Logic and Language

Logic and Language

Copyright © James R Meyer 2012 - 2017 www.jamesrmeyer.com

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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. *

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 |

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 |

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.

There is a new addition to the page Yet another flawed incompleteness proof, where Berto’s proof of incompleteness in his book *There’s something about Gödel* comes under scrutiny.

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).

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.

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.

13 May 2015 Good Math, Bad Math?

16th Mar 2015 Bishops Dancing with Pixies?

23rd Feb 2015 Artificial Intelligence

31 Mar 2015 Cranks and Crackpots

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 page relating specifically to the Gödel mind-machine debate:

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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.

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Copyright © James R Meyer 2012 - 2017

www.jamesrmeyer.com