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. 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.
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.
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. 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 except Sobel applies this to modern cosmology, which flies in the face of the consensus of modern cosmological scholarship.
 1) Whatever begins to exist has a cause. 2) The universe began to exist. 3) Therefore, the universe had a cause.
 Paul Copan and William Lane Craig, Creation out of Nothing: A Biblical, Philosophical, and Scientific Exploration (Grand Rapids, MI: Baker Academic, 2005), 200.
 William Lane Craig, “J. Howard Sobel on the Kalam Cosmological Argument.” Canadian Journal of Philosophy 36 (2006): 565-569.
 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.
 See Mark Nowacki, “Assessing the Kalam Cosmological Argument,” Philosophia Christi 12 (2010): 201-212.