The Rejection of Pascal's Wager
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Kalam Cosmological Argument

William Craig in his book The Kalam Cosmological Argument (1979), revived an old sixth century version of the cosmological argument. The argument actually originated from a Christian philosopher in Alexandria in the sixth century but was later developed by medieval Islamic theologians of the Kalam school.

The Basic Argument of the Kalam

The basic argument of the Kalam is as follows:
1. Everything that begins to exists has a cause for its existence
2. The universe began to exist (i.e. it is not infinite)
Therefore: The universe has a cause of its existence.

The first premise states that nothing which originates in time can be causeless. In other words, if it begins to exists at a certain point in time, something must have caused it to begin existing.

The second premise is rooted in the Kalam school's skepticism of the concept of infinity. They argued that while infinity may be possible in the mathematician's mind it is not a property of the real world. According to Craig the crux of the whole argument lies in this premise. He provided two basic groups of "proofs" as to why the universe has to be of finite duration:

1. A priori Proofs

Craig claims that even in mathematics, infinity has paradoxical implications. And although it may form a coherent mathematical system, it has no bearing on the existence of actual infinity in the real world. He gives an example of how thinking about an actual infinity leads to absurd implications. Consider a library that contains an infinite number of books. Each book is sequentially numbered in a one to one correspondence with natural numbers (i.e. 1,2,3 and so on). This means that every possible natural number is printed on some book. Now if one were to add another book to the library it would be impossible to allocate a natural numbers to it since all the numbers have already been taken. This, according to Craig is absurd, "since entities that exist in reality can be numbered".

Another example Craig gives is that of succesive addition. For every number n, one can always add "1", n + 1. Thus one can never reach infinity by successive addition.

2. Empirical/Scientific Proofs

Craig argues that evidence from the sciences actually supports a finite (in time) universe. The science of modern cosmology, the "Big Bang Theory", actually supports the hypothesis that the universe had a beginning at a finite point in the past, some fifteen billion years ago. Furthermore, the second law of thermodynamics predicts that if the universe is infinitely old, it would have reached maximum entropy
[a] (or chaos) long time ago. Yet we are obviously still in a stage of low entropy, since the stars still shine and we are still here. Thus the universe must have a beginning. [1]

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A Critique of the Kalam Cosmological Argument

It should first be noted that even if the Kalam argument is successful, it can prove, at most, that the universe is caused. It could not show if the universe had a single cause, or if it was caused by a single (or multiple) personal agent(s) or even that the cause of the universe is the first cause. It certainly does not show that the cause is what we would define as God.

We will see that even this modest goal has not been achieved.

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. [2]

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! [3]. Is causation an inductive principle? In other words, is it somethign 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.[b] 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. [4] 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. [5]

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.[6]


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.

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a.Entropy is mathematically represented as the ratio of the change of energy over temperature (dQ/T). It is a measurement of "reversibility" and is a measure of a very fundamental fact of nature. Things left to themselves tend to degrade. Thus a hot cup of coffee left at room temperature will cool down to room temperature. In short, it measures the natural decay of order into chaos.
b.See for instance "The Contrarian Theological Afterword" in the book The Whole Shebang (1998) by Timothy Ferris.


1.Martin, Atheism, A Philosophical Justification: p101-103
2.ibid: p103-105
3.Poidevin, Arguing for Atheism: p10-22
4.Gribbin, In Search of the Big Bang: p372-375
5.Ferris, The Whole Shebang: p247
6.ibid: p247

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