An Infinite Universe is Impossible

 

The idea of a universe that is not past-eternal is held by most theists who believe that God created the universe. By contrast, many atheists believe in a past-eternal universe, which presumably rules out the need for any creator. So while the topic of this post is not explicitly regarding the existence of God, it is still of key theological importance. For instance, the second premise of the traditional Kalam Cosmological argument states, "The universe began to exist."

Putting aside strong scientific evidence for the fact that the universe began to exist, such as the BVG theorem, the idea of a past-eternal universe is logically impossible. In short, the universe cannot be past-eternal because the present moment could never have arrived if we had to traverse an actual infinite. Kant said this much more eloquently than me:

"If we assume that the world has no beginning in time, then up to every given moment an eternity has elapsed, and there has passed away in that world an infinite series of successive states of things. Now the infinity of a series consists in the fact that it can never be completed through successive synthesis. It thus follows that it is impossible for an infinite world-series to have passed away, and that a beginning of the world is therefore a necessary condition of the world's existence."

In other words, the past cannot be eternal, because an actual infinite cannot be formed via successive addition. Actual infinites are also shown to be absurd via thought experiments such as Hilbert's Hotel and the Tristam Shandy paradox. 

Secondly anything that is extended in space is by its very nature contingent, mutable. It owes its existence to something else and is in a state of change, therefore constantly changing its essence and identity; therefore, not eternal. Therefore the physical universe cannot be eternal nor can there be more than one eternal being or “thing”.

Can multiple gods or items exist?

If there were multiple eternal beings they would need to be omnipotent, omniscient, and omnipresent to possess externality - their simultaneous existence would impinge on each other. Their common existence would be metaphysically and logically impossible.