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 – 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 Neo- Platonist. 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 ( ).

Among those who opposed the O.A. were Gaunilo de Marmoutiers (11 th. 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 (11 th. 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.

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 ( ): “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.

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.

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”.

“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 ( ). 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 20 th. 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.

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.

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 ( ) 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 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.