• Use Tab, Shift + Tab keys to traverse the main menu. To enter a sub-menu use the Right Arrow key. To leave a sub-menu use the Left Arrow or the Escape key.
• The Enter or the Space key opens the active menu item.
• To get back to the top of the page anytime, press the Home key.

Note: Full functionality of this web page requires JavaScript to be enabled in your browser.

# Gödel, Minds, and Machines - Web links

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: here), and also in the logic of various other incompleteness proofs (see Analysis of Incompleteness Proofs: 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.

## 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 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 Minds, Machines and Gödel: a Retrospect (PDF) Ethics & Politics, V (2003) 1 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 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 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 Bojadziev, Damjan Article in 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) Chalmers, David J 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 How Subtle is Gödel’s Theorem (PS file): here but only as a postscript file Behavioral and Brain Sciences (1993) 16 pp 611-612. Davis, Martin Is Mathematical Insight Algorithmic? Available online Is Mathematical Insight Algorithmic? (PS file): here but only as a postscript file Behavioral and Brain Sciences 13.4 (1990): 659-660. 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 Free will and modern science (2011) OUP for the British Academy, London 102 Feferman, Solomon 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 Engineering Applications of Artificial Intelligence (1999) 12:5 pp 655-659 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 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 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 Krebs, Peter Turing Machines, Computers, and Artificial Intelligence PDF 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 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 Between the motion and the act Psyche (1996) 2 pp 40-51 McCarthy, John Awareness and understanding in computer programs Psyche 2.11 (1995) McCullough, Daryl Can humans escape Gödel? Psyche 2.4 (1995). McDermott, Drew Penrose is wrong Psyche 2:66-82 (1996) Moravec, Hans 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 (PDF) 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 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 Tennant, Neil On Turing Machines Knowing Their Own Gödel-Sentence PDF Philosophia Mathematica 9, no. 1 (2001) pp 72-79. 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), 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

 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 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 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 Landau, L J Penrose’s philosophical error Concepts for Neural Networks (1998) Springer pp 171-223 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 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

## NEWS

### Lebesgue Measure

There is now a new page on a contradiction in Lebesgue measure theory.

### Illogical Assumptions

There is now a new page Halbach and Zhang’s Yablo without Gödel which analyzes the illogical assumptions used by Halbach and Zhang.

### Easy Footnotes

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).

### O’Connor’s “computer checked” proof

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.

### Previous Blog Posts

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:

Gödel, Minds, and Machines

### Printer Friendly

All pages on this website are printer friendly, and will print the main content in a convenient format. Note that the margins are set by your browser print settings.

Note: for some browsers JavaScript must be enabled for this to operate correctly.

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.

If you prefer to ask me directly about the material on this site, please send me an e-mail with your query, and I will attempt to reply promptly.

Feedback about site design would also be appreciated so that I can improve the site.