First Cause Argument: Finite Universe

A Finite Universe: A Premise for a First Cause 

There are two main schools of thought regarding the origins of the universe: Either the universe has always existed with an infinite past, or the universe was at one point created and thus finite. I will contain my response as another essay to support the premise of a finite universe in linear form and why the universe could not have always existed in a state of actual infinity. This essay will not address causal loops - that is addressed here.

Before we even dive into the why's and why not's of an infinite universe, we need to understand a basic idea of Mathematical Set Theory. Below are two mathematical sets, labeled "A" and "A1", and we will use them to explain the basic ideas of what we will be discussing later:

A - {0,1,2,3,4 ...}

A1 - {0,2,4,6,8 ...}

As you can see set "A" contains all numbers up to infinity, while set "A1", a sub set of "A", contains all the even numbers up to infinity. What has been presented is one Mathematical Set and one Mathematical Subset. For anything to be a subset every member in that subset must be contained in the parent set. So if subset "A1" has the letter "a", then "A1" could not be a subset of "A" because set "A", the parent set, does not have the letter "a" as a member.

Now here is a question. If set "A" and subset "A1" are actual infinity, which is larger? The answer is that they are equal. This conclusion is derived from the fact that each member of both sets can be evenly paired.

A -   { 0 , 1 , 2 , 3 , 4 ...}

A1 - { 0 , 2 , 4 , 6 , 8 ...}

Since these two sets continue on for infinity they would continue to be paired equally.

On the other hand, outside of actual Infinity, there is potential infinity. A potential infinity designates a set of numbers which can be continually added, but is unlike actual infinity in that the subsets are not equal to the parent set. The latter is seen in every day life, the prior, I will contend, does not exist.

The first argument is that actual infinity cannot exist in our universe. In actual Infinity, the old saying, "The whole is greater than its parts", is false because the parts are equal to the whole. I am going to give a couple of examples to show the nature of actual infinity:

Imagine a library that contains an infinite amount of red books and an infinite amount of black books. Each book contains an infinite amount of pages. There are two specific assertions that we will be taking note of. First, the total combined amount of infinite red and black books would equal the amount of infinite red books. Secondly, if we read every page in the library, consisting of an infinite amount of pages, it would be equal to reading only one book with the infinite amount of pages. As you can see, actual infinite decimates addition, subtraction, multiplication, and division.

Another example of a part being equal to its whole is in the affirmation that one-billionth of an inch would have an equal amount of points as the universe does in its totality. Again, every part, in actual infinity, is equal to the whole. This again is not possible because in our universe we have accumulation (ie. added parts equals a whole, not every part equaling a whole).

The second argument against an actual infinite universe is noting that infinity is Non-Transversal. What this means is that if our universe always existed, the universe should have an infinite past. With the premise established, we can say that, if the past could not be transversed, then we do not have the present; for the present equals the past transversed.

When we see a plane flying over head we can assume a chain of past causes had to be tansversed to the point of the present state. For the plane to be flying we could assume that the pilot got into the plane. Perhaps we could also assume that the plane needed fuel before departing the airport. In any assumption we make, we can assume that there has been a series of past events which were transversed and lead up to the present plane flying over head.

The next thing we must consider is the idea of counting to infinity. You may have pulled this one out during a game of hide-and-seek where you tell the counter to count up to infinity so you have enough time to find the awesome hiding spot everyone knows about. The problem is if you count for the duration of your life you will never reach infinity. Why? This is what we call potential infinity. The mathematical set we deal with in this equation is concerning the possibility of continual addition. Meaning the numbers are finite, but can always be continually added by 'x' number. An easy rule is if you can state the number it is finite because you can always add 1 to it; which you cannot add 1 to infinity and change its nature. You cannot count up to infinity and likewise you cannot count down from it.

With these two premises, that you have chained events and that you cannot count up or down from infinity, tells us one thing. If the past was infinite, an infinite chain, you cannot transverse the infinite as you similarly could not do so in counting. The conclusion is that the past could not have been transversed and thus we could not have the present. The past would still be continuing and we would not have a present state (Remembering that the present is equal to the past transversed). Of course this is not so and another reason why the universe is not infinite.

As Blaise Pascal stated, "The finite are annihilated in the presence of the infinite." Whenever the actual infinite are applied to the finite application of our day-to-day universe, we find not only no ability to tend the actual infinite, but if it were applicable, time itself would cease to exist. The most classic example is Zeno's puzzle. If actual infinity did exist, we could not even declare motion as being real because we would have to transverse infinity in each step we took - again 1) we know motion does exist and 2) it isn't possible for actual infinity to exist.

Hope this helps.