I want to throw this little argument out for comment. (This type of argument was first suggested to me in correspondence with Mike Almeida. My colleague, Michael Tooley, thinks that an argument along these lines is sound.)
The argument implicitly assumes two things.
1. Time is infinitely divisible.
2. There is no least amount of time that it would take God to create a hotel room.
If these assumptions are granted, then it seems that God could not only create a Hilbert’s Hotel, but could do so by successive addition. As I’ll describe the scenario, God does it in two hours.
During the first hour, God creates the first room. During the next half hour, He creates the second room, during the next fifteen minutes, He creates the third room, during the next seven and a half minutes, He creates the fourth. He continues in this manner until two hours have elapsed. At that point, God has created infinitely many rooms.
We’re (obviously) dealing with an actual infinite here, since the two hours have elapsed, and all the rooms have been created. So it looks as if an actually infinite number of “room creations” have taken place and an actually infinite number of rooms exist at the end of the two hours.
This sort of scenario has a familiar air of Zeno-like paradox. Add the following twist on it to bring out the weirdness. Suppose that there’s a switch with just two positions: ON and OFF. At the start of the process, the switch is in the OFF position. Every time God creates a room, He changes the position of the switch. Will the switch be ON or OFF at the end of the process?
This question is not answerable, given merely what’s specified in the scenario as I have described it. The infinite series of switchings does not entail either that the switch will be ON or that it will be OFF. It could be either.
Does this show that the whole scenario is impossible?
In his discussion of “supertasks” in an appendix to The Kalam Cosmological Argument, Craig discusses scenarios like this one, and declares them to be impossible. Why? Because the position of the switch at the end of the two hours must be causally determined by what went on during the two hours. The only way for that to be so is for there to have been an “infinitieth” change in the position of the switch. But there can’t be any such number. At any point during the series of switchings the number that have occurred is finite.
I am not satisfied with this response. What does “must” mean in “must be causally determined by what went on during the two hours?” In order to show that the scenario involving God is impossible, it must have the force of metaphysical necessity. So understood, I don’t think Craig’s claim is true.
Craig’s claim might be true if we were dealing with a merely natural process (in which, among other things, nothing can travel faster than the speed of light). But a God who can create the entire universe out of nothing need not be bound by the causal rules that hold in the world He has created. So I don’t see why God couldn’t simply settle the matter. If God so chooses, the switch is in the ON position at the end of the process. If God so chooses, it is in the OFF position. If God so chooses, the switch ceases to exist altogether. The fact that the scenario by itself doesn’t tell us which position the switch will be in does not therefore show that the scenario metaphysically impossible.
As far as I can see, the only way to block the argument as I’ve stated it is to reject the claim that time is infinitely divisible. If, for example, you thought that any finite chunk of duration was necessarily made up of finitely many temporal atoms each of which comes into being all at once and ceases to be all at once, then the scenario would be impossible. Even an omnipotent God would run out of sets of temporal atoms in which to create hotel rooms.
I’m not a philosopher of time, but it does seem to me that this solution isn’t very plausible. Others may have more sophisticated thoughts.