Is It Possible To Have An Actually Infinite Number of Things? (Part 1)

In a recent post, I talked about the impossibility of an infinite regression based on the "who designed the designer?" question.  In this post, I wanted to expand upon the idea of an actually infinite number of things, showing in brief how such a concept is impossible.

When discussing the idea of an actually infinite number of things, we are not talking about a theoretical idea such as "all real numbers".  Everyone can agree that the set "all real numbers" is theoretically infinite (in other words, there is no "last number" to this set because we can always add 1 more to it).  Instead, what we're talking about is the idea that no real-world example of a infinite number of things exists.  As an example, think about the number of days that preceded this one.  Is it possible that an infinite number of days preceded this one?  Or what about an infinitely long row of dominoes?  Can such a row of dominoes exist in reality?  What about a hotel with an infinite number of rooms? These are what we mean when we talk of an actually infinite number of things.

When we look at these 3 examples we see a few different things.  We see, first of all, the need for a "first thing" to get the entire series started.  And we also see that logical contradictions emerge.  This is, admittedly, a difficult topic.  But it becomes important when talking about questions such as "Did the universe have a beginning?".  Some people will claim that the universe is simply infinitely old.  But as we'll see, this is an impossibility because an actually infinite number of things is impossible (and an infinite number of days in the past would involve an actually infinite number of things...namely, an infinite number of days).

It also becomes important when attempting to answer someone who is asking "who designed the designer?" (more on that below).

To explain this topic, I'm going to leverage a lengthy quote from Dallas Willard.  In his book Knowing Christ Today, he does a good job of illustrating the impossibility of an actually infinite number of things using the domino example from above.  On page 105 of his book, he says:

"To aid our comprehension, consider the following familiar image.  You have a line of dominoes standing on end in such a way that if one is pushed over, it knocks over the next one in the direction it falls, and so on down the line.  Now imagine a line of dominoes falling toward your right and a line of those already having fallen dissappearing over the horizon to your left.  Someone suggests that the line to your left has no first member.  They are saying that for every fallen domino in the sequence to your left there is another fallen domino beyond it to your left, which made it fall.  That is to say, the sequence of falling dominoes leading up to this one now falling right before you here is unlimited. infinite, with no first member.  That amounts to the claim that there is no domino that falls without being knocked over by another domino falling upon it.  But if there were no first domino to fall, not knocked over by another domino, there would be no last one before this one, to make this one fall, and so it would not fall.  But it does fall.  There is such a last one, so there is a first one, a first domino to fall.

"If there were no first domino to fall, the sequence of falling dominoes to the left would be unlimited or infinite, and it would never 'reach' the domino that, just having fallen, knocks over the one falling here and now in front of you.  Viewed from the point of view of the progressively falling dominoes coming from the left - from the 'other end,' as it were - there would always be more dominoes to fall before this one."

I know that's difficult to fully grasp, but spend some time reviewing it.  Read it several times.  The point is this...it is impossible for there not to be a "first domino".  This is necessary for any of the dominoes to begin falling.  If there is no "first domino", then the entire series of dominoes can never start falling.  In the same way, if people ask you "who designed the designer", the answer is simple...there must be a starting point or nothing else would have ever come into existence.  That necessary being (a being that must exist), is God.

While we've not gone into a great deal of description about the characteristics of God with this discussion, we are already able to see one thing...He is a necessary being.  God must exist.  It is literally impossible for him not to exist.

Another example on infinity next time.  This time dealing with infinite hotels.

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