The Kalam Cosmological argument, by showing that the universe began to exist, demonstrates that the world is not a necessary being and, therefore, not self-explanatory with respect to its existence.  This is one form of the cosmological argument that is much neglected by philosophers and cosmologists today, but is, nevertheless, of great historical importance.  The aim of this argument is to show that the universe had a beginning in time.  The argument originates from the efforts of Christian theologians to refute the Greek doctrine of the eternity of matter and was developed and reformulated by medieval Islamic and Jewish theologians, who in turn, passed it back to the Latin West. Dr. Willian Lane Craig, a Christian apologist, has authored books and given public treatments of the argument.  He is the argument's greatest proponent.  The argument has inter-sectarian appeal, because it is defended by Muslims, Jews, Catholics and Protestants.  The argument proceeds as follows:

1. Whatever begins to exist has a cause of its existence.
2. The universe began to exist.
   *Argument based on the impossibility of an actual infinite.  (An actual infinite cannot exist.  An infinite temporal regress of events is an actual infinite.  Therefore, an infinite temporal regress of events cannot exist.)
   *Argument based on the impossibility of the formation of an actual infinite by successive addition.  (A collection formed by successive addition cannot be actually infinte.  The temporal series of past events is a collection formed by successive addition.  Therefore, the temporal series of past events cannot be actually infinite.)
3. Therefore, the universe had a cause of its existence.

The argument clearly lies in (2).  But let us have a clear understanding of the terms involved.  A 'potential infinite' is a collection which is incresing towards infinity as a limit but never reaches that point.  Such a collection is really indefinite, not infinite.  An antual infinite is a collection in which the number of members is really infinite.  The collection is not growing towards infinity; it is 'complete' in this sense.  The argument maintains that an actual infinte cannot exist.  A great illustration of this is Hilbert's Hotel.  This is a hotel wherein the number of rooms and people occupying those rooms are actually infinite.  Every room is full.  In a situation like this, though, a hotel manager could still manage to fit in another person.  Simply have each guest slide 'down' one room.  The new guest can check into room 1 and the remainder of the guest finds accommodations in the room next to them.  In fact, the hotel manager could manage to fit in an infinite busload of guests into the hotel.  He could simply have his guests move into the room that is twice the number of their orginal room.  This would open up an infinite number of rooms.

The Kalam cosmological argument has not been undisputed.  Several modern philosophers and the scientific community in general have raised points as to the arguments' soundness.  In general, though, I feel that this particular cosmological argument is sound and is very defendable.

I think this argument for the existence of God is interesting for the simple fact that it uses a bit of set theory.  The crux of the argument lies not on some complex, philosophical argument, but rather on the reality and structure of numbers and sets.  For the individual who spent his school days complaining about the uselessness of mathematics, the Kalam argument presents quite a twist.

"Man is equally incapable of seeing the nothingness from which he emerges and the infinity in which he is engulfed." - Blaise Pascal

Author: Clarence L. Terry

References:
<http://www.geocities.com/Athens/8160>
<http://www.origins.org/truth>
<http://www.str.org>