Gödel, Minds, and Machines - Web links
For the past fifty years there has been a continuing argument as to whether Gödel's 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 follows 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 here), and also in the logic of various other incompleteness proofs (see here) 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.
Links to freely available online material on the Gödel, Minds, and Machines argument.
See 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 (PDF) | 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 | 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 | 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 | 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 | The Gödelian argument: Turn over the page | a talk by J R Lucas (1996) |
| Lucas, J R | A Simple Exposition of Gödel's Theorem | a talk by J R Lucas, (1997) |
| Lucas, J R | 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 | A paper read to the Turing Conference at Brighton on April 6th, 1990 | |
| Lucas, J R | Commentary on Turing's 'Computing Machinery and Intelligence' | a comment (2005) on Turing's paper Computing Machinery and Intelligence |
| Lucas, J R | A response to a paper by Professor Feferman (PDF) | a response to Feferman's paper, Gödel's incompleteness theorems, free will and mathematical thought (PDF) |
| Penrose, Roger | Beyond the Doubting of a Shadow | Psyche (1996) 2 (23) pp 89-129 - a reply to the various reactions (see P1 P2 P3 P4 P5 P6 P7 P8 P9 below) to his book Shadows of the Mind, see P10 below for details of the book |
Other authors
| Baars, Bernard J [P1] | Can physics provide a theory of consciousness? | |
| Benacerraf, Paul | God, the devil, and Gödel (MS Word doc file) | The Monist (1967) 51 pp 9-32 |
| Bojadziev, Damjan | Mind versus Gödel | Book: Mind Versus Computer, IOS Press (1997) pp 202-210 |
| Bringsjord, Selmer | Is Gödelian model-based deductive reasoning computational? (PDF) | Philosophica (1998) 61 pp 51-76 |
| Bringsjord, Selmer & Xiao, H | A refutation of Penrose's new Gödelian case against the computational conception of mind (PDF) | Journal of Experimental and Theoretical Artificial Intelligence (2000) 12 pp 307–329 |
| Bruni, Riccardo | Gödel, Turing, the Undecidability Results and the Nature of Human Mind (PDF) | (2006) |
| Burgess, John | On the Outside Looking In: A Caution about Conservativeness (MS Word doc file) | Kurt Gödel: Essays for his Centennial, pub Cambridge University Press, 2010, ISBN-13: 978-0521115148 |
| Chalmers, David J [P2] | Minds, machines, and mathematics | 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 | The Mathematical Objection: Turing, Gödel, and Penrose on the Mind (PDF) | Machinery (2008) July, pp 1-14 |
| Davis, Martin | How Subtle is Gödel's Theorem Available online here but only as a postscript file | Behavioral and Brain Sciences (1993) 16 pp 611-612. |
| Davis, Martin | Is Mathematical Insight Algorithmic? Available online here but only as a postscript file | |
| 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 | The Four Sons of Penrose (PDF) | Lecture Notes in Computer Science (2005) vol 3835, pub Springer-Verlag, Berlin pp 125–138 |
| Edis, Taner | How Gödel's theorem supports the possibility of machine intelligence (PDF) | Minds and Machines (1998) 8 (2) pp 251-262 |
| Feferman, Solomon | Gödel's incompleteness theorems, free will and mathematical thought (PDF) | (2011) |
| Feferman, Solomon [P3] | Penrose's Gödelian argument (PDF) | Psyche (1996) 2 pp 21–32 |
| Gaifman, H | What Gödel's incompleteness result does and does not show (PDF) | Journal of Philosophy (2000) 97 (8) pp 462-471 |
| George, A & Velleman, Daniel J | Leveling the playing field between mind and machine: A reply to McCall (PDF) | Journal of Philosophy (2000) 97 (8) pp 456-452 |
| 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 | Gaps in Penrose's toiling (PDF) | Book: Conscious Experience (1995) pub Schoningh |
| Hutton, Anthony | This Gödel is killing me (MS Word doc file) | Philosophia (1976) 6 pp 135-144 |
| Jacquette, Dale | Metamathematical criteria for minds and machines (PDF) | Erkenntnis (1987) 27 (July) pp 1-16 |
| Jongeneel, Christian & Koppelaar, H | Gödel pro and contra AI: dismissal of the case | |
| Ketland, Jeffrey | Deflationism and Tarski's paradise (PDF) | Mind (1999) 108 pp 69-94 |
| Ketland, Jeffrey & Raatikainen, Panu | Truth and provability - again (PDF) | a reply to a paper by Lucas and Redhead see [LR1] below for details of that paper |
| King, D | Is the human mind a Turing machine? (PDF) | Synthese (1996) 108 (3) pp 379-89 |
| Kirk, Robert E | Mental machinery and Gödel (PDF) | Synthese (1968) 66 (March) pp 437-452 |
| Klein, Stanley A [P4] | Is quantum mechanics relevant to understanding consciousness? | |
| Krebs, Peter | Turing Machines, Computers, and Artificial Intelligence (PDF) | an MA thesis (2002) |
| LaForte, G, Hayes, P J & Ford, K M | Why Gödel's Theorem Cannot Refute Computationalism: A reply to Penrose (PDF) | Artificial Intelligence (1998) 104 pp 265-286 |
| Landau, L J | Penrose's Philosophical Error | |
| 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 [P5] | Between the motion and the act | Psyche (1996) 2 pp 40-51 |
| McCarthy, John [P6] | Awareness and understanding in computer programs | |
| McCullough, Daryl [P7] | Can humans escape Gödel? | |
| McDermott, Drew [P8] | Penrose is wrong | |
| Moravec, Hans [P9] | Roger Penrose's gravitonic brains | |
| Putnam, Hilary | Review of Shadows of the Mind (PDF) | Bulletin of the American Mathematical Society (1995) 32.3 pp 370–373 |
| Raatikainen, Panu | McCall's Gödelian argument is invalid (PDF) | Facta Philosophica (2002) Vol 4, No 1 pp 167-169 |
| Raatikainen, Panu | On the philosophical relevance of Gödel's incompleteness theorems (MS Word doc file) | Revue Internationale de Philosophie (2005) 59 (4) pp 513-534 |
| Raatikainen, Panu | Truth and provability: A comment on Redhead (PDF) | British Journal for the Philosophy of Science (2005) 56 (3) pp 611-613 |
| Seager, William E | Yesterday's algorithm: Penrose and the Gödel argument (PDF) | Croatian Journal of Philosophy (2003) 3 (9) pp 265-273 |
| Shapiro, Stewart | Incompleteness, Mechanism, and Optimism (PDF) | Bulletin of Symbolic Logic (1998) Vol 4-3 pp 273-302 |
| Sloman, Aaron | The emperor's real mind (PDF) | Book: Artificial Intelligence and Its Applications (1986) pub John Wiley and Sons |
| Smart, J J C | Gödel's theorem, Church's theorem, and mechanism (PDF) | Synthese (1961) 13 pp 105-110 |
| Tassinari, R P & D'Ottaviano, I M. L | Cogito ergo sum non machine (PDF) | Anti-mechanist article |
| van de Putte, Xandra | Is Lucas' Gödelian argument valid? (PDF) | (2005) |
| Yu, Qiuen | Consistency, mechanicalness, and the logic of the mind (PDF) | Synthese (1992) 90 (1) pp 145-79 |
| Yu, Qiuen | Further Explanations of the Gödel Scenario of the Mind - a Reply to Prof Graham Priest (PDF) | Synthese (1992) 95-3, pp 461-465 |
Books and non-free online material
The principal anti-mechanist authors
| Lucas, J R | The Freedom of the Will | Book: Oxford University Press (1970), ISBN13: 978-0198243434 details |
| Lucas, J R | Metamathematics and the Philosophy of Mind: A Rejoinder | Philosophy of Science (1971) 38 (2) pp 310-13 details |
| Lucas, J R and Redhead, Michael [LR1] | Truth and Provability | British Journal for the Philosophy of Science (2007) 58 (2) pp 331-332 details |
| McCall, Storrs | Can a Turing machine know that the Gödel sentence is true? | Journal of Philosophy (1999) (10) pp 525-32 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 details |
| Penrose, Roger [P10] | Shadows of the Mind: A Search for the Missing Science of Consciousness | Book: Oxford University Press, (1994) ISBN 0-19-853978-9 details |
| Redhead, M | Mathematics and the Mind | British Journal for the Philosophy of Science (2004) 55 (4) pp 731-737 details |
Other authors
| Bowie, G Lee | Lucas' number is finally up | Journal of Philosophical Logic (1982) 11-3 pp 279-285 details |
| Boyer, David L R | Lucas, Kurt Gödel, and Fred Astaire | The Philosophical Quarterly (1983) 33, No. 131 pp 147-159 details |
| Chari, C T K | Further comments on minds, machines and Gödel | Philosophy (1963) 38 (April) pp 175-8 details |
| Chihara, C | On alleged refutations of mechanism using Gödel's incompleteness results | Journal of Philosophy (1972) 69 pp 507-26 details |
| Copeland, Jack | Turing's o-machines, Searle, Penrose, and the brain | Analysis (1998) 58 (2) pp 128-138 details |
| Hadley, Robert F | Gödel, Lucas, and mechanical models of mind | Computational Intelligence (1987) 3 pp 57-63 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 details |
| Lindstrom, Per | Remarks on Penrose's new argument | Journal of Philosophical Logic (2006) 35 (3) pp 231-237 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 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 details |
| Martin, J & Engleman, K | The mind's I has two eyes | Philosophy (1990) 65 (264) pp 510-515 details |
| Priest, Graham | Gödel's theorem and the mind... again | Kluwer Philosophical Studies Series, (1994) Volume 60 pp 191-201 details |
| Putnam Hilary | Reflexive reflections | Erkenntnis (1985) 22, 1/3, Jan details |
| Robinson, William S | Penrose and mathematical ability | Analysis (1992) 52 (2) pp 80-88 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 details |
| Shapiro, Stewart | Mechanism, Truth, and Penrose's New Argument | Journal of Philosophical Logic (2003) 32 (1) pp 19-42 details |
| Slezak, Peter | Artificial Intelligence, Gödelian Arguments Against | Encyclopedia of Cognitive Science (2006) details |
| Slezak, Peter | Descartes' diagonal deduction | British Journal for the Philosophy of Science (1983) 34 pp 13-36 details |
| Slezak, Peter | Gödel's theorem and the mind | British Journal for the Philosophy of Science (1982) 33 pp 41-52 details |
| Slezak, Peter | Minds, machines and self-reference | Dialectica (1984) 38 pp 17-34 details |
| Webb, Judson | Metamathematics and the philosophy of mind | Philosophy of Science (1968) 35 pp 156-78 details |
| Whitely, C | Minds, machines and Gödel: A reply to Mr Lucas | Philosophy (1962) 37 pp 61-62 details |
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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.
