The good way to answer to the question is to view the content of the conference "Beyond Belief 2006" and then ask it again. After having viewed this content (all of it) I think there are six answers to the question. I think answers 4, 5 and 6 are most interesting. The idea of multiple answers beyond three was reinforced strongly by my experience in viewing the conference. So here are the answers:
- I do not know.
- I do not understand the question.
- It can be show using mathematics that an extended version of answer 4 is the best response. (The extended version of 4 is "Neither I nor you understand the question.")
- There is good medical evidence that the urge to ask and respond to this question is a physiological artifact of the operation of the human brain.
My favorites now are 5 and 6.
When I was a teenager, and after going through the Piaget level, number two was my best response with lots of supporting evidence on my part. This response was coupled with huge shouting matches with my father that frequently ended in me storming away in tears and in long and very careful discussions with my grandparents.
As I got older number three was my choice but I was never happy with it.
Recently (before watching the conference) my best choice was five. And after watching the conference six has been added. Just after watching the conference I started reading "Shadows of the Mind" by Rodger Penrose.
I do think that Gödel's basic result can be improved on by more carefully thinking about Logic and in particular how we define the Natural Numbers and Arithmetic. This improvement could make answer five incorrect and leave only answer six.
Additionally I think a lot about a different question than the one presented here, and it has the answer "42".