Richard Dawkins, in his book The God Delusion, gives a novel argument for the thesis that God is improbable. Al Plantinga, in his review, criticizes this argument. I’ve claimed that Plantinga’s criticism is correct; here I’ll defend my claim (with some nuances).

Here’s how Plantinga summarizes Dawkins’ argument:

So why does [Dawkins] think theism is enormously improbable? The answer: if there were such a person as God, he would have to be enormously complex, and the more complex something is, the less probable it is: “However statistically improbable the entity you seek to explain by invoking a designer, the designer himself has got to be at least as improbable. God is the Ultimate Boeing 747.” The basic idea is that anything that knows and can do what God knows and can do would have to be incredibly complex. In particular, anything that can create or design something must be at least as complex as the thing it can design or create. Putting it another way, Dawkins says a designer must contain at least as much information as what it creates or designs, and information is inversely related to probability. Therefore, he thinks, God would have to be monumentally complex, hence astronomically improbable; thus it is almost certain that God does not exist.

Let me start with a point that Plantinga doesn’t make — when Dawkins talks about a hypothesis being improbable, what interpretation of probability is he using? It’s a standard problem when people give unsophisticated probabilistic arguments — they don’t make clear how we’re supposed to understand these probabilistic claims. 

Plantinga pushes two lines of criticism: 

But why does Dawkins think God is complex? And why does he think that the more complex something is, the less probable it is?

With regard to the first line of criticism, Plantinga writes:

First, is God complex? According to much classical theology (Thomas Aquinas, for example) God is simple, and simple in a very strong sense…

As Vic Stenger has aptly pointed out to me, Plantinga’s move here could be questioned. One could hold that, sure, the God of classical theology is simple, but the God that the intelligent design proponents are arguing for can’t be simple, since that God intervenes in various ways in the world, and has a hand in making complex creatures like us. Perhaps Dawkins is just arguing against that sort of complex God, not against the God of classical theology. (Or perhaps Dawkins would hold that even the God of classical theology is complex.) 

My personal opinion is that judgements of complexity and simplicity are subjective — what seems complex to us might seem simple to a creature with a different cognitive constitution. But I won’t pursue this line of reasoning here. 

Instead, let’s step back: why does it matter if God is (objectively) complex? Dawkins says that it follows from that claim that God is improbable. But I don’t see why this follows — I don’t see why something complex is more improbable than something simple. Here’s what Plantinga says:

Given materialism and the idea that the ultimate objects in our universe are the elementary particles of physics, perhaps a being that knew a great deal would be improbable—how could those particles get arranged in such a way as to constitute a being with all that knowledge? Of course we aren’t given materialism. Dawkins is arguing that theism is improbable; it would be dialectically deficient in excelsis to argue this by appealing to materialism as a premise. Of course it is unlikely that there is such a person as God if materialism is true; in fact materialism logically entails that there is no such person as God; but it would be obviously question-begging to argue that theism is improbable because materialism is true.

So why think God must be improbable? According to classical theism, God is a necessary being; it is not so much as possible that there should be no such person as God; he exists in all possible worlds. But if God is a necessary being, if he exists in all possible worlds, then the probability that he exists, of course, is 1, and the probability that he does not exist is 0. Far from its being improbable that he exists, his existence is maximally probable. So if Dawkins proposes that God’s existence is improbable, he owes us an argument for the conclusion that there is no necessary being with the attributes of God—an argument that doesn’t just start from the premise that materialism is true. Neither he nor anyone else has provided even a decent argument along these lines; Dawkins doesn’t even seem to be aware that he needs an argument of that sort.

I agree with Plantinga’s responses here, but I want to emphasize my basic response: why should we think that something complex is more improbable that something simple? I don’t see any even prima facie clear argument for a link between complexity and improbability in Dawkins’ discussion. Moreover, for those who think that there is a link between complexity and improbability, what interpretation of probability should we use to understand that claim?