Alvin Plantinga on Naturalism as Self-Defeating
From a theistic point of view, we'd expect that our cognitive faculties would be (for the most part, and given certain qualifications and caveats) reliable. God has created us in his image, and an important part of our image bearing is our resembling him in being able to form true beliefs and achieve knowledge. But from a naturalist point of view the thought that our cognitive faculties are reliable (produce a preponderance of true beliefs) would be at best a naïve hope. The naturalist can be reasonably sure that the neurophysiology underlying belief formation is adaptive, but nothing follows about the truth of the beliefs depending on that neurophysiology. In fact he'd have to hold that it is unlikely, given unguided evolution, that our cognitive faculties are reliable. It's as likely, given unguided evolution, that we live in a sort of dream world as that we actually know something about ourselves and our world.
If this is so, the naturalist has a defeater for the natural assumption that his cognitive faculties are reliable — a reason for rejecting that belief, for no longer holding it. (Example of a defeater: suppose someone once told me that you were born in Michigan and I believed her; but now I ask you, and you tell me you were born in Brazil. That gives me a defeater for my belief that you were born in Michigan.) And if he has a defeater for that belief, he also has a defeater for any belief that is a product of his cognitive faculties. But of course that would be all of his beliefs — including naturalism itself. So the naturalist has a defeater for naturalism; naturalism, therefore, is self-defeating and cannot be rationally believed.
The real problem here, obviously, is Dawkins' naturalism, his belief that there is no such person as God or anyone like God. That is because naturalism implies that evolution is unguided. So a broader conclusion is that one can't rationally accept both naturalism and evolution; naturalism, therefore, is in conflict with a premier doctrine of contemporary science. People like Dawkins hold that there is a conflict between science and religion because they think there is a conflict between evolution and theism; the truth of the matter, however, is that the conflict is between science and naturalism, not between science and belief in God.