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 |
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.
Site Mission
Please see the menu for numerous articles of interest. Please leave a comment or send an email if you are interested in the material on this site.
Interested in supporting this site?
You can help by sharing the site with others. You can also donate at _{} where there are full details.