Following the last set of posts on the Kalam Cosmological Argument (KCA), we have…well, what do we have?

Suppose you are skeptical – that may be fair.  Which premise do you object to, and why?

For the skeptic, that is the only course of action here.  The logic can’t be denied (unless you want to deny logic).  Even for a hobbyist of philosophy, that’s pretty easy to see.

Let’s just say, for the sake of explanation, that you don’t like the first premise, “Whatever begins to exist has a cause.”  You think, vaguely (as I do),* that quantum mechanics must reveal some exception to this rule, or that somewhere down the line, we’ll find something truly astounding, which can’t be anticipated by this kind of logic.  Maybe in a Universe with different rules of physics, there are also different rules of logic.

Aside from taking the opportunity to use a phrase like “atheism-of-the-gaps,” what I would point to is the notion that we don’t need 100% certainty of the argument for it to be successful.  We just need the premises to be more plausibly true than their denials.

Is it more plausibly true, I would ask, that “Whatever begins to exist has a cause,” or rather, “Some things begin to exist without a cause”?  If you think the second statement is true, or just more plausibly true than the first, what example would you give?

If you can’t give an example, why think that some things begin to exist without a cause?  Why prefer this over the premise, “Whatever begins to exist has a cause”?

Suppose you can’t find any exceptions or successful objections to either premise.  Is this any reason to jump to the conclusion that you must believe in the God of the Bible?

No.  I am one of the two Catholic guys, but my aim here is not to make you a Catholic, or Christian, or Jew.  What I aim to offer is that belief in God is more rational than the absence of belief.  That, I think, is one of the fruits of the KCA – the conclusion, it seems to me, is much more rational than the denial of the conclusion.

Keep in mind, Krauss offers that the multiverse is (perhaps) more rational than the absence of the multiverse.  Nevermind that there’s no evidence for its existence^ – it is simply a hypothesis to make sense of the evidence we do have.  And I have no interest or need to deny that hypothesis, except that we may be able to explain things without it.

Though no objections have surfaced in previous posts as of this writing, I realize some may come up when there is time for various readers to comment.  I’m interested in that conversation.

However, for the sake of this series, I want to continue with this assumption:  The KCA is more plausibly true than false.  Now what?

*In a bit of permitted confusion, what I mean to say here is that I think vaguely about quantum mechanics, but not that QM will someday prove that things can begin to exist without causes.

^As far as I have read/heard.  I suspect we’ll all know it if any evidence does materialize.

We’ve been considering the concept of infinity as it relates to the Kalam Cosmological Argument (KCA) and the existence of God.

Imagine you’re stranded in a town in the middle of nowhere.  It’s getting dark, and you need a place to stay for the night.  You come to a 10 room hotel and ask the clerk for a room.  He says, “Unfortunately, every room is booked.  You might try Hilbert’s Hotel down the road.  They’re full right now, but they always have room.”

You can feel your face wrench into a puzzled expression, and the clerk merely shrugs and goes back to his business.  You figure, in any event, that Hilbert’s Hotel might be the only other place in town, and it might be worth suffering some word play in order to find a place to sleep.

As you go, you seem dimly that Hilbert’s Hotel is quite a long building.  It seems to go on forever toward the horizon, or as much of the horizon as you can still make out.  You step inside.

“Hi, I’d like a room.  The gentleman down the road said you were full, but might have a room anyway?”

The proprietor smiles at you.  ”Yes, yes, come on in!  We have an infinite number of rooms – and an infinite number of guests – but no problem!  Will it just be you?”

“Yes,” you say, apprehensively, “but if you’re full, how will I-”

“It is nothing!” he says with unbounded enthusiasm.  ”Here, I will show you.”

He leads you to Room 1, and knocks.  A woman answers, and he says, “Would you kindly move over to Room 2?”

The woman, having been afforded the same courtesy earlier, obliges.  When she gets there, she passes on a similar request:  ”The manager has asked me to move to Room 2.  Would you please move to Room 3, and pass it on?”

In just this way, every guest shifts to the next room up.  You now have a room, and no one has to leave, since there are still an infinite number of rooms.

This is surely an eerie phenomenon, so you decide to explore the building a bit after settling into your room.  And as you walk (Room 167…513…2,134…) you have no sense that the building will ever end.  There is no sense that the architects grew tired of designing the building, no sense that the builders experienced fatigue and began to fail in their workmanship.  It actually seems to continue forever, and now the quest of finding an end to this building has become decidedly futile.  You are tired, and a little overwhelmed, and so you return to your room to retire.

Just as you get back, the smiling manager approaches you.

“Great news!  We have a large party here seeking rooms for every member – it’s a party of infinity!”

You unconsciously shake your head, like you’ve been struck blind.  And there certainly are a lot of people, running clear out the door and as far as you can tell, on down the street.  Even if this is a thousand, how will they all fit?

“No problem!” says the manager, perhaps reading your mind.  ”Sir-” now he’s addressing you “-will you please move to Room 2?”

In a state of bewilderment, though certainly not belligerence, you move to Room 2.  When you get there, you pass on the manager’s instructions – Move to the room number which is double your current room number.  You also inform the guest in Room 3, and so the shift occurs as follows:  Room 1 moves to Room 2 – Room 2 moves to Room 4 – Room 3 moves to Room 6…

Once it is complete, all of the odd numbered rooms are open.  Not only that, but there are an infinite number of odd numbers, and so the entire party of infinity guests can be easily accommodated!

This is really too much, and so you decide to close your eyes and see if a night’s sleep will clear your mind and make sense of all this.

In the morning, you discover that guests have begun to check out.

First of all, that party of infinity has already left.  Yet, though an infinite number of people have left, there are still an infinite number of people still staying at the hotel!

But the manager does not like the appearance of a half-empty hotel (all the odd-numbered rooms are empty, after all) and so he asks everyone to return to the rooms they occupied before they moved last night (last night, of course, they all moved to the room number which was double the number they occupied at the time the infinite party checked in.  Now they move to the room number which is half of their current room number).

Then, you discover that before you had arrived, there was a previous party of infinity that had checked in.  In fact, at the beginning of the previous day, there were only three guests, one in each of the first three rooms.  There was no shifting required for that first infinite party!

Now, everyone from Room 5 and up is checking out.  (You’ll recall, when you arrived, that everyone had to shift over one room).  There are just four guests left.

This is a puzzle, you think.  How could you have two infinite departures – both representing an infinite number of people checking out – and while the first time there remained an infinite number of people, now there remain only four?

Now here is the main point of this wild illustration, originally the brainchild of mathematician David Hilbert:  To the extent that it is wild, and absurd, it is also unlikely to manifest in any way in reality.  (I say unlikely, but I believe there are serious thinkers who would say “impossible.”  I am only trying to be cautious).

This is not simply because the hotel is impossibly long, or because it’s impossible for us really to conceive of an actual infinite.  It’s also because the math doesn’t make sense.

For example, consider the guests checking in.

When you checked in, there were already infinity guests, and we will represent infinity as N.  You were alone.  By this math, we have to say that:

N = N,

and N + 1 = N

Then, when infinity guests arrive:

N = N 

and N + N = N

Then, when guests start checking out:

N – N = N

  and N – N = 4.

But our equations are obviously true, if we take seriously what infinity means.  If N stood for any number other than infinity, these equations would be puzzling, because they’d be false (except for the equations of identity, which only show how the subsequent equations are unusual).

There are yet more things to say about infinity, but we will move on.  This post and the previous two serve as supports to Premise 2 of the KCA – The Universe began to exist – as a way of demonstrating that the Universe could not exist from the eternal past, but must have had a beginning a finite time ago.

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!