The First Cause Argument

Okay, this is well-known, so I’ll review the obvious points quickly, then get to how my own special theories help with the issue.

The first cause argument:

The universe must have had a cause. If the universe had a cause, that cause was God. So God exists.

Obvious question: Why think (2)?

Maybe we could just define “God” to be that which created the universe, but then we can’t be sure that “God” is even a conscious being, let alone that it has the traditional properties of God.

Maybe you could just argue that something like God is the only reasonable theory anyone has devised for what might have created the universe, if anything did.

Be that as it may, most debate traditionally concerns #1. Traditionally, theists assume the universe needs a cause, while atheists say it need not have a cause since it might have just always existed, for infinite past time. People like Bertrand Russell say (my paraphrase): “If everything needs a cause, then what caused God? If you say that God could exist with no cause, then I can just say the universe exists with no cause.”

William Lane Craig gives some interesting arguments for #1. They’re fun and interesting because they have to do with infinity. Basically, he cites some paradoxes of the infinite to argue that there can’t be an actual infinity, or a completed infinity.

Example 1: Hilbert’s Hotel: You have a hotel with infinitely many rooms, all full. But yet you can still fit an infinite number of additional guests in it: just tell every guest to move from room number n to room 2n (where n is their current room #). Then you have infinitely many vacant rooms, which you use to accommodate the new guests. You’re supposed to think this is crazy, and then infer that “actual infinities” are impossible.

I’m not all that impressed by this one, myself. But there are other, more bizarre paradoxes of the infinite.

Example 2: Thompson’s lamp: A lamp starts out on. After ½ hour, it is switched off. After another ¼ hour, it’s switched back on, and so on, for infinitely many switchings. At the end of 1 hour, is it on or off?

Example 3: Benardete’s paradox. There’s an opaque black slab, ½ foot thick. On top of it is a white slab, ¼ inch thick. On top of that, another black one, 1/8 inch thick. And so on. If you stand over the pile and look down, what do you see?

There are many more examples in my book, Approaching Infinity.

If the universe always existed, then its history would be an actual, completed infinity. Since such a thing is impossible, the universe must have begun at some time. Or so the argument goes. It’s then plausible that it could not have just started existing with no cause.

Objection: Actual Infinities Are Possible

If the claim is that there can’t be an actual infinity, there seem to be plenty of counter-examples. E.g., the set of natural numbers is an actual infinity (provided you accept, as you should, that numbers exist). There are many other examples involving abstract or semi-abstract objects (universals, possible worlds, propositions, other mathematical objects).

If you don’t like those, there is space, which is infinitely extended. It also seemingly contains infinitely many parts within any given region, since it’s infinitely divisible.

The same is true of time, which is infinitely extended and infinitely divisible. The First Cause people of course dispute that the past is infinite. Perhaps they would also claim that the future is not an actual infinite because the future is only “potential”, not actual. Even so, time seems to be infinitely divisible, which is enough.

Plus, there is one other, super-important counterexample, if you’re a theist: God.

Math trivia: Georg Cantor’s purpose in developing the theory of transfinite numbers was to show that actual infinities are perfectly coherent, because he thought that God was infinite.

God is infinite in various respects, as traditionally understood. E.g., He is infinitely powerful, and he has an infinite amount of knowledge (knowing infinitely many propositions). So I think a theist had best not claim that actual infinities are impossible. (Craig tries to address this on his web page, but I couldn’t really make sense of it.)

It might still be open, however, to claim that a completed infinite series is impossible. That’s enough, since the theist would say that if the universe goes back forever, then its history is a completed infinite series.

Objection: Completed Infinite Series Are Actual

The problem: the Zeno series is a completable infinite series. It’s possible for an object to move one meter. When it does so, it goes half a meter, then another quarter meter, then another eighth of a meter, and so on. That’s an infinite series of sub-motions. And that infinite series gets completed every time an object moves 1 meter. So completed infinite series are possible.

What About the Paradoxes?

Problem

You shouldn’t be happy at this point, though. What about the paradoxes of the infinite? They were supposed to motivate us to reject actual infinities or completed infinities. If we accept actual, completed infinities, how can we avoid the paradoxes?

Lame response

The usual view for atheists and mathematicians is to boldly embrace paradox. E.g., in the Hilbert’s Hotel case, just say, “Yep, you can have a full hotel, and yet still fit infinitely many more people. Isn’t infinity wonderful?”

Note: In that case, I think this is actually correct. More precisely, I think there is a version of the Hotel scenario that is in principle possible, and it works as advertised. But the other paradoxes are more problematic.

In the Thomson Lamp case, one says something like, “Well, it’s indeterminate: in some possible worlds the lamp ends up on, and in some possible worlds it ends up off. There’s no way of determining which would happen.”

Because this way of treating the infinite is very intuitively unsatisfying, the First Cause theist still appears to maybe have a point.

Correct response

But when you see the correct response, you’ll see that the First Cause Argument fails. The correct response to the paradoxes is not “actual infinities are impossible”, nor is it “completed infinities are impossible”. It is “Infinite intensive magnitudes are impossible”.

Roughly, intensive magnitudes are magnitudes that do not add across the parts of a thing. Example: temperature (the temperature of the left half of a room plus the temperature of the right half does not equal the temperature of the room). Contrasted with extensive magnitudes (e.g., length, where the length of the left half of a pencil + the length of the right half = the length of the pencil).

The reason the Thomson Lamp scenario is impossible is that it requires various intensive, physical magnitudes to be infinite. Most obviously, you need infinite energy density in the spacetime region of the switch during the hour that it gets switched back and forth infinitely many times.

By contrast, the Zeno series is okay, because none of the physical magnitudes in the story need be infinite. E.g., distance, time, velocity, total energy, energy density, etc., are all finite.

Also, infinite space is okay because that is an infinite extensive magnitude (volume), not intensive.

For more on this, including treatment of all the various paradoxes and the theoretical rationale for banning infinite intensive magnitudes, see again my book, Approaching Infinity.

Back to the First Cause

Now, applying the correct treatment of the infinite to the first cause argument: The argument is mistaken in assuming that there can’t be an infinite history of the universe. Duration is an extensive magnitude, not intensive, so there is no problem with an infinite past. There is also no problem with an infinite cardinal number, so no problem with an infinite number of causes. Again, that’s illustrated by the Zeno series. The same theory we use to explain why the Zeno series can be completed also applies to the series of past causes in the history of the universe.

Conclusion: the First Cause Argument doesn’t work. I haven’t proved that the universe wasn’t created, but there’s no reason why it had to be. There’s no reason that I can see why it couldn’t have just always existed.