alt Hacker NewsI have tried to read some articles and watch some videos "explaining" Godel but never really understood it. Everyone seems to be explaining the mechanics of what Godel did but explaining the Why is lacking i.e. What was it in mathematics that got him even thinking on these lines in the first place? Can this problem be demonstrated with a simple toy axiomatic formal system? How did he hit upon his approach? Answers to these sort of questions is what seems to me the most important thing to understand before following his arguments.
I recently came to know of The Annotated Godel: A Reader's Guide to his Classic Paper on Logic and Incompleteness by Hal Prince which i think i need to sit with :-)
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To me the mechanics and the why are closely intertwined. If you feel like self-referentiality is a way to demonstrate a problem (this is the “why”), it is not a long step to the mechanics of encoding.
The work is in creating the theorem / contradiction from that point, but in the big picture, the approach doesn’t have to come from nowhere.
I think that Gödel did all of this stuff because of David Hilbert basically posing the challenge to make maths' foundations consistent and complete.
https://en.wikipedia.org/wiki/Hilbert's_program