Consider the following two premises that are accepted by several theistic philosophers:
- God is a being than which no greater can be conceived.
- An actual infinite is logically absurd.
I contend that if one wants to accept Premise 1, then one must reject Premise 2 (along with any argument that relies on it). Why? Well, I think that if Premise 1 is true, then God can count to infinity. To see why, let’s suppose that Premise 1 is true.
Now, if there was a limit to the speed at which a certain being could think or speak, then I could conceive of a greater being — one that could think or speak faster. Therefore, since we are assuming Premise 1 is true, there is no limit to how fast God could think or speak. So now consider the following scenario:
- At one minute to midnight, God says “one”.
- Half a minute later, he says “two”.
- A quarter of a minute later, he says “three”.
- An eighth of a minute later, he says “four”.
- And on, and on…
- For good measure, at midnight he says “infinity”.
By midnight, he would have counted through all the natural numbers: 1, 2, 3, 4, 5, …… and got to infinity. Not a single number would have been left out. Even if God did not actually carry out such a task, the fact remains that he could do it if he wanted to. It follows that an actual infinite (which would supposedly have been completed if someone spoke the name of all the natural numbers) is logically possible. And this implies that Premise 2 is false.