Dr. Craig's main argument for the existence of God has been the Kalam Argument. He worked on it for his Ph.D. in philosophy.
It goes like this.
1. Whatever begins to exist has a cause
2. The Universe began to exist
Conclusion: The Universe had a cause
He explains that Premise 1 is well accepted by philosophers as not only true, but necessarily true (meaning that it cannot be false)
He gives two arguments from science and two arguments from mathematics that the physical world cannot be eternal in the past but must have had a beginning. He says that the conclusion of this argument lets you draw a lot of conclusions about the Creator: that He is spaceless, timeless, extraordinarily powerful, and personal.
However, he said that it does not prove that God exists necessarily (that He cannot not exist)
So I asked him: "Why not? If the mathematical arguments are sound, then it is impossible for any physical world to be eternal in the past. If so, then both premises are not just true, but necessarily true. Which means the conclusion is necessarily true."
Or more specifically: Any possible world in which anything physical exists must have a transcendent personal creator.
A smile crept on Dr. Craig's face as he told me: "That's...true. Did you think of that yourself or did someone tell you this?"
I told him that I thought of this myself.
He then said: "I never thought of that before, and no one told me it, either. I'm going to add that to my presentations on the Kalam Argument"
It's really awesome being able to make a contribution to the philosophy of religion field.