Can There Be An Infinite Series of Escapes From Kalam?

by Glenn Smith

One of the demonstrations for the existence of God is the Kalam Cosmological Argument, which claims that the universe had a beginning, and therefore needed a beginner. At its root, it is quite simple, for anything that comes to be must have a cause. Of itself, the Kalam demonstration does not get us the God of the Bible, but further reasoning after the Kalam can get us to God’s attributes.

One of the supports for the demonstration is that there cannot be an infinite series of moments prior to now, so there must be a beginning.  Most of the arguments about infinites in Kalam are dealt with by those philosophically trained theists who understand the Kalam. Perhaps the leading supporter of Kalam is William Lane Craig, whose book The Kalam Cosmological Argument has a lengthy section on infinity. Craig also includes 25 pages of detailed defense of his position on infinity in The Blackwell Companion to Natural Theology.

Skeptics and atheists are not silent on this point, of course, and have fun entangling theists in conundrums about infinites. I’m convinced most of them do not read the detailed explanations in the writings of men like Craig, but either get their information from popular online sources such as YouTube or do not listen to theists at all, but merely pass around criticisms among themselves. If they would have read the detailed explanations of Kalam, they would not make the same mistakes over and over.

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One of the key positions of the Kalam argument is that the there cannot be an infinite series of moments prior to now, so there must be a beginning. One of the supports for this is the following:

  • A collection formed by successive addition cannot be an actual infinite.
  • The temporal series of events is a collection formed by successive addition.
  • Therefore, the temporal series of events cannot be an actual infinite. (Craig, Natural Theology, p.117)

Skeptics respond with a series of criticisms, most of which are off point. They give arguments such as infinity being used in mathematics. Indeed, interesting and odd things can be found when one tries to nail down the properties of infinity. For example, the mathematician Bolzano (1781 – 1848) pointed out that if we take the simple function y=2x, and apply it to all the numbers between 0 and 1, then “every real number between o and 1 is assigned a unique companion between 0 and 2. Therefore, Bolzano concluded, there are as many numbers between 0 and 1 as there are in the interval 0 to 2, which has twice the length of the 0 to 1 interval.” (Aczel, The Mystery of the Aleph, p.61).

Further, we can take an infinite set of whole numbers, and compare it to an infinite set of odd numbers, and an infinite set of squared numbers, and the different sets will be the same size: infinite. Such are the games people play with defining infinity…

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