Monday, December 19, 2011

Interlude: God is infinite

This is a continuation of "A few things wrong about the cosmological argument," an ongoing series. This will be a lighter post.

In William Lane Craig's formulation of the Kalam Cosmological argument, he argues that infinities cannot exist, therefore the universe began, therefore God exists.

But... surely God is infinite?  You know... actually infinite.

This seems like such a jarring inconsistency in the argument.  I give William Lane Craig more credit than that, and I'm sure he has a functional response somewhere.  Let's just pretend that I've put in the effort to find his response, and that I've been suitably convinced that of all the problems with the cosmological argument, this is not one of them.  *wink*

As many of you know I went to a Catholic high school.  It wasn't so bad.  Actually a really good high school, run by Jesuits.  But yes, it was a religious education.  Morning prayers.  Religiously infused mission statement.  Monthly services.  Retreats.  A few teachers who were Jesuits.  I was Catholic at the time, so I didn't mind. Except for the monthly services.  Mass is boring!

I also took some religious classes, learning about the Bible, social justice, and apologetics.  They didn't call it apologetics, but that's what it was.  The teacher for that class was pretty good.  He had a flair for the dramatic and comedic.  He used lots of creative teaching techniques, and frequently showed videos.  From a high schooler's perspective, showing videos in class was like the best thing ever.

I think he was a fan of William Lane Craig.  When I later encountered Lane Craig's arguments, they seemed utterly familiar to me.  I consider them to be classic apologetic arguments, though this is perhaps only my perception.  "Classic" is just whatever I learned about in high school.

Along the same lines, I also believe that one of the "classic" understandings of God is The Infinite.  God isn't merely infinite, God is The Infinite.  You can't possibly comprehend God with your finite mind!  That would be like trying to comprehend the integers, or quantum field theory!  (Silly physicists...)

I took all this stuff with just a grain of salt, but he said one thing that really bothered me.  Paraphrased from memory fragments:
God is defined as The Infinite.  Suppose there were two gods.  Then there would be two infinites.  But there can only be one infinity, because all infinities are overlapping and identical.  Therefore, there can only be one God.
Arrrgh!  I mean, I don't mind arguing for a single God.  Whatever.  But man, that is some bad math!  The set of even numbers and the set of odd numbers are both infinite but they don't overlap!  Also, neither odd nor even numbers are identical to God.  This got me to thinking along other lines, like what is God's cardinality?  Does God's power set have greater cardinality than God?

This series on the cosmological argument is in about the same spirit.  I don't particularly care if people argue for the existence of God.  I definitely don't care if people argue about whether God is single or multiple.  At least, I don't care in the abstract.  But sometimes I see these arguments, and wow!  Bad math, bad physics, bad argumental form.  If someone argues that we're justified in believing an invisible conscious being that can only touch us in our "hearts", that's okay on some level.  (Well, no, it's ridiculous.)  But when you start talking bad math?  Blasphemy!

A few people have accused me of hiding behind lots of complicated logic, math, and physics.  It's all an attempt to dazzle people in to agreeing with me.  But that's not the point.  The point is to trick you all into reading about logic, math, and physics, when you just wanted a refutation of the cosmological argument.  Ha!  Ha ha ha!

Tune in next time for more of...

"A few things wrong about the cosmological argument"
1. Actual and potential infinities
2. Actual infinities in physics
3. What is real?
4. The "absurdity" of Hilbert's Hotel
5. Interlude: God is infinite
6. Forming Infinity, one by one 
7. Uncertain beginnings
8. Entropy: The unsolved problem
9. Kalam as an inductive argument
10. Getting from First Cause to God  


drransom said...

Craig does in fact have an answer to this question:

. . . the key to your question [i.e., how God can be actually infinite] is to understand that the mathematical notion of an actual infinite is a quantitative concept. It concerns a collection of definite and discrete elements that are members of the collection. But when theologians speak of the infinity of God, they are not using the word in a mathematical sense to refer to an aggregate of an infinite number of elements. God's infinity is, as it were, qualitative, not quantitative. It means that God is metaphysically necessary, morally perfect, omnipotent, omniscient, eternal, and so on.

So it appears that there's no contradiction, because when Craig describes God as "infinite" he doesn't actually mean that God is infinite. But if he doesn't mean that God is infinite, why use the term? He doesn't explain.

Seems like a huge morass of conceptual confusion, but not actually a contradiction.

miller said...

From your link:

Really "infinity" is just a sort of umbrella term used to cover all of God's superlative attributes.

That's funny because in math, infinity is not a superlative, and there are always larger infinities. I guess this is a case of people trying to use impressive mathematical terms that they don't actually understand very well.

I am who I am said...

> The set of even numbers and the set of odd numbers are both infinite but they don't overlap!

They do both have bijections into the natural numbers and in that sense they are the same infinity. What is overlapping than to say each can cover the other? Is this not exactly the idea behind Schroeder-Bernstein that two injections between sets entails a shared cardinality? In that way they are identical when considered purely as being manifestations of "infinities". Of course you can put other structures on top of them which would serve to differentiate them in other ways. But oddly I think you could still consider them as identical and overlapping, perhaps as co-sets in the additive group of naturals (again different manifestations of the same thing). But I guess you could justify any view with enough thought.

miller said...

By "overlapping" I meant "having a non-empty intersection".

drransom said...

WLC says all infinites are "overlapping and identical," so I wonder if he means something by "overlapping" that makes it non-redundant with "identical"? Though I'm at a loss to think what that would be.

miller said...

I think he's confusing "identical" with "equinumerous", which is not redundant with "overlapping". WLC probably thinks an ant is identical to an elephant because they are both single-element sets. It's like the old joke about topologists, and how they can't tell the difference between a donut and a coffee mug.

Larry, The Barefoot Bum said...

The way I heard it, a topologist can't tell the difference between his ass and a hole in the ground, but he can tell the difference between his ass and two holes in the ground.