as follows:
A being is maximally excellent in a world W if and only if it is
omnipotent, omniscient, and morally perfect in W; and
A being is maximally great in a world W if and only if it is maximally
excellent in every possible world.
Thus, maximal greatness entails existence in every possible world:
since a being that is maximally great at W is omnipotent at every
possible world and non-existent beings can't be omnipotent, it follows
that a maximally great being exists in every logically possible world.
Accordingly, the trick is to show that a maximally great being exists
in some world W because it immediately follows from this claim that
such a being exists in every world, including our own. But notice that
the claim that a maximally great being exists in some world is
logically equivalent to the claim that the concept of a maximally
great being is not self-contradictory; for the only things that don't
exist in any possible world are things that are conceptually defined
in terms of contradictory properties. There is no logically possible
world in which a square circle exists (given the relevant concepts)
because the property of being square is inconsistent with the property
of being circular.
Since, on Plantinga's view, the concept of a maximally great being is
consistent and hence possibly instantiated, it follows that such a
being, i.e., God, exists in every possible world. Here is a schematic
representation of the argument:
The concept of a maximally great being is self-consistent.
If 1, then there is at least one logically possible world in which a
maximally great being exists.
Therefore, there is at least one logically possible world in which a
maximally great being exists.
If a maximally great being exists in one logically possible world, it
exists in every logically possible world.
Therefore, a maximally great being (that is, God) exists in every
logically possible world.
It is sometimes objected that Plantinga's Premise 4 is an instance of
a controversial general modal principle. The S5 system of modal logic
includes an axiom that looks suspiciously similar to Premise 4:
AxS5: If A is possible, then it is necessarily true that A is possible.
The intuition underlying AxS5 is, as James Sennett puts it, that "all
propositions bear their modal status necessarily." But, according to
this line of criticism, Plantinga's version is unconvincing insofar as
it rests on a controversial principle of modal logic.
To see that this criticism is unfounded, it suffices to make two
observations. First, notice that the following propositions are not
logically equivalent:
PL4 If "A maximally great being exists" is possible, then "A maximally
great being exists" is necessarily true.
PL4* If "A maximally great being exists" is possible, then it is
necessarily true that "A maximally great being exists" is possible.
PL4 is, of course, Plantinga's Premise 4 slightly reworded, while PL4*
is simply a straightforward instance of AxS5. While PL4 implies PL4*
(since if A is true at every world, it is possible at every world),
PL4* doesn't imply PL4; for PL4 clearly makes a much stronger claim
than PL4*.
Second, notice that the argument for Premise 4 does not make any
reference to the claim that all propositions bear their modal status
necessarily. Plantinga simply builds necessary existence into the very
notion of maximal greatness. Since, by definition, a being that is
maximally great at W is omnipotent at every possible world and a being
that does not exist at some world W' cannot be omnipotent at W', it
straightforwardly follows, without the help of anything like the
controversial S5 axiom, that a maximally great being exists in every
logically possible world.
Indeed, it is for this very reason that Plantinga avoids the objection
to Malcolm's argument that was considered above. Since the notion of
maximal greatness, in contrast to the notion of an unlimited being as
Malcolm defines it, is conceived in terms that straightforwardly
entail existence in every logically possible world (and hence eternal
existence in every logically possible world), there are no worries
about whether maximal greatness, in contrast to unlimitedness, entails
something stronger than eternal existence.
IV. Is the Concept of a Maximally Great Being Coherent?
As is readily evident, each version of the ontological argument rests
on the assumption that the concept of God, as it is described in the
argument, is self-consistent. Both versions of Anselm's argument rely
on the claim that the idea of God (that is, a being than which none
greater can be conceived) "exists as an idea in the understanding."
Similarly, Plantinga's version relies on the more transparent claim
that the concept of maximal greatness is self-consistent.
But many philosophers are skeptical about the underlying assumption,
as Leibniz describes it, "that this idea of the all-great or
all-perfect being is possible and implies no contradiction." Here is
the problem as C.D. Broad expresses it:
Let us suppose, e.g., that there were just three positive properties
X, Y, and Z; that any two of them are compatible with each other; but
that the presence of any two excludes the remaining one. Then there
would be three possible beings, namely, one which combines X and Y,
one which combines Y and Z, and one which combines Z and X, each of
which would be such that nothing … superior to it is logically
possible. For the only kind of being which would be … superior to any
of these would be one which had all three properties, X, Y, and Z;
and, by hypothesis, this combination is logically impossible.… It is
now plain that, unless all positive properties be compatible with each
other, this phrase [i.e., "a being than which none greater can be
imagined"] is just meaningless verbiage like the phrase "the greatest
possible integer."
Thus, if there are two great-making characteristics essential to the
classically theistic notion of an all-perfect God that are logically
incompatible, it follows that this notion is incoherent.
Here it is important to note that all versions of the ontological
argument assume that God is simultaneously omnipotent, omniscient, and
morally perfect. As we have seen, Plantinga expressly defines maximal
excellence in such terms. Though Anselm doesn't expressly address the
issue, it is clear (1) that he is attempting to show the existence of
the God of classical theism; and (2) that the great-making properties
include those of omnipotence, omniscience, and moral perfection.
There are a number of plausible arguments for thinking that even this
restricted set of properties is logically inconsistent. For example,
moral perfection is thought to entail being both perfectly merciful
and perfectly just. But these two properties seem to contradict each
other. To be perfectly just is always to give every person exactly
what she deserves. But to be perfectly merciful is to give at least
some persons less punishment than they deserve. If so, then a being
cannot be perfectly just and perfectly merciful. Thus, if moral
perfection entails, as seems reasonable, being perfectly just and
merciful, then the concept of moral perfection is inconsistent.
The problem of divine foreknowledge can also be seen as denying that
omniscience, omnipotence, and moral perfection constitute a coherent
set. Roughly put, the problem of divine foreknowledge is as follows.
If God is omniscient, then God knows what every person will do at
every moment t. To say that a person p has free will is to say that
there is at least one moment t at which p does A but could have done
other than A. But if a person p who does A at t has the ability to do
other than A at t, then it follows that p has the ability to bring it
about that an omniscient God has a false belief – and this is clearly
impossible.
On this line of analysis, then, it follows that it is logically
impossible for a being to simultaneously instantiate omniscience and
omnipotence. Omnipotence entails the power to create free beings, but
omniscience rules out the possibility that such beings exist. Thus, a
being that is omniscient lacks the ability to create free beings and
is hence not omnipotent. Conversely, a being that is omnipotent has
the power to create free beings and hence does not know what such
beings would do if they existed. Thus, the argument concludes that
omniscience and omnipotence are logically incompatible. If this is
correct, then all versions of the ontological argument fail.
5. References and Further Reading
Anselm, St., Anselm's Basic Writings, translated by S.W. Deane, 2nd
Ed. (La Salle, IL: Open Court Publishing Co., 1962)
Aquinas, Thomas, St., Summa Theologica (1a Q2), "Whether the Existence
of God is Self-Evident (Thomas More Publishing, 1981)
Barnes, Jonathan, The Ontological Argument (London: MacMillan
Publishing Co., 1972)
Broad, C.D., Religion, Philosophy and Psychical Research (New York:
Routledge & Kegan Paul, 1953)
Findlay, J.N., "God's Existence is Necessarily Impossible," from Flew,
Antony and MacIntyre, Alasdair, New Essays in Philosophical Theology
(New York: MacMillan Publishing Co., 1955)
Gale, Richard, On the Nature and Existence of God (Cambridge:
Cambridge University Press, 1991)
Hartshore, Charles, The Logic of Perfection (LaSalle, IL: Open Court, 1962)
Hegel, Georg Wilhelm Friedrich, Lectures on the History of Philosophy,
translated by E.S. Haldane and F.H. Simson (London, Kegan Paul, 1896)
Kant, Immanuel, Critique of Pure Reason, translated by J.M.D.
Meiklejohn (New York: Colonial Press, 1900)
Leibniz, Gottfried Wilhelm, New Essays Concerning Human Understanding,
translated by A.G. Langley (Chicago, IL: Open Court Publishing, 1896).
Malcolm, Norman, "Anselm's Ontological Argument," Philosophical
Review, vol. 69, no. 1 (1960), 41-62
Miller, Ed L., God and Reason, 2nd Ed. (Upper Saddle River, NJ:
Prentice-Hall, Inc., 1995)
Pike, Nelson, "Divine Omniscience and Voluntary Action," Philosophical
Review, vol. 74 (1965)
Plantinga, Alvin, God, Freedom, and Evil (New York: Harper and Row, 1974)
Plantinga, Alvin, The Ontological Argument from St. Anselm to
Contemporary Philosophers (Garden City, NY: Doubleday, 1965)
Pojman, Louis, Philosophy of Religion (London: Mayfield Publishing Co., 2001)
Rowe, William, "Modal Versions of the Ontological Argument," in
Pojman, Louis (ed.), Philosophy of Religion, 3rd Ed. (Belmont, CA:
Wadsworth Publishing Co., 1998)
Sennett, James F., "Universe Indexed Properties and the Fate of the
Ontological Argument," Religious Studies, vol. 27 (1991), 65-79
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