Transcript The Ontological Argument for the existence of God

The Ontological Argument for
the existence of God
Pedro M. Guimarães Ferreira S.J.
PUC-Rio
Boston College, July 13th. 2011
• The ontological argument (henceforth, O.A.)
for the existence of God has a long history. It
was proposed (firstly) by St. Anselm of
Canterbury (c. 1033 – 1109). Some
researchers say that Ibn Sina, died in 1037,
was the first. Others say that the argument
may have been implicit in the works of Greek
philosophers such as Plato and the NeoPlatonist.
• As said by someone, fascination with the
ontological argument stems from the effort
to prove God's existence from simple but
powerful premises.
• In his Proslogion Anselm presents
two O.A.’s . The first one, in
chapter 2, is on the existence of
God, and the second one, in
chapter 3, is on the necessary
existence of God.
• In the first argument he says that God is “that
than which nothing greater can be thought”.
In other words, one cannot conceive a being
greater than God. But besides existing in our
understanding, he has to exist in the reality,
because existing in the understanding and in
the reality is greater than existing only in our
understanding. In other words, if that Being
would exist only in our understanding, we
could think of another being who would exist
in the reality also, and this would be greater
than that one.
• And that is the proof!
• In chapter 3 he argues that if x is
such that x can be conceived not to
exist, then x is not that than which
nothing greater can be thought.
Consequently, that than which
nothing greater can be thought
cannot be conceived not to
exist. (And that is equivalent to
saying that God is necessary).
• See the Word document, p. 1
• The O.A. was accepted (and formulated
in different ways) as well as denied by
many of the greatest philosophers in
history.
• The argument has a platonic flavor. As
said before, it may have been implicit in
the works of Greek philosophers such as
Plato and the Neo-Platonist
• After Anselm, the argument was
assumed, among others, by Descartes
(1596 – 1650), Spinoza (1632 – 1677),
Leibniz (1646 – 1716), Hegel (1770 –
1831) and more recently the argument
was recovered, among others, by Charles
Hartshorne (1897 – 2000), Kurt Gödel
(1906 – 1978), Norman Malcolm (1911 –
1990) and Alvin Plantinga (1932 - ).
• Among those who opposed the O.A.
were Gaunilo de Marmoutiers (11th.
century), Saint Thomas Aquinas
(1225 – 1274), David Hume (1711 –
1776), Kant (1724 – 1804) and, more
recently, Gottlob Frege (1848 –
1925) and Bertrand Russell (1872 –
1970).
Gaunilo de Marmoutiers (11th. century) is not
noticed in the history of philosophy, except for
his argument against the O.A . He wrote that if
it were valid, one could prove anything with
the idea of most perfect. And he exemplified:
one can conceive the most perfect island, then
it should exist.
But those who support the O.A. argue: what
would be the most perfect island? Temperate
or tropical? What amount of land compared
to the earth’s surface, etc?
• Saint Thomas Aquinas (1225 – 1274) rejected
the O.A. with few words, but those were
considered devastating: Anselm says that a
non-existent God is not intelligible, but from
this it does not follow that someone may not
think that God does not exist or deny the
existence of God.
• Saint Thomas Aquinas (1225 – 1274) rejected
the O.A. with few words, but those were
considered devastating: Anselm says that a
non-existent God is not intelligible, but from
this it does not follow that someone may not
think that God does not exist or deny the
existence of God.
• I would say that for Thomas, existence
precedes ontologically the essence of a thing;
in fact, for him, essence is the limitation of
existence, so existence is not included in the
essence of a thing, hence it does not make
sense for him to say that a thing has to exist in
order that its essence be most perfect.
• David Hume (1711- 1776): “Whatever we
conceive as existent, we can also conceive as
non-existent. There is no being, therefore,
whose non-existence implies a contradiction.
Consequently there is no being, whose
existence is demonstrable”.
• With respect to the first statement above,
there is an obvious counter-example: what we
conceive as necessarily existent cannot be
conceived as non-existent.
• Kant (1724 – 1804). He denied that
existence is a property, so rejecting the
O.A. So, it seems to me that his position
on this regard is essentially the same
which I commented on that of Aquinas.
• Gottlob Frege (1848 – 1925) states that
existence is a predicate of second order,
hence statements of first order about
existence are meaningless.
• Bertrand Russell (1872 – 1970): In his Hegelian
youth he exclaimed: “Great God of boots! The
O.A. is sound!” Having become an atheist, he
observed that it is much easier to be
persuaded that O.A.’s are no good than it is to
say exactly what is wrong with them.
• Bertrand Russell (1872 – 1970): In his Hegelian
youth he exclaimed: “Great God of boots! The
O.A. is sound!” Having become an atheist, he
observed that it is much easier to be
persuaded that O.A.’s are no good than it is to
say exactly what is wrong with them.
• And it is commented that this helps to explain
why ontological arguments have fascinated
philosophers for almost a thousand years.
Indeed, it would be the case to quote Kant in
this context: “Human reason poses problems
to itself which it cannot avoid (to pose) and
does not know how to answer them”.
• René Descartes (1595 – 1650). Aquinas’ criticism of
the O.A. was considered so devastating, that it took
more than 350 years for no one less than Descartes
to resume the O.A.
• Descartes wrote more than one O.A. Instead of
considering the “greatness” of God, Descartes'
argument, in contrast, is grounded in two central
tenets of his philosophy — the theory of innate ideas
and the doctrine of clear and distinct perception. He
purports not to rely on an arbitrary definition of God
but rather on an innate idea whose content is
“given.”
• His version is also extremely simple. God's
existence is inferred directly from the fact that
necessary existence is contained in the clear
and distinct idea of a supremely perfect being.
Indeed, on some occasions he suggests that
the so-called ontological “argument” is not a
formal proof at all but a self-evident axiom
grasped intuitively by a mind free of
philosophical prejudice.
• His version is also extremely simple. God's existence
is inferred directly from the fact that necessary
existence is contained in the clear and distinct idea of
a supremely perfect being. Indeed, on some
occasions he suggests that the so-called ontological
“argument” is not a formal proof at all but a selfevident axiom grasped intuitively by a mind free of
philosophical prejudice.
• Descartes argues that necessary existence cannot be excluded
from the idea of God anymore than the fact that in a triangle
the sum of its angles equal two right angles. The analogy
underscores once again the argument's supreme simplicity.
God's existence is purported to be as obvious and self-evident
as the most basic mathematical truth.
• Leibniz (1646 – 1716) is considered one of the
great philosophers, one of the three most
important logicians of history – together with
Aristotle and Gödel – and he was the “hero” of
the last.
• For Leibniz, the perfect being is by definition the
being that has all the positive predicates
(“perfections”) and only those predicates. But
existence is a positive predicate and then the
perfect being exists necessarily.
• He says in a text:
“Elsewhere I have already given my opinion of St.
Anselm’s proof of the existence of God, which was
revived by Descartes. The substance of it is that that
which includes all perfections in its idea, or the
greatest of all possible beings, also includes existence
in its essence, since existence is one of the perfections,
and otherwise something could be added to that which
is perfect. I occupy a middle ground between those
who consider this argument to be a sophism, and the
opinion [which] considers it a perfect proof. That is, I
agree that it is a proof, but I disagree that it is perfect,
since it presupposes a truth which still deserves to be
proved. For it is tacitly supposed that God, or rather
the perfect being is possible. If this point were also
proved, as it should be, it could be said that the
existence of God would be proved […]”.
• And he continues:
“And this shows, as I have already said, that one can
only reason perfectly on the basis of ideas when
one knows their possibility”. [That is one thing I
don’t understand. If p is necessary, how it can
possibly be not possible?]. “However, he
continues, one can say that this proof is still
worthy of consideration, and has, so to speak, a
presumptive validity; for every being should be
considered possible till its impossibility is proved.
[…]. However that may be, one could form an
even simpler proof by not talking at all of
perfections, so as to avoid being held up by those
who think fit to deny that all perfections are
compatible, and consequently that the idea in
question is possible”.
• But in another text he apparently has a proof of
the possibility:
“I call a perfection every simple quality which is
positive and absolute, i.e. which expresses
whatever it expresses without any limitations.
But since such a quality is simple, it follows that it
is unanalysable, i.e. indefinable; for if it is
definable, it will either not be one simple quality,
but an aggregate of many; or if it is a single
quality, it will be defined by its limitations, and
hence will be understood through negations of
further progress; but this goes against the initial
assumption, which was that it is purely positive.
From this it is not difficult to show that all
perfections are compatible with each other, i.e.
that they can co-exist in the same subject”.
• “For let there be a proposition of the following
sort: A and B are incompatible (understanding by A
and B two simple forms of this sort, i.e. perfections
[…]). It is obvious that this proposition cannot be
proved without analyzing either or both of the terms
A and B; […].
• But (ex hypothesi) they are unanalysable. Therefore
this proposition cannot be demonstrated of them.
But if it were true, it certainly could be demonstrated
of them, because it is not true by itself. ([…]
necessarily true propositions are either provable or
known by themselves)”.
• “Therefore this proposition (“A and B are
incompatible”) is not necessarily true — in
other words, it is not necessary that A and B
are not in the same subject. Therefore
they can be in the same subject, and since the
same reasoning is valid for any other qualities
of this sort you might choose, it follows that
all perfections are compatible with each
other”.
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• “Therefore this proposition (“A and B are incompatible”) is not
necessarily true — in other words, it is not necessary that A
and B are not in the same subject. Therefore they can be in
the same subject, and since the same reasoning is valid for
any other qualities of this sort you might choose, it follows
that all perfections are compatible with each other”.
• Notice that according to this Leibniz’s statement, ¬ Np → Mp,
i.e. if p is not necessary, then, it is possible (möglich).
We may think that this does not make sense: a thing may be
neither necessary nor possible. Moreover, the statement
above is logically equivalent to ¬ Mp → Np, which more
clearly would not make sense: if it is not possible, how can it
can imply necessity?
So, it seems that the universe of this discourse does not
include contradictory things (which in fact are “not-beings”
according to the classical philosophy), and in this case, if
something is not necessary, it has to be possible.
• “Therefore there is, or [better] can be
understood, the subject of all perfections, or a
most perfect being.
• From which it is obvious that he also exists,
since existence is included in the number of
perfections”.
• Hegel (1770 - 1831). Considered in general
one of the most important philosophers in
history. In the last year of his life he affirmed
repeatedly in his Conferences that there exists
a successful O.A., but this is not shown in any
of his texts. For Hegel, what is rational is real
and what is real is rational (“Was vernünftig
ist, das ist wirklich; und was wirklich ist, das ist
vernünftig”).
• (Every (or almost every) western thinker
would agree with the second statement, but
only a platonic mind agrees with the first). So
it is not surprising that some scholars say that
the whole Hegel’s work is an O.A.
• Charles Hartshorne (1897 – 2000). American
philosopher, he is considered by many
scholars one of the most important
metaphysicians and philosophers of religion in
the 20th. Century.
• His philosophy is teo-centric, defended the
rationality of theism and is one that
rediscovered St. Anselm’s O.A.
• He argues that Hume's and Kant's criticisms of
the ontological argument of St. Anselm are
not directed at the strongest version of his
argument found in Proslogion, chapter 3.
Here, he thinks, there is a modal distinction
implied between existing necessarily and
existing contingently. Hartshorne's view is that
existence alone might not be a real predicate,
but existing necessarily certainly is. (And this
sounds a reply to Frege).
• That is, contra Kant and others, Hartshorne
believes that there are necessary truths
concerning existence.
• He assumes here that there are three
alternatives for us to consider: (1) God is
impossible; (2) God is possible, but may or
may not exist; (3) God exists necessarily. The
ontological argument shows that the second
alternative makes no sense. Hence, he thinks
that the prime task for the philosophical theist
is to show that God is not impossible.
• Kurt Gödel (1906 – 1978) is considered one of three
most important logicians in history, together with
Aristotle and Leibniz. According to Feferman, he is by
far the most important logician of our times. In 1931
he proved an absolutely unexpected result by the
leading mathematicians and logicians of the time, a
result that is difficult to accept by everyone who would
hope that mathematics is the ultimate fortress of our
certitudes: the famous incompleteness theorem, that
states that it is impossible, with any given axioms,
establish all the theorems of mathematics. (And he
proved it for the simplest mathematical structure, that
of the integers).
• Well, this man who showed in a dramatical way the
limits of the human mind, proposed an O.A. for the
existence of God! Good for those who believe!
• His O.A. was never published and its
reconstitution is difficult and disputed among
experts who have tried to recover it. The
argument is found dispersed in many sketchy and
sometimes cryptical notes that he wrote for
himself.
• There is a small, but steadily growing, literature
on the ontological arguments which Gödel
developed in his notebooks, but which did not
appear in print until well after his death. These
arguments have been discussed, annotated and
amended by various leading logicians: the upshot
is a family of arguments with impeccable
logical credentials.
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There follows Gödel’s O.A., as presented by Anderson:
Definition 1: x is God-like if and only if x has as essential properties those
and only those properties which are positive
Definition 2: A is an essence of x if and only if for every
property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is
necessarily exemplified
Axiom 1: If a property is positive, then its negation is not positive.
Axiom 2: Any property entailed by—i.e., strictly implied by—a positive
property is positive
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is positive
Axiom 6: For any property P, if P is positive, then being necessarily P is
positive.
Theorem 1: If a property is positive, then it is consistent, i.e., possibly
exemplified.
Corollary 1: The property of being God-like is consistent.
Theorem 2: If something is God-like, then the property of being God-like is
an essence of that thing.
Theorem 3: Necessarily, the property of being God-like is exemplified.
• An expert says about the argument that “given
a sufficiently generous conception of
“properties”, and granted the acceptability of
the underlying modal logic, the listed theorems
do follow from the axioms. […]. Some
philosophers have denied the acceptability of
the underlying modal logic. And some
philosophers have rejected generous
conceptions of properties in favor of sparse
conceptions according to which only some
predicates express properties. […]. One
important point to note is that no definition of
the notion of “positive property” is supplied
with the proof. At most, the various axioms
which involve this concept can be taken to
provide a partial implicit definition.
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If we suppose that the “positive properties” form
a set, then the axioms provide us with the
following information about this set:
If a property belongs to the set, then its negation
does not belong to the set.
The set is closed under entailment.
The property of having as essential properties
just those properties which are in the set is itself
a member of the set.
The set has exactly the same members in all
possible worlds.
The property of necessary existence is in the set.
If a property is in the set, then the property of
having that property necessarily is also in the
set.”
• Corollary 1 follows from Thm. 1 and Axiom 3.
• Gödel uses the axioms of modal logic for the
argument.
• Might those “positive properties” be Leibniz’s
“perfections”? Recall that for Leibniz,
a perfection is every simple quality which is
positive and absolute, i.e. which expresses
whatever it expresses without any limitations.
• Or might the positive properties be the
ontological transcendentals of classical
philosophy, that is, unity, intelligibility,
desirability and beauty?
• Alvin Carl Plantinga (1932 - ) is currently Professor
Emeritus at the University of Notre Dame. His O.A. is
inspired in that of Hartshorne:
• 1. A being has maximal excellence in a possible world W
if and only if it is omnipotent, omniscient and completely
good.
• 2. A being has maximal greatness if it has maximal
excellence in all possible worlds.
• 3. (Premise): It is possible that there exists a being with
maximal greatness.
• 4. Hence it is possibly necessarily true that there exists a
being that is omnipotent, omniscient and completely
good.
• 5. Hence it is necessarily true that there exists a being
that is omnipotent, omniscient and completely good.
• 6. Then there exists a being that is omnipotent,
omniscient and completely good. (See Word document, p. 2).
• Plantinga has another O.A., which is a formalization of
Anselm’s:
• 1. (Hypothesis): God exists in our knowledge, but not in
reality.
• 2. (Premise): Existing in reality and in our knowledge is
greater than existing only in our knowledge.
• 3. (Premise): We can think of a being which has all God’s
properties and existence.
• 4. Hence a being having all God’s properties plus is greater
than God in view of 1. and 2.
• 5. As a consequence, a being greater than God can be
conceived.
• 6. But from God’s definition, it is false that a being greater
than God can be conceived.
• 7. Hence it is false that God can be conceived in our
understanding, but not in reality.
• 8. But God does exist in our knowledge.
• 9. Hence God does exist in reality.