Language, Logic and Understanding
The quest for greater understanding of logic and language
Gödel links
You will find numerous references to Gödel and his Incompleteness Theorem. Some of them are listed 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
| http://www.cosmicfingerprints.com/incompleteness/ | An attempt to apply Gödel's Incompleteness Theorem to the universe |
| http://math.stanford.edu/~feferman/papers/Godel-IAS.pdf (PDF) | On Gödel's incompleteness theorems by Solomon Feferman |
| http://www.math.hawaii.edu/~dale/godel/godel.html | Brief notes about Gödel's Incompleteness Theorem and other things, by By Dale Myers |
| http://plato.stanford.edu/entries/goedel/ | Stanford Encyclopedia of Philosophy entry on Gödel's Incompleteness Theorem |
| http://plato.stanford.edu/entries/self-reference/ | Stanford Encyclopedia of Philosophy entry on paradoxes arising from self-reference |
| http://www.cs.auckland.ac.nz/~chaitin/georgia.html | Just one of many articles by G Chaitin |
| http://tachyos.org/godel.html | Webpage about Gödel's Incompleteness Theorem by a Stephen Lee on Gödel's Incompleteness Theorem, appears to be attempting to write a computer proof of incompleteness. |
| http://www.sciencemag.org/content/298/5600/1899.full.pdf (PDF) | Science magazine article on Gödel's Incompleteness Theorem |
| http://www.bbc.co.uk/programmes/b00dshx3 | BBC page with link to a broadcast on Gödel's Incompleteness Theorem |
| http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html | Entry on Gödel's Incompleteness Theorem in Wolfram's Mathworld |
| http://www.myrkul.org/recent/godel.htm | Claims that the incompleteness concept appears in Zen Buddhism |
| http://www.ltn.lv/~podnieks/gt5.html | Webpage on incompleteness by K Podnieks |
| http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Godel.html | Biography and other information about Kurt Gödel |
| http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems | Wikipedia entry |
| http://blog.plover.com/math/Gdl-Smullyan.html and http://www.sikharchives.com/?p=1417 |
These pages claim to be the 'World's shortest explanation of Gödel's theorem' but they are nothing of the sort, see the article here |
| http://rationalwiki.org/wiki/Essay:Gödel... | Trite and superficial |
| http://www.encyclopedia.com/topic/Kurt_Godel.aspx | Encyclopedically article on Kurt Gödel |
| http://www.britannica.com/EBchecked/topic/236770/Kurt-Godel | Encyclopedia Britannica article on Kurt Gödel |
| http://simplycharly.com/godel/roger_penrose_godel_interview.html | Roger Penrose On Kurt Gödel on the Simply Charly website |
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. See also [WNP1] WNP2 [WNP3] [WNP4] [WNP5] [WNP6] |
| Floyd, Juliet & Putnam, Hilary | Bays, Steiner, and Wittgenstein's 'notorious' paragraph about the Gödel theorem (PDF) | Journal of Philosophy (2006) 103 (2). See also [WNP1] [WNP2] [WNP3] WNP4 [WNP5] [WNP6] |
| Davis , Martin | The Incompleteness Theorem (PDF) | Notices of the AMS vol 53 no 4 (2006), p414 |
| György, Sereny | Godel, Tarski, Church, and the Liar | Arxiv (1999) |
| György, Sereny | Boolos-style proofs of limitative theorems | Arxiv (2003) |
| Kikuchi, Makoto; Tanaka, Kazuyuki | On formalization of model-theoretic proofs of Gödel's theorems | Notre Dame Journal of Formal Logic (1994) 35 (3): 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, pp245–260 |
| Charles Sayward | Steiner Versus Wittgenstein: Remarks on Differing Views of Mathematical Truth | Theoria (2005) 20 (3) pp 347-352. See also [WNP1] [WNP2] [WNP3] [WNP4] [WNP5] WNP6 |
| 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, pp411–447 |
| 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): 211–259 |
Books and non-free online articles on Gödel and/or his Incompleteness Theorem
| Berto , Francesco | There's Something about Gödel: The Complete Guide to the Incompleteness Theorem | (2010) John Wiley and Sons details |
| Boolos, George | A New Proof of the Gödel Incompleteness Theorem | (1989) Notices of the AMS v 36, pp388–390 and p676, reprinted 1998 in Boolos: Logic, Logic, and Logic, Harvard University Press ISBN 0674537661 details |
| Charlesworth, Arthur | A Proof of Gödel's Theorem in Terms of Computer Programs | (1980) Mathematics Magazine, v 54 no 3, pp 109–121 details |
| Dawson, John W Jr | Logical Dilemmas: The Life and Work of Kurt Gödel | (1997) AK Peters, Wellesley Mass, ISBN 1-56881-256-6 details |
| Floyd, Juliet & Putnam, Hilary | A Note on Wittgenstein's 'Notorious Paragraph' About the Gödel Theorem | (2000) Journal of Philosophy v 97 n 11, pp624–632. See also WNP1 [WNP2] [WNP3] [WNP4] [WNP5] [WNP6] |
| Franzén, Torkel | Gödel's Theorem: An Incomplete Guide to its Use and Abuse | (2005) AK Peters ISBN 1568812388 details |
| Goldstein, Rebecca | Incompleteness: the Proof and Paradox of Kurt Gödel | (2005) W W Norton & Company ISBN 0-393-05169-2 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), pp451–468 |
| Hofstadter, Douglas | Gödel, Escher, Bach: An Eternal Golden Braid | (1979) Vintage Books ISBN 0465026850 1999 reprint: ISBN 0465026567 details |
Hofstadter, Douglas |
I Am a Strange Loop | (2007) Basic Books ISBN 9780465030781 details |
| Hopcroft, John & Ullman, Jeffrey | Introduction to Automata theory | (1979) Addison-Wesley, ISBN 0-201-02988-X |
| Kleene, Stephen Cole | Mathematical Logic | (1967) Reprinted in 2002: Dover, ISBN 0-486-42533-9 details |
| Kleene, Stephen Cole | Recursive predicates and quantifiers | (1943) Transactions of the AMS, v 53 n 1, pp41–73 reprinted in 1965: The Undecidable (Martin Davis) pp255–287 details |
| Nagel, Ernest & Newman, James Roy | Gödel's Proof | (1958) 2002 Revised ed: ISBN 0814758169 details |
| Priest , Graham | Logic of Paradox Revisited | (1984) Journal of Philosophical Logic, v 13, n 2, pp153–179 |
| Priest, Graham | In Contradiction: A Study of the Transconsistent | (2006) Oxford University Press, ISBN 0-199-26329-9 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, pp279–313 details See also [WNP1] [WNP2] [WNP3] [WNP4] WNP5 [WNP6] |
| Rosser , J B | Extensions of some theorems of Gödel and Church | (1936)Journal of Symbolic Logic vol 1 pp87–91 reprinted in 1965: The Undecidable (Martin Davis) pp230–235 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) pp53–60, in Martin Davis 1965, The Undecidable pp223–230 details |
| Rucker. Rudy | Infinity and the Mind: The Science and Philosophy of the Infinite | (1982) Princeton University Press details |
| Shankar, N | Metamathematics, Machines and Gödel's Proof | (1994) Vol 38, Cambridge Tracts in Theoretical Computer Science ISBN 0521585333 details |
| Shapiro, Stewart | Incompleteness and Inconsistency | (2002) Mind, v 111, pp 817–32 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 details |
| Smorynski, C | The incompleteness theorems | (1982) Handbook of Mathematical Logic, ed J Barwise, North-Holland 1982 ISBN 978-0444863881, pp821–866 |
| Smullyan, Raymond | Diagonalization and Self-Reference | (1994) Oxford University Press 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 details See also [WNP1] [WNP2] WNP3 [WNP4] [WNP5] [WNP6] |
| 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 |
| Wang, Hao | A Logical Journey: From Gödel to Philosophy | (1997) MIT Press ISBN 0262231891 details |
| Wang, Hao | A Logical Journey: From Gödel to Philosophy | (1996) MIT Press, Cambridge MA, ISBN 0-262-23189-1 details |
| Willard, Dan E | Self-Verifying Axiom Systems, the Incompleteness Theorem and Related Reflection Principles | (2001) Journal of Symbolic Logic, v 66 n 2, pp536–596 details |
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NEW
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 –
– and a link relating specifically to the Gödel mind-machine debate –
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NEWS
New paper on an error in a proof of Incompleteness
A paper is now available detailing an error in an incompleteness proof by Boolos.
There is now a total of seven papers on flaws in incompleteness proofs other than Gödel's original paper, including three 'computer checked' proofs. See here.
Interview
Simply Charly has posted an interview on
Gödel and incompleteness on their website, see here.