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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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 –

Gödel Links

 

– and a link relating specifically to the Gödel mind-machine debate –

Gödel, Minds, and Machines

 


 

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