Dear Dr Craig
I am a devout Christian and I read your Q&A every week. I have read Q#323 today and I was totally surprised by it because it is basically exactly what I have been thinking about for the last couple of days. Infinity is a concept that has been driving me nuts as I cannot completely fathom it. A few comments I want to make:
1. Is it possible that God could have counted the whole set of natural numbers? The answer according to me is no. Why? Because the set of natural numbers is infinite. You will never stop counting. So even though God is almighty, He cannot do things like these. It simply doesn't make sense. It's like saying God can create a rock that He cannot lift. It's a logical incoherent statement.
2. Regarding the existence of abstract objects: One thing that has bugged me about this is the whole thing about infinity. Does it exist? I have read some of your comments on this, namely that you say that infinity is a mere concept of the mind that doesn't exist in the real word. This makes sense to me. So if there are an infinite amount of natural numbers, how could they all exist? Well I believe numbers exist in two to three ways:
a. Since numbers are mere concepts, they exist in our minds as we think about them.
b. Numbers exist conceptually as real world objects represent them. I.e. the number of planets in the solar system.
c. They exist conceptually as symbols on a piece of paper (or computer screen).
Because only a finite amount of thoughts, objects and written symbols exist, it follows that only a finite amount of real numbers exist in the real world.
3. Abstract objects aren't limited to numbers. It includes things like music, literature and other forms of art. Now there are an infinite amount of songs that can be composed. Do they all exist? Again the same line of reasoning goes. A tune lives in the mind of the one that composed it and the ones who hear it. It is a concept, an idea which didn't exist before someone thought about it. So there are only a finite number of art forms in the real world and always will be even though the number increases all the time.
4. Now I want to say something about the future. God as we know can foresee the future. This is what makes prophecy possible. We know that the world has a beginning, and it will have an end in this age as the Bible predicts, but the age to come will have no end. So the number of future events counts up to infinity. Now is it possible for God to know everything in the future? Again as explained above this is impossible. One cannot know an infinite amount of things. It is simply an illogical thing to ask from someone like God, even though He is almighty, and I am not trying to limit Him in any way. So God knows the future. How much and how far? Well as much as He chooses or as far He deems necessary.
These are my comments. I therefore believe God is almighty, but He cannot do illogical things, or know things that do not exist. Thanks for reading and please let me know if you agree with my views. Also please tell me of articles I can read which might give me more insight into these things.
Finally I want to thank you for the work you're doing. I think you're making a big difference in many people's lives.
Click HERE to read Dr. Craig's answer