William Lane Craig’s “J. Howard Sobel on the Kalam Cosmological Argument”–A Review

by Max Andrews

A Review of William Lane Craig’s “J. Howard Sobel on the Kalam Cosmological Argument.” Canadian Journal of Philosophy 36 (2006): 565-584.

William Lane Craig formulates retort to J. Howard Sobel’s objection to kalam as he typically formulates it.[1] Premise 1 seems obviously true—at least, more than its negation.  To suggest that things could just pop into being uncaused out of nothing is to quit doing serious metaphysics and is a premise that Sobel acknowledges to be true.  Sobel’s objection is with 2—that the universe began to exist.  This would then run into an infinite regress, which is philosophically and mathematically untenable.  Because an actually infinite number of things cannot exist, the series of past events must be finite in number and, hence, the temporal series of past, physical events is not without beginning.[2]

Before getting into the exchange on actual infinites in fieri they seem to focus attention on Thomas’ arguments on contingency.  Sobel seems to want to apply another Cantorian set to his association of numbers.  Sobel seems to confuse Aquinas’ mathematico-metaphysical claim that there are no infinite numbers with some sort of stricture on the use of words. One can re-define “number” to mean “natural number” if desired, and then Thomas would agree that there is no “number” associated with an infinite multitude.[3]

There is a difference between an actual infinite and a concept of indefinite quantity.  A א cannot actually be formed because a series of events, (E), is formed by successive addition.    A collection formed by successive addition cannot be actually infinite and therefore, a series of events cannot be actually infinite.  For an actual infinite to be spatiotemporally actual א would be equivalent to any set (E).  To illustrate this absurdity:  א=(E), and א=(E+1), and א=(E-1) would all have to hold the same truth-value and the same actual collection of events, which is completely unintelligible.

What is true is the idea of ∞=E.  Consider an illustration of a line with three points A, B, and C.  A and B are twice as close to each other as C is to B.  No matter how many times the distance between any of these points are divided, it will never come to an absolute end of division.[4]  The distances between the points are indefinite, not infinite.  However, consider A, B, and C as spatiotemporal physical points.  The concept of infinity is still there, but one may actually travel that distance—the distance is not without end.  The idea of an indefinite quantity, ∞, possibly existing does no justice to defeating the argument.  What Sobel needs to do to refute the argument is to prove that א is actually possible.  The philosophical and mathematical evidence suggest that an actual infinite is impossible, thus, the series of causes for the universe had a beginning.

Craig devotes much attention to the philosophical and mathematical ramifications to an actual infinite.  Sobel makes a suggestion that there was initial time prior to the creation of this universe.  To use the conical illustration of space-time, Sobel’s understanding of the initial time would run perpendicular to the present conical plane from the cone’s initial singularity.  The time posited is a metaphysical time.  Craig’s response is that to suggest that a metaphysical time be inclusive with the metaphysical claim that nothing can begin to exist uncaused is still metaphysically inconsistent and Sobel’s positing of such time is not needed and does not really advance his argument.  Craig then proceeds to provide a counterpoint argument based on contemporary cosmology and the big bang standard model.

What is interesting about Sobel’s metaphysical time is that he posits a beginningless series on metaphysical grounds respective to the actual physics.  His argument, if the metaphysical principle Craig responds with stands true, is really self-defeating.  It is interesting to see this posit of metaphysical time rather than the popular geometric time advocated by other objectors to kalam.  Craig harshly criticized Sobel for his radical revisions of contemporary cosmology.

Craig’s summation and responses to Sobel are the same that Craig gives in the rest of his aggregate literature concerning kalam.  He will address the particular objection and tie it back to an initial principle premised in his formulation of the argument.  Sobel’s attempt is similar to the Nowacki-Guminski dialogue concerning Cantorian sets[5] except Sobel applies this to modern cosmology, which flies in the face of the consensus of modern cosmological scholarship.


[1] 1) Whatever begins to exist has a cause. 2) The universe began to exist. 3) Therefore, the universe had a cause.

[2] Paul Copan and William Lane Craig, Creation out of Nothing:  A Biblical, Philosophical, and Scientific Exploration (Grand Rapids, MI:  Baker Academic, 2005), 200.

[3] William Lane Craig, “J. Howard Sobel on the Kalam Cosmological Argument.” Canadian Journal of Philosophy 36 (2006): 565-569.

[4] Some physicists may object to this notion, Zeno’s paradox, by stating that if this line were to exist in a spatiotemporal dimension with physics at are currently known then this point cannot be smaller than any Planck distance.

[5] See Mark Nowacki, “Assessing the Kalam Cosmological Argument,” Philosophia Christi 12 (2010):  201-212.


7 Comments to “William Lane Craig’s “J. Howard Sobel on the Kalam Cosmological Argument”–A Review”

  1. Craig’s own theory appears to be that infinite regress is avoided by postulating a deity that exists outside of time. However, this creates its own problem. Creation requires the existence of time. How does this deity create a universe and create time itself if it exists outside of time? How is an uncaused being any less of a problem than an uncaused universe?

    And if one further claims that this being is perfect – as Craig does – then one has another problem – if this being creates something, It must have desired to create it (unless the creation was against Its own will). A being with desires cannot be complete and therefore cannot be perfect.

    • Eloquent refutation. LOVE IT! (although I think it might be more intellectually stimulating to try to address real problems instead of refuting the ramblings of idiots)

  2. @Andrew Ryan

    “How is an uncaused being any less of a problem than an uncaused universe?”

    The first premise of the argument is not that *everything* that exists has a cause, but that everything that *begins to exist* has a cause. The problem is that the ‘uncaused’ universe has a beginning, while the former being does not, and hence it requires a cause of its existence, while the former one does not.

    “And if one further claims that this being is perfect – as Craig does – then one has another problem – if this being creates something, It must have desired to create it (unless the creation was against Its own will). A being with desires cannot be complete and therefore cannot be perfect.”

    Why should I believe that a being with desires cannot be perfect? That’s just an unsupported assertion in your argument, and rather circular if that’s what you’re trying to prove. Let’s say that a being B desires those things which are morally good. Does this desire make B any less perfect? I don’t think so. Let’s say this being B desires to make creatures with the freedom to do moral choices. Does this desire make B any less perfect? Clearly not.

    I’m not quite sure why you mean by ‘complete.’ If by ‘complete’ you mean God *requires* the existence of creation and creatures, then that is simply false. There are possible worlds where God abstains from creation, hence the orthodox theological position that God’s act of creation is one from which God could have *chosen* to abstain.

    Desire and necessity are very different things, Andrew. I could desire something, but that in no way means that I *must* have or somehow depend on that something.

    • Nope, the distinction you make between desires makes no difference to my argument. If you desire something then simple logic dictates you can’t be perfect.

      An eternal universe can endlessly spawn new universes in a cycle of big bangs and subsequent crunches.

      There are severe problems in postulating a timeless being creating anything, especially time itself.

    • “I could desire something, but that in no way means that I *must* have or somehow depend on that something”

      If you want a soda, that means you think a soda would improve your situation – whether you actually depend on it, or feel you *must* have it, is irrelevant to that point. There are two scenarios – one where you have the soda, the other without, and the former is better than the latter.

      Given that, you cannot claim your present situation is ‘unimprovable’, since you know a way it can be improved.

      WLC has actually been confronted with this argument and his reply was that God created us for OUR benefit, not his own. However, this doesn’t solve the problem. If you want that soda for your friend, not yourself, it doesn’t affect the point that you still want that soda, even if it’s for someone else.

      • Please Andrew Ryan, give me an example of how big bangs could continue to cycle big bangs and subsequent crutches. Are there any examples of this being seen? We know that a Big Bang most likely took place, but unless something created it or caused it, it continues to be an issue of an infinite regress. A big bang would cause a big band, which would cause a big bang, etc. but what caused the first one? It couldn’t be chance-chance is a nonpower and a nonpower cannot bring something into existence. Nothing cannot create something, and if there were constantly big bangs spawning new universes, there would be no explanation as to the beginning of those big bangs. You have not answered the question regarding the issue of an infinite regress. Unless there is a being creating and causing the universe to take place, it continues to be illogical. The being exists outside of time, and without the dimension of time, there is no cause and effect. All things that could exist in such a realm would have no need of being caused, but would have always existed. This being that created the universe would have no need of being created, but, in fact, created the time dimension of our universe so that cause and effect would exist for us. Since God created time, cause and effect would never apply to His existence. The only answer for someone doubting this would be the invention of a kind of super universe, which can never be confirmed experimentally (hence it is metaphysical in nature, and not scientific).

        • “The being exists outside of time, and without the dimension of time, there is no cause and effect.”

          Then it would be impossible for this being to create anything – even time itself – as that would require time.
          Positing an eternal being is no less problematic than positing an eternal universe. In fact it’s MORE problematic – we at least know the universe exists!

          “…but what caused the first one?”

          If it’s eternal then there would BE no ‘first one’.

          “You have not answered the question regarding the issue of an infinite regress.”

          I have.

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