The Modal Ontological Argument

Arguments for and against the existence of God constitute one of the main topics in philosophy over the last few thousand years. By far, one of the craziest family of arguments is ontological arguments. They claim that the concept of God entails his actual existence. God is, by definition, the supreme being, the greatest conceivable being, the maximally great being, the perfect being, the being greater than which none can be thought. But if our conception of God is that he doesn't exist, he wouldn't be the greatest conceivable being since we could conceive of him existing and hence being even greater. Therefore, God must exist. Right? Anyone? Hello?

Ontological arguments sound like riddles, but some of the greatest intellects throughout history have defended them. Just in the last 100 years we've had Kurt Gödel (inarguably the greatest logician of the 20th century), Norman Malcolm, Alvin Plantinga, and Charles Hartshorne all defending versions of it. The standard objection to ontological arguments, from Kant, is that they treat existence as if it were a property a being could have or fail to have. But a being that failed to have existence wouldn't be a being at all. The recent counterargument is that this would only apply to Descartes's ontological argument, not to those of others, like Anselm's (or, for that matter, Kant's).

The contemporary versions use modal logic. This is basically the logic of possibility and necessity. If it's logically possible for you to do or be something -- say, waking up one morning as a giant cockroach -- then you have the modal property of "possibly existing as a cockroach." The weird thing is that, if it is possible for you to wake up one morning as a cockroach, then this modal property would not itself be a possible property you may or may not have, it would be an actual property. If something is possible, then its possibility is necessary (possible in all possible worlds), and if it's necessary, it's actual. So if it's possible you may wake up as a cockroach, then you actually have the modal property of "possibly existing as a cockroach." This sounds weird but it's a basic premise in modal logic (axiom S5) and as far as I know, it is uncontested in logical and philosophical circles.

So: say God is the maximally great being -- he has all positive properties, has them without limit, and has no negative properties. If this is logically possible, then God exists in at least one possible world. Now say God exists in only one possible world. Then he would lack the modal property of "possibly existing in world 2," and so wouldn't be maximally great. OK, so he has the property of possibly existing in worlds 1 and 2 and that's it. But then he lacks the modal property of "possibly existing in world 3." Now say he has the modal properties of "possibly existing in all possible worlds but one." Then he would lack the modal property of "possibly existing in that one world," and by lacking that modal property, wouldn't be maximally great. So if God exists in one possible world, he exists in all possible worlds. And the real world is a possible world, since if something is actual, it must be possible. Another way to say this is that any maximally great being worth its salt would exist necessarily, not just contingently; and if a necessarily existing being exists in one possible world, it exists in all possible worlds. Here's a rundown.

1. A maximally great being (God) is logically possible.
2. Therefore, a maximally great being exists in at least one possible world.
3. Therefore, a maximally great being exists in all possible worlds (otherwise he wouldn't be maximally great).
4. Therefore, a maximally great being exists in the actual world.
5. Therefore, a maximally great being (still God) exists.

There are some very interesting things about this, each one leading to the next. First, virtually every step in this argument is uncontroversial among logicians and philosophers, including atheists. But, second, there's a way to avoid the conclusion: deny the first premise. Deny that God, a maximally great being, is logically possible. Then God doesn't exist in any possible world. In fact, Plantinga, one of this argument's advocates, explicitly makes this point. Third, this means that God either exists in no possible worlds or all possible worlds. He either can't exist or can't not exist. He's either logically impossible or logically necessary. Fourth, since in order to say that God does not exist we have to say God cannot exist, the atheist bears the burden of proof. They must show that it is logically impossible for God to exist, that a maximally great being entails a logical contradiction. The theist only has to maintain that it's logically possible. But you don't have to prove something is logically possible unless you have a reason to think it may not be.

Naturally, one of the main objections to God is precisely that a maximally great being entails logical contradictions. For example, such a being would be maximally merciful but also maximally just. But these are, allegedly, incompatible since perfect justice would conflict with perfect mercy. Some individual traits are accused of being incoherent: could a maximally powerful (omnipotent) being create a stone so big that even he couldn't move it? If he can't, then there's something he can't do: make that stone. If he can, then there's something he can't do: move that stone. Either way, there's something he can't do and so omnipotence is a chimera. Naturally again, there are plenty of counterarguments and countercounterarguments and countercountercounter . . . . etc. Regardless, the modal ontological argument is fascinating, not least because it makes denying God's existence much more problematic.