Many of the arguments pro-religious belief presented in TGD would form a nice corpus in a dictionary of critical analysis for the entry on "begging the question". However, Prof. Dawkins studiously avoids the phrase despite its rampant, repeated and some would say wanton applicability, and if I were ever asked to predict why (I haven't been, I just like the sound of my keyboard) I'd say that it's because the phrase is so frequently misused on both sides of the Atlantic ocean.
Indeed, when I was taught the phrase, the example I was given is that of proof of the existence of god: we can see the results of god's creation all around, therefore god created them, therefore god exists. That's about as short - and absurd - an example of the technique as can be demonstrated. In ordinary speech, people use the phrase "begging the question" to mean: the argument I have just heard is incomplete or fallacious, because it appears not to answer (or to directly raise) the following problem. Where the problem was not explicitly part of the argument. However, the meaning of the word "beg" should not be overlooked, and is key when calling an argument out as one that begs the question. In fact, it isn't the argument that begs the question: it's the conclusion which does so, and the conclusion is begged from the question. In other words, the meaning of the phrase is that an argument draws to a conclusion which already existed in its assumptions or axioms. My Latin isn't very good, but I might describe this kind of argument as QEQ - Said that which was said.
Let's look at, for example, the argument for the existence of purgatory (it's quite near the end of TGD which makes it easy for me to remember). The conclusion is that purgatory exists, and the justification is that people everywhere are praying for the souls of the dead because they believe that the souls are in purgatory, and surely prayer isn't pointless. I hope that going all slanty made the point in the argument where the conclusion was codified apparent - the reason we can be sure that purgatory exists because we are sure that purgatory exists. QEQ.
I realise that this had little to do with the thesis of TGD, but to beg the question is a cool phrase which should be used less, but with higher accuracy.