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I highly recommend getting Godel's proof[1] and reading it. It's an amazing journey and quite understandable from the start (the first half of the book is intr

by kruhft 10y ago

I highly recommend getting Godel's proof[1] and reading it. It's an amazing journey and quite understandable from the start (the first half of the book is introduction), and I've never been able to read proofs very well. It takes concentration, but once you get it (at '17 GenR') it's almost like a symphony going off. The crystalline brilliance of the "System P" decomposition is worth it just to see how math as a process could be reduced to a such simple, clear and concise set of symbol manipulations...and then the rest shows how that could be used topple itself. Incredibly philosophically insightful. [1] https://www.amazon.ca/Undecidable-Propositions-Principia-Mathematica-Mathematics-ebook/dp/B00A44R3E8/ref=sr_1_1?ie=UTF8&qid=1489447527&sr=8-1&keywords=on+formally+undecidable+systems+godel https://www.amazon.ca/Undecidable-Propositions-Principia-Mat...

ucarion 10y ago
I can't speak for Godel's original proof since I haven't seen it before, but I certainly found Computability and Logic [1] to be pretty approachable. It's the textbook used for UC Berkeley's "Intermediate Logic" philosophy course (in other words, it's so easy even philosophy majors can understand it! :P). From my understanding, C&L diverges from Godel's original proof technique in order to make it easier to follow, but it's much more rigorous and explicit than what you'd find in Godel, Escher, Bach or something. It's still a textbook. [1]: https://www.amazon.com/Computability-Logic-George-S-Boolos/dp/0521701465 https://www.amazon.com/Computability-Logic-George-S-Boolos/d...
cgh 10y ago
I try to read Godel's Proof once a year or so. You might also be interested in Gregory Chaitin's Meta Math! The Quest For Omega, which relates the halting problem (among other things) to Godel. A word of warning though, the book is rather idiosyncratic, as you might have seen from the title.
- kruhft 10y ago
  Got it years ago and loved it. Have to give it another read some day.

by kruhft 10y ago

ucarion 10y ago

I can't speak for Godel's original proof since I haven't seen it before, but I certainly found Computability and Logic [1] to be pretty approachable. It's the textbook used for UC Berkeley's "Intermediate Logic" philosophy course (in other words, it's so easy even philosophy majors can understand it! :P). From my understanding, C&L diverges from Godel's original proof technique in order to make it easier to follow, but it's much more rigorous and explicit than what you'd find in Godel, Escher, Bach or something. It's still a textbook. [1]: https://www.amazon.com/Computability-Logic-George-S-Boolos/dp/0521701465 https://www.amazon.com/Computability-Logic-George-S-Boolos/d...

cgh 10y ago

I try to read Godel's Proof once a year or so. You might also be interested in Gregory Chaitin's Meta Math! The Quest For Omega, which relates the halting problem (among other things) to Godel. A word of warning though, the book is rather idiosyncratic, as you might have seen from the title.

kruhft 10y ago
Got it years ago and loved it. Have to give it another read some day.