If Actual Infinites Cannot Exist, How Can We Say God Is Infinite?
by Evan Minton
In defense of the Kalam Cosmological Argument, apologists such as William Lane Craig, Frank Turek, and myself will argue for the second premise (i.e that the universe had a beginning to its existence) by arguing that an actually infinite number of things are impossible. If an actually infinite number of things are impossible, then a beginningless universe cannot exist since it would involve an actually infinite number of things existing, namely, past events. If you’ve read my book Inference To The One True God, you’ll know that the reason to believe an actually infinite number of things cannot exist is that if they could, various absurdities would result. For example, if I had an actually infinite number of CDs all with an infinite number of songs on them, if you listened to only one CD, you would hear the same number of songs as you would if you had listened to every CD in my collection.
The problem though is that this argument seems to help the Christian in one area, but hurts him in another, for if actual infinities cannot exist, in what way can we say that God is infinite? Isn’t God infinitely powerful, infinitely good, and knows an infinite number of truths? It would seem that we would either have to backpedal and say actual infinities really can exist after all, or we would have to say that God is not a Maximally Great Being. Frankly, the former is preferrable After all, we could still affirm the second premise of the Kalam argument by means of The Big Bang, the second law of thermodynamics, and the impossibility of traversing infinities. However, the arguments against actual infinities existing seem compelling…
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