God cannot be omniscient or omnipotent

In classical theology, God is held to be 3-O: omniscient, omnipotent and omnibenevolent. For centuries, critics of theism have argued against the coherence of this picture of God by invoking the Problem of Evil. In this context, evil should be understood as not only malicious acts by humans, but anything that causes suffering, including tsunamis, droughts and other types of "natural evil". The Problem of Evil can be stated as follows:

1. If God is omniscient, he is aware when evil is about to take place.
2. If God is omnipotent, he is able to prevent evil from taking place.
3. If God is omnibenevolent, he would act to prevent evil from taking place.
4. Evil takes place.
5. Therefore, God cannot be all three of omniscient, omnipotent and omnibenevolent.

Apologists respond to the Problem of Evil with theodicies - arguments that, for example, the evil that takes place in the world is part of a greater good, or it is necessary for character-building, and so on. None of these arguments strike me as convincing, or indeed as anything more than ad-hoc and somewhat desperate attempts to shore up the classical theological understanding of God.

Alvin Plantinga has put forward a rather technical free-will defense which purports to let God off the hook. The details aren't important here. While not everyone accepts the validity of Plantinga's argument, the focus seems to have shifted from the Logical Problem of Evil (why is there any evil at all) to the Evidential Problem (why is there so much evil in this world).

It should be pointed out that if you use any free will-based theodicy, you're backing away from the assumption that God is omnibenevolent. He is only benevolent up to a certain point. He looks for a trade-off between benevolence and humans having free will. So, as far as I'm concerned, a strictly 3-O god is still logically inconsistent.

However, in the present post, I want to leave omnibenevolence aside and saw off the other two legs of the stool - omniscience and omnipotence. I intend to do this by invoking the Butterfly Effect, which has entered the realm of pop culture (it's even the title of an Ashton Kutcher movie) but is actually a profound mathematical result regarding the limits of what can in principle be known about the world.

The effect is usually stated in terms of a butterfly flapping its wings in the Amazon rainforest, resulting in a tornado forming a few days later in Texas. It's important not to think of this in classical terms of a chain of cause and effect, with each link in the chain pointing unambiguously to the next and previous links. Chaotic systems - the kind we are talking about here - don't work like that.

Imagine two scenarios which are identical except that in one scenario the butterfly flaps its wings at a certain instant, and in the other, the butterfly doesn't flap its wings at that instant. The two scenarios evolve differently due to this tiny difference in initial conditions. The difference amplifies exponentially due to the nonlinear feedback in the system, with the result that in one scenario a tornado occurs, and in the other, there is no tornado. This is what scientists call sensitive dependence on initial conditions, and it is the hallmark of chaotic systems.

Now, the point is that at the instant the butterfly flaps its wings, there is no way to know that a tornado will result. In another scenario, the flap of the butterfly's wings might actually prevent a tornado that would otherwise have occurred. There's just no way to predict the behavior of the system with any accuracy more than a few days ahead of time, because the slightest rounding error will amplify exponentially until it overwhelms the predicted solution, making it radically different from the actual behavior.

"But," says the apologist, "God is infinitely more powerful than all the computers that humans have created."

It's not a question of throwing more computing power at the problem. If you used all the computers on earth to predict the weather, you might gain an extra day of accuracy. Double the number of computers, and you might gain an extra few hours. Double it again, and you might gain a few minutes. But there is a fundamental mathematical restriction on how far in advance you can predict the weather, and even God is subject to this restriction, because the atmosphere is a nonlinear chaotic system.

With me so far? Now, what about omnipotence?

Lack of omnipotence follows logically from lack of omniscience. Suppose God wanted to cause or avert a tornado a week from today. He wouldn't know how to do it, because he wouldn't know which butterfly might become a causal factor by flapping or not flapping its wings.

And the atmosphere is not the only nonlinear chaotic system. The solar system is also chaotic. During its early history, there may have been hundreds of Mars-sized planets which were constantly colliding. It would have been impossible to predict in advance that the earth would have a large moon which stabilizes its rotation and gives us seasons, that it would have oceans due to bombardment by icy comets, that the dinosaurs would be wiped out by an asteroid collision 65 million years ago, and so on. So if God was planning since before the Big Bang that the earth would eventually support human life, it's a fantastic coincidence that his plans actually came to fruition.

At this point, the sophisticated theologian would typically sniff haughtily and say something like: "Once again you show your narrow, limited understanding of God. Obviously he isn't bound by petty scientific restrictions. He exists beyond space and time, and sees the whole history of the universe at a glance."

I'm not sure such airy assertions are even meaningful, let alone true. How can a conscious being exist outside of time? Consciousness is by definition a temporal sequence of brain states. If there is no time, there is no change in brain states and therefore no consciousness. The only kind of thing I can imagine existing outside of time and space is an abstract concept such as a mathematical theorem, not a conscious being with which one can have a personal relationship.

Anyway, my main point is that there are limits to God's knowledge - he can't be omniscient, because it's not possible, even in principle, for anyone to be omniscient. The cost of gaining knowledge of even the gross future behavior (let alone the fine details) of a chaotic system increases exponentially, and you hit a wall long before you get anywhere near omniscience. And since perfect control requires perfect knowledge, omnipotence is not possible without omniscience.

In conclusion, not only is omnibenevolence on shaky ground but omnipotence and omniscience aren't looking too good either. 3-O God doesn't have a leg to stand on!