Time may be infinite; but, it must have a beginning. It is often argued that the universe has no beginning and that it has just always existed. I will explore a few points that, I believe, show how absurd this view really is.
Actualizing Infinity
Hilbert’s Paradox of the Grand Hotel
Imagine a hotel with infinitely many rooms. A guest arrives, however, there are no vacancies. Each room is occupied. But, the man at the front desk tells the guest not to worry. He’ll make room for him. He has each guest move to the room that is one greater than his own. Essentially, N+1. Room 1 becomes vacant and the hotel is able to accommodate the new guest.
Now, imagine that an infinite number of guests arrives. The man at the front desk tells them not to worry; he has the guest in Room 1 move to Room 2, the guest in Room 2 to Room 4. Essentially, the guests in Room N to 2N. In doing so, all of the odd numbered rooms become vacant and the infinite number of guests are able to be accommodated. Yet, remember. The hotel was full when the guests arrived.
Strangely enough, imagine that an infinite number of guests decide to check out the next morning. For example, all of the guests in the odd numbered rooms. So, the hotel had no vacancies, infinitely many guests check out, infinitely many guests remain and infinitely many vacant rooms remain from the guests that checked out. So, infinity – infinity = infinity.
Furthermore, imagine that all of the guests in rooms greater than three check out. So, infinitely many guests check out and three remain. Infinity – infinity = 3.
It’s easy to see that an actually infinite number of things is self-contradictory.
Attempting to form a set of actually infinite things by N+1…
…is impossible. For example, consider time. An infinite past implies an infinite set of past of events; it implies an actual infinite.
- The series of events in time is a collection formed by adding one member after another.
- A collection formed by adding one member after another cannot be actually infinite.
- Therefore, the series of events in time cannot be actually infinite.
Premise (1) relies on what J.M.E. McTaggart calls the “A-Theory” of time. That is, that the past no longer exists and the future does not yet exist; only now exists. Premise (2) can be explained as the problem of traversing the infinite. We can consider time as a series of event-states. This current event-state was preceded by and could have only come about because of the previous event-state. The previous event-state comes about after another preceding one. However, if the preceding event-states were infinite, as we traverse back we would find that no event could have come to be without a prior event first taking place. So, as William Lane Craig put it, “if the series of past events were beginningless, the present event could not have occurred, which is absurd.” If premises (1) and (2) are true, the conclusion, that the series of of events in time cannot be infinite, follows logically.
Consider a line which extends infinitely in both directions. At any point at which you may count the preceding event states on the line, you have a line segment showing a finite amount of time between that event-state and your current event-state. However, prior to the earliest event-state we can conceive of, the line extends infinitely. That means, before we could have reached the the earliest conceivable event-state, an infinite number of event-states must have already occurred. Everything should have already happened.
God and Infinity
We have seen the paradoxes Hilbert’s hotel has presented us and the problem of traversing the infinite past. Now, one may wonder if God could have always existed. Hasn’t God had to traverse an infinite number of event-states before reaching this point, which renders Him impossible? No. God exists outside of space and time. The Standard Model of the universe (also known as the Big Bang) is the most scientifically accepted model of the universe. This model explains that space and time came into existence at the moment the “Big Bang” occurred. God, being the creator of the universe, cannot be bound by it. Since time has a beginning and God created time God must exist outside of time. For all we know, our entire existence is His now.
Infinite Future
As a Christian, I believe that I have an infinite future. This is possible. That is because at any point in time only a finite amount of time has existed. The finite is actually possible. Time may extend infinitely into the future but it must have a beginning.
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