## Philosophical Arguments that the Universe had a Beginning

*by Allen Hainline*

This is my last blog dealing with the origin of the universe as an argument for the existence of God. I’ll examine the issue of whether new physics might be discovered to enable the universe to be past eternal. I’ll offer a couple of philosophical arguments against the possibility of an eternal past. If these arguments succeed we can be confident that no scientific discoveries could ever show that the universe has existed forever. Indeed if these arguments are sound, the scientific evidence I’ve offered so far would become superfluous.

If the universe has existed forever, this would entail an actually infinite number of past events. I use the term “actually infinite” to distinguish it from a potential infinite quantity. No one doubts that the number of future events can grow without limit but this is merely a potential infinite. Any finite time in the future there would still have been a finite number of events since the current time so the infinity is just potential – it represents an unattainable limit as this article by George Ellis, a prominent cosmologist, indicates.

##### Is it possible for actually infinite numbers of entities to be realized in the actual world?

One of the greatest mathematicians of all-time, David Hilbert, certainly didn’t think so: “the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought.“ Georg Cantor established a mathematically rigorous way of dealing with the concept of infinity that is very useful for mathematical and scientific calculations. Although Hilbert defended Cantor’s work, he argued that infinities couldn’t exist in the actual world or they would lead to absurdities.

Some readers may be thinking that if it is mathematically possible it has to be physically possible. But not everything used in mathematics necessarily implies a direct correspondence with physical ontology (nature of being). Infinitesimals are mathematically feasible and highly useful in calculus, but modern physics holds that everything is quantized. Mathematical consistency and coherence doesn’t necessarily imply physical realization – there are abstract mathematical systems that can be constructed that are coherent but not all of them are necessarily realized anywhere in physics. In computer science we often choose between multiple mathematically equivalent but quite different ways of computing things – they can’t all correspond to physical ontology because they entail fundamentally different ways of modeling reality. Infinities that show up in physics equations are considered problematic unless and until some type of renormalization can be performed.

So if we can show that absurdities result if actual infinites exist, then we have good reasons for rejecting the possibility of an actually infinite number of past events – even if it is mathematically feasible. Here is how philosopher Peter S Williams makes this argument to a lay audience…