An Introduction to Gödel's Theorems

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1. aragoniteMar 2024
   Gödel Without (Too Many) Tears, by Peter Smith. Also his An Introduction to Gödel’s Theorems.

   https://www.logicmatters.net/books/

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2. jimhefferonAug 2017
   Lots of reading are available to technical people who are willing. People elsewhere in this thread have mentioned Nagel and Newman, and also Smullyan. Here are two more:

   1) Smith's Introduction to Godel's Theorems http://www.logicmatters.net/igt/ is a great book, with all the mathematics but willing to go into the philosophy.

   2) Franzen's Gödel's Theorem: An Incomplete Guide to Its Use and Abuse http://www.ams.org/notices/200703/rev-raatikainen.pdf is enlightening in a different way.

   I'll also mention a favorite author around here http://www.scottaaronson.com/blog/?p=710 .

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3. jimhefferonMar 2017
   I'm not sure why you have it in quotes. But FWIW, most of my questions were cleared up by these two wonderful books: Peter Smith's An Introduction to Gödel's Theorems and Torkel Franzén's Gödel's Theorem: An Incomplete Guide to Its Use and Abuse
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4. ionfishMay 2012
   Do you have a decent understanding of first order logic? If not, sort that out first. Peter Smith has a good list of books to choose from:

   http://www.logicmatters.net/2012/05/teach-yourself-logic-1-f...

   Then get Smith's book An Introduction to Gödel's Theorems. It explains Gödel's results in great detail and doesn't assume too much background knowledge. A certain amount of perseverance will, of course, be required…

   There's some supplementary material on his website: http://www.logicmatters.net/igt/

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5. manifestsilenceOct 2018
   I agree that it's way over-long and rambling, but it was my introduction to the topic. Where it really shines is his interesting and controversial thesis that connects Godel's proof with the Church-Turing thesis and other things to form a theory of consciousness as pattern and make the claim that a sufficiently powerful AI is as sentient and meaningful a consciousness as we are.

   I read Godel's Proof after though, and I agree that it is a far clearer introduction to Godel's theorems.

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