The Ontological Argument

Disclaimer: There is very little that can be known with absolute certainty. Logical and mathematical proofs might be among them, but almost any proposition can be shot down with enough hyperskepticism. I could deny many propositions that virtually everyone else would agree are true; that other minds exist, that the outside world is real, that George Washington was the first US President. While there is no absolute proof that these things I might be trying to deny are true, there is good reason to believe them, because the evidence better supports them than it supports their negations.

Deductive logic operates on deriving a conclusion from premises. If each premise is more plausible than its negation, and the connection between the premises and the conclusion is valid, then the conclusion follows logically and inescapably.

Here are the Big Four arguments in natural theology and what they attempt to demonstrate:

Kalam Cosmological Argument: There cannot be an actually infinite number of past events, therefore, matter cannot be eternal. There was a first event. The first event had to be caused. The cause for the first event had to be uncaused, nonphysical and had to have the properties of volition and causal potency.

Teleological Argument: That from which reality came had to possess intelligence, volition, and causal potency

Ontological Argument: The greatest possible being actually exists in all possible worlds

Moral Argument: Objective morality exists, and that from which objective morality came had to possess the property of morality


The Set-Up
The Ontological Argument is a very brainy argument that at first seems like a philosophical trick. Yet, to those that understand it, this is the most powerful argument in all of natural theology. Unfortunately, without some background in modal logic, this argument is unintelligible, so I am going to give a crash course in modal logic before presenting this argument.

Possible Worlds
A possible world is basically a hypothetical situation. Calling it a possible world is not to say that such a world actually exists. It's just a description of what reality might be; a way for philosophers to see what ideas are coherent and what ideas are not. If something is possible, then we say that it exists in some possible world.

Possibility, Necessity, and Contingency
In metaphysics, the term "possible" has an entirely different meaning than in epistemology. In epistemology, you could look at a difficult math problem and say "it's possible that there is a solution for it" which is like saying "for all I know, there is a solution to this problem." In metaphysics, something is possible if it is logically coherent. For example, my wearing a red shirt is possible, but the existence of square circles is not possible.

Possible - If something is possible, it exists in some possible world.
Necessary - If something is necessary, it cannot not exist, so it exists in all possible worlds. Logical and mathematical truths exist necessarily.
Contingent - If something is contingent, it exists in some possible worlds but not in others. This is to say that it is possible but not necessary.
Impossible - If something is impossible, it exists in no possible worlds. Logically contradictory things like married bachelors are impossible.

For this argument, we are using the metaphysical definition of "possible" so if I say "it's possible that 1+1=2" this doesn't imply "it's possible that 1+1 does not equal 2" Something can be both possible and necessary.

Entailment
To say that A entails B is to say that if A is true, then B has to be true.

Perfection
Perfection - A property that it is better to have than to lack
Imperfection - A property that it is better to lack than to have
Neutral - A property that is neither a perfection nor an imperfection

Maximal Greatness
Maximal Greatness - The state of having all perfections. A maximally great being would have properties such as omnipotence, omniscience, moral perfection, and necessary existence, to name a few. Nothing that exists contingently can be Maximally Great. This is not to say that something has to exist to be Maximally Great. Instead, if something that is Maximally Great exists, then it exists necessarily.

The Ontological Argument
This argument is a deductive argument with 5 premises, that if true, entail the conclusion.

Premise 1: It is possible that a Maximally Great Being (MGB) exists
Premise 2: If it is possible that a MGB exists, then a MGB exists in some possible world
Premise 3: If a MGB exists in some possible world, then a MGB exists in all possible worlds
Premise 4: If a MGB exists in all possible worlds, then a MGB exists in the actual world
Premise 5: If a MGB exists in the actual world, then a MGB exists
Conclusion: A MGB exists.

Interestingly enough, premises 2 through 5 are pretty uncontroversial. They are more or less restatements of the laws of modal logic, and are accepted by theist and atheist philosophers alike.
Premise 2 is just a restatement of what it means for something to possibly exist.
Premise 3 restates the definition of what Maximal Greatness is. If something exists contingently, then it cannot be Maximally Great. Therefore, its existence is either necessary or impossible.

So the question remains: is it possible that a Maximally Great Being exists? Generally, the atheist position has been: "no", but recently the logician Robert Maydole slammed the door on that position by showing that such a response leads to a contradiction.

Why it is Possible that a Maximally Great Being Exists
(A) If a property (P) is a perfection, its negation (~P) is an imperfection
(B) If a property P is a perfection and P entails Q, Q is not an imperfection
(C) Maximal Greatness (we'll call it M) is a perfection
Conclusion 1: M cannot entail ~M

Here's the reason: If a property is a perfection, anything it entails not an imperfection. But since a perfection's negation is an imperfection, no perfection can entail its own negation.

Here is why this is relevant:

It is perfectly within the laws of modal logic for a property (which is not a perfection) to entail its negation. If a property is an incoherent (or impossible) property (square-circleness is an example, so we'll call this S), then it's necessary that everything has the negation of S (we'll call this ~S) as a property. That's what it means for a property to be impossible. But if everything has ~S, that means that every property entails ~S. If it didn't, then something could have some other property and not have ~S, which means it would have S, which means S would be a possible property. But if every property entails ~S, then S also entails ~S. This is consistent with the Principle of Explosion, which states that if you assert a contradiction, you can logically infer anything from it.

So if Premise 1 of the Ontological Argument is false, then
(X) It is not possible that something with M exists; which is the same as saying
(Y) Necessarily, all things have ~M; and if that's the case, then
(Z) All properties entail ~M; and since M is a property, then
Conclusion 2: M entails ~M
But we just established that M cannot entail ~M
So Premise 1 of the Ontological Argument cannot be false.

For the minority of philosophers who do not believe in the Principle of Explosion, here is another way to think of it:

If M is an impossible property, then everything necessarily has ~M. This means that every property entails ~M. ~M is an imperfection, and perfections cannot entail imperfections. This means that if M is impossible, then no property is a perfection. This means that there are no good properties, only bad ones. But this is ridiculous. Aren't some properties, like goodness, intelligence, and wisdom better to have than to lack?
So again, Premise 1 of the Ontological Argument cannot be false.

The Consequences
But if that is the case, then it is possible that a being with Maximal Greatness exists. But then that entails that this Maximally Great Being exist in some possible world, which means that it exists in all possible world, which means that it exists in this world.

Which means that a Maximally Great Being exists. And since this being must exist in all possible worlds, including ones with odd space/time curvatures and worlds that lack space itself, this being transcends physical limitations, and therefore cannot be physical. And since some of these properties such as omnipotence, omniscience, and moral perfection entail personality, then it follows that this Maximally Great Being must be personal. But that's the definition of a personal God.

Conclusion
The greatest possible being actually exists in all possible worlds, which means that a personal God exists in this world. His existence is as necessary and certain as the laws of logic themselves, and atheism is a logical impossibility.

Objections
Most objections to the Ontological Argument try to parody the argument to show that it proves too much. Let's see if any of them are sound.

Dawkins' Delusion
In The God Delusion, Richard Dawkins attempts to use this argument to disprove the existence of God. He says that if God is the greatest possible being, then wouldn't it be greater for God to not exist and still bring the universe into being? But far from undermining the Ontological Argument, it shows its coherence.

To answer Dawkins: Greater? Maybe. Possible? No. For in what possible world does a non-existent being exist?

A Maximally Great Island
What if I state that a Maximally Great Island (MGI) exists by its definition? Wouldn't its Maximal Greatness entail its existence?

First, we have already established that anything which is Maximally Great cannot be physical, due to the problem of space. But this concept also fails because a MGI is incoherent. While the properties that make up a Maximally Greatness have maximum values (knowledge tops out at omniscience), the properties that make an island great do not. You could always add more good things (beverages, dancing, etc.) to any given island to make it greater.

A Quasi-Maximally Great Being
What if a being has all the other perfections but did not exist in every possible world? Or what if this necessary being had all the perfections except one, such as omniscience? Neither one is possible. Here's why:

Some of the properties possessed by a Maximally Great Being cannot exist in more than one being in any possible world. Omnipotence is one example. If multiple beings are omnipotent, then a logical contradiction follows if their wills come into conflict. If one omnipotent being chooses to bring about a state of affairs where a green elephant exists, then such a state of affairs will be actualized. But if another omnipotent being in the same world wants to bring about a state of affairs where a green elephant does not exist, then that state of affairs will be actualized. So in this world, a green elephant would both exist and not exist, but no possible world can contain such a contradictory state of affairs. So no possible world can have multiple omnipotent beings.

But what if it was metaphysically impossible that their wills could come into conflict? If it is not even possible that the wills of these two omnipotent beings could come into conflict, then we are not talking about two different wills, but one will being described two ways. And if there is only one will, then that collapses the two beings into one.

And if the Quasi Maximally Great being was not omnipotent, then that being cannot exist necessarily. If an omnipotent being exists, then nothing else can exist except by the will of the omnipotent being. Since the Maximally Great being is by definition omnipotent and personal, it would be able to refrain from allowing anything else to exist, so there would be possible worlds where only the Maximally Great Being exists.

So no Quasi Maximally Great being can exist necessarily.

This has the side effect of eliminating polytheism. If God exists, then other gods (who by definition have to exist necessarily in order to be gods) cannot exist. So when an atheist tells you "You don't believe in Thor or Wotan. So when you understand why you reject those gods, you'll understand why I reject yours" you will know how to respond.

For further reading on this subject, the Blackwell Companion to Natural Theology is now available.