Incompleteness
Maarten Maartensz
maartens at xs4all.nl
Wed Jan 23 14:14:42 UTC 2002
Hello,
Craig Latta and Ken Kahn discussed incompleteness and Goedel's Theorem.
(I'll forego the Umlaut).
For what it is worth: Some mathematical logicians get the shakes from
reading Nagel and Newman on Goedel and are not greatly impressed if amused
by Hofstadter's book. Here are references that REALLY explain it
1. Raymond Smullyan: Goedel's Incompleteness Theorems
ISBN 0-19-504672-2
(Oxford Logic Guides #19)
2. Raymond Smullyan: What's the name of this book?
ISBN 0-13-955088-7
(Hardcover edition)
3. Raymond Smullyan: The Lady or the Tiger and other Logic Puzzles
ISBN 0-394-51466-1
(Hardcover edition)
4. Hao Wang: Reflections on Kurt Goedel
ISBN 0-262-23127-1
5. Hao Wang: Logic, Computers and Sets
(can't find my copy on the moment)
I could flood you with much more if you like it. Smullyan is a great
mathematical logician, and (1) requires some logic, but (2) and (3) are
extra-ordinary logic puzzles around Goedelian themes in English of great
originality and wit (There are more of these by Smullyan, and all have
paperback editions. I listed my original hardcover ones.)
Hao Wang was a mathematical logician who was one of the few personal
friends of Goedel (Einstein was another), and (4) requires no logic while
explaining a lot. His (5) is a collection of his beautiful very clear
papers in the fields mentioned in the title.
In any case: If you liked Hofstadter, take a peep at one of Smullyan's
logic puzzle books. Amazon probably lists quite a few of these. They are a
joy to read and only require a clear mind and no mathematics or logic at all.
Regards,
Maarten.
------------------------------------------
Maarten Maartensz. Homepage:
http://www.xs4all.nl/~maartens/
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