To answer the OP:
I think Dawkins’ argument is terrible, and hardly the beacon of rational thinking that many assume him to be.
First off, it is worth considering what Dawkins means when he says “there is no evidence for God”. Human history, if nothing else, is full of stories of miraculous things happening which demonstate the existence of some higher power. Some are widely believed, some not. Some are personal to the people who tell the stories, some not. To merely hand-wave and say that none of these accounts existist is ludicrous.
But of course that isn’t what Dawkins means. Dawkins is operating from what you could call a “Scienceist” (as dsitinct from scientist or science) point of view which says that only things that can be empirically verified are true. If it can’t be empirically verified then it must be at best undecided or worse false. Working from this method of determining truth, since none of the accounts of God’s actions can be empirically verified, then they must all be false. Therefore the term “no evidence” means that there is no evidence that he deems credible. Not that there is no evidence ever presented, but that there is no evidence that he accepts.
The question then of course is, his “Scienceist” view of truth reasonable. IMHO no. First off it has the problem that it is overly restrictive. Not all true things can be demonstarted to be true through empirical observation. There are other ways of demonstrating truth, such as inference. So to take the Scienceist view is to effectively deny that all of what we know of history is true. History is discovered through inference, not through empiricism. You can’t experiment on the past to see if what you think you know about it is true. You can’t devise an experiment to test for instance that Napoleon was defeated at Waterloo. We can infer that is what happened through what we observe now, but we can’t empirically verify that is actually the case.
It is somewhat ironic because much of Dawkins own speciality, evolution, relies on inference and not on empiricism. Because the mechanism of evolution is so slow, much of what know is not through direct experimentation, but through inference looking at the fossil record. Dawkins, if he was being consistent, should discount much if not all of this since this inference is not strictly empirical. Note that I am not trying to disprove evolution, merely pointing out that Dawkins method of determining truth is too restrictive.
Secondly though, it has the other flaw his Scienceist view holds that all things happen through a uniform set of cause and effect laws. That is the whole basis of empiricism. God or gods however, are not thought of to be bound by those laws. So if we decide a priori as Dawkins does that only things that can be explained by natural laws happen, then we are effectively not giving God any room to reveal himself. If it can be explained by natural laws then it is not evidence of God. And if it can’t be explained by natural laws then it didn’t really happen. It makes it impossible for there to be any evidence of God because God cannot fit in this narrow view of truth.
But that is how Dawkins effectively gets to his “no evidence” claim. He dismisses any account of the supernatural because it can’t be verified empirically. Of course if it was verified empirically then it wouldn’t be supernatural. It’s like asserting that squares can only exist if they have three sides. If they don’t have three sides they don’t exist, and if they have three sides then they are really a triangle.
So that is the problem with Dawkins argument (at least the main one). It is entirely dependant on his unproven and IMHO unreasonable assumption that only things that are empirically verifiable can be true. In the end his argument is nearly circular, in that he claims that there is no evidence of the supernatural, yet his whole view of truth is constructed so that no supernatural things are possible.
Bob