Gödel links
Page last updated 07 Jul 2023
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 at Gödel’s Proof - English translation. Links that are principally about the Gödel, Minds, and Machines question are listed on a separate page, see Gödel, Minds, and Machines.
There is a plethora of articles about Gödel’s theorem, which might seem to indicate that it is of great importance - but even if there were a genuine mathematical equivalent of the expression “This sentence is unprovable in English”, it’s difficult to fathom why that might be considered important. It seems that you can say almost anything about Gödel’s proof, provided you avoid any mention of the ultimate taboo – that is, you never suggest that there might be an error in Gödel’s logic. For example, Gödel’s ‘theorem’ has been used to claim that it shows that god exists, and to claim that it shows that god does not exist, see Religions Wiki: Gödel incompleteness and On the Philosophical Relevance of Gödel’s Incompleteness.
There are also wacky pseudo-scientific claims; an example is given by a professor of economics Sheri Markose, who claims that because she can’t think of any other way to explain a certain biological process, she concludes that it must be because the process is using Gödel’s theorem - in other words, a “God of the gaps ” type of argument, see the papers Genomic Intelligence as Über Bio-Cybersecurity: The Gödel Sentence in Immuno-Cognitive Systems and Complexification of eukaryote phenotype: Adaptive immuno-cognitive systems as unique Gödelian blockchain distributed ledger. Although they are published in journals whose editors ostensibly consider the journals to be scientific, the notion that Gödel’s theorem is involved in the biological process is completely untestable - it fails the Popperian test for falsifiability.
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Links to webpages on Gödel and/or his Incompleteness Theorem
Links to freely available online papers on Gödel and/or “Gödel’s Incompleteness Theorem”
| Bays, Timothy | PDF On Floyd and Putnam on Wittgenstein on Gödel | Journal of Philosophy (April 2004) pp 197-210. |
| Bays, Timothy | PDF Floyd, Putnam, Bays, Steiner, Wittgenstein, G̈odel, Etc | Online |
| Davis, Martin | PDF The Incompleteness Theorem | Notices of the AMS vol 53 no 4 (2006), p414 |
| György, Sereny | Gödel, Tarski, Church, and the Liar | Arxiv (1999) |
| György, Sereny | PDF Boolos-style proofs of limitative theorems | Arxiv (2003) |
| Jaki, Stanley | PDF A Late Awakening to Gödel in Physics | Sensus communis 5 (2004), pp 153-162. |
| Ketland, Jeffrey | PDF Deflationism and Tarski’s Paradise | Mind 108, no. 429 (1999) pp 69-94 |
| Ketland, Jeffrey | PDF Deflationism and the Gödel phenomena: Reply to Tennant | Mind 114, No. 453 (2005) pp 75-88 Deflationism… Reply to Tennant: Details |
| Kikuchi, Makoto; Tanaka, Kazuyuki | PDF On formalization of model-theoretic proofs of Gödel’s theorems | Notre Dame Journal of Formal Logic (1994) 35 (3) pp 403-412 |
| O’Connor, Russell | Essential Incompleteness of Arithmetic Verified by Coq | Lecture Notes in Computer Science (2005) v 3603, pp 245-260 |
| Rucker. Rudy | Infinity and the Mind: The Science and Philosophy of the Infinite | (1982) Princeton University Press |
| Sayward, Charles | Steiner Versus Wittgenstein: Remarks on Differing Views of Mathematical Truth | Theoria (2005) 20 (3) pp 347-352. |
| Tennant, Neil | PDF Carnap, Gödel, and the Analyticity of Arithmetic | Philosophia Mathematica 16, no. 1 (2008) pp 100-112 |
| Tennant, Neil | PDF Deductive Versus Expressive Power: A Pre-godelian Predicament | The Journal of philosophy (2000) pp 257-277 |
| Tennant, Neil | PDF Deflationism and the Gödel Phenomena | Mind 111, no. 443 (2002) pp 51-582 |
| Tennant, Neil | PDF Deflationism and the Gödel Phenomena: Reply to Cieśliński | Mind 119, no. 474 (2010) pp 437-450 |
| Tennant, Neil | PDF Deflationism and the Gödel Phenomena: Reply to Ketland | Mind 114, No. 453 (2005) pp 89-96 |
| Vidal-Rosset, Joseph | PDF Does Gödel’s Incompleteness Theorem Prove That Truth Transcends Proof ? | from Book: The Age of Alternative Logics (2006) pp. 51-73. Springer |
| Wigderson, Avi | PDF The Gödel Phenomena in Mathematics: A Modern View | from Book: Kurt Gödel and the Foundations of Mathematics: Horizons of Truth (2010) Cambridge University Press |
| Zach, Richard | PDF Hilbert’s program then and now | from Book: Philosophy of Logic, Dale Jacquette (ed), Handbook of the Philosophy of Science (2006) v 5, Elsevier, pp 411-447 |
| Zach, Richard | PDF Kurt Gödel 1931 | from Book: Landmark Writings in Mathematics (2004) pub North-Holland pp 917-925 |
| Zach, Richard | PDF The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert’s Program | Synthese (2003) 137 (1) pp 211-259 |
Books and non-free online articles on Gödel and/or “Gödel’s Incompleteness Theorem”
The articles are not available free online, except at sci hub, see Current sci-hub active links or Latest Sci Hub Links and Download Research Papers and Scientific Articles for free.
| Berto, Francesco | There’s Something about Gödel: The Complete Guide to the Incompleteness Theorem | (2010) John Wiley and Sons, DOI:10.1002/9781444315028 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, DOI:10.2307/2689794 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 | 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 |
| Jaki, Stanley | On A Discovery About Gödel’s Incompleteness Theorem | Pontifical Academy of Sciences, Acta 18, Vatican City (2006) |
| 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 |
| Lindström. Per | Aspects of Incompleteness | Lecture Notes in Logic (1997) v 10 |
| 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 |
| 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 | (2013) Cambridge University Press ISBN: 9781107683464 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 |
Rationale: Every logical argument must be defined in some language, and every language has limitations. Attempting to construct a logical argument while ignoring how the limitations of language might affect that argument is a bizarre approach. The correct acknowledgment of the interactions of logic and language explains almost all of the paradoxes, and resolves almost all of the contradictions, conundrums, and contentious issues in modern philosophy and mathematics.
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