One who hits on the truth by a wild guess does not know what he believes.
Knowledge is true belief supported by good reasons. In an important article, "Justified True Belief", Edmund Gettier produced a number of counterexamples to this traditional model. For instance, suppose I believe that the market went up yesterday, because I read that it did in the copy of the WSJ. I have true belief, supported by good reasons. However, suppose that my actual copy of the WSJ was replaced by a prankster with a phony copy, full of misinformation (except that, by chance, the phony copy correctly states that the market went up. In this case, I do not know that the market went up -- the truth of my belief is a lucky accident.
Knowledge is a true belief that has been caused by the corresponding fact in the right way, in a way that reliably produces true beliefs.
Knowledge can be defeated in two ways: by a rebutting defeater, and by an undercutting defeater.
For example: an alibi is a rebutting defeater of the prosecution's case (a reason for thinking that the accused is innocent), while impugning the reliability of a key witness is an undercutting rebuttal (it doesn't give reason to believe the accused to be innocent, but it casts doubt on the reasonableness of believing him -- on the basis of this testimony -- to be guilty).
Anything that casts doubt on the reliability of one of our cognitive faculties is an undercutting defeater for beliefs produced by that faculty.
An undercutting defeater of belief B is a piece of evidence that raises reasonable doubts about whether B was caused in a reliable, knowledge-conferring way.
Defeaters can themselves be defeated: if my neighbor tells me that he substituted a fake WSJ for the real one, I have a defeater. If I learn that my neighbor has falsely claimed to have pulled this trick many times in the past, then I have a defeater for my defeater.
So, Knowledge = True belief + Reliable mode of caustion + No (undefeated) defeaters
If naturalism were true, then rational knowledge would be impossible. So, for rational knowledge (knowledge by rational inference) to be possible, naturalism must be false.
This doesn't prove theism (since naturalism & theism aren't the only alternatives), but it does give a reason for thinking naturalism to be false: we do have rational knowledge, so naturalism must be false.
He wants to establish: it is impossible to believe rationally in naturalism. Belief in naturalism leads to an epistemic catastrophe (in which nothing we believe is rational).
This isn't a transcendental argument. Naturalism could be true, and we could have rational beliefs, so long as we didn't believe naturalism to be true.
However, it does create obvious problems for the naturalist. At the very least, it should motivate the naturalist to look at alternative worldviews that avoid this catastrophe.
Five or six reasons to doubt that natural selection favors true beliefs (= "Darwin's Doubt").
If either (1) we judge the probability P(R/N) to be low, or (2) we are agnostic about the probability P(R/N) (we decide that we can't discover it), then we have reason to doubt the reliability of our own cognitive faculties. This doubt acts as an "undercutting defeater" to defeat any inference we draw.
Plantinga: naturalism cast doubt on the reliability of all of our faculties. Thus, any belief in naturalism results in a defeaters of all our knowledge. So, a naturalist cannot know anything at all.