First of all, I will mention that the entire book can be found at
https://www.andrew.cmu.edu/user/jksadegh/A Good Atheist Secularist Skeptical Book Collection/The God Delusion by Richard Dawkins.pdf although I don't know whether that violates any kind of law.
Search for the phrase "the ultimate Boeing 747"
This will put you at the start of his long, rambling "proof." His proof consists of an argument
against the argument of improbability. This is the
modus operandi of his book. Since there are objections to the argument of improbability (objections that may or may not be valid – experts disagree), it is not absolutely necessary for someone to accept the argument of improbability. Therefore, Darwinism.
That's the logic of the entire book. The only part that kind of deviates from this theme is the "anthropic principle." Scan for the phrase "Gap theologians who may have given up on" and you will find yourself at the start of the section. You can read on, if you like, or skip ahead to the phrase:
"This objection can be answered by the suggestion, which Martin Rees himself supports, that there are many universes, co-existing like bubbles of foam, in a 'multiverse' (or 'megaverse', as Leonard Susskind prefers to call it).*"
What's the point of the argument? It is this: Even though it is quite improbable that any of what he postulates could have happened, if you postulate an infinite number of universes, why it must have happened in one of them. Then, therefore, it is not surprising that we would find ourselves in the universe where it did happen because (drumroll) the anthropic principle.
Of course this "proof" could easily be applied to anything, really. Yes, it's extremely unlikely that a young Joseph Smith ran into an angel who gave him golden plates written in an ancient language. It's also extremely unlikely that he was able to translate these writings into our modern language using little more than a few rocks and a hat. However, if we postulate an infinite number of universes, why it was certain to happen in one of them, and it's not surprising that we are in the universe where Mormonism is the one true religion because (drumroll) the anthropic principle!! If we hadn't been in the right universe, we never would have heard of old Joe Smith and his Book of Mormon.
Would you similarly like me to prove that Jesus really was God, that Mohammed really did talk to Allah, and that Bigfoot exists?
Again, the main point of Dawkins' argument seems to be that since you can postulate infinite numbers of universes, Darwinism is not completely falsified outright. Since it has not been proven completely false, it
must be true.
Dawkins senses, in a certain naive way, that people might balk at his argument and so includes this doozy:
"It is tempting to think (and many have succumbed) that to postulate a plethora of universes is a profligate luxury which should not be allowed. If we are going to permit the extravagance of a multiverse, so the argument runs, we might as well be hung for a sheep as a lamb and allow a God. Aren't they both equally unparsimonious
ad hoc hypotheses, and equally unsatisfactory? People who think that have not had their consciousness raised by natural selection. The key difference between the genuinely extravagant God hypothesis and the apparently extravagant multiverse hypothesis is one of statistical improbability. The multiverse, for all that it is extravagant, is simple. God, or any intelligent, decision-taking, calculating agent, would have to be highly improbable in the very same statistical sense as the entities he is supposed to explain."
This is what we call
special pleading. He is entitled to make completely unsupportable hypotheses that save his pet theory from falsification. However, his opponents are denied the same opportunity.