An Analysis of the Ontological Argument for the Existence of God

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An Analysis of the Ontological Argument for the Existence of God Logical Theist

In this episode, I analyze one of the most interesting arguments for the existence of God, the ontological argument. Read the corresponding blog post here. Podcast theme music by Transistor.fm. Learn how to start a podcast here.

One of the most interesting arguments for the existence of God is what is known as the ontological argument. (Ontological just means referring to the study of existence.) One of the things that makes this argument so interesting and so unique is that it attempts to argue for the existence of God from completely rational premises, rather than empirical observations, such as in the cosmological and teleological arguments for the existence of God, which start from natural observations. However, this argument is also one of the least used and one of the least known, especially compared to arguments from design. This is likely because of the deeply philosophical nature of the argument and the difficulty in immediately grasping every aspect of the argument. With that said, I will attempt here to explain the argument simply and clearly and to analyze it objectively and rationally.

ANSELM’S FIRST ONTOLOGICAL ARGUMENT

It is generally recognized that Anselm of Canterbury, a Catholic monk and theologian who lived in the late 11th and early 12 centuries, was the first to formulate the argument; and he actually came up with two forms of the argument. The first can be summarized as follows:

1. God is defined as that than which none greater can be conceived.
2. If someone can think of a being greater than that than which none greater can be conceived, then that is actually that than which none greater can be conceived.
3. If that than which none greater can be conceived only exists in the mind, then it cannot be that than which none greater can be conceived, since it is greater to exist both in the mind and in reality than only in the mind.
4. Thus, that than which none greater can be conceived must exist both in the mind and in reality.
5. Therefore, God, that than which none greater can be conceived, exists in reality.

People will of course have varying reactions to hearing this argument. Many will find this argument silly at first. Others may balk at the argument as just feeling wrong, although they cannot quite articulate why it feels so wrong. And there may be some who find this argument intriguing and convincing. Perhaps, the reason this argument seems so wrong is that it appears to be defining God into existence; that is, the argument appears to be saying that God must exist by definition just as a triangle must by definition have three sides and three angles. An issue that I had with it upon first looking at it is that it appear to be circular in its reasoning. In other words, it looked as if it were attempting to say that God exists because God exists. The argument also attempts to trap one in a corner. If someone admits that they can conceive of a being that than which none greater can be conceived, even if only in that person’s own mind, then they are forced to admit that God exists both in the mind and in reality, since a being that exists only in the mind but not in reality is not as great as a being that exists in both. This would appear to force one to imagine God into existence.

However, as one analyzes the argument more meticulously, that person will find that the argument is much more complex and much more complicated than this. The argument appears completely valid and sound, since every premise follows from the preceding premise coherently and since the conclusion does seem to naturally follow from the steps leading up to it. Nevertheless, there is one key flaw which was pointed out by Immanuel Kant in this particular version of the argument, and this flaw is that the argument assumes that existence is a property which can makes one greater or lesser depending on the degree of existence. This can be expressed grammatically in that saying that God exists is the same as saying that God is. Existence is not a property that someone or something possesses in the same way that the number of sides is a property of a triangle. A triangle can described as having three sides or as being three-sided. In the case of existence, existence is not a predicate but a verb that links the subject and the predicate. For example, in the statement, a triangle is three-sided, there is a subject (triangle), a linking verb (is), and a predicate (three-sided). One could replace the verb is with exists as so that the sentence would read: a triangle exists as three-sided, or exists as being three-sided. Therefore, existence is not a property and, thus, cannot be used to make anything greater or lesser.

ANSELM’S SECOND ONTOLOGICAL ARGUMENT

Anselm’s second version of the ontological argument seems to get around this problem. It can be summarized thus:

1. God is defined as that than which none greater can be conceived.
2. Necessary existence is greater than unnecessary existence.
3. If a being can be conceived which exists only in the mind but not necessarily in reality, than a greater being can be conceived, namely, a being that necessarily exists in reality.
4. Thus, God must have necessary existence.
5. Therefore, God exists.

The reason that adding necessary to existence is not subject to the same flaw as the first of Anselm’s ontological arguments can be expressed grammatically in the statement: God is necessary. In other words, necessary existence does imply a predicate so that necessary existence can be considered a property, unlike mere existence, which is demonstrably not a property. However, this argument still makes an error. It remains unclear as to why necessary existence is relevant to every possible world. A possible world is simply any world that is logically possible. For example, it does not seem as if the existence of goblins is logically impossible. Therefore, it can be stated that goblins exist in some possible world, for example, in the fictional world of J. R. R. Tolkien, the author of The Lord of the Rings. Now, if God exists in some possible world, it does not follow that this it is relevant that he must exist in every possible world, including the actual world.

PLANTINGA’S MODAL ONTOLOGICAL ARGUMENT

The 20th century philosopher Alvin Plantinga formulated the ontological argument using modal logic. Modal logic essentially deals with different modes of expression, such as necessary and possible. In the case of arguing for the existence of God, Plantinga makes the following argument (which I have summarized in a shortened form):

1. A maximally great being is possible.
2. A maximally great being is possibly necessary.
3. Thus, it is necessary that a maximally great being exists.
4. Therefore, a maximally great being exists.

If you are wondering how one can get from step 2 to step 3, this was done by using the S5 axiom. The S5 axiom in modal logic is basically eliminating modes in a chain of expressions. For example, to say that something is necessarily possible is the same as stating that it is possible. In other words, the S5 axiom eliminates the extra modal expression. To say that something is necessarily possible and that this same thing is possible essentially means the same thing. Now, for those interested, the way that this axiom works mathematically can be found on Wikipedia.

Although the S5 axiom makes sense in going from necessarily possible to possible, it does not seem to make quite as much sense to say that something which is possibly necessary is necessary. However, Plantinga has attempted to explain why this does make sense, in saying that if something is necessary in one possible world (which it would be if it is possible), then it must be necessary in all possible worlds, including the actual world. The reason that this works is that in modal logic, to be necessary means to be true in all possible worlds.

It should also be noted that Plantinga is defining a maximally great being as having maximal excellence in every possible world. Maximal excellence is defined as being omnipotent, omniscient, and omnibenevolent, that is, all-powerful, all-knowing, and all-good, respectively. Many critics of the Plantinga’s ontological argument argue that these three cannot possibly all be possessed by the same being and that, therefore, maximal excellence is impossible. And if maximal excellence is impossible, then a maximally great being is not possible, showing the first premise to be unsound. However, I do not wish to address the possibility of maximal excellence here, since my thoughts on it are not fully formed. But I do wish to show that the argument has another flaw. Now, before I do so, I want to make it clear that I do believe in the existence of God, whether this argument is valid or not. It is completely possible to disagree with this argument and still believe in the existence of God. In fact, this argument has been criticized by theists and atheists alike.

With all of that said, we can now examine whether Plantinga’s argument is sound. The premise that a maximally great being is possibly necessary is not substantially different than the premise that a maximally great being is necessary, by axiom S5. However, a maximally great being is defined as a being that is maximally excellent in all possible worlds. If a maximally great being is defined as necessary, but the argument seeks to prove that a maximally great being is necessary, the argument appears to beg the question, which is another way of saying that it is circular. Also, since saying saying that something is necessary is to say that it necessarily exists or simply that it exists, then the conclusion also seems to essentially be saying the same thing as the premise. As one can see, the argument is circular. It is basically stating that a maximally great being exists because a maximally great being exists.

Now, there is of course a reason that Plantinga insisted that a maximally great being, if it can possibly exist at all, is necessary. A maximally great being is said to be necessary because necessary existence is better than unnecessary or contingent existence. In other words, it would be illogical to say that a maximally great being is not necessary, since such a being would not be maximally great. If this is the case, then that a maximally great being is necessary can be shown in that the negation would be logically impossible. However, as I said earlier, necessary existence is not a great-making property because whether something is necessary in one world is irrelevant, in terms of greatness, as to whether it is necessary in another possible world. Therefore, a maximally great being is not necessary, since maximal greatness is irrelevant across possible worlds.

To understand this flaw, we must first also understand what makes something necessary in modal logic. If necessity is defined as the quality of being true in all possible worlds, then it follows that something which is necessary is either true or false in all possible worlds. In other words, a truth is a necessary truth if the negation of that truth is logically impossible. For example, the statement a is equal to a is a truth. The negation of this is that a is not equal to a. However, this is like saying that one is not equal to one, which is not possible. Therefore, the truth that a is equal to a is necessary, that is, it is true in all possible worlds. On the other hand, the truth that I ate today is a contingent truth, a truth that is true in some but not all possible worlds, because it is possible that I could have chosen to not eat today. With this in mind, in order to show that a maximally great being is necessary, it would have to first be shown that non-existence of a maximally great being is impossible.

CONCLUSION

Although I have attempted to show that the ontological argument is does not work, it does not mean that I do not believe in the existence of God. What I hope this shows is that I am willing to analyze arguments and to be willing to disagree with them, even if it is attempting to demonstrate a position I already hold. I believe that God exists based on other arguments. It should also be noted that demonstrating that the ontological argument is faulty does not mean that God is not maximally great but only that maximal greatness does not imply necessity. Finally, the ontological argument can be quite complex, and it is possible that I missed something or that I made a subtle misunderstanding, and I would be willing to change my views on this argument after discussing it further or after doing more research and thinking more deeply about it. For now, however, I am not convinced that the ontological argument is sound.

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