The stock arguments do not prove that god exists. Recall that the conclusion of a deductively valid argument necessarily follows from the premises, but for an argument to be sound, the premises must be true. Even WLC's Kalam makes assumptions that cannot be verified. He makes several assumptions that take advantage of our cognitive biases and limited intuitions, but the history of science shows us (doesn't it?) that our middle-world intuitions are sometimes false. Galileo demonstrated that despite our intuition to the contrary, objects of different mass fall at the same rate. Einstein showed us that time and space are not absolute but relative to one's reference frame. Bohr revealed that in quantum mechanics the act of observation itself causes a wave to collapse. It is conceivable that Craig is right, but for his argument to be a proof, he must demonstrate that the premises are true.
For example, "Everything that begins to exist has a cause" We have no experience of things beginning to exist out of nothing. Therefore, we do not know that this is a coherent idea. How does Craig know that "everything that begins to exist has a cause"? Has he ever seen something begin to exist out of nothing? Furthermore, even if it were a coherent idea, we have not established that the universe began to exist at the Big Bang. All that physics tells us is that there was an expansion. We have not reached point zero. We cannot rule out a contraction phase before the Big Bang (see Vilenkin's correspondence with Victor Stenger).
Furthermore, Craig's argument rests on the notion of "personal causation" as opposed to "scientific causation," but cognitive science shows us that there is no difference between personal causation and scientific causation (see Daniel Dennett, "Consciousness Explained" and "Freedom Evolves"); in other words, mind and body are not ontologically distinct kinds of entities.
The presupposition underlying Craig's notion of personal causation is mind-body dualism. "In philosophy of mind dualism is the position that mental phenomena are, in some respects, non-physical, or that the mind and body are not identical." [Crane, Tim; Patterson, Sarah (2001). "Introduction".History of the Mind-Body Problem. pp. 1–2. "the assumption that mind and body are distinct (essentially, dualism)"]
Craig assumes that dualism is true, that the mind is non-physical (on Craig's view, humans possess a non-physical soul, so this is not surprising). Craig even describes the personal cause of the universe as "a disembodied mind":
"...because there are only two accepted types of
explanations, personal and scientific, and this can't be a scientific explanation. Also, the only
things that might be immaterial, timeless, and spaceless are abstract objects or
disembodied minds, but abstract objects cannot cause things, so it must be a disembodied
mind. Finally, only personal agency can explain how a temporal effect could come from a
changeless cause." [Craig & Sinclair, 2009]
Craig commits the fallacy of "failure of imagination as insight into necessity." In other words, he cannot imagine how the universe could have a non-personal cause; therefore, he concludes that it must be personal and non-physical. But we know that when talking about cosmology, the answer, whatever it may be, is going to be "mind-boggling" as Dennett puts it, so "mind-boggling" cannot be our test of what is possible. All I need to do to show that Craig's argument is not a proof is to show that at least one or more of his premises is not necessarily true. I have done that. Thoughts?