Godel’s Theorem and it Linkage to our pursuit
4January 30, 2012 by styagi68
The objective of this blog is to explore the nature of truth through reasoning. That broadly means that one starts with as few axioms (accepted truths) and builds a system of theorems (derived truths) which is complete and consistent.
A few days back, I was watching the videos of Godel, Escher, Back: Douglas Hofstadter’s classic about finding the root of self through mathematics, music and drawing. (side note, Open Courseware from MIT is a fantastic program. In 2007, there was a seminar on GEB and the videos are available for free on youtube, just search for Godel Escher Bach in youtube!). Godel’s incompleteness theorem states that no formal system can be complete and consistent.
Complete means that it contains all truths and conistent means that no two theorems are in contradiction. It got me started thinking about the objective of this blog. If we can’t construct a number theory which is consistent and complete then how can we aspire to “find the truth through reasoning.” Many mystics have stated that in the path of self realization, one can only progress when you leave thinking behind and move with intuition. That has always seemed to me as a cop out. However, does Godel’s theorem lead us to the same conclusion—just more rigorously.
Analytical Faith 
A man is sitting on a boat in a pond. He holds a cup in his hand. Fills the cup from one side of the boat and drops on the other side. Would he be ever able to measure how many glasses of water this pond contains?
No, as his apparatus for measuring a system is itself a part of the system.
And we are sitting not in a pond but in an ocean.
Dear Jatinder,
Thank you for your comment. Your comment is in line with the mystical tradition (and may well be ultimately the reason). Godel’s Incompleteness typically refers to the problem of self reference. Consciousness can’t meditate on itself, kind of issue.
Regards.
Sandeep
As I see it, absolute truth is an ideal. There is no limit to how many truths you can find but there is probably no way all truths can be known (for practical and physical reasons). I would say that only 1/3 of all the truths can be known. 🙂 Otherwise you risk to get a complete system that makes no sense, it is a compromise. Sorry I don’t make much sense, it is a bit late. But interesting article.
I love that reply! Did you just come up with it?