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!

And so, what can be said about the Kalam Cosmological Argument in particular?

Some rather intriguing things, if you ask me.  The following exposition is heavily informed by what William Lane Craig has to say about this argument, in support of it and in anticipation of possible objections.  You may, without too much exercise of the mind, still find an objection; you may also depend on the notion that Dr. Craig has fielded it, or readily will.

Premise 1 – Whatever begins to exist has a cause.

Another way of saying this is, “Nothing comes from nothing.”  In the last post, I linked to the Wikipedia page for Lawrence Krauss, a theoretical physicist who authored the book, A Universe from Nothing.  In it, according to the NYT, he proposes a “deeper nothing,” from which even the laws of physics are absent, and out of this nothing the Universe was born.  But then, he doesn’t actually mean “nothing” – we might have been spawned by the multiverse, which even the layman realizes is a whole lot of something.

By “nothing,” Dr. Craig says, we actually mean “not anything.”

And this seems to be true, in the sense that Stephen Hawking (also linked last time) theorizes that there is a boundary to spacetime, beyond which there is really nothing…except that he also admits something, namely the laws of physics.  To these he ascribes potential creative power (namely, causal power) whereas they have usually been seen as descriptions of our observations, and not things existing as causal agents.

What’s interesting to note is that neither of these theoretical physicists deny Premise 1.  They have some strange ideas about nothing – which is to say, they identify something and call it “nothing” – and yet they try to extract something from that nothing in order to provide a cause for everything.

Premise 2 – The Universe began to exist.

Nevertheless, it appears there really is a hard beginning to the Universe, which theorem has stood against alternative explanations.  If the Universe began thus, and there is no explanation which space, time, energy, or matter can provide, what do we suppose could have caused it?

Nothing comes from nothing, after all.  We must therefore posit an “abstract” something, or as we have said, something which transcends the Universe.

Those last two links are tough.  I admit to reading only what appears to be standard English, having to look up some of the technical terms (geodesic!) and taking only a cursory glance at the geometry.  I admit that they appear less clearly stated than the way Craig employs them, but he understands the field better than I do.  Would love to learn more about this.

What I understand better are the philosophical arguments against an actual infinity, which we’ll look at next time.

There’s a TED talk in which Alain de Botton said (in effect):  I’m not here to discuss whether there’s a God or not.  We know there’s no God.  Let’s also admit that militant atheism doesn’t really get us anywhere.  Instead, let’s move on and talk about how we’re going to live our lives in a world without God.

His primary objective, to restate the paraphrase, was to envision an entirely secular culture, one that might even borrow from the “good things” he had seen religion doing.  An interesting perspective, if you’re curious.

In a similar fashion, my primary objective in this series is not to prove that God exists.  I did say that I’ve been studying the question, with all of the focus and spare time afforded to a father employed in a field far from Philosophy.  I do say, so far as I can tell, that God’s existence seems to me more plausible than not.  And not just by a little, but overwhelmingly so.

Further, as an autobiographical aside, I don’t believe my purpose is to go about proving that God exists.  I think there are minds at work which fare far better than mine, and their arguments range from simple (as we have seen with the Kalam Cosmological Argument) to quite difficult to follow.

So, as de Botton looks at life in the absence of God, and seeks fulfillment, I now take a contrary tack.  There is a God, a greatest of all possible beings, a mind so powerful and intelligent as to defy all comprehension except His own.  Now what?

The proofs for God’s existence are instructive for my primary objective, and that is why they will show up from time to time.  I do hope to give my agnostic and atheist friends exposure to them, to observe a depth of mind not often found in popular culture.  (EDIT:  There are similarly deep and profound insights offered by atheists and agnostics as well, and taken together with the theists’ insights, these represent thought far beyond what our televisions typically showcase).  I also aim to discuss the subject in such a way that it is not too pious for my A&A friends, though I have been guilty of that charge from time to time.

The very tip of the point of this series, then, is this:  To explore the nature of God through the analogy of an author.  More broadly, this might be called a “conceptual analysis,” which we have already done in brief:  If conditions are such that X exists, then what can we know about X?

In this manner, we learned what we did in 3.0.  In later posts, we’ll introduce the concept of “God as author” and begin to explore what this can tell us about God and how to live our lives.

In our last exciting installment, I said that skeptics (and believers) often have a view of God which is painfully small, especially for human minds.  I noted that those human brains are often seen as bearing no significance at all, none to speak of anyway, when compared with the size of the Universe.  What, then, could set the Universe in motion?  How much greater must that intelligence and power be, compared even with our wild imaginations?

I submitted that this power (whatever its source) is something beyond comprehension, whether it comes from God or else a natural cause.  I think we must say the same for that intelligence – this is almost easier to recognize, though still beyond comprehension – though I do not necessarily mean that we must therefore admit a God.

I don’t know what else you’ll say could manifest that intelligence, but I’m listening.

Even with a view toward modern science (let alone “God”), I am looking through the glass dimly, and still can appreciate what a startling display of intelligence has been required to understand the cosmos, to draw conclusions about its origins and to sketch out what are the laws of physics.  There are people out there inventing mathematics to explain it, and talking about equations so difficult that we might never solve them.

What?

This does not compute with a Universe tumbling into existence on the same mechanics as a roulette wheel.  That Universe would not require or condone complex, logical equations.  It would require a deck of cards and a lot of time.

But that’s not what smart atheists are saying now, so let’s do away with straw men.

Smart atheists are trying to find a way around this:

Premise 1 – Whatever begins to exist has a cause.

Premise 2 – The Universe began to exist.

Conclusion – The Universe has a cause.

Again, the conclusion is not:  “God exists.”  It is rather, “The Universe has a cause.”

The Big Bang theory does not quibble with this, but some physicists do.  Other physicists say the Universe began to exist, but without a God.

William Lane Craig, the contemporary champion of the Kalam Cosmological Argument, rightly points out that, since the argument is sound, the burden is on atheists to refute one or both of the premises.  If the argument is successful, it would seem to demonstrate a cause which transcends those things by which we define the Universe – space, time, energy, and matter.  It is further suggested that this cause must be personal (that is, a person) because the act of creation would have been a choice, and only persons make choices.

If you would, how would you refute them?

In the preceding post I attempted to refute the idea that anyone can consider the question of God’s existence to be trivial.  While it seems to be a question of utmost importance to theists and atheists alike, there are some who find themselves feeling blase about it.  I hope those who find themselves indifferent will become convinced that the question is worth exploring.

Granting that the question is important – how to begin?

The second obstacle I have noticed is that many A&A (agnostics and atheists) have not really considered who God is, or who God would be if he existed.  They often set up a strawman, or a teapot, and suppose that by logic or mockery they have eliminated the possibility of God’s existence.

But I can’t put all of the blame for this particular fallacy on the skeptics.  They typically reference believers whom they know, and point out the sorts of things those believers do and say (Westboro Baptist comes to mind as an extreme example, but the bulk of the criticism is aimed at more mundane practices).  Believers are not well represented, for example, in suggesting that the athletic team of their choice was specially chosen by God to win a particular contest.  This is not because the thing is necessarily false, but because it too often represents a high water mark of the person’s religious expression.

So in the first place, we had a misplacement of malaise; now we have a deficiency in discernment.  If we want to argue over the existence of a God who resembles a teapot and principally brings his power to bear on sporting events – well, I don’t much care for that debate, either.

What, then, are we talking about?

It has been noted that some cosmologists – the late Carl Sagan appears to be a prime example – deify the Universe in the absence of a belief in God.  And not without cause.  Newton and Einstein – scientists who have lent their names to models of nature – both regarded the Universe as something unimaginably complex and deep – and ordered.

Some skeptics point to our size – our physical bodies, the size of our planet, even the location of our solar system in the galaxy – and appeal to the unimaginable immensity of the Universe by comparison.  Their point being, of course, that our insignificant size and location correspond to any possible significance we might have in the purpose of the Universe, a point easily dismissed.  Yet the skeptics and I agree, in any case, that the size of the Universe is actually far, far beyond our comprehension, much the way we cannot really comprehend infinity.  Much less could we comprehend the power that set it in motion (whether natural or supernatural).

If we consider just these two categories of things – that is, the complexity, depth, and order of the Universe, and again, the size of the Universe and the kind of power required to set it in motion – we will have two things to say about God, starting from the premise that He created everything seen and unseen.  We may say that God is all-knowing and all-powerful.

This is not how one begins a description of a teapot.

This aims to be a humble post, not standing up to the enormous significance of the subject.  Still, something of some significance might be said, and if not, you can have your money back.  (No refunds on time)

First of all, as I’ve been casually studying proofs for the existence of God, a proof against, and the objections and rebuttals besides, one thing can probably be said without controversy:  There are some people who think deeply about this subject, and in fact are consumed by it.  Others do not and are not, and they have reached their conclusions by whatever means each one found persuasive.

I am speaking, then, more toward the second group.  To the first group, I wouldn’t have anything to say which has not, most likely, already been dealt with.  Instead, among them, I am an observer and a student.

I share with them the conviction that this is a subject of first importance, and with that conviction I come to the second group.  However, as I’ve begun talking to some of my agnostic and atheist friends, I’ve learned that most of them just don’t find the question significant.

Bear in mind – I am not yet challenging the process by which they became agnostics or atheists, but only the importance of the subject as a whole.  On this, for example, even Daniel Dennett would agree with me.

How do these atheists and agnostics come to think the question is passe, as though God’s (non)existence as a fact can either be fashionable or out of fashion?

The best I can tell (and I would be very interested to have further explanations of this) is that they are misplacing their disinterest.  They are actually disinterested (disillusioned?) with the debate; even that is not precisely true, I don’t think. They are disillusioned with conflicts and debates surrounding religion, where things can be so subjective, irrational, heavy-handed…and complicated, nuanced, demanding…and where there does not seem to be any end in sight.

When, for example, will the majority of rational creatures agree on which is the correct religion?  On what bases?  Does the truest possible religion yet exist?

Barring a grand consensus, they think, the debates over religion are simply so open-ended as to be meaningless.  Therefore, there is no reason to engage the debate over God’s existence, since it falls under the purview of religion.

 

There is likely to be more to the answer than that, but let’s deal with this first.

If it is truly a misplacement of disillusionment – whether or not it is done consciously – then we ought to re-evaluate the subject in question.  One’s bias toward the religion debates should not necessarily be cast upon the debate over the existence of God – namely, the importance of the latter debate.

So, taken aside from religion, as much as possible; taken from the point of view of an alien, for example, who wanted to talk to you about whether God exists, who otherwise knows nothing of our world’s religions – is it an important question?

 

Here, as I said, Dennett and I agree that the answer is yes.  We would, however, have divergent reasons for saying so.

As best I can tell, Dennett would say the question is important because people have done such great harm in the name of God.  Atheists must, he would say, press the case that there is no God, thereby pulling the plug on religiously motivated crimes against humanity.  While he seems to focus on the large crimes – war, oppression, discrimination, torture – he would probably add that religious people in general tend to be noxious, that wherever and whenever they are actively living out their faith, they are a stain on society.  He has likened religious instruction for children to child abuse.

I am not here to make hay out of Dennett’s excesses, though.  I only want to point out that he feels very strongly about the subject.  It might be possible – there is a possible world, perhaps – that humanity would reach such a state of independence from religion that the question would fade into obscurity, and at that point Dennett might simply want to make sure “God” was dead and buried, never to rise again.

This, come to think of it, is where my A&A friends may have progressed to, intellectually.  They are done fighting over it; they have their answer.  Now, they simply endure the religious fanatics (as do we all) and act as though they, at any rate, have already reached Dennett’s desired destination.  Anyone else, they might say, is free to believe in God, so long as it doesn’t have any negative impact on them.  (I must speak broadly, intending my words to cover a wide range of possibilities – but raise any objection you like).

I agree with Dennett, and essentially present a converse case:  If there is a God, there can be no greater pursuit than to worship Him, to know His will, and to decide whether to follow it.  I use “Him,” but not to impose my understanding of God; let’s go further and attempt to cleanse the statement from the vestiges of religion.

Imagine you are at a baseball game at Wrigley Field on a sunny day.  Ryan Braun of the Milwaukee Brewers steps up to the plate and you think, “This guy is Superman.  How do you pitch to him?  Hard to buy the idea that he hasn’t used steroids…”

Just then, the Cubs’ manager walks out to the pitcher’s mound and calls for a relief pitcher, a righty.  Out of the bullpen comes…Superman.

There’s a bubbling laughter in the crowd as everyone responds to the announcer.  Superman?  The intoxicated guy behind you makes a dumb joke about cryptonite.

Lo and behold, the relief pitcher veritably floats across the field to the mound.  He’s not wearing a glove.  The catcher takes up a stance behind the batter’s box opposite Braun.  He holds his glove out tentatively, and the umpire, seeing this, takes up his stance behind the catcher.  There’s no one standing behind the plate.

Braun takes his stance, and Superman delivers the pitch – it is past Braun and buried into the brick wall of the backstop before Braun ever swings.  Strike 1.

The crowd goes wild.  You sense the excitement, even within yourself, but immediately become more reflective.  After a series of very natural questions – what are they paying him?, for example – you realize that the excitement over Superman’s performance for the Cubs will diminish very quickly.  You will get tired of 200 mph fastballs.  The Cubs will win the World Series, and there’s no hint of uncertainty about that.  This is not the way you wanted the Curse to end.

Superman strikes Braun out, and after a feverish cheer from the crowd, he addresses them without the aid of a microphone.

“People of Chicago – indeed, people of Earth!  I am the one you predicted, but never expected, in your stories about Superman.  While I will now retire from baseball, I will immediately begin to serve you all in the name of peace and justice!  Together, we will not only strike out crime, but we will feed the hungry, and build up our schools…”

You zone out.  It’s too much to believe, though he is as real as Ryan Braun.  Later, you tell me the story (though I have heard it on the news) and amid your bewilderment, I say, “Well, it doesn’t really matter whether Superman is here or not.”

How would you respond to this?

I would have to think that your response is, “Of course it does!  This is Superman!  This is the most incredible thing that could have happened, and how fortunate for us that he wants to help us, rather than oppress us!”

I start to say that he might very well oppress us with his figures of speech, but you won’t hear any of it.

 

Or have I put too many words in your mouth?  Would you in fact take my side, and say that it does not matter very much that Superman is real, much less what his intentions may be?  Does it not seem important to you to stay on the right side of the law, since he will set out to “strike out crime”?

And I say, all the more for whether God exists.  You may multiply Superman’s good intentions, his power, his intelligence, his speed (or ability to be in multiple places in a very short time) – all of this, you may multiply by infinity, and now we are talking about God.  If God exists, I have to say it is a fact of the highest priority, and one which must be responded to.