In the last post we saw (in brief) how the Kalam Cosmological Argument (hereafter, KCA) interacts with physics – namely, how it is supported by the fundamental acceptance of causality in science (or science would soon die) and how the evidence seems to point to an absolute beginning of the Universe.

In light of this evidence (and the evidence for fine-tuning), many theorists have posited some form of a multiverse, the idea that though we are causally isolated from all other universes (often thought of as bubbles in a great foaming sea), ours is only one of many possible worlds. Perhaps infinitely many, which would wash out much of the significance of the fine-tuning argument.

But let’s pause and consider – is it possible for an actually infinite number of things to exist?

Interesting as it is to apply this question to the multiverse, we should prefer to handle one argument at a time. If someone responds to Premise 2 of the KCA – The Universe began to exist – by saying it might not have, but rather, it could be past-eternal, we come to the question at hand: Can an actually infinite number of things (in this case, past events) exist?

Suppose you are walking along one day, and you hear a man counting down: “…-6, -5, -4, -3, -2, -1, 0!” You ask him what he was doing, and he says, “I just finished counting down from negative infinity!”

Whatever your philosophical leanings, this has to strike you as preposterous, and perhaps humorously so. With a smile, you ask, “When did you start?”

(This is not how the argument is supposed to go, actually, but the question occurred to me and it makes a point).

Rather, you ask yourself, “Why did he finish today? Why not yesterday or the day before?”

And as you think about it, you wonder why it wasn’t last week, or last decade, or last millennium. After all, no matter which date in the past that you pick, he would have had an infinite time in the past from which to count down from negative infinity. No matter how far back you go, he should already be done counting!

But there’s a further difficulty – suppose he starts today, and says to himself, “Negative infinity!” What is the next number down that he’ll count?

This obstacle is called “traversing the infinite,” and it’s understood as an impossibility. This point might be easier to make in the opposite direction.

Say you are immortal, and you start counting today from zero. Imagine, if you like, that you are able to count one million (or billion, or quadrillion) numbers a second. When will you reach infinity? What is the number you will say just before you get to infinity?

There is no such number, and in fact, whether you count a million numbers a second or just one per second, you will be equally “close” to your goal (which is to say, not making any progress at all).

What does this mean for our present discussion? Simply imagine that the past runs to “negative infinity” and today is Day 0. But you can’t count down to zero from negative infinity. It means if the past really were infinite, we would never have reached today – you would never have lived to talk about it. A past-eternal world is like a treadmill that always runs faster than you can.

A natural question, almost a reflex, is to ask, “What about the future, isn’t it infinite?”

It may, in fact, be infinite – but it is not infinite yet, and since we are able to count the days, it can only be considered a “potential infinite.” And the question before us is whether there can be an “actual infinite.”

I really enjoy thinking about this stuff, much as it tends to twist my brain in knots. And there’s at least one more post on infinity!