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Gödel links

You will find numerous references to Gödel and his incompleteness theorem. Some of them are listed here. You can see an English translation of his proof Gödel’s Proof - English translation: here. Links that are principally about the Gödel, Minds, and Machines question are listed on a separate page, see Gödel, Minds, and Machines.

 

If you think an item should be included on this page please let me know.

 

Please note: Inclusion in this list does not mean I recommend any of the items in this list.

 

Links to Web pages on Gödel and/or his Incompleteness Theorem

Cosmic fingerprints website on incompleteness
An attempt to apply Gödel’s Incompleteness Theorem to the universe
The nature and significance of Gödel’s incompleteness theorems PDF
An article by Solomon Feferman
Dale Myers on Gödel
Brief notes about Gödel’s Incompleteness Theorem and other things, by Dale Myers
Stanford Encyclopedia entry on Gödel’s Incompleteness Theorem
Stanford Encyclopedia entry on paradoxes arising from self-reference
An article by G Chaitin on Gödel’s Theorem
Just one of many similar articles on Gödel’s Theorem by Chaitin
Webpage about Gödel’s Incompleteness Theorem by Stephen Lee
appears to be attempting to write a computer proof of incompleteness
Science Magazine article on Gödel’s Incompleteness Theorem PDF
BBC page with link to a broadcast on Gödel’s Incompleteness Theorem
Entry on Gödel’s Incompleteness Theorem in Wolfram’s Mathworld
Webpage on incompleteness by K Podnieks
Biography and other information about Kurt Gödel
Wikipedia entry on Gödel’s incompleteness theorems

A claim to be the ‘World’s shortest explanation of Gödel’s theorem’

The above webpage claims to be the ‘World’s shortest explanation of Gödel’s theorem’ but it is nothing of the sort, see World’s shortest explanation of Gödel’s theorem?: here

Trite and superficial attempt to explain Gödel’s Theorem
encyclopedia.com article on Gödel
Encyclopedia Britannica article on Gödel

 

Links to freely available online papers on Gödel and/or his Incompleteness Theorem

Bays, Timothy On Floyd and Putnam on Wittgenstein on Gödel PDF

Journal of Philosophy (April 2004) pp 197-210.

Bays, Timothy Floyd, Putnam, Bays, Steiner, Wittgenstein, G̈odel, Etc PDF

Online

Davis , Martin The Incompleteness Theorem PDF Notices of the AMS vol 53 no 4 (2006), p414
György, Sereny Gödel, Tarski, Church, and the Liar Arxiv (1999)
György, Sereny Boolos-style proofs of limitative theorems Arxiv (2003)
Jaki, Stanley A Late Awakening to Gödel in Physics Sensus communis 5 (2004), pp 153-162.
Jaki, Stanley On A Discovery About Gödel’s Incompleteness Theorem Pontifical Academy of Sciences, Acta 18, Vatican City (2006)
Ketland, Jeffrey Deflationism and Tarski’s Paradise Mind 108, no. 429 (1999) pp 69-94
Kikuchi, Makoto; Tanaka, Kazuyuki On formalization of model-theoretic proofs of Gödel’s theorems Notre Dame Journal of Formal Logic (1994) 35 (3) pp 403-412
Lindström. Per Aspects of Incompleteness Lecture Notes in Logic (1997) v 10
O’Connor, Russell Essential Incompleteness of Arithmetic Verified by Coq PDF Lecture Notes in Computer Science (2005) v 3603, pp 245-260
Sayward, Charles Steiner Versus Wittgenstein: Remarks on Differing Views of Mathematical Truth Theoria (2005) 20 (3) pp 347-352.
Tennant, Neil Carnap, Gödel, and the Analyticity of Arithmetic PDF Philosophia Mathematica 16, no. 1 (2008) pp 100-112
Tennant, Neil Deductive Versus Expressive Power: A Pre-godelian Predicament PDF The Journal of philosophy (2000) pp 257-277
Tennant, Neil Deflationism and the Gödel Phenomena PDF Mind 111, no. 443 (2002) pp 51-582
Tennant, Neil Deflationism and the Gödel Phenomena: Reply to Cieśliński PDF Mind 119, no. 474 (2010) pp 437-450
Tennant, Neil Deflationism and the Gödel Phenomena: Reply to Ketland PDF Mind 114, No. 453 (2005) pp 89-96
Vidal-Rosset, Joseph Does Gödel’s Incompleteness Theorem Prove That Truth Transcends Proof? from Book: The Age of Alternative Logics (2006) pp. 51-73. Springer
Wigderson, Avi The Gödel Phenomena in Mathematics: A Modern View PDF from Book: Kurt Gödel and the Foundations of Mathematics: Horizons of Truth (2010) Cambridge University Press
Zach , Richard Hilbert’s program then and now PDF from Book: Philosophy of Logic, Dale Jacquette (ed), Handbook of the Philosophy of Science (2006) v 5, Elsevier, pp 411-447
Zach , Richard Kurt Gödel 1931 PDF from Book: Landmark Writings in Mathematics (2004) pub North-Holland pp 917-925
Zach, Richard The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert’s Program PDF Synthese (2003) 137 (1) pp 211-259

 

Books and non-free online articles on Gödel and/or his Incompleteness Theorem

The articles are not available free online, except at sci hub, http://sci-hub.bz/ or http://sci-hub.cc/.

 

Berto , Francesco There’s Something about Gödel: The Complete Guide to the Incompleteness Theorem (2010) John Wiley and Sons There’s Something about Gödel: Details
Boolos, George A New Proof of the Gödel Incompleteness Theorem (1989) Notices of the AMS v 36, pp 388-390 and p676, reprinted 1998 in Boolos: Logic, Logic, and Logic, Harvard University Press ISBN 0674537661 A New Proof of the Gödel Incompleteness Theorem: Details
Charlesworth, Arthur A Proof of Gödel’s Theorem in Terms of Computer Programs (1980) Mathematics Magazine, v 54 no 3, pp 109-121 A Proof of Gödel’s Theorem in Terms of Computer Programs: Details
Dawson, John W Jr Logical Dilemmas: The Life and Work of Kurt Gödel (1997) AK Peters, Wellesley Mass, ISBN 1-56881-256-6 Logical Dilemmas: The Life and Work of Kurt Gödel: Details
Floyd, Juliet & Putnam, Hilary A Note on Wittgenstein’s ‘Notorious Paragraph’ About the Gödel Theorem (2000) Journal of Philosophy v 97 n 11, pp 624-632.
Floyd, Juliet & Putnam, Hilary Bays, Steiner, and Wittgenstein’s ‘notorious’ paragraph about the Gödel theorem PDF

Journal of Philosophy (2006) 103 (2)

Franzén, Torkel Gödel’s Theorem: An Incomplete Guide to its Use and Abuse (2005) AK Peters ISBN 1568812388 Gödel’s Theorem: An Incomplete Guide to its Use and Abuse: Details
Goldstein, Rebecca Incompleteness: the Proof and Paradox of Kurt Gödel (2005) W W Norton & Company ISBN 0-393-05169-2 Incompleteness: the Proof and Paradox of Kurt Gödel: Details
Hellman, Geoffrey How to Gödel a Frege-Russell: Gödel’s Incompleteness Theorems and Logicism Noûs Vol 15, No 4, Special Issue on Philosophy of Mathematics (Nov 1981), pp 451-468
Hofstadter, Douglas Gödel, Escher, Bach: An Eternal Golden Braid (1979) Vintage Books ISBN 0465026850
1999 reprint: ISBN 0465026567 Gödel, Escher, Bach - Hofstadter: Details

Hofstadter, Douglas

I Am a Strange Loop (2007) Basic Books ISBN 9780465030781 I Am a Strange Loop: Details
Hopcroft, John & Ullman, Jeffrey Introduction to Automata theory (1979) Addison-Wesley, ISBN 0-201-02988-X
Ketland, Jeffrey Deflationism and the Gödel phenomena: Reply to Tennant Mind 114, No. 453 (2005) pp 75-88 Deflationism ... Reply to Tennant: Details
Kleene, Stephen Cole Mathematical Logic (1967) Reprinted in 2002: Dover, ISBN 0-486-42533-9 Mathematical Logic: Details
Kleene, Stephen Cole Recursive predicates and quantifiers (1943) Transactions of the AMS, v 53 n 1, pp 41-73
reprinted in 1965: The Undecidable (Martin Davis) pp 255-287 Recursive predicates and quantifiers: Details
Nagel, Ernest & Newman, James Roy Gödel’s Proof (1958)
2001 Revised ed: New York University Press, ISBN 0814758169 Nagel and Newman, Gödel’s Proof: Details
Priest , Graham Logic of Paradox Revisited (1984) Journal of Philosophical Logic, v 13, n 2, pp 153-179
Priest, Graham In Contradiction: A Study of the Transconsistent (2006) Oxford University Press, ISBN 0-199-26329-9 In Contradiction: A Study of the Transconsistent: Details
Putnam, Hilary Minds and Machines (1960) Dimensions of Mind, a Symposium, New York University Press, reprinted in 1964: Minds and Machines, pub Prentice-Hall
Rodych, Victor Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein (2003) Dialectica v 57 n 3, pp 279-313 Misunderstanding Gödel: Details
Rosser , J B Extensions of some theorems of Gödel and Church (1936)Journal of Symbolic Logic vol 1 pp 87-91
reprinted in 1965: The Undecidable (Martin Davis) pp 230-235 Extensions of some theorems of Gödel and Church: Details
Rosser, J B An Informal Exposition of proofs of Gödel’s Theorem and Church’s Theorem (1939) Reprinted from the Journal of Symbolic Logic, vol 4 (1939) pp 53-60, in Martin Davis 1965, The Undecidable pp 223-230 The Undecidable, Martin Davis: Details
Rucker. Rudy Infinity and the Mind: The Science and Philosophy of the Infinite (1982) Princeton University Press Infinity and the Mind: Details
Shankar, N Metamathematics, Machines and Gödel’s Proof (1994) Vol 38, Cambridge Tracts in Theoretical Computer Science ISBN 0521585333 Metamathematics, Machines and Gödel’s Proof: Details
Shapiro, Stewart Incompleteness and Inconsistency (2002) Mind, v 111, pp 817-32 Incompleteness and Inconsistency: Details
Shoenfield,Joseph R Mathematical Logic (1967) Reprinted by AK Peters for the Association of Symbolic Logic, 2001 ISBN 978-156881135-2
Smith, Peter An Introduction to Gödel’s Theorems (2007) Cambridge University Press An Introduction to Gödel’s Theorems: Details
Smorynski, C The incompleteness theorems (1982) Handbook of Mathematical Logic, ed J Barwise, North-Holland 1982 ISBN 978-0444863881, pp 821-866
Smullyan, Raymond Diagonalization and Self-Reference (1994) Oxford University Press Diagonalization and Self-Reference: Details
Smullyan, Raymond Gödel’s Incompleteness Theorems (1991) Oxford University Press
Steiner, Mark Wittgenstein as his Own Worst Enemy: The Case of Gödel’s Theorem Philosophia Mathematica 9 (2001) pp 257-279 Wittgenstein as his Own Worst Enemy: The Case of Gödel’s Theorem: Details
Tourlakis, George Lectures in Logic and Set Theory, Volume 1, Mathematical Logic (2003) Cambridge University Press ISBN 978-0-52175373-9
van Heijenoort, Jean Gödel’s Theorem in Focus ( 1963) Edwards, Paul, ed, Encyclopedia of Philosophy, Vol 3 Macmillan: 348-57
Various Kurt Gödel: Essays for his Centennial (2010) Cambridge University Press ISBN 978-0521115148 Kurt Gödel: Essays for his Centennial: Details
Wang, Hao A Logical Journey: From Gödel to Philosophy (1997) MIT Press ISBN: 9780262231893 Wang, A Logical Journey: Details
Willard, Dan E Self-Verifying Axiom Systems, the Incompleteness Theorem and Related Reflection Principles (2001) Journal of Symbolic Logic, v 66 n 2, pp 536-596 Self-Verifying Axiom Systems and the Incompleteness Theorem: Details

The Lighter Side

 

NEWS

Lebesgue Measure

There is now a new page on Lebesgue measure theory and how it is contradictory.

 

 

Illogical Assumptions

There is now a new page Halbach and Zhang’s Yablo without Gödel which demonstrates the illogical assumptions used by Halbach and Zhang.

 

 

Peter Smith’s ‘Proof’

It has come to my notice that, when asked about the demonstration of the flaw in his proof (see A Fundamental Flaw in an Incompleteness Proof by Peter Smith PDF), Smith refuses to engage in any logical discussion, and instead attempts to deflect attention away from any such discussion. If any other reader has tried to engage with Smith regarding my demonstration of the flaw, I would be interested to know what the outcome was.

 

 

Easy Footnotes

I found that making, adding or deleting footnotes in the traditional manner proved to be a major pain. So I developed a different system for footnotes which makes inserting or changing footnotes a doddle. You can check it out at Easy Footnotes for Web Pages (Accessibility friendly).

 

 

O’Connor’s “computer checked” proof

I have now added a new section to my paper on Russell O’Connor’s claim of a computer verified incompleteness proof. This shows that the flaw in the proof arises from a reliance on definitions that include unacceptable assumptions - assumptions that are not actually checked by the computer code. See also the new page Representability.

 

 

New page on Chaitin’s Constant

There is now a new page on Chaitin’s Constant (Chaitin’s Omega), which demonstrates that Chaitin has failed to prove that it is actually algorithmically irreducible.

 

Previous Blog Posts  

 

13 May 2015 Good Math, Bad Math?

 

30 Apr 2015 The Chinese Room

 

31 Mar 2015 Cranks and Crackpots

 

16th Mar 2015 Bishops Dancing with Pixies?

 

23rd Feb 2015 Artificial Intelligence

 

Links  

 

For convenience, there are now two pages on this site with links to various material relating to Gödel and the Incompleteness Theorem

 

– a page with general links:

Gödel Links

 

– and a page relating specifically to the Gödel mind-machine debate:

Gödel, Minds, and Machines

 

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Comments

 

Please note that this web site, like any other is a collection of various statements. Not all of this web site is intended to be factual. Some of it is personal opinion or interpretation.

 

If you prefer to ask me directly about the material on this site, please send me an e-mail with your query, and I will attempt to reply promptly.

 

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