Sunday, February 25, 2007

"Spirit" -> The Paradox Of Free Will

Kurt Godel saved me from Jacobus Arminius and John Calvin, and I thank him for it.

I have written before on the nature of Calvinism vs Arminianism and free will. However, I didn't state what I believed in. While I do tend to switch to the simple Arminianist viewpoint for witnessing, I do not hold this viewpoint.

I hold to both, which is a paradox. If not for our modern world, I couldn't have held this viewpoint.

Before, the 20th century, the Protestant church leaned in two directions:

1. Freewill means that God can't control everything (and you go on to try and harmonize the "difficult" verses that seem to indicate that God controls everything). Calvinist hate this viewpoint since it removes the sovereignty of God.

2. If God has total omniscience and total omnipotence, he can't allow freewill for salvation (and you go on to try and harmonize the "difficult" verses that seem to indicate that God allows freewill). The Arminianist hate this because it makes God responsible for all misery that we experience. In fact, it makes God responsible for only saving some people, and for creating evil.

[There is a new movement in the church toward ultra-free will called open theism. In this viewpoint God limits himself completely from knowing the future. If you think Calvinist have a problem with Arminianist, then you haven't seen anything. In a similar vein, Orthodox Churches are much more biased toward Free Will, but I will not address these in these posts.]

This is my beliefs: God has absolute control over everything while I still retain my right to freely chose.

Now, if God controls everything, then I should not have the right to freely chose. But if I don't have the right to freely chose, why would I spend any time worrying about free will? If we had no choice in the matter, the last thing we would do is worry that we had no choice.

The arguments for free will is very strong. The thing to be reconciled is the idea that God has directed every footstep. That he knows the future completely. That all things work together for the glory of God. If by free will, we chose to believe the Bible, we must find someway of reconciling the obvious fact of free will to the statements in Pslam 139:

All the days ordained for me
were written in your book
before one of them came to be

So, the way that I reconcile free will and God's sovereignty is to hold both. Now, you may state that my belief is not logical, and I will agree. It fundamentally breaks set theory (logic is just a subset of set theory). As logic is the basis of all rational thought, therefore, I am being irrational. Right?

Well, before we jump into this, I think we should first see what paradox precedent we have.

Really, the question is "are paradoxes allowed?" If we are to ask this, then I think we should jump to the most famous of modern paradoxes: Russell's paradox.

The picture to the right is one of Russell, one of the most famous atheists that have ever lived. Interesting, that I should say that Russell could have helped me with my theology, but he does. Russell, beyond arguing against God, was a very good mathematician. One of the ways of attacking logic is to define sets. Sets are objects that all have the same properties. Normally, with the Russel paradox, we use teacups.

So, lets say that you have a teacup. Let's say that I have a teacup. Timu-chan has a teacup. Paula has a teacup. My children and wife have teacups. The world has teacups. If we gather all of these teacups into a mathematical expression, we can call them a set. In this case, we'll call the set "R."

So, I say R and you should imagine the idea of "every teacup everywhere." It is the idea of a group of all teacups. Another way of saying this is to think of a crowd. A crowd is a set of people. When we say "crowd behavior" we think of something other than the behavior of people. We see the crowd having a personality in and of itself. (Not a perfect analogy for set theory, but this gets the flavor across.)

Now, we get a bit tricky, while R represents every teacup in the world, it is not a teacup. (In a similar fashion, a crowd contains people, but a crowd is not a person.) What is R? Well R is simply a logical construct.

We may chose to define another set and call it "S." We can define S as the set of all cups.

Now, we can see that R is a subset of set S. They are basically mathematical constructs. They are not teacups. They are simply concepts. However, a concept is still a thing.

Now, Russel started to think about this, and he said, "well I can define sets."

So, he said, "I'll define Z as the set of sets that are not members of themselves."

So, let's go back to R. Remember we said that R was not a teacup? R was simply a logical construction. So R is not a member of itself since it is not a teacup. We have a pretty good idea of what a teacups is, and now we know that the R is not a teacup therefore, it is not in itself. Therefore, the set of Z does have R in it.

However, let's talk about the set of "all ideas." We will call this set Y. This will be a very, very big set indeed! Every idea is in this set. Like pizza? This idea is in there. Like art? This idea is in there. All ideas are there. What about the idea of sets? Well, yes, if you think about it, the idea of sets is inside the set of all ideas. Because Y is inside Y, it does not below in Z.

So, we look to have a pretty good system.

Z has R in it.
Z does not have Y in it.

Then Russell thought, where does the set Z belong?

If Z is not in itself, then it belongs in Z.
But if Z is in itself, then it shouldn't be in itself.

Now, we are in trouble. As soon as we put Z somewhere, it instantly belongs somewhere else! Or some people have called this idea of being both entirely true and entirely false at the same time!

Although paradoxes had been documented since the Greeks, here we have a real problem. The type of paradoxes that Zeno came up with really were not paradoxes, they were word games. Once we got a piece of graph paper, we could show that Achilles and the tortoise did cross over (one of Zeno's paradoxes).

The problem with Russell's paradox is that you sit down with a formally equivalent mathematical system, and you needs to stay away from certain operations that yielded gibberish. Math and logic, which has solved the greek paradoxes, now have yielded paradoxes themselves.

Russell tried to get around this by limiting self reference. If you do any computer science, self reference commonly shows up in recursion algorithms. Therefore, the idea of staying away from self reference would knock the stuffing out of your programming.

Kurt Godel finally showed up and showed that all formal, complete systems will yield paradoxes. (An over simplification, but close enough for this post.) Godel's work is similar to other work by computer scientist. Remember that computers often use self reference, so you might expect that they to will run into issues.

Hilbert, who is pictured to the left, came up with the Entscheidungsproblem, which was the mother problem of computer science. I have talked about Hilbert and his problem before. As mentioned in my previous post, his problem was wrestled to the ground in Turing Halting Problem and Church's Lambda Calculus. They both proved for computer science what Godel proved for math. You should be able to see a braid here, that I am not the first or the last to notice.

Faith -> Math -> Computer Science -> Incomplete or Paradoxes -> Chance -> Faith

There are themes that weave themselves together.

Net-net, humans have been able to derive that we can't find the answer to all questions. We have found out that it is impossible to know in some cases!

This line of thought and understanding is only found in the 20th century. Until we had developed the math and the computer science, we simply did not explore these types of thoughts because they were illogical. They simply did not make sense.

After the 20th century, the church as freedom to say:

God has allowed total freewill and yet has total omniscience and total omnipotence. Now, mind you, there will be some that say that I have committed a gross foul, and I might as well pick up the flack for this.

While there is good evidence that paradoxes exist in all formal mathematical systems that are complete and there is also multiple ways of showing that the Entscheidungsproblem is unsolvable, there is nothing (and I mean nothing) to say that free will and sovereignty should be considered in this class. It is a little bit like saying that somebody didn't come home because I discovered that "flat tires have proven to happen" and then I suggest that the reason that somebody didn't home is because they got a flat tire. There are a variety of reasons that somebody may have not come home, just one of them is the idea that they got a flat tire.

However, for me, as I read the scriptures this is what I think is the best answer.

CS Lewis stumbled across some of this in his own thinking, although he couldn't do mathematics worth beans. He simply stated that as to his own failing he was going to think as somebody who has total freewill. He said that his faults was all his own.

To the goodness that happened anywhere else, it was because of omnipotent hand of God, and had nothing to do with freewill.

I can hardly think of better advice for our own lives.


Joshua said...

This is a really thoughtful post, and I think you're right and that paradox and wisdom are the only ways of understanding a good number of things in Scripture (i.e. How should parents treat children that stray? Should parents wait for their children to come home, like the father of the prodigal son, or should they track down their children like the shepherd that leaves the ninety-nine to find the one that is lost? Or, how is it that the Prince of Peace did not come to bring peace, but a sword?).

I'm interested to hear what you think the concept of time has to do in your discussion of free will and God's sovereignty. Does God create our lives in real time, or are we living out something like a recording of what He has already determined to be? While I think that Scripture clearly presents God as a crafty and wise God, we can also find examples of God graciously reneging on things He has declared to be (i.e. His promise to destroy the city of Nineveh, the declared goodness of man in Genesis, various demands of Old Testament prophets that He graciously relents of when questioned).

Although a rather simplistic response, I think that one of the main problems with Calvinist theology is that it is preoccupied with the power of God, sometimes to the point of excluding His goodness. I haven't done any kind of case study, but in a tertiary reading of the OT (and certaily the NT), the writers of Scripture are more concerned with Yah's goodness than His strength. While it's kind of a strange distiction to make, God's power is certainly controlled by His goodness. God certainly has the power to destroy the faithful and send them to hell, but His goodness and His promises in sacrament and Christ sway Him against ever doing such a thing.

Regardless, thanks for this article.

Take care, and I'll see you in a few weeks!


Theologic said...


I look forward to a few nights of philosophical talk when you are in town. Perhaps we can table some of these questions until then. (We can also discuss what music is worth listening to.)

Maybe just one comment on one of your questions:

Jonah's message in the NASB: "Then Jonah began to go through the city one day's walk; and he cried out and said, "Yet forty days and Nineveh will be overthrown."

This is the story in the NIV: "Forty more days and Nineveh will be overturned."

In the King James, "Yet forty days, and Nineveh shall be overthrown."

And Ninevah was overthrown, without blood or destruction. Their sin was overthrown because of repentance. God called it right.

As always your affectionate,
Uncle Teddy