tive and hopelessly paradoxical. If we are to accept the existence of infinity, we are being asked to accept absurdity. Therefore, it is argued, actual infinity cannot be possible.
             Craig does not deny that the idea of an actual infinite is impossible. A definition of the 'actual infinite' proposed by nineteenth century mathematician Georg Cantor shows the concept to be conceptually coherent. But because of the absurdities and paradoxes Craig observes in applying this definition in reality, he denies that this mathematically derived concept of an actual infinite can find any example in the real world (Craig 1993a, p. 10).
             For example, if a library existed with an infinite number of books, each numbered with a natural number, when we add one more book we have no remaining natural numbers available to assign to it (Craig 1993a, p. 12f). By removing the infinite number of even-numbered books we are still left with an infinite number of odd-numbered books, but by removing the infinite set of books numbered 4 and upwards, we are left with only 4 books with natural numbers. If one more guest arrives at a completely full and infinitely-roomed hotel ( 'Hilbert's Hotel'), all of the guests could be moved to the infinite number of rooms from room two onwards, and the new guest would be able to be accommodated in room one. So, the number of occupied rooms both increases by one and remains steady at infinity (Craig 1993a, p. 13f).
             Do these examples prove the absurdity of an actual infinite that exists in the real world? The central reason Craig's examples appear to be absurd is that he is applying the rules of the finite world to the infinite world (Mackie, p. 93; Smith 1996). Whereas, these rules simply do not apply to the infinite world. So it is not an actually infinite world that has a problem, it is Craig's methodology that has the problem. It is as though Craig is using a thermometer to ...