Before the 19th century it was commonly understood that only God (or perhaps the “gods”) were actually infinite. If one spoke about the actual infinite, one was doing theology. In mathematics infinity was considered a manner of speaking, which was clarified in the early 19th century with the careful definition of limits.
In the late 19th century Cantor’s infinite sets were seen as a challenge to this because they treated infinite sets as complete entities. But there is still no need to consider this essentially different from the relative manner infinity is treated elsewhere in mathematics.
The idea that the universe may be eternal is ancient but there has never been a comprehensive treatment of what this would mean. Theologians are still struggling to understand in what sense time could exist before the creation. Nonmetric time seems to be the best solution.
The burden is on anyone who speaks of a physical infinite to explain in detail what they mean. Otherwise, they’re just throwing words around.
August 2014