In a real library, removing a certain number of books reduces the overall collection. But if infinites are actual, a library with an infinite number of books would not be reduced in size at all by removal of a specific number of books, such as all the red books or those with even catalogue numbers.

Since conclusion 8 follows validly, if premises 6 and 7 are true the argument is sound. In defense of premise 6, he defines an actual infinite as a determinate totality that occurs when a part of a system can be put into a one-to-one correspondence with the entire system (Craig and Sinclair 2009: 104). Craig argues that if actual infinites that neither increase nor decrease in the number of members they contain were to really exist, rather absurd consequences would result. For example, imagine a library with an actually infinite number of books. Suppose that the library also contains an infini...