Hilbert's paradox of the Grand Hotel is a mathematical veridical paradox (a non-contradictory speculation that is strongly counter-intuitive) about infinite sets presented by German mathematician David Hilbert (1862–1943). David Hilbert posed this paradox in the 1920s to illustrate the mysterious properties of the infinite.

Consider a hypothetical hotel with countably infinitely many rooms, all of which are occupied – that is to say every room contains a guest. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms.

Suppose a new guest arrives and wishes to be accommodated in the hotel. Because the hotel has infinitely many rooms, we can move the guest occupying room 1 to room 2, the guest occupying room 2 to room 3 and so on, and fit the newcomer into room 1. By repeating this procedure, it is possible to make room for any finite number of new guests.

It is also possible to accommodate a countably infinite number of new guests: just move the person occupying room 1 to room 2, the guest occupying room 2 to room 4, and in general room n to room 2n, and all the odd-numbered rooms will be free for the new guests.

William Lane Craig (born August 23, 1949) is an American analytic philosopher, philosophical theologian, and Christian apologist. He is known for his work in the philosophy of religion, philosophy of time, and the defense of Christian theism. One of his most notable contributions to the philosophy of religion is his defense of the Kalām cosmological argument, which is the most widely discussed argument for the existence of God in contemporary Western philosophy. In theology, he has also defended Molinism and the belief that God is, since Creation, subject to time.

Craig has authored or edited over 30 books, including The Kalām Cosmological Argument (1979), The Cosmological Argument from Plato to Leibniz (1980), Theism, Atheism, and Big Bang Cosmology (with Quentin Smith, 1993), Philosophical Foundations for a Christian Worldview (with J.P. Moreland, 2003) and Reasonable Faith: Christian Truth and Apologetics (3d edition, 2008).

Craig received a Bachelor of Arts degree in communications from Wheaton College, Illinois, in 1971 and two summa cum laude master's degrees from Trinity Evangelical Divinity School in Deerfield, Illinois, in 1975, in philosophy of religion and ecclesiastical history. He earned a Ph.D. in philosophy under John Hick at the University of Birmingham, England in 1977 and a Th.D. under Wolfhart Pannenberg at the University of Munich in 1984.