From: - Kalam Cosmological Argument
The basic argument of the Kalam is as follows:1. Everything that begins to exists has a cause for its existence2. The universe began to exist (i.e. it is not infinite)Therefore: The universe has a cause of its existence.
Craig's Mistaken Concept of Infinity
We will look at the second premise of the argument first. It is strange that Craig is trying to prove infinity is impossible by pointing out oddities which are already well known to mathematicians and logicians. Just because a feature is odd does not mean it involves a contradiction.First in his example of the infinite library of books. His argument is flawed because we can simply remove the books from the library, add the new books together with the ones in it and then reassign natural numbers to each book. No problem, no absurdity.
With respect to the problem of successive addition. You can get infinity if you construct a successive addition that has no beginning, i.e. it already reaches out into infinity.
The Universe Being Finite in Time:
Craig's use of science is really a double edged sword. He claims that science supports the finiteness of the universe. Actually it does not do that at all. All it shows is that our current state of the universe had a beginning about fifteen billion years ago. It does not show that it was the absolute beginning. For instance Stephen Hawking has proposed a four dimensional universe. In this model the universe goes through a period of increasing entropy during an expansionary phase and a period of reducing entropy during the contractionary phase. Furthermore the jury is still out as to whether the universe will end in a contraction (a "big crunch") or whether it will continue to expand forever. If the former is the case, there is every possibility that ours is merely a cycle (of big bangs and big crunches) within an infinite series of cycles.
The Concept of Causation
With this we go to the first premise. Is causation an a priori necessity? In other words, can it be shown that it is logically contradictory to speak of ubncaused things, the way it is logically contradictory when we speak of husbands as unmarried spouses? The answer is no. We can conceive of something as being uncaused, it involved no contradiction. As proof, theist conceive of God as being uncaused. Is causation an inductive principle? In other words, is it something which science can show to be true? If it is something which can be resolved inductively, the answers seems to be causation is not a universal principle of science. We note first and foremost cosmologists seem very comfortable with the idea that the universe could have come into existence uncaused. In fact some scientists have suggested that the Big Bang began with a quantum fluctuation. The principle of quantum mechanics allow virtual pairs of quantum particles to appear and exist for a short time before annihilating. In December 1973, in an article for Nature, Edward Tryon of the City University of New York proposed the idea that the universe is "a fluctuation of the vacuum". He showed that such a fluctuation does not violate the conservation of energy. When Tryon's hypothesis is combined with the inflationary theory of the big bang a viable model of creation literally ex nihilo can be constructed.  Secondly causation is not a universally observed fact. In the realm of subatomic particles, quantum mechanics dominate. Yet quantum mechanics lead to many non-causational observations that are probabilistic in nature.
As Timothy Ferris explains:
The radioactive isotope radium-224 has a half life of 3.64 days. So if we study an atom of radium-224 for 3.64 days we will have an even chance of witnessing its decay. But we cannot know just when it will decay-this particular atom might wait for years-nor can we, in principle or in practice, assign a causeto its decay. All we can know are probabilities.
Note that he mentioned it is not even possible in principle. In other words quantum mechanics, one of the most widely confirmed scientific theories known, says that it is simply not possible to do, not that our equipment or knowledge is incomplete. Thus causation seems to break down in the subatomic realm. Yet this is exactly the condition the universe was in at the beginning. The universe, was in the domain of quantum mechanics at the beginning, the domain where causality breaks down.
Thus in conclusion, the basic premises of the Kalam cosmological argument are either invalid or not proven:
Craig's concept of infinity is mistaken.
The universe may or may not have a beginning in time.
The verdict is still out, thus it cannot be used as a premise to prove his argument.
Causation is not an a priori principle.
Causation is not a universally valid empirical principle, as quantum mechanics have shown.
"So Long and Thanks for all the Fish"