by Patrick Julius

Created on: June 09, 2007

Anselm's version of the ontological argument has been perfectly well refuted to the satisfaction of nearly every philosopher alive today. Change the argument to "the being than which nothing more unicorny can be conceived" to prove the Invisible Pink Unicorn's existence, and it will be obvious to you that the argument is fallacious.

Plantinga's modal ontological argument is far stickier, because it is hidden in a long and complicated treatise ("The Nature of Necessity," 1974), and makes extensive use of theoretical modal logic that most people do not take the effort to really understand.

The argument goes something like this:

1. If God exists, he exists necessarily.
2. It is possible that God exists.
3. Therefore it is possible that God exists necessarily.
4. (S5) If it is possible that an entity X has a property P necessarily, then X has P necessarily.
5. Therefore God exists necessarily.
6. Anything that exists necessarily exists.
7. Therefore God exists.

What exactly is being said here? Well, a careful reading of Plantinga's S5-based theory of modal logic (which is to say, the standard theory of modal logic, much to my chagrin) shows that he is using a *possible worlds semantics,* namely, he is saying that "possible" implies "true in at least one world" and "necessary" implies "true in all worlds."

If we reformulate the argument in these terms, it comes out like this:

1. If God exists, he exists in all worlds.
2. God exists in at least one world.
3. Therefore God exists in all worlds, in at least one world.
4. If a thing X has a property P in all worlds, in at least one world, then X has P in all worlds.
5. Therefore God exists in all worlds.
6. Anything that exists in all worlds exists.
7. Therefore God exists.

Obviously this entire argument is valid; indeed, the idea of something "existing in every possible worlds, in at least one world" is so fundamentally weird that one wonders why we even bother with the idea. "Possibly necessary" in possible-worlds semantics means exactly the same thing as "necessary."

The problem is, premises 1 and 2 are absolutely unfounded! They pop out of thin air, and no rational or evidential argument is given to support them. Neither is something that any atheist or agnostic would concede is true; indeed, I'm not even sure most theists would agree with the first premise. The argument completely begs the question.

Why, then, does it have any credibility at all? Because the language of modal logic is slippery. If we think of "possible" in the sense

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