Michael Martin briefly addresses the Kalam Cosmological Argument in his book, “Atheism: A Philosophical Justification.” In particular, he critiques William Lane Craig’s defense of the argument as found in his book, “The Kalam Cosmological Argument.”
Martin’s first round of responses are attempts to demonstrate that the Cosmological Argument does not establish the God of Christian theism. I find this general claim to be unproblematic, however, as I will grant that the argument fails to establish all of the attributes of the God of classical theism. However, Martin’s skepticism on this account causes him to give the argument much less credit than it deserves.
He first complains that “Craig cannot validly conclude that a single agent is the creator.”  I have always been rather surprised that atheists are so willing to use this argument in order to undermine theistic arguments. After all, whether or not there is one God or one thousand gods, atheism is still false. So, I can hardly see the practicality of this objection, other than to try to avert the inference to monotheism by any means necessary.
Furthermore, and even more damaging, theistic philosophers- including Craig himself- have in fact supported the contention that a single Creator is the most reasonable hypothesis given Occam’s razor. According to this principle, we should prefer the simplest hypothesis. Why, then, should we posit 10 creators when 1 will do the job? In fact, Occam’s razor is commonly appealed to in order to support atheistic contentions, and the principle itself is nearly universally regarded as generally plausible.
Martin next faults Craig for claiming that the Cosmological Argument demonstrates that something greater than and beyond the universe must have created the universe. He points out that sometimes, effects are greater than their causes (he mentions the example of a parent who gives birth to a child greater than she). Here I will admit that Craig has overstepped the bounds of the argument, as I can’t think of a strictly logical reason why the cause of the universe would necessarily have to be greater than it, although it does seem quite likely. I would simply deny that the Cosmological Argument demonstrates anything in particular about the Creator’‘s power; such a demonstration will need to rely on other arguments, or remain undefended. 1
Martin also takes issue with Craig’s claim that the Creator must create the universe ex nihilo. Yet, Craig’s contention here is due to the evidence for the Big Bang that emerged out of the initial singularity, which emerged out of nothing (a.k.a., ex nihilo). Therefore, it is most likely that the Creator created the universe ex nihilo. However, even if it is hypothesized, as Martin posits, that the Creator used previously existing materials in order to accomplish His goals, I can hardly see that this would weaken the case for theism. In fact, if anything, it would help to rebut charges that some have made (though ineffective for other reasons) that creation ex nihilo is absurd. So, even if Martin is right on this account, he has only succeeded in giving theistic philosophers another defense against the supposed infeasibility of God’s creative act.
In Craig’s defense of the universe’s finite past, he cites both philosophical and scientific reasons to believe that the universe in fact began to exist. Martin’s critique here seems to be quite lazy, frankly. He claims that “Craig’s a priori arguments are unsound or show at most that actual infinities have odd properties. This latter fact is well known, however, and shows nothing about whether it is logically impossible to have actual infinities in the real world.”  However, his defense of this claim is particularly unimpressive, as he cites only one supposed problem with only one of Craig’s arguments on this issue. Craig’s writings contain a plethora of arguments against the possibility of an actual infinite, and it hardly seems sufficient to critique one argument and imply that the issue is closed. In fact, Craig has admitted elsewhere that “…the above argument for the impossibility of the real existence of the actual infinite is, in my opinion, one of the most tentative I presented…” 2
So what is the argument? Martin addresses Craig’s example of a library that contains an actually infinite number of books, which use up the entire number system. Craig argues that it would be impossible to add another book to the library, which is absurd, since there is nothing to stop somebody from doing such a thing. Martin claims, however, that the books could simply be renumbered, and thus avoid the problem. It appears, though, that Craig has already attempted a reply to such reasoning,
“It might be suggested that we number the new book ‘I’ and add one to the number of every book thereafter. This is perfectly successful in the mathematical realm, since we accommodate the new number by increasing all the others out to infinity. But in the real world this could not be done. For an actual infinity of objects already exists that completely exhausts the natural number system- every possible number has been instantiated in reality on the spine of a book. Therefore, book I could not be called book 2, and book 2 be called book 3, and so on, to infinity. Only in a potential infinite, where new numbers are created as the collection grows, could such a re-count be possible. But in an actual infinite, all the members exist in a determinate, complete whole, and such a re-count would necessitate the creation of a new number. But this is absurd, since every possible natural number has been used up.” 3
Thus, Craig has already rebutted Martin’s attempted refutation of one of his weakest arguments for the impossibility of an actual infinite. This hardly inspires confidence in Martin’s case.
Martin then counters Craig’s claim that an actual infinite cannot be formulated by successive addition. He formulates Craig’s argument thusly:
1. For any point, it is impossible to begin at that point and construct an actual infinity by successive addition.
2. In order to construct an actual infinity by successive addition, it is necessary to begin at some point.
3. Therefore, an actual infinity cannot be constructed by successive addition.
Martin says that “It should be clear that (2) begs the question, since there is an alternative- namely, that an actual infinity can be constructed by successive addition if the successive addition is beginningless.” 
As far as I read Martin here, his claim is essentially that an actual infinite can be constructed if it has an ‘infinite’ core (since, it seems, addition that is truly beginningless must be infinite). If my analysis here is correct, then Craig has actually already dealt with this objection as well. He states:
“The only way a collection to which members are being successively added could be actually infinite would be for it to have an infinite ‘core’ to which additions are being made. But then it would not be a collection formed by infinite addition, for there would always exist a surd infinite, itself not formed successively but simply given, to which a finite number of successive additions have been made. But clearly the temporal series of events cannot be so characterized, for it is by nature successively formed throughout.” 4
In any case, I would be more than happy to let all this pass. Perhaps an actual infinite is possible. This would not show that it is actual. And, much to the chagrin of non-theists, scientific evidence points almost unavoidably to a beginning of the universe so that, even if all of the arguments against the existence of an actual infinite are unsound, we would be justified in believing that the universe did begin to exist.
Much to my surprise, Martin simply denies the possibility of scientific inference to a beginning. He states that, “To say that the universe had an absolute beginning would preclude any scientific investigation of this beginning.”  Yet I can hardly even conceive of what Martin is trying to claim here. One piece of scientific evidence for the beginning of the universe is found in the science of thermodynamics. Since thermodynamics imply that entropy (or disorder) will always increase, the universe is unavoidably hurdling towards a future of “equilibrium,” or heat death. This implies that the universe must have had a beginning, for if it had always existed, then we would already be in this state of equilibrium. Yet we are not, so the universe began to exist.
So, given this piece of evidence, what does Martin really mean when he says that science cannot establish a beginning to the universe? Clearly it can. Scientific evidence (laws of thermodynamics, observations that the universe is not in a state of equilibrium, etc.) lead to the inevitable conclusion (the universe had a beginning). On what basis does Martin deny this inference?
Even granting Martin’s dubious claim, the Cosmological Argument is not necessarily weakened the slightest. I would cheerfully grant that science proper does not permit the conclusion that the universe began, and instead claim that philosophy shows the conclusion true. Perhaps we could say that the argument from thermodynamics is a philosophical argument. The fact remains that the evidence points to a beginning of the universe and nonbelievers are going to have to explain it, like it or not.
Next Martin weakly claims, “Of course, given the present state of scientific theory there may be no scientific explanation of what came before the beginning of the universe. But the possibility cannot be excluded that further developments in science will provide answers.”  Yet I can hardly understand how this claim has anything whatsoever to do with the Cosmological Argument. Of course it is “possible” for future scientific discoveries to naturalistically explain the universe. But such mere possibilities do not equate with likelihood or even plausibility. If Martin wishes to provide a “Philosophical Justification” for atheism, then he must do more than appeal to “possible” future scientific discoveries in order to avert the inference to theism.
Moreover, it is indeed unlikely that future scientific discoveries will furnish a naturalistic explanation of the universe, for two reasons. First, the evidence for the universe’s origin is extremely compelling. Second, attempts to avert the beginning of the universe (such as the steady-state and oscillating models) have been thoroughly demolished by physicists and philosophers (including Craig) on the basis of evidence and lack of internal consistency.
However, even if Martin is right about the scientific evidence, the Cosmological Argument is still successful if the arguments against the actual infinity are sound. But, we have already seen that Martin fails miserably to even address, let alone refute, most of these arguments.
Martin mentions in passing that some scientists have entertained the possibility of an uncaused origin of the universe, thus countering Craig’s claim that such speculations are incapable of sincere affirmation. First of all, every model that Martin mentions has been crushed by Craig and others in print 5, and since Martin doesn’t even try to vindicate these models, the point is moot. But secondly, it seems to me that the “sincere affirmation” of the universe coming into existence out of nothing is more likely due to the necessity of such a postulation given the evidence for a beginning of the universe, if these thinkers wish to avoid the inference to theism. As Martin would probably admit, people will believe strange things when their worldview starts crumbling.
1. As I note in my article concerning the proper way to define God, it seems to me strictly impossible, even in theory, to know that God is actually omnipotent, omniscient, or omni-benevolent. For example, if God wished to prove to us that He was omnipotent, He may perform some incredible act. Yet, it seems that it will always be possible for a human to imagine some thing God could do that would be more incredible and require more power. Thus, omnipotence is strictly impossible to prove. However, as I explain in the article, Richard Swinburne has argued that omnipotence is more simple than near-omnipotence, and thus the preferred hypothesis.
2. Craig, William and Quentin Smith. Theism, Atheism, and Big Bang Cosmology (Oxford: 1993) p. 97
3. Ibid, p. 96
4. Ibid, p. 34
5. See Craig’s articles at http://www.leaderu.com/offices/billcraig/menus/existence.html.