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Monday, February 18, 2008

Faith in Axioms

I happened to notice a line in the post here that translates to something like: "theology begins from faith". An analogy to explain this would be that in Mathematics, NO theorems can be proven without "believing in" axioms. We need to believe in certain axioms that CANNOT be proven. For example, a line is straight. A "point" is the (smallest) precise location on a plane. Mathematics begins here, in these beliefs !

Going by the ways of an atheist - It is possible to realize even smaller points. So "a point can never be a point" as per its definition. And as for line - since quantum physics defines constituents of an atom using a "probability" of finding each of them at a particular place, I wonder how perfectly straight a straight line can possibly be (All straight lines are in reality "broken" lines).

However, if we were to have always debated over mathematical axioms, we would never have had mathematics. This fate was never reached because the capability to make a fair judgement between axioms and theorems has been well within the human intellectual capability. Humans could judge what could be assumed (eg: Mathematics limits which tend to infinity / zero but are neither infinity / zero) and what must be proven. In school, I used to have friends for whom the axioms of mathematical Limits were too incomprehendible to have put their belief in. I have often felt that their behaviour in a calculus class or in a class on N-dimensional mathematics can be compared to those of an atheist listening to a preacher.

If God is really as great as we think (say, a lot greater than mathematics), then comprehending him will demand faith in a lot more axioms than the silly mathematics axioms that we (although not all humans) can comprehend.

(This is not entirely my original thought)

1 comment:

സഞ്ചാരി @ സ്വര്‍ഗ്ഗീയം said...

Thanks for your serious attention to my post and the link. You clarified it more in scientific terms beautifully and precisely.
Certainly everything has its own limits of methods and principles. Nothing is autonomous except God. All human sciences and discoveries are coming under these limitations. For example, the very structure of which allows a bird to fly limits its ability to swim, whereas, conversely a fish's structure which allows it to swim but not usually to fly. Quantum Physics proved these limitations in scientific way.
In the past many scientists believed that nature is written in mathematical symbols and the mathematical formulation of scientific theories represents 'Reality' in itself. But, how is it possible? As Russell wrote, " is it possible for a physicist to predict something, calculate equations which describe it, and still not know what he is talking about". As you wrote clearly they are also starting from some kind of ‘blind faith’ or ‘hope’.
I believe that all these sciences are complimentary to each other in order to explain the Mystery of Reality (for me it’s GOD) in a better way. The famous scientist William Pollard says, “We are not speaking of a mystery of anything unknown at all. Rather we are speaking of the mysteriously amazing character of the known. There is a truer mystery of the known and our modern knowledge in science confronts us with that mystery very strongly.” Theology is also doing the same from known to the Unknown, especially a religion like Christianity. They start from the belief that God revealed everything in Christ and through Him they reach to God.