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TMA | KCA 19 | Traversing The Infinite | Part 3

Welcome to Tuesday Morning Apologetics (TMA). We’re talking about the Kalam Cosmological Argument (KCA):

1. Whatever begins to exist has a cause.

2. The universe began to exist.

3. Therefore, the universe has a cause.

Our focus is now on the second premise of the KCA. Which is leading us on a little excursus exploring a challenge against Naturalism. Specifically, the apparent difficulties that arise from the combination of there being:

(1)an actually infinite number of Events contained in any Finite Interval


(2)the apparent fact that we routinely traverse those actually infinite sets.

Last week, I said that one of the reasons that problems arise is due to the nature of infinity itself. Specifically, its endlessness. This week I want to mention a different problem that arises from this attribute of infinity.

I’m going to bring back Finite Intervals and the Events associated with them. To make it a little easier to visualize, let’s define "Finite-Interval-1" as one minute. We’ll just say that it’s the minute of 12:00 and 12:01.

Now, we know that it takes sixty seconds to get from 12:00 to 12:01, but we are not interested in seconds. We are interested in Events. I am not using “Events” to denote some new increment of our measurement of Time. By “Event” I mean any kind of progression or change. In previous posts I defined it as a description of some cause and effect. And that's what I mean here. By "Event", I'm talking about the actualization of some potential and any kind of "duration" is not required, but not excluded either.

Last week we granted the notion that there is an actually infinite number of Events contained in any Finite Interval. Therefore, in Finite-Interval-1 we see that Event-1 exists and is followed by Event-2, then Event-3, then Event-4 and so on. Going out to infinity until we eventually start Finite-Interval-2 (which, in this case, would be defined as proceeding from 12:01 to 12:02). So, once we understand that we can begin our march.

But… before we can take our first step we run into a problem. Stepping from Event-1 to Event-2 is, itself a Finite Interval. That means that we must traverse an actually infinite number of Events in order to go from Event-1 to Event-2.

We can label these Events as so:

Event-1 followed by Event-1-1, then Event-1-2 then Event-1-3 and so on unto infinity then we can finally get to Event-2.

But, once again, we run into the same problem. Because stepping from Event-1 to Event-1-1 is yet another Finite Interval.

So, maybe:

Event-1 followed by Event-1-0-1, then Event-1-0-2, then Event-1-0-3…

But we just run into it again and again going out to infinity. As you can see:

Event-1 followed by Event-1-0-0-1, then Event-1-0-0-2….

But before we can step from Event-1 to Event-1-0-0-1 we first have to get through:

Event-1 followed by Event-1-0-0-0-1, then Event-1-0-0-0-2….

But before we can step from Event-1 to Event-1-0-0-0-1 we first have to get through:

Event-1 followed by Event-1-0-0-0-0-1, then Event-1-0-0-0-0-2….

But before we... And I think you get it... ad infinitum...

The problem that should be coming apparent is that there can be no motion or change and, therefore, no Time, because there is no Event that we can step off of Event-1 onto. There is no “next” Event.

However, that runs in direct contradiction to the motion and change I'm experiencing all the time. I mean, like, right now... as I’m typing. So, how do we account for that?

In light of last week’s consideration, and this week’s, I’m inclined to believe that it’s impossible for every Finite Interval to contain an infinite number of Events AND that we are able to traverse them. So, how do we get around this problem? I think there are a few different options.

1. Finite Intervals do not contain an infinite number of events. OR

2. Finite Intervals do contain an infinite number of Events but the vast majority are ignored. Those Events aren’t “counted”. OR

3. Our experience of motion and change is an illusion.


4. Reality is often counterintuitive, deal with it.

I explain why I don’t think (3) is a viable option in my series on Time. And, to me, (4) is just silly. Ignoring problems do not beget answers. So that leaves (1) and (2). And we’ll save the discussion on those for next week.

What do you think? In light of this consideration do you think that there is an infinite number of Events contained within each Finite Interval? Do you think it could ever be proven one way or another? Let me know!

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