Aristotle thought that the universe was infinitely old and that it will continue to exist infinitely. John Philoponus, a Christian, argues against this by saying that this is impossible. It goes like this:
(1) If the world had an infinite past, then it got to today by traversing an infinite number of days
(2) It is impossible to traverse an infinite number of days
(3) The world has not traversed an infinite number of days
(4) Therefore, the world is not infinitely old, but finitely old
(2) is the crucial premise and is doing all the work. It can be illustrated like this though: If I asked you to travel to a place that was infinitely far away, could you ever actually get there? I think Philoponus is right, if the universe really was infinitely old, then we would never have gotten to today, but we did so it’s not.
Some people think that this is similar to one of Zeno’s paradoxes. And if kind of is. Zeno thought that you couldn’t walk across a room because if you walked half the distance every time, you would approach the limit of the other side of the room, but never cross it. From this he concluded that there is no change and the real world was static, much like Parmenides. Can this be applied to this argument? The problem with Zeno’s paradox is that if we just make the distance we travel constant, then we can cross the room. But either way we cut the infinite distance, we are still going to have to cross and infinite. Half of an infinite is still an infinite.
So I think this is a good argument.
