The actual infinity of the universe
The universe has existed for an infinite time because for each day, there is a preceding day. In Aristotle's opinion, however, this is a potential infinity, as these days do not co-exists at the same time, an actual infinity - in which an infinite number of things all exists at the same time - is impossible.
There has been a conflicting point of view about the infinity of Universe. The eastern and Western philosophers always had conflicting theories. The arguments become more complexed when thinkers debated about potential infinity and actual infinity. According to Aristotle the infinite is what has no limit. For instance, the sequence of numbers is infinite, because for each number, there is another higher number that follows. Similarly, the universe has existed for an infinite time because for each day, there is a preceding day. In Aristotle's opinion, however, this is a potential infinity, as these days do not co-exists at the same time, an actual infinity - in which an infinite number of things all exists at the same time - is impossible.
Philoponus and his thirteenth century followers however think that this argument presents problems that Aristotle had not noticed. They point to the fact that he believes that all the types of living beings in the universe has always existed. If this very true, they say, it would mean that there were already an infinite number of human beings, by the time Socrates was born - because if they have always existed, they existed then. But since Socrates time, many more humans have been born, and so the number of humans born up until now must be greater than infinity. But no number can be greater than infinity.
In addition, these writers add, Christian thinkers believe that human souls are immortal. If this is so, and infinity number of humans has already existed, there must be an infinity number of human souls in existence now. So there is an actual infinity of souls, not a potential infinity ; and Aristotle has said actual infinity is impossible. The eastern philosophers have explained this phenomenon by apparent and dormant forms of souls.
With theses two arguments using Aristotle's own principles as a starting point, Philoponus and his followers were confident that they had demonstrated that the universe cannot always have existed. Aristotle was wrong that Universe is not eternal and this fits perfectly with the christian doctrine, that God created the world.
Aquinas has little time for this kind of reasoning. He points out that Universe could have existed forever but that species such as humans and other animals might had a beginning so the difficulties raised by Philoponus and his followers can be avoided. Despite his defence of Aristotle's reasoning Aquinas does not accept Aristotle assertion that the Universe is eternal because the Christian faith says otherwise but he does not think that Aristotle's position is illogical.