The Infinite Hotel: William Lane Craig’s Ingenious Argument for a Finite Universe

In the years since its publication, William Lane Craig’s The Kalām Cosmological Argument has become a favorite of Christian apologists—and has been subject to fierce debate with prominent atheists such as Christopher Hitchens and Sam Harris.
In the book, Craig attempts to demonstrate that, at some point, the universe began to exist. This seems simple, but by doing so, he can then argue that the universe was caused to exist by a creator. To prove that the universe had a beginning, Craig employs a paradox conceived by the German mathematician David Hilbert:

 Let us imagine a hotel with a finite number of rooms, and let us assume that all the rooms are occupied. When a new guest arrives and requests a room, the proprietor apologizes, ‘Sorry—all the rooms are full.’

Of course, if this hotel contained an inifinite number of rooms, this wouldn’t be a problem . . . even if all the rooms were full. Craig explains:

When a new guest arrives and asks for a room, the proprietor exclaims, ‘But of course!’ and shifts the person in room one to room two, the person in room two to room three, the person in room three to room four, and so on . . . The new guest then moves into room one, which has now become vacant as a result of these transpositions.

Because there is an infinite number of rooms in the hotel, the proprietor can continue to shift the guests around in order to free up rooms—even though every room is full! If that concept doesn’t make your brain hurt, perhaps the next part will:

But now let us suppose that an infinite number of new guests arrive, asking for rooms. ‘Certainly! Certainly!’ says the proprietor, and he proceeds to move the person in room one into room two, the person in room two into room four, and the person in room three into room six, the person in room four into eight, and so on . . . In this way, all the odd-numbered rooms become free, and the infinity of new guests can easily be accommodated in them.

If you’re having trouble keeping track of all this gerrymandering, don’t feel alone. Mathematicians, philosophers, and theologians have long puzzled over this paradox, but they are in agreement on one thing: such an absurd hotel could never actually exist.
And that is precisely Craig’s point. This seems like a simple conclusion to draw from such a complex, mind-bending thought experiment.  However, it has profound implications. Craig argues that physicists and philosophers who propose a beginningless universe simply cannot be right.
Here’s how he puts it in his introduction to apologetics, Reasonable Faith:

If the universe never began to exist, then prior to the present there have existed an actually infinite number of previous events. Thus, a beginningless series of events in time entails an actually infinite number of things, namely, events.

However, as the paradox of Hilbert’s hotel demonstrates, such a notion is absurd. Having established that the universe must have had a beginning, Craig is free to argue that someone must have caused the universe to exist, namely, God.

Save on the Select Works of William Lane Craig!

Including The Kalām Cosmological Argument and The Cosmological Argument from Plato to Leibnizi, this collection is a great introduction to the work of an influential apologist.