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If you want to learn thoroughly about Godel's Incompleteness Theorem, and all its implications, nothing is better than Godel, Escher, Bach: An Eternal Golden Br

by truth_ 5y ago

If you want to learn thoroughly about Godel's Incompleteness Theorem, and all its implications, nothing is better than Godel, Escher, Bach: An Eternal Golden Braid by Hofstadter. This book is quite outdated in both approaches and ideas about computers, and computer-aided approaches to Artificial Intelligence, this book still has to offer a lot. It is one of the most impactful books I have read.

ruslan 5y ago
Fascinating book indeed. I read it when I was a student some twenty years ago, I had been astonished by simple and clever trick Godel used to prove his theorem - to digitize everything, then operate with just numbers.
alok-g 5y ago
Does it explain the proof itself in it's full glory? I had read "Godel's Proof" by Ernest Nagel et al [1] and it fell short. [1] https://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/0814758371/ https://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/08147583...
- truth_ 5y ago
  You mention in another comment that it skipped some part of the proof and that you were disappointed. Do you still recommend the book?
  - alok-g 5y ago
    If you are mathematically-inclined and are looking forward to understanding the proof itself, the book won't do much better than the following video [1] taken from a comment in this thread [2]. Disappointed, I attempted to read Godel's original papers. That has it's own challenge as it refers to Principia Mathematica. I started reading that. Only to fimd that it uses older mathematical notation not in use today. In short, I haven't found any source that explains the proof in reasonable detail. If you want to understand the thought process of axiomatic reasoning (and with less extrapolations to consciousness et al) it is a good book. Note: I had read a long time back, so do not remember the details. [1] https://www.youtube.com/watch?v=HeQX2HjkcNo https://www.youtube.com/watch?v=HeQX2HjkcNo [2] https://news.ycombinator.com/user?id=littlecranky67 https://news.ycombinator.com/user?id=littlecranky67
adverbly 5y ago
It tops my list of impactful books for sure. I feel like GEB can't even properly be described as being "about" anything in particular. It seems to evade capture in the same way that the formal systems that it describes evade capture. It is almost "about" what "meaning" itself is... Nothing quite like it.

by truth_ 5y ago

ruslan 5y ago

Fascinating book indeed. I read it when I was a student some twenty years ago, I had been astonished by simple and clever trick Godel used to prove his theorem - to digitize everything, then operate with just numbers.

alok-g 5y ago

Does it explain the proof itself in it's full glory? I had read "Godel's Proof" by Ernest Nagel et al [1] and it fell short. [1] https://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/0814758371/ https://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/08147583...

truth_ 5y ago
You mention in another comment that it skipped some part of the proof and that you were disappointed. Do you still recommend the book?
- alok-g 5y ago
  If you are mathematically-inclined and are looking forward to understanding the proof itself, the book won't do much better than the following video [1] taken from a comment in this thread [2]. Disappointed, I attempted to read Godel's original papers. That has it's own challenge as it refers to Principia Mathematica. I started reading that. Only to fimd that it uses older mathematical notation not in use today. In short, I haven't found any source that explains the proof in reasonable detail. If you want to understand the thought process of axiomatic reasoning (and with less extrapolations to consciousness et al) it is a good book. Note: I had read a long time back, so do not remember the details. [1] https://www.youtube.com/watch?v=HeQX2HjkcNo https://www.youtube.com/watch?v=HeQX2HjkcNo [2] https://news.ycombinator.com/user?id=littlecranky67 https://news.ycombinator.com/user?id=littlecranky67

adverbly 5y ago

It tops my list of impactful books for sure. I feel like GEB can't even properly be described as being "about" anything in particular. It seems to evade capture in the same way that the formal systems that it describes evade capture. It is almost "about" what "meaning" itself is... Nothing quite like it.