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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)