Incompleteness: The Proof and Paradox of Kurt Godel

One book leads to another.  That’s the way it goes.  Since I was a child, I allowed myself no gaps between the end of one book and the beginning of another.  In many cases, there would be direct causal connections to the choices.  Sometimes there would be jumps and starts, but overall, themes would build and become supported by a continuum of developed and borrowed ideas.

This is the case with Godel.  As stated below, I read and thoroughly enjoyed Anathem, by Neal Stephenson.  I was also deeply impressed with the process that Stephenson constructed and consolidated philosophical parallels between our world and his (in his story).  This was done, in part, because of the work in mathematics and logic by Kurt Godel.  Of course, intent and outcome are rarely coincidental.   As a result, I was attending a very fun and beautiful wedding in New Jersey and one of our friends sitting at the table took out a book and proclaimed that it was one of her favorites and that she had just had it returned to her from a friend.  She wanted to pass it around the table, and since we had just returned from the buffet line and were beginning to eat, it increased the potential for deep conversation at such a festive event.  Most people politely looked at the book (pictured above) and nodded silent approval while moving it passively around the table.  When it got to me, I exclaimed, “GODEL!”, which drew the attention of everyone at our table and the near vicinity.  Being somewhat introverted but also somewhat intellectually isolated with my friends, I pounced on the opportunity to bring a philosophical conversation to the surface.   As a result of my display, I came away from the wedding with a pleasant night of smiles and memories, and a book on Godel.

Trying to understand Godel is another thing entirely.  I needed to build a language in order to understand the concepts while also trying to construct a context to fit that language in.  This is very difficult, since the theories on which Godel’s logic is based call into question how we are able to know that anything is true at all.  Wittgenstein and other colleagues (Einstein for one) also shaped Godel’s thoughts.  Currently, I am still in the process of reading the book, deconstructing my philosophical neural-networks, and replacing them with something that adds ‘incompleteness’ to the logic of existence.  Wish me luck.