This chapter considers the response of St. Thomas to objections to the doctrine that the world could be infinite in past time. His argument was immediately attacked and continues to be so, but the criticisms are unfounded. The chapter concentrates on one major line of attack, put forward by van Steen-berghen, who has argued that Thomas is guilty of an inconsistency inasmuch as his position concerning the eternity of the world is incompatible with his position concerning the possibility of an actual infinite multitude. It begins by looking briefly at the historical background; then argues that St. Thomas's arguments concerning the acceptability of the traversal argument are sound. Finally, the chapter suggests some reasons for rejecting the claim of inconsistency. With hindsight we can see that Aquinas's argument does not tell against actual infinities, for the heart of his argument is this: every kind of multitude must belong to a species of multitude.