Tuesday, June 28, 2016

Consistent and Complete

Kurt Gödel's incompleteness theorem proved that the title of this post is impossible for any set of axioms that you adopt.

On one of my many walks between home and office, I thought about the significance of this and the human psyche.  I place myself, and the axioms and tenets that I adopt, into an incomplete category.  This is where I have found the most comfort. I am more comfortable in a framework that is consistent in my day-to-day learning and understanding of the world. Incompleteness isn't comfortable by any means, but I've accepted the fact that there are things that are true within my system that cannot be proven within that system.  This means, confusingly, that I cannot accept some "truths" as true, since I do not have the capability of knowing them to be "true."

Then I began to think of those who take more comfort and embrace a complete system of axioms and tenets. Within their system, these people have the ability to accept "truths" that I cannot accept, because they can be proven and are acceptable within their system.  However, this complete system of theirs is inconsistent, and hence has contradictions by Gödel's theorem.

Nobody likes inconsistencies, either.  So, those that take more comfort in a complete system either go the Walt Whitman route: "Do I contradict myself? Very well, then I contradict myself, I am large, I contain multitudes," or they take the following stance.

Life is full of complete and consistent people. Whichever one you are, we need to remind ourselves that the other person could be inconsistent or incomplete, and that there's no changing that.

There is at least one important thing I've learned as a consistent person who accepts his incompleteness, and that is there are a lot of complete people out there that do not want to hear about nor accept how inconsistent they are.

Which are you?

I'm reading Gödel, Escher, Back: An Eternal Golden Braid again this summer because I love this book, and it fosters thought experiments like these.

1 comment:

  1. Great application of a complex idea. I really hadn't thought about it, but I think I'm with you: I prefer consistency to completeness, and can deal with knowing my way of looking at life doesn't account for every eventuality.