Both the Bible and the earliest Greek philosophers begin with accounts of the world's genesis. It is thus not surprising that medieval cosmological thought was preoccupied, perhaps obsessed, with the issue of creation. But what about the end of the world? If the universe had a beginning, does it necessarily have an end? Does creation imply destruction? On this topic the Bible is not so explicit and unambiguous. Greek philosophy, however, was virtually unanimous in claiming that whatever has a beginning will have an end, and that whatever will have an end had a beginning. If this cosmological principle is construed strictly, then the world's past and its future are essentially and necessarily linked together, such that the finitude of one entails the finitude of the other. This would mean that if the temporal history of the world is finite a pane ante, then by virtue of this cosmological principle it will have a temporal end a pane post. The most vigorous and detailed defense of the strict interpretation of this general principle was given by Aristotle, who attempted to prove it in his treatise On the Heavens. Henceforth, I shall refer to this principle as “Aristotle's theorem.”