Just to be clear, I didn't quite summarise the whole of Craig's version of the Cosmological argument. The first part is the Kalam Cosmological Argument, which appears in my opening post: Everything that begins to exist has a cause. The universe began to exist. Therefore, the universe has a cause. Up to this point, if the argument is accepted, it has only been shown that the universe has a cause. The nature of that cause is not specified. But Craig goes on to conclude: 4. The cause of the universe is God. His justification for that conclusion is as follows, approximately: 4a. If the universe has a cause, then an uncaused, personal Creator of the universe (God) exists, who did not begin to exist, is changeless, immaterial, timeless, spaceless and enormously powerful. 4b. The universe has a cause (based on the Kalam Cosmological Argument given previously). 4c. Therefore God exists. Craig bases 4a on what he says is an "ontological analysis" that draws on the Kalam argument. Needless to say, premise (4a) is also open to criticism on a number of grounds. For example, it seems difficult to justify the assumptions that there must be a single creator of the universe, and that that creator must be a conscious or "personal" agent.