Please refer to Kelly's post

Pluralism: The Solution to the ID Debate?[This post is actually a reply to an interesting proposal by Kelly on his blog. Supposedly, I am doing this because there is a bit of a technical problem interfering with the display on his page. Actually, I just spent so much time writing this, that I wanted to kill two birds with one stone by getting my comment and my post in at the same time.]

Very interesting post, Kelly! You may be onto something.

Here is my recent train of thought:

Euclid's book, the

*Elements*, introduced a system of geometry from which he deduced the properties of geometric objects from a set of only 5

postulates. He had invented a method of proving numerous truths about geometry and numbers that rocked the world. What was truly fascinating about his achievement was how he proved so many theorems (things proved) from such a small number of postulates or axioms.

His method was so nifty -- so frikkin' cool -- it inspired both geniuses and crackpots throughout the ages to use it as the model for almost any endeavor that required deductive reasoning, or the creation of proofs.

Today, modern math and logic make extensive use of the axiomatic system to prove whatever it is that they are concerned with proving. Informal logic is also heavily influenced by Euclid's great idea.

Euclid's idea was so impressive, that people tried to apply it to just about every area of human reasoning. Sometimes with absurd results. Several years ago, I encountered a book in a public library that was written in the 1800's (I think), and purported to teach chess as an axiomatic system. As far as I could tell, the book was complete nonsense.

The problem with incredibly brilliant ideas that rock the world, however, is that people don't often see their limitations. Sometimes for centuries -- or even millenia. They introduce notions that may become so pervasive, so much a part of our basic assumptions about reality, that we don't even notice them, let alone question them.

And that is what happened when people became so enamored with the axiomatic system. They thought it should be able to prove everything. All you had to do was to find the right basic set of axioms, and apply the right reasoning, and eventually you could prove all the truths in the system.

This idea was so pervasive, that it permeated virtually all of Western philosophy and science. [Okay, you should call me on this last statement.] And so did the fallacy that any truth should be provable if you just had the right axioms and the right method. Of course, there were always paradoxes and weirdities that occured in every tightly expressed logic or mathematical system. Like

Bertrand Russell and a paradox involving the logic of classes. I just remember it had something to do with a class of all classes. I'm too tired think it through, so you can look it up yourself, if you want.

Anyway, as far as I remember learning it, Russell set out to try to resolve all the paradoxes. He hoped to come up with a complete little axiomatic system that resolved all paradoxes, and could prove all the truths of the system. He ended up producing the massive Principia Mathematica (with Alfred North Whitehead), which managed to avoid many paradoxes and problems of logic. It was a huge effort. But it was incomplete.

But he must have felt rather disappointed when

Kurt Goedel came up with a proof that showed a that Russel never could have accomplished some of the goals that it aimed to do. He proved that it is impossible for any logic system (of a non-trivial size) to eliminate all paradoxes. He also showed that no logic system could be complete based on a limited number of axioms. There would always we truths that could not be proven from the axioms. If you wanted to prove them, you would have to increase the axioms. But then you will just get more paradoxes and more truths that are known to exist, but can not be proven.

And in one fell swoop, he knocked down some of the key assumptions driving western logic systems for the previous 2000+ years. In my opinion, it was a feat at least as important as Einstein's Theory of Relativity.

The problem is, that so many people didn't get the memo.

What does this have to do with anything? Well, it seems to me that this relates to the ID vs Evolution debate, epistimology, and whatever else you want to throw into the mix. (I am getting very, very sleeeepy).

It's the problem of there always being truths out there that can not be proven. We may know that there are such truths. We may suspect we know which truths they are. But we can not use deduction from any finite set of known axioms, or already proved things, to prove that they are true. So, if I understand Godel correctly (and I very well may not), it seems to me that there will always be these gaps in what the Scientific Method can and can't prove. (By the way, I should add that, because of Godel's proof, it does not seem to be a valid criticism of any theory that there are truths that it can not prove.)

But just as important, we have to ask the question, if it is proved that there will always be truths that the Scientific Method can not prove, then what options are open to us? Is religion the appropriate method for finding those truths?

I don't know. I guess that's a question to be answered in Kelly's epistemology class.

*Disclaimer -- I make no pretense of having doublechecked any of the above facts, or even having thought my conclusions and interpretations over in any detail. Please feel free to correct me if you have better knowledge than I.*