Logic and Language
Load the menuLoad the menu


Copyright   James R Meyer    2012 - 2024 https://www.jamesrmeyer.com

BANNER CONTENT

Gödel, Minds, and Machines - Web links

Page last updated 18 Sept 2023

 

For the past fifty years there has been a continuing argument as to whether Gödel’s incompleteness proof shows that minds are more than mere machines (albeit complex ones). A common line of argument is that a human can ‘see’ that the ‘Gödel sentence’ is ‘true’ but a machine could not have this ‘insight’, since a machine must always follow definite rules, just like a formal system. And even after fifty years of argument neither side is prepared to concede defeat and lay aside their cherished beliefs. Those advocating this viewpoint are commonly called ‘anti-mechanists’, while those opposing it are called ‘mechanists’.

 

As you can see by the number of links below, there is a plethora of articles on this subject, of various degrees of quality. 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.

 

It doesn’t seem to occur to anyone that the continuing conflict of viewpoints and the heated debate over the issue might indicate a problem in Gödel’s proof, rather than a problem in its interpretation. It is somewhat ironic that the mechanists are as definitive as the anti-mechanists in their deeply held belief that there cannot possibly be any error in Gödel’s proof. The demonstration that there is actually a fundamental flaw in the logic of Gödel’s proof (see The flaw in Gödel’s proof), and also in the logic of various other incompleteness proofs (see Analysis of Incompleteness Proofs) settles the question at once, since, at a stroke, it pulls out the principal cornerstone of the anti-mechanist argument.

 

Below are links to various articles on the Gödel, Minds, and Machines question. Links to articles on other aspects of Gödel’s theorem can be found on this page: Gödel Links. 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.

 

Online material on the Gödel, Minds, and Machines argument

See further down the page below for books and non-free online material

 

Note: The principal anti-mechanists are John Randolph Lucas, Roger Penrose, Michael Redhead and Storrs McCall. There are many more pro-mechanists. The articles by the principal anti-mechanists are listed first - this is for the convenience of the reader only, and does not indicate any partiality towards these authors.

 

The principal anti-mechanist authors

Lucas, J R Minds, Machines and Gödel Philosophy 36 (1961) pp 112-127
Lucas, J R Satan Stultified: A Rejoinder To Paul Benacerraf The Monist, vol.52, 1 (1968) - a response to Beancerraf’s paper God, the devil, and Gödel (MS Word doc file)
Lucas, J R Human and Machine Logic: a Rejoinder (doc file) British Journal for the Philosophy of Science, 19 (1968) pp 155–156 - a response to Good’s paper Human and machine logic (MS Word doc file)
Lucas, J R PDF Mechanism: A Rejoinder Philosophy 45, (1970) pp 149-151 - a response to Coder’s paper Gödel’s theorem and mechanism (MS Word doc file) and Lewis’ paper Lucas against mechanism (MS Word doc file)
Lucas, J R PDF This Gödel is Killing Me: a Rejoinder Philosophia, 6, no.1 (1976) pp 145-148 - a response to Hutton’s paper This Gödel is killing me (MS Word doc file)
Lucas, J R Review of Mechanism, Mentalism and Metamathematics (Judson Webb) The British Journal for the Philosophy of Science, 33 (1982) pp 441-444
Lucas, J R A paper read to the Turing Conference at Brighton on April 6th, 1990 a talk by J R Lucas (1990)
Lucas, J R PDF The Gödelian argument: Turn over the page a talk by J R Lucas (1996)
Lucas, J R PDF A Simple Exposition of Gödel’s Theorem a talk by J R Lucas, (1997)
Lucas, J R PDF The Implications of Gödel’s Theorem a talk by J R Lucas, (1996 - 1998)
Lucas, J R The Implications of Gödel’s Theorem (more technical) a talk by J R Lucas, (1998)
Lucas, J R The Implications of Gödel’s Theorem - handout handout for the above talk
Lucas, J R PDF Minds, Machines and Gödel: a Retrospect Ethics & Politics, V (2003) 1
Lucas, J R Commentary on Turing’s ‘Computing Machinery and Intelligence’ A comment by Lucas (2007) on Turing’s 1950 paper PDF Computing Machinery and Intelligence, both are chapters in the book “Parsing the Turing Test”, Springer, 2009, Parsing the Turing Test: details.
Lucas, J R A response to a paper by Professor Feferman A response (2009) to Feferman’s paper, PDF Gödel’s incompleteness theorems, free will and mathematical thought
Penrose, Roger Beyond the Doubting of a Shadow Psyche (1996) 2 (23) pp 89-129 - a reply to the various reactions (see Baars, Bernard: P1, Chalmers, David: P2, Feferman, Solomon: P3, Klein, Stanley: P4, Maudlin, Tim: P5, McCarthy, John: P6, McCullough, Daryl: P7, McDermott, Drew: P8, Moravec, Hans: P9 below) to his book Shadows of the Mind (see below for details of the book).

 

Other authors

Baars, Bernard J [Return to link: P1] Can physics provide a theory of consciousness? Psyche 2.8 (1995)
Benacerraf, Paul God, the devil, and Gödel (MS Word doc file) The Monist (1967) 51 pp 9-32
Bringsjord, Selmer PDF Is Gödelian model-based deductive reasoning computational? Philosophica (1998) 61 pp 51-76
Bringsjord, Selmer & Xiao, H PDF A refutation of Penrose’s new Gödelian case against the computational conception of mind Journal of Experimental and Theoretical Artificial Intelligence (2000) 12 pp 307-329
Bruni, Riccardo PDF Gödel, Turing, the Undecidability Results and the Nature of Human Mind (2006)
Chalmers, David J [Return to link: P2] PDF Minds, machines, and mathematics: A Review of Shadows of the Mind by Roger Penrose Psyche (1996) 2 pp 11-20
Coder, David Gödel’s theorem and mechanism (MS Word doc file) Philosophy (1969) 44 pp 234-237
Copeland, Jack PDF The Mathematical Objection: Turing, Gödel, and Penrose on the Mind Machinery (2008) July, pp 1-14
Davis, Martin PDF Is Mathematical Insight Algorithmic? Behavioral and Brain Sciences 13.4 (1990): 659-660.
Davis, Martin How Subtle is Gödel’s Theorem: Available online only as a ps file at How Subtle is Gödel’s Theorem? Behavioral and Brain Sciences (1993) 16 pp 611-612.
Dennett, Daniel C Murmurs in the cathedral: Review of R Penrose, The Emperor’s New Mind The Times Literary Supplement, September 29 (1989)  
Dershowitz, Nachum PDF The Four Sons of Penrose Lecture Notes in Computer Science (2005) vol 3835, pub Springer-Verlag, Berlin pp 125-138
Edis, Taner PDF How Gödel’s theorem supports the possibility of machine intelligence Minds and Machines (1998) 8 (2) pp 251-262
Feferman, Solomon PDF Gödel’s incompleteness theorems, free will and mathematical thought Free will and modern science (2011) OUP for the British Academy, London 102
Feferman, Solomon [Return to link: P3] PDF Penrose’s Gödelian argument Psyche (1996) 2 pp 21-32
Gaifman, H PDF What Gödel’s incompleteness result does and does not show Journal of Philosophy (2000) 97 (8) pp 462-471
Good, I J Human and machine logic (MS Word doc file) British Journal for the Philosophy of Science (1967) 18 (August) pp 145-6
Grush, Rick & Churchland, Patricia PDF Gaps in Penrose’s toiling Book: Conscious Experience (1995) pub Schoningh
Hutton, Anthony This Gödel is killing me (MS Word doc file) Philosophia (1976) 6 pp 135-144
Jongeneel, Christian & Koppelaar, H Gödel pro and contra AI: dismissal of the case Engineering Applications of Artificial Intelligence (1999) 12:5 pp 655-659
Ketland, Jeffrey PDF Deflationism and Tarski’s paradise Mind (1999) 108 pp 69-94
Ketland, Jeffrey & Raatikainen, Panu PDF Truth and provability Again a reply to a paper by Lucas and Redhead see below for details of that paper.
Klein, Stanley A [Return to link: P4] Is quantum mechanics relevant to understanding consciousness? Psyche 2.3 (1995)
Krajewski, Stanisław On Gödel’s Theorem and Mechanism: … Fundamenta Informaticae (2007) 81.1 pp 173-181
Krajewski, Stanisław PDF On the anti-mechanist arguments based on Gödel’s theorem Studia Semiotyczne (2020) 34(1), 9-56
Krebs, Peter PDF Turing Machines, Computers, and Artificial Intelligence MA thesis (2002)
LaForte, G, Hayes, P J & Ford, K M PDF Why Gödel’s Theorem Cannot Refute Computationalism: A reply to Penrose Artificial Intelligence (1998) 104 pp 265-286
Landau, L J PDF Penrose’s philosophical error Concepts for Neural Networks (1998) Springer pp 171-223 Penrose’s philosophical error: Details
Lewis, David K Lucas against mechanism (MS Word doc file) Philosophy (1969) 44 231-233
Makey, Jeff Gödel’s Incompleteness Theorem is Not an Obstacle to Artificial Intelligence (1981)
Maudlin, Tim [Return to link: P5] Between the motion and the act Psyche (1996) 2 pp 40-51  
McCarthy, John [Return to link: P6] Awareness and understanding in computer programs Psyche 2.11 (1995)
McCullough, Daryl [Return to link: P7] Can humans escape Gödel? Psyche 2.4 (1995).
McDermott, Drew [Return to link: P8] Penrose is wrong Psyche 2:66-82 (1996)
Moravec, Hans [Return to link: P9] Roger Penrose’s gravitonic brains  
Putnam, Hilary PDF Review of Shadows of the Mind Bulletin of the American Mathematical Society (1995) 32.3 pp 370-373
Raatikainen, Panu PDF McCall’s Gödelian argument is invalid Facta Philosophica (2002) Vol 4, No 1 pp 167-169
Raatikainen, Panu PDF On the philosophical relevance of Gödel’s incompleteness theorems Revue Internationale de Philosophie (2005) 59 (4) pp 513-534
Raatikainen, Panu PDF Truth and provability: A comment on Redhead British Journal for the Philosophy of Science (2005) 56 (3) pp 611-613
Shapiro, Stewart PDF Incompleteness, Mechanism, and Optimism Bulletin of Symbolic Logic (1998) Vol 4-3 pp 273-302
Sloman, Aaron PDF The Emperor’s Real Mind Book: Artificial Intelligence and Its Applications (1986) pub John Wiley and Sons
Tennant, Neil PDF On Turing Machines Knowing Their Own Gödel-Sentence Philosophia Mathematica 9, no. 1 (2001) pp 72-79.
Tassinari, R P & D’Ottaviano, I M. L PDF Cogito ergo sum non machine Anti-mechanist article
van de Putte, Xandra PDF Is Lucas’ Gödelian argument valid? (2005)

 

Books and non-free online material

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.

 

The principal anti-mechanist authors

Lucas, J R The Freedom of the Will Book: Oxford University Press (1970), ISBN‑13: 978‑0198243434 The Freedom of the Will: Details
Lucas, J R Metamathematics and the Philosophy of Mind: A Rejoinder Philosophy of Science (1971) 38 (2) pp 310-13 Metamathematics and the Philosophy of Mind: A Rejoinder: Details
Lucas, J R and Redhead, Michael Truth and Provability British Journal for the Philosophy of Science (2007) 58 (2) pp 331-332 Truth and Provability: Details
McCall, Storrs Can a Turing machine know that the Gödel sentence is true? Journal of Philosophy (1999) (10) pp 525-32 Can a Turing machine know that the Gödel sentence is true? Details
Penrose, Roger The Emperor’s New Mind: Concerning Computers, Minds and The Laws of Physics Book: Oxford University Press, (1989) ISBN 0-198-51973-7 The Emperor’s New Mind: Details
Penrose, Roger Shadows of the Mind: A Search for the Missing Science of Consciousness Book: Oxford University Press, (1994) ISBN 0198539789 Shadows of the Mind: Details
Redhead, M Mathematics and the Mind British Journal for the Philosophy of Science (2004) 55 (4) pp 731-737 Mathematics and the Mind: Details
Seager, William E Yesterday’s algorithm: Penrose and the Gödel argument

Croatian Journal of Philosophy (2003) 3 (9) pp 265-273 Yesterday’s algorithm: Penrose and the Gödel argument: Details

 

Other authors

Bojadziev, Damjan Article in book: Mind Versus Computer Book: Mind Versus Computer, IOS Press (1997) pp 202-210 Mind versus Computer: Details
Bowie, G Lee Lucas’ number is finally up Journal of Philosophical Logic (1982) 11-3 pp 279-285 Lucas’ number is finally up: Details
Boyer, David L R Lucas, Kurt Gödel, and Fred Astaire The Philosophical Quarterly (1983) 33, No. 131 pp 147-159 Lucas, Kurt Gödel, and Fred Astaire: Details
Chari, C T K Further comments on minds, machines and Gödel Philosophy (1963) 38 (April) pp 175-8 Further comments on minds, machines and Gödel: Details
Chihara, C On alleged refutations of mechanism using Gödel’s incompleteness results Journal of Philosophy (1972) 69 pp 507-26 On alleged refutations of mechanism using Gödel: Details
Copeland, Jack Turing’s o-machines, Searle, Penrose, and the brain Analysis (1998) 58 (2) pp 128-138 Turing’s o-machines, Searle, Penrose, and the brain: Details
George, A & Velleman, Daniel J Leveling the playing field between mind and machine: A reply to McCall Journal of Philosophy (2000) 97 (8) pp 456-452 Leveling the playing field: reply to McCall: Details
Hadley, Robert F Gödel, Lucas, and mechanical models of mind Computational Intelligence (1987) 3 pp 57-63 Gödel, Lucas, and mechanical models of mind: Details
Jacquette, Dale Metamathematical criteria for minds and machines Erkenntnis (1987) 27 (July) pp 1-16 Metamathematical criteria for minds and machines: Details
King, D Is the human mind a Turing machine? Synthese (1996) 108 (3) pp 379-89 Is the human mind a Turing machine? Details
Kirk, Robert E Mental machinery and Gödel Synthese (1968) 66 (March) pp 437-452 Mental machinery and Gödel: Details
Krajewski, Stanislaw On Gödel’s Theorem and Mechanism: Inconsistency or Unsoundness is Unavoidable in any Attempt to ‘Out-Gödel’ the Mechanist Fundamenta Informaticae (2007) 81, 173-181 On Gödel’s Theorem and Mechanism: Details
Lindstrom, Per Remarks on Penrose’s new argument Journal of Philosophical Logic (2006) 35 (3) pp 231-237 Remarks on Penrose’s new argument: Details
Lyngzeidetson, A E Massively parallel distributed processing and a computationalist foundation for cognitive science British Journal for the Philosophy of Science (1990) 41 (March) pp 121-127 Massively parallel distributed processing: Details
Lyngzeidetson, A E & Solomon, Martin K Abstract complexity theory and the mind-machine problem British Journal for the Philosophy of Science (1994) 45 (2) pp 549-54 Abstract complexity theory and the mind-machine problem: Details
Martin, J & Engleman, K The mind’s I has two eyes Philosophy (1990) 65 (264) pp 510-515 The mind’s I has two eyes: Details
Priest, Graham Gödel’s theorem and the mind … again Kluwer Philosophical Studies Series, (1994) Volume 60 pp 191-201 Gödel’s theorem and the mind … again: Details
Putnam Hilary Reflexive reflections Erkenntnis (1985) 22, 1/3, Jan Reflexive reflections: Details
Robinson, William S Penrose and mathematical ability Analysis (1992) 52 (2) pp 80-88 Penrose and mathematical ability: Details
Serény, György How do We Know that the Gödel Sentence of a Consistent Theory Is True? Philosophia Mathematica (2011) Volume 19 (1) Oxford University Press How do We Know that the Gödel Sentence of a Consistent Theory Is True? Details
Shapiro, Stewart Mechanism, Truth, and Penrose’s New Argument Journal of Philosophical Logic (2003) 32 (1) pp 19-42 Mechanism, Truth, and Penrose’s New Argument: Details
Slezak, Peter Artificial Intelligence, Gödelian Arguments Against Encyclopedia of Cognitive Science (2006) Artificial Intelligence, Gödelian Arguments Against: Details
Slezak, Peter Descartes’ diagonal deduction British Journal for the Philosophy of Science (1983) 34 pp 13-36 Descartes’ diagonal deduction: Details
Slezak, Peter Gödel’s theorem and the mind British Journal for the Philosophy of Science (1982) 33 pp 41-52 Gödel’s theorem and the mind: Details
Slezak, Peter Minds, machines and self-reference Dialectica (1984) 38 pp 17-34 Minds, machines and self-reference: Details
Smart, J J C Gödel’s theorem, Church’s theorem, and mechanism Synthese (1961) 13 pp 105-110 Gödel’s theorem, Church’s theorem, and mechanism: Details
Webb, Judson Metamathematics and the philosophy of mind Philosophy of Science (1968) 35 pp 156-78 Metamathematics and the philosophy of mind: Details
Whitely, C Minds, machines and Gödel: A reply to Mr Lucas Philosophy (1962) 37 pp 61-62 Minds, machines and Gödel: A reply to Mr Lucas: Details
Yu, Qiuen Consistency, mechanicalness, and the logic of the mind Synthese (1992) 90 (1) pp 145-79 Consistency, mechanicalness, and the logic of the mind: Details
Yu, Qiuen Further Explanations of the Gödel Scenario of the Mind - a Reply to Prof Graham Priest Synthese (1992) 95-3, pp 461-465 Further Explanations of the Gödel Scenario of the Mind - a Reply to Prof Graham Priest: Details

 


 

Interested in supporting this site?

You can help by sharing the site with others. You can also donate at Go Get Funding: Logic and Language where there are full details.

 

 

As site owner I reserve the right to keep my comments sections as I deem appropriate. I do not use that right to unfairly censor valid criticism. My reasons for deleting or editing comments do not include deleting a comment because it disagrees with what is on my website. Reasons for exclusion include:
Frivolous, irrelevant comments.
Comments devoid of logical basis.
Derogatory comments.
Long-winded comments.
Comments with excessive number of different points.
Questions about matters that do not relate to the page they post on. Such posts are not comments.
Comments with a substantial amount of mathematical terms not properly formatted will not be published unless a file (such as doc, tex, pdf) is simultaneously emailed to me, and where the mathematical terms are correctly formatted.


Reasons for deleting comments of certain users:
Bulk posting of comments in a short space of time, often on several different pages, and which are not simply part of an ongoing discussion. Multiple anonymous user names for one person.
Users, who, when shown their point is wrong, immediately claim that they just wrote it incorrectly and rewrite it again - still erroneously, or else attack something else on my site - erroneously. After the first few instances, further posts are deleted.
Users who make persistent erroneous attacks in a scatter-gun attempt to try to find some error in what I write on this site. After the first few instances, further posts are deleted.


Difficulties in understanding the site content are usually best addressed by contacting me by e-mail.

 

Based on HashOver Comment System by Jacob Barkdull

Copyright   James R Meyer   2012 - 2024
https://www.jamesrmeyer.com