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.
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.
The problem, of course, is that these are mathematical abstracts, not actual infinity. Craig’s point in Kalam is not denying that we can do slippery things in mathematics with infinity – no one in apologetics denies that. The Kalam denies actual infinity that is reached by successive addition. This is a very different thing than abstract infinity in math formulas, or possible numbers between two points. We can indeed do math that shows an infinite set of numbers within an inch. However, no matter how hard we try, we cannot add an infinite number of sheets of paper into a one-inch binder. No matter how thin the paper, or how hard we squeeze, we can only add a finite number of sheets of paper into one inch.
The Kalam also deals with successive addition. It is a brute fact that in a series derived by successive addition, we always have an ever-increasing finite, not an infinite. As Craig explains:
It follows, then, that the temporal series of events cannot be actually infinite. The only way a collection of which members are being successively added could be actually infinite would be for it to have an infinite tenselessly existing “core” to which additions are being made. But then, it would not be a collection formed by successive 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. (Natural Theology, 124-125)
As apologists, we find ourselves repeatedly having to explain that in dealing with objects in the universe being measured by moments of time, we are dealing with actual, real things, not abstract distances between two points on an imaginary timeline. We are dealing with actual, real things that are occurring successively. Adding to very large finites merely gives us bigger finites.
There is a group that is trying to build a clock that will run for 10,000 years. Let’s say they succeed. We can be sure of two things. First, it may run for a long time, but it will not run forever, for eventually the forces of nature will stop it. Second, if someone finds it someday, they will be able to conclude that since it is running, someone had to start it. It could not have been running for an infinite amount of time.
In the work of Craig and other theists who specialize in the Kalam, they deal with much more detail than can be done on this blog. I still wonder if the skeptics have truly read the detailed explanations of Kalam. I also wonder if they truly believe their positions, or if they just like to have fun slipping around in the world of abstract infinity. In the end, the Kalam Argument is a valid demonstration that shows the universe had a beginning and therefore needed a Beginner.