The Ontological Argument

© 2011 By Paul Herrick

Issues in Philosophy of Religion

3. The Ontological Argument

Anselm of Canterbury (1033-1109) was the first major philosopher of the High Middle Ages, roughly the eleventh through the thirteenth centuries in European history. Born in the Italian town of Aosta, located in the province of Turin, Anselm left home while still in his teens and for three years wandered alone through Europe in search of the highest truth. From a very early age, he is said to have been filled with both an intense love of learning and a desire to know about God. His journey ended on the coast of Normandy, France, at the Benedictine monastery at Bec, headed by the famous scholar Lanfranc (1005-1089). Here Anselm settled into a monastic life of prayer, works of charity, active participation in the community…and the disciplined study of philosophy.

Can God’s Existence Be Definitively Proven?

Among the issues that absorbed Anselm during his early years of study were questions about the nature and existence of God, including these: Can the existence of God be proven by unaided reasoning, independent of the Bible or of organized religion or unquestioned authority? Is there an independent argument, a logical proof, that proves not only God’s existence but God’s nature as well? In other words, an argument that demonstrates not only that God is but what God is like? From premises acceptable to any rational person, not just “believers”?

As Anselm pondered these questions, a single idea kept forcing itself on his mind: The concept of God is the concept of a being who is so great, so perfect in every way, that nothing could even possibly be greater or more perfect. God would not only be the greatest being in the actual world, or the most perfect actual being, but the greatest possible being, the most perfect being there could possibly be. This concept of the greatest possible being, the most perfect being possible, is a different concept altogether than that of the greatest or most perfect actual being.

But, of course, a definition of the concept alone doesn't prove God exists. The if-then statement (if God exists, God is the greatest, most perfect being possible) is about a possibility, and as everyone knows, just because something is possible does not mean it is real or actual. Lots of things are possible but not actual, for instance, Santa Claus, unicorns, lepruchauns, and the Grinch Who Stole Christmas.

However, while meditating on the idea of the greatest possible being, another idea kept pushing its way into his thought as well: Absolutely unsurpassable greatness or perfection includes existence. For it seems that a being couldn't be unsurpassably great, or be the most perfect possible, while at the same time being nonexistent or merely imaginary.

This connection between unsurpassable greatness and existence seemed seductive, but Anselm kept rejecting it as a  fallacious inference. Absolute, unsurpassable greatness or perfection is one thing, he thought, and real or actual existence is another thing entirely. And there is no reason to think the latter logically implies the former. And so Anselm resisted the inference from greatest possible being to actual and real being.

However, the more he thought about it, the more the inference seemed self-evident and logically necessary: Absolute, unsurpassable perfection includes or implies real existence. But this implies that an unsurpassably perfect being must actually exist. For it would seem to be contradictory to suppose that an unsurpassably perfect being lacks existence, i.e., does not exist. That would be like saying that a square lacks four equal sides. Impossible. Anselm gave in, accepted the inference, and produced one of the most famous, intriguing, challenging, and fascinating arguments in the history of philosophy, an argument that was later named the “ontological argument” (from the Greek word ontos. “Ontological” means “the study of being itself”).

In 1078 Anselm wrote his philosophical “discovery” in a meditation titled the Proslogion (Latin: “An address”). In the preface he states that his argument is written for anyone who is “striving to elevate his own mind to the contemplation of God.” A few preliminaries are in order before the argument can be presented. First, Anselm supposed that if something is thought of, then it exists in the mind as an object of thought, as an object thought of. He contrasted this “existence in the understanding,” which can also be called “subjective existence,” with "real existence” or “actual existence,” which is existence outside the mind, i.e., existence in objective reality, existence in the real or actual world, so to speak. The example he gave is interesting: Before the artist paints a picture, the painting exists in the artist's understanding, as an idea in the mind. This idea in the understanding cannot be touched, it cannot be seen by others, etc. However, once the painting is finished, that idea exists in objective reality, i.e., in realty outside the mind—as well as in the understanding. For now it exists on the canvas, which is part of objective reality, or reality outside the mind, and yet it also exists subjectively in the mind, as an object of thought.

Using Santa Claus as an example, we might say: Santa Claus exists as a subjective idea in the mind, as something thought of, but he does not exist in objective reality, in actuality, in the “real world;” he is only a “figment of the imagination.” On the other hand, the Taj Mahal exists both as an idea in the mind and as a really existing object outside the mind, i.e., as a monumental building in reality, in India.

Next, Anselm's argument takes the logical form of a reductio ad absurdum argument, also known as an “indirect proof.” A “reductio” has an interesting logical structure. As in all arguments, you begin by defining your terms. Next, you assume the logical opposite of what you seek to prove. In the rest of the argument, you “reduce the assumption to an absurdity;” in other words, you demonstrate that the assumption logically implies a contradiction. Since only a contradiction can imply a contradiction, this proves (given that the premises are true) that the assumption is a contradiction, which in turn implies that the assumption is false (since all contradictions are false). It logically follows that the opposite of the assumption must be true, which means the conclusion you originally sought to prove must be true.

In his ontological proof, Anselm argued similarly that although some people say, “There is no God,” in other words, that “God does not exist,” if you logically analyze the very concept of God, as it is understood within classical theism, if you probe beneath the surface, you will see that the claim that God does not exist is itself a contradiction. But this implies that the opposite must be true, i.e., that God must exist. In short, Anselm offered a proof for the following claim: We cannot deny God’s existence without contradicting ourselves; therefore, God (as defined within classical theism) must exist. Here is one way to summarize Anselm's full argument:

  1. The term God is understood by everyone, theist and atheist alike, as meaning “that than which nothing greater or more perfect can be thought.”

    Gloss: Anselm is simply defining his terms here. If we do not define our terms at the beginning of an argument, we won’t agree on what it is we are talking about.

  2. The phrase “Something than which nothing greater or more pefect can be thought” is understood when it is heard.

    Gloss: Surely the atheist understands the meaning of the definition when he says, “There is no such being.”

  3. Whatever is understood exists in the understanding.

    Gloss: So God at least exists subjectively, as an idea in the mind, as a thought or mental image in the mind.

  4. Whatever exists in the understanding either exists in the understanding alone, as only an idea in the mind, or it exists both in the understanding subjectively and in objective reality outside the mind, in actuality, as well.

  5. Assumption: Let us assume God exists in the understanding alone, as an idea in the mind alone, and not in objective reality, not in actuality or reality. In other words, let us assume God does not really exist.

    Gloss: This is the assumption to be “reduced.”

  6. But God can at least be thought to exist in objective reality as well as in the mind, which is greater or more perfect, for it is greater or more perfect to exist both in the understanding subjectively and in reality objectively, in actuality outside the mind, than to exist in the understanding alone.

    Gloss: The claim here is that it is a greater or more perfect mode of existence or mode of being to exist both subjectively as an idea in the mind and objectively in actuality outside the mind as well, in reality, than to only exist subjectively, as a mere idea in the mind, all else equal.

  7. So, if God exists in the understanding alone, as an idea only, as a mere figment of our imagination, and not also in objective reality as an actual entity outside the mind, then God is that than which a greater can be thought.

    Gloss: In this case God, is that than which a greater can be thought because we can easily think of something greater, namely, a being just like God but existing in objective reality as a real thing outside the mind in addition to existing subjectively in the mind.

  8. Therefore that than which a greater cannot be thought is that than which a greater can be thought.

  9. This is a contradiction.

    Gloss: Anselm derived a contradiction from his assumption. The contradiction follows from the assumption alone, since the definition of God is used consistently throughout the argument and is not in dispute in the argument. (The atheist implicitly accepts the common definition of God when he says, “There is no such being as that.” The contradiction is God is that than which a greater cannot be thought, and God is that than which a greater can be thought. In other words, God is that than which a greater cannot be thought, and it is not the case that God is that than which a greater cannot be thought.

  10. So without doubt, something than which nothing greater can be thought exists both in the understanding and in objective reality. In other words, God, as defined, actually and really exists.

    Gloss: Since the assumption has been “reduced to an absurdity,” Anselm logically asserted the opposite. What do you think of Anselm’s argument?

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A priori vs. a Posteriori Arguments

Logicians call Anselm’s ontological argument an “a priori argument.” The term is Latin for “prior to sense- experience.” An a priori argument is one all of whose premises can be known to be true on the basis of pure, unaided reasoning alone, independent of (without using) information provided by the physical senses of sight, touch, taste, sound, and smell. All arguments in pure mathematics are a priori, as are many arguments in philosophy.

In contrast, an a posteriori argument (Latin for “after the senses”) contains at least one premise that can be known to be true only on the basis of sense experience (of the material world), in other words, on the basis of information provided by our physical senses. The cosmological and teleological arguments for God’s existence, as well as the atheological argument from evil, are all a posteriori arguments. (Can you explain why?)

The following are examples of propositions most philosophers would agree are known a priori, by pure reasoning alone, independently of sense experience:

  • The whole is always greater than the part.
  • 1+ 1 = 2
  • All triangles have three sides.
  • The square root of 2 is irrational.
  • If x is a number greater than y, and y is a number greater than z, then X is greater than Z.

The following are propositions known a posteriori:

  • Water boils at 212 degrees Fahrenheit under standard conditions.
  • Ripe lemons are normally yellow and taste sour.
  • Sugar tastes sweet.
  • Mount Rainier has snow on it.
  • The Moon has craters.
  • The universe exists.
  • The universe is an orderly place.

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Guanilo’s Critique of Anselm’s Argument

Guanilo’s “On Behalf of the Fool”

Nearly every great philosopher since Anselm has commented on his ontological argument, some defending it (Descartes and Leibniz, among others) and some critiquing it (Kant and Russell, among others). The first person to write a critique of Anselm’s argument was Guanilo, a monk from a nearby abbey. Guanilo attacked Anselm’s argument using the “method of parody.” What is this?

A parody of an argument X is “an argument that uses the same logical structure as X to reach an obviously absurd conclusion, thus suggesting that there is something wrong with the logic of argument X!” More specifically, a refutation by logical parody has the following structure:

  1. A parody of the target argument is constructed in such a way that the parody and the target argument share a common logical structure, but the parady argument reaches an absurd conclusion.
  2. This suggests that the parody argument must contain a fallacy or logical flaw somewhere.
  3. Since the parody and the target arguments share the same logical structure, it follows that the target argument probably has faulty or fallacious reasoning as well.

Guanilo argued that we can adapt Anselm’s form of reasoning to prove the existence of all sorts of absurd things, things we know do not exist. For instance, he argued, the form of reasoning employed by Anselm’s ontological argument can be adapted and used to prove the existence of a perfect island, a perfect mountain, a greatest dog, and so on. But it is absurd to suppose such things exist. Therefore Anselm’s reasoning must be flawed.

Here is one way to formalize Guanilo’s argument in more detail:

  1. Let us define “Lost Island” as the greatest possible island, an island so excellent no island could be more excellent.
  2. We understand the idea of the most perfect island.
  3. Therefore, it exists as an idea in our “understanding,” i.e., in our minds.
  4. Assume Lost Island does not exist.
  5. But it is “more excellent to exist not merely in the understanding, but also in reality” outside the mind in the real world.
  6. Therefore, it is possible there is an island greater than Lost Island, namely, one just like Lost Island except that it really exists.
  7. This is a contradiction.
  8. Therefore, Lost Island must exist in reality, outside the mind, in actuality.
  9. Surely this is “foolish” reasoning.
  10. But Anselm’s ontological argument employs the same form of reasoning.
  11. Therefore, Anselm’s argument is foolish as well. That is, it too must contain a flaw somewhere and therefore is not worthy of our acceptance.

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Anselm’s Reply

In reply, Anselm argued that the reasoning of his ontological argument could not properly be applied to contingent things. But islands, mountains, and other physical things within the material world are all contingent things. The reasoning of the ontological argument, Anselm argued, can legitimately be applied only in one very unique case: in the case of a greatest possible being. Therefore, the reasoning of the ontological argument dodges the parody, its reasoning is not parallel to the parody argument, and it cannot be used to prove the existence of a lost island or a perfect mountain. In short, argued Anselm, the parody fails.

In support of Anselm, some modal logicians argue along the following lines: A contingent entity, even if it is a perfect examplar of the kind of thing it is, for instance, even if it is a perfect island, is still a logically contingent thing. Thus, it exists in some possible circumstances, and it fails to exist in other possible circumstances. It follows that even if it is possible there is a perfect island, that is, even if there are possible circumstances in which a perfect island would exist as a perfect thing of its kind, that alone does not prove that those possible  circumstances include the present circumstances, i.e., the actual circumstances in which we live, the circumstances we call “the actual world.” Thus, the mere possibility of a perfect island does not prove the actuality of such a thing; it does not prove such a thing really exists.

On the other hand, argues the defender of Anselm, the mere possibility of a greatest possible being does entail the actuality of such a being, i.e., does entail its real existence, and for the following reason: If there is even one possible circumstance in which an absolutely perfect being would exist, such a being exists in the present circumstance, in the circumstance we call the actual world, for ultimate perfection of existence entails necessary existence, which is existing in all possible circumstances, not in just a few. Thus, if an absolutely unsurpassably perfect being even possibly exists, then it necessarily actually exists.

Modal logic is required for any in-depth analysis of the ontological argument, Guanilo’s objection, and the back and forth argument that Anselm’s argument generated.

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The Charge of Contradiction

Another way to attack Anselm’s argument is to argue that the traditional concept of God is self-contradictory or incoherent. For if the concept of God as the greatest possible being there could be is contradictory, then God is not even a possibility; the very concept of God is a contradiction in terms, in which case a key step in the reasoning of the ontological argument is refuted. This is also one of the most fundamental criticisms of traditional theism, for if the concept of God is a contradiction in terms, then it is irrational to believe in God. 

An example of a self-contradictory, or incoherent, concept is the concept of a square circle. Nothing could possibly be both square and circular at the same time, for a circle is a locus of points all equidistant from a single point, while a square is not such a locus of points.

If it could be established that the concept of a most perfect being contains or entails a contradiction, then the concept of God is as contradictory as the concept of a square circle. It would follow that God—as conceived within traditional theism—is an impossibility. The Paradox of the Stone is a classic argument for the claim that the traditional concept of God is contradictory. Here is one way to put the argument:

The Paradox of the Stone

According to traditional theism, God is omniptent and omnipotence means the power to do anything. So, can God make a stone so heavy God can't lift it? If the theist's answer is no, then it follows that there's something God can't do, namely, make such a stone. If the theist's answer is yes, then there's still something God can't do, which is to lift such a stone. The theist must answer either yes or no. But either way, there's something God can't do. So the theist must say that an omnipotent being can do anything, and the theist must also say it is not the case God can do anything. Contradiction. Therefore, the traditional concept of God contains a contradiction.

Reply

In order to avoid the contradiction, the theist needs to clarify and revise the definition of omnipotence so that the paradox no longer arises. Essentially, this requires specifying in logically consistent terms the scope of God's omnipotent power. Consider this revision:

A being is omnipotent just in case it can bring about anything that is logically possible.

The scope of God's omnipotence, on this account, covers every logical possibility, but it does not extend to the impossible. Thus, to say that God is omnipotent is not to say that God can do the impossible.i Using this revised definition of omnipotence, the theist may reply to the paradox of the stone this way:

Omnipotence should not be thought of as the power to do absolutely anything.  Rather, it is the power to do anything logically possible.  Now, if a being is omnipotent, it certainly has the power to raise any stone of any weight and it has the power to create a stone of any weight. Therefore, the phrase "a stone so heavy it can't be lifted by an omnipotent being" is itself a contradiction in terms, for a stone so heavy it can't be lifted by an omnipotent being would be a stone so heavy it can't be lifted by a being who can lift stones of any weight. The phrase "a stone so heavy it can't be lifted by a being who can lift stones of any weight" is thus a string of words that cannot refer to anything (since contradictions are impossible). The reply to the paradox is thus: there cannot possibly be such a stone. The fact that God cannot bring about an impossibility represents no deficiency in God's power, for an impossibility is not a “something,” and hence is not something anything could be expected to be able to do. No power could encompass the impossible—there’s nothing there to encompass.

This solution to the paradox of the stone has a long history. For instance, the greatest philosopher of the Middle Ages, St. Thomas Aquinas (1224-1274) argued that it is not possible for an omnipotent being to bring about an impossible state of affairs, for if omnipotence included the power to do the impossible, then it would be possible for an impossibility to be, and this would be a contradiction.

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Other Contradiction Arguments

A number of other arguments allege that the traditional concept of God is contradictory. For example:

The Watusi Argument

  1. God is said to be an immaterial being.
  2. God is said to be able to do anything possible. (This is omnipotence.)
  3. A human being can dance the Watusi. So dancing the Watusi is possible.
  4. But God, being an immaterial being, has no body and so cannot dance.
  5. So there is something God cannot do, namely, dance.
  6. So God cannot possibly be omnipotent.

The L.A. Freeway Argument

  1. God is said to know everything. (This is omniscience.)
  2. God is said to be able to do anything possible. (This is omnipotence.)
  3. A human being can get lost. So getting lost (for instance, on the L.A. Freeway system) is possible.
  4. But God, being omniscient, cannot get lost.
  5. So there is something God cannot do, namely, get lost.
  6. So God cannot be both omnipotent and omniscient at the same time.

How might a defender of the traditional concept answer these arguments?


i For more on the definition of omnipotence, see the readings on omnipotence in Linwood Urban and Douglas Walton, The Power of God.

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