For some reason I always feel the need to say Richard Dawkins is a man of intelligence before I criticize any of his arguments. It's the same with Stephen Hawking and Lawrence Krauss. Some are critical of those who criticize their arguments, since they're not professional philosophers. Poetically, that's entirely the point. Not only are they not professional philosophers, but they've shown very little evidence that they've studied philosophy to any reasonable extent. However, whenever a person enters into the world of philosophy, they had better be prepared for some philosophical critiques. Can you imagine me, as a scientific layman, writing a book called The Science Delusion, and then making excuses for why I shouldn't debate the leading scientists of the day? Dawkins has done just that with William Lane Craig for years now. Nevertheless, let's take a quick look at the argument that Dawkins considers a knockdown argument for atheism.
1. One of the greatest challenges to the human intellect has been to explain how the complex, improbable appearance of design in the universe arises. (Premise)
2. The natural temptation is to attribute the appearance of design to actual design itself. (Premise)
3. The temptation is a false one because the designer hypothesis immediately raises the larger problem of who designed the designer. (Premise)
4. The most ingenious and powerful explanation is Darwinian evolution by natural selection. (Premise)
5. We don't have an equivalent explanation for physics. (Premise)
6. We should not give up the hope of a better explanation arising in physics, something as powerful as Darwinism in biology. (Premise)
7. Therefore, God almost certainly does not exist. (Conclusion)
Now, anyone even remotely familiar with logic will say that the conclusion that "God almost certainly does not exist" is a complete non sequitur. Even if one grants all six of Dawkins's premises - even the most dubious ones, such as (3) - the conclusion is simply not a cogent inference. Let's say the design argument fails, and let's grant that arguments concerning law-like behavior and the fine-tuning of the universe's initial conditions fail. So what? These are largely inductive arguments, whereas Thomism and other philosophical traditions offer mostly deductive arguments for God's existence.
Dawkins only offers a couple pages dedicated to the proofs of Thomas Aquinas, and he misinterprets them for the most part. For example, with respect to the first three ways Dawkins states on p. 101 that, "[Thomists] make the entirely unwarranted assumption that God himself is immune to the regress." Unfortunately, had Dawkins taken the time to read Thomas Aquinas's reasons for concluding to an Unmoved Mover, an Uncaused Cause, and a Necessary Being, he would have realized that the causal premises require that the First Cause be uncaused.
Dawkins continues, "Even if we allow the dubious luxury of arbitrarily conjuring up a terminator to an infinite regress and giving it a name, simply because we need one . . ."
I'm going to stop right there and point out that Thomas offers three distinct arguments against an infinite regress of essentially-ordered causes. There's nothing arbitrary about it.
Continuing, "there is absolutely no reason to endow that terminator with any of the properties normally ascribed to God: omnipotence, omniscience, goodness, creativity of design, to say nothing of such human attributes as listening to prayers, forgiving sins and reading innermost thoughts."
At this point, one can only wonder: did Dawkins just read the five ways in the Summa Theologiae (literally a summary of theology) and simply gloss over Thomas's arguments for God's omnipotence, and so forth?
Next, "Incidentally, it has not escaped the notice of logicians that omniscience and omnipotence are mutually incompatible. If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. But that means he can't change his mind about his intervention, which means he is not omnipotent."
First, what logicians is Dawkins referring to? He makes no citations and only adds a little poem by Karen Owens to confirm his point. Secondly, God cannot do what is logically impossible. He cannot create a square-circle, and no, he cannot change his mind, since he is immutable. This fits quite nicely with the actual definition of omnipotence (the ability to do whatever is logically possible) and can only be used as an argument against God by adopting a caricature of the term.
Finally, "To return to the infinite regress and the futility of invoking God to terminate it, it is more parsimonious to conjure up, say, a 'big bang singularity', or some other physical concept as yet unknown."
This is the definitive proof that Dawkins doesn't understand Thomas's arguments. Thomas argues that the universe must have a First Cause in the order of essentially-ordered causes, or sustaining causes. This is entirely different from the originating cause of the kalam cosmological argument that Dawkins conflates with the Thomistic proofs. As far as Thomas is concerned, a universe infinite in the past still requires a First Cause in the order of sustaining causes. It's one thing to ask why something begins to exist, and quite another to ask why it continues to exist. For defenders of the kalam argument, I'll leave it to you to explain what's obviously wrong with Dawkins's alternative "big bang singularity" being the cause of anything.