Monothestic Religion and Science

Normally I don’t like to talk much about religion, but I came across an idea last night that was so interesting I thought I had to write it down. Simply put, the idea is that science is an unintentional side effect of a religious system that believes in a single god.

The argument goes something like this. Think of a society that believes in lots of gods, one that believes each rock, tree, animal, river etc has its own spirit to diety controlling it. You could easially think of two rivers, one flowing upstream, and the other flowing downstream, because that’s how each god wanted to run their river. If you accept that as a part of the belief system, you will never try and look for common behaviour in all rivers, because it just wouldn’t make sense. Every river has its own god, and every river has its own behaviour, based on that god.

Then by contrast, think about a society such as Christianity, which believes in (one) God. God decides how all the rivers work, and because of this, all rivers work the same. Once you have the concept that all things sharing some property also share behaviour, you start trying to explain that behaviour, to understand it, to predict it. As soon as you start trying to do that, science as we know it soon follows.

The familiar process then often follows, whereby we look at something, create some ideas as to how it works, that seems to successfully predict it, and then we think “hey, this explanation doesn’t need a God to make sense”. Before long there are all sorts of tensions between the scientists and the religious believes, but that’s another story…

By |October 10th, 2006|General|3 Comments

Can we trust logic – revisited

A few days ago (well, more than a few days ago, but some technical problems got in the way since I wrote this post) I wrote about how logic cannot be conclusively shown to be correct. I mentioned that the argument is explained better in the book Gödel, Escher, Bach. I knew it was actually an application of Gödel’s theorem.

That night I went to bed, and picked up my book, “The music of the primes”. I turned to the next chapter, and what do I discover, an analysis of Gödel’s theorem! So I can now explain with a bit more accuracy the history.

I had thought that the theorem was originally presented in terms of sets, but in fact it was originally presented in terms of mathematical axioms. Maths, like any logical system is defined by axioms and rules. The axioms set out a list of facts, things that are “true” by definition. The rules allow you to modify the axioms to create theorems, statements that can be derived from axioms. For a long time, one of the biggest questions for mathematicians was “are our axioms consistent”. That is to say, is it possible to construct two different theorems from the axioms that contradict each other? This is another way of asking if mathematics works. If maths allows us to produce two theorems that contradict each other we cannot trust either of them. We would not be able to allow ourselves to trust any result in mathematics. Unless we simply accept that the axiom’s are consistent.

Gödel’s theorem, in its original form, shows that no set of axioms and rules, can be used on their own, to prove that those axioms are consistent. Mathematics alone cannot prove that mathematics is consistent, that it is valid, and that it works. A greater system is needed, one that encompasses the axioms of mathematics, maybe it produces them as theorems, or has them as axioms itself. Logic is this system. But how to we to be sure the axioms of logic are consistent…

By |October 10th, 2006|General|1 Comment