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Summary Godelian arguments use Godel's incompleteness theorems to argue against the possibility of human-level computer intelligence.  Godel proved that any number system strong enough to do arithmetic would contain true propositions that were impossible to prove within the system. Let G be such a proposition, and let the relevant system correspond to a computer.  It seems to follow that no computer can prove G (and so know G is true), but humans can know that G is true (by, as it were, moving outside of the number system and seeing that G has to be true to preserve soundness).  So, it appears that humans are more powerful than computers restricted to just implementations of number systems.  This is the essence of Godelian arguments. Many replies to these arguments have been put forward.  An obvious reply is that computers can be programmed to be more than mere number systems and so can step outside number systems just like humans can.  
Key works Probably the central paper using Godelian arguments against AI is Lucas 1961. Another good paper is Benacerraf 1967.  For what is often regarded as the classic reply to Lucas, see Putnam 1960.
Introductions Penrose 1994 and Penrose 1989.
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  1. added 2020-09-13
    Remarks on the Gödelian Anti-Mechanist Arguments.Panu Raatikainen - forthcoming - Studia Semiotyczne.
  2. added 2020-07-25
    Was bedeuten Parakonsistente, Unentscheidbar, Zufällig, Berechenbar und Unvollständige? Eine Rezension von „Godels Weg: Exploits in eine unentscheidbare Welt“ (Godels Way: Exploits into a unecidable world) von Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160p (2012).Michael Richard Starks - 2020 - In Willkommen in der Hölle auf Erden: Babys, Klimawandel, Bitcoin, Kartelle, China, Demokratie, Vielfalt, Dysgenie, Gleichheit, Hacker, Menschenrechte, Islam, Liberalismus, Wohlstand, Internet, Chaos, Hunger, Krankheit, Gewalt, Künstliche Intelligenz, Krieg. Las Vegas, NV , USA: Reality Press. pp. 1171-185.
    In "Godel es Way" diskutieren drei namhafte Wissenschaftler Themen wie Unentschlossenheit, Unvollständigkeit, Zufälligkeit, Berechenbarkeit und Parakonsistenz. Ich gehe diese Fragen aus Wittgensteiner Sicht an, dass es zwei grundlegende Fragen gibt, die völlig unterschiedliche Lösungen haben. Es gibt die wissenschaftlichen oder empirischen Fragen, die Fakten über die Welt sind, die beobachtungs- und philosophische Fragen untersuchen müssen, wie Sprache verständlich verwendet werden kann (die bestimmte Fragen in Mathematik und Logik beinhalten), die entschieden werden müssen, indem man sich anschaut,wie wir Wörter in bestimmten (...)
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  3. added 2020-06-13
    Что означают парапоследовательные, неопределимые, случайные, вычислительные и неполные? Обзор: “Путь Годеля - Приключения в неопределенном мире” (Godel's Way: Exploits into an undecidable world) by Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160p (2012) (обзор пересмотрен 2019).Michael Richard Starks - 2020 - In ДОБРО ПОЖАЛОВАТЬ В АД НА НАШЕМ МИРЕ : Дети, Изменение климата, Биткойн, Картели, Китай, Демократия, Разнообразие, Диссигеника, Равенство, Хакеры, Права человека, Ислам, Либерализм, Процветание, Сеть, Хаос, Голод, Болезнь, Насилие, Искусственный интелле. Las Vegas, NV USA: Reality Press. pp. 171-186.
    В «Godel's Way» три видных ученых обсуждают такие вопросы, как неплатежеспособность, неполнота, случайность, вычислительность и последовательность. Я подхожу к этим вопросам с точки зрения Витгенштейна, что есть две основные проблемы, которые имеют совершенно разные решения. Есть научные или эмпирические вопросы, которые являются факты о мире, которые должны быть исследованы наблюдений и философские вопросы о том, как язык может быть использован внятно (которые включают в себя определенные вопросы в математике и логике), которые должны быть решены, глядят, как мы на самом деле (...)
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  4. added 2020-04-28
    The Significance of Evidence-Based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences.Bhupinder Singh Anand - manuscript
    In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...)
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  5. added 2020-03-18
    Reseña de ‘Soy un Bucle Extraño’ ( I am a Strange Loop) de Douglas Hofstadter (2007) (reseña revisado 2019).Michael Richard Starks - 2020 - In Comprender las Conexiones entre Ciencia, Filosofía, Psicología, Religión, Política, Economía, Historia y Literatura - Artículos y reseñas 2006-2019. Las Vegas, NV USA: Reality Press. pp. 265-282.
    Último sermón de la iglesia del naturalismo fundamentalista por el pastor Hofstadter. Al igual que su mucho más famoso (o infame por sus incesantemente errores filosóficos) trabajo Godel, Escher, Bach, tiene una plausibilidad superficial, pero si se entiende que se trata de un científico rampante que mezcla problemas científicos reales con los filosóficos (es decir, el sólo los problemas reales son los juegos de idiomas que debemos jugar) entonces casi todo su interés desaparece. Proporciono un marco para el análisis basado (...)
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  6. added 2019-12-19
    Revisão de ‘Eu sou um Loop Estranho’ (I am a Strange Loop) por Douglas Hofstadter (2007) (revisão revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 112-128.
    Último sermão da Igreja do naturalismo fundamentalista pelo pastor Hofstadter. Como o seu muito mais famoso (ou infame por seus erros filosóficos implacáveis) Godel, Escher, Bach, ele tem uma plausibilidade superficial, mas se se compreende que este é um scientismo desenfreado que mistura questões científicas reais com os filosóficos (ou seja, o somente as edições reais são que jogos da língua nós devemos jogar) então quase todo seu interesse desaparece. Eu forneci um quadro para análise baseada na psicologia evolutiva e (...)
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  7. added 2019-06-07
    Gaps in Penrose's Toiling.Rick Grush & Patricia Smith Churchland - 1995 - Journal of Consciousness Studies 2 (1):10-29.
    Using the Godel incompleteness result for leverage, Roger Penrose has argued that the mechanism for consciousness involves quantum gravitational phenomena, acting through microtubules in neurons. We show that this hypothesis is implausible. First the Godel result does not imply that human thought is in fact non-algorithmic. Second, whether or not non-algorithmic quantum gravitational phenomena actually exist, and if they did how that could conceivably implicate microtubules, and if microtubules were involved, how that could conceivably implicate consciousness, is entirely speculative. Third, (...)
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  8. added 2019-06-06
    What Godel's Incompleteness Result Does and Does Not Show.Haim Gaifman - 2000 - Journal of Philosophy 97 (8):462.
    In a recent paper S. McCall adds another link to a chain of attempts to enlist Gödel’s incompleteness result as an argument for the thesis that human reasoning cannot be construed as being carried out by a computer.1 McCall’s paper is undermined by a technical oversight. My concern however is not with the technical point. The argument from Gödel’s result to the no-computer thesis can be made without following McCall’s route; it is then straighter and more forceful. Yet the argument (...)
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  9. added 2019-06-06
    Minds, Machines and Godel.F. H. George - 1962 - Philosophy 37 (139):62-63.
    I Would like to draw attention to the basic defect in the argument used by Mr J. R. Lucas. Mr Lucas there states that Gödel's theorem shows that any consistent formal system strong enough to produce arithmetic fails to prove, within its own structure, theorems that we, as humans, can nevertheless see to be true. From this he argues that ‘minds’ can do more than machines, since machines are essentially formal systems of this same type, and subject to the limitation (...)
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  10. added 2019-06-06
    Minds, Machines and Gödel.John R. Lucas - 1961 - Philosophy 36 (137):112-127.
    Gödei's Theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met. This I attempt to do.
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  11. added 2019-06-05
    Folk Psychology as Mental Simulation.Luca Barlassina & Robert M. Gordon - 2004 - The Stanford Encyclopedia of Philosophy.
    Mindreading (or folk psychology, Theory of Mind, mentalizing) is the capacity to represent and reason about others’ mental states. The Simulation Theory (ST) is one of the main approaches to mindreading. ST draws on the common-sense idea that we represent and reason about others’ mental states by putting ourselves in their shoes. More precisely, we typically arrive at representing others’ mental states by simulating their mental states in our own mind. This entry offers a detailed analysis of ST, considers theoretical (...)
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  12. added 2019-06-05
    Leveling the Playing Field Between Mind and Machine: A Reply to McCall.Alexander George & Daniel J. Velleman - 2000 - Journal of Philosophy 97 (8):456.
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  13. added 2019-02-23
    Review of I Am a Strange Loop by Douglas Hofstadter (2007) (Review Revised 2019).Michael Starks - 2019 - In Suicidal Utopian Delusions in the 21st Century-- Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2019 4th Edition Michael Starks. Las Vegas, NV USA: Reality Press. pp. 217-235.
    Latest Sermon from the Church of Fundamentalist Naturalism by Pastor Hofstadter. Like his much more famous (or infamous for its relentless philosophical errors) work Godel, Escher, Bach, it has a superficial plausibility but if one understands that this is rampant scientism which mixes real scientific issues with philosophical ones (i.e., the only real issues are what language games we ought to play) then almost all its interest disappears. I provide a framework for analysis based in evolutionary psychology and the work (...)
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  14. added 2018-10-27
    On the Question of Whether the Mind Can Be Mechanized, II: Penrose’s New Argument.Peter Koellner - 2018 - Journal of Philosophy 115 (9):453-484.
    Gödel argued that his incompleteness theorems imply that either “the mind cannot be mechanized” or “there are absolutely undecidable sentences.” In the precursor to this paper I examined the early arguments for the first disjunct. In the present paper I examine the most sophisticated argument for the first disjunct, namely, Penrose’s new argument. It turns out that Penrose’s argument requires a type-free notion of truth and a type-free notion of absolute provability. I show that there is a natural such system, (...)
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  15. added 2018-08-18
    On the Question of Whether the Mind Can Be Mechanized, I: From Gödel to Penrose.Peter Koellner - 2018 - Journal of Philosophy 115 (7):337-360.
    In this paper I address the question of whether the incompleteness theorems imply that “the mind cannot be mechanized,” where this is understood in the specific sense that “the mathematical outputs of the idealized human mind do not coincide with the mathematical outputs of any idealized finite machine.” Gödel argued that his incompleteness theorems implied a weaker, disjunctive conclusion to the effect that either “the mind cannot be mechanized” or “mathematical truth outstrips the idealized human mind.” Others, most notably, Lucas (...)
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  16. added 2018-07-08
    Gödel’s Disjunction: The Scope and Limits of Mathematical Knowledge. [REVIEW]Panu Raatikainen - 2018 - History and Philosophy of Logic 39 (4):401-403.
  17. added 2018-02-17
    Can a Turing Machine Know That the Gödel Sentence is True?Storrs McCall - 1999 - Journal of Philosophy 96 (10):525-532.
  18. added 2017-08-07
    Turing Machines and Semantic Symbol Processing: Why Real Computers Don’T Mind Chinese Emperors.Richard Yee - 1993 - Lyceum 5 (1):37-59.
    Philosophical questions about minds and computation need to focus squarely on the mathematical theory of Turing machines (TM's). Surrogate TM's such as computers or formal systems lack abilities that make Turing machines promising candidates for possessors of minds. Computers are only universal Turing machines (UTM's)—a conspicuous but unrepresentative subclass of TM. Formal systems are only static TM's, which do not receive inputs from external sources. The theory of TM computation clearly exposes the failings of two prominent critiques, Searle's Chinese room (...)
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  19. added 2017-02-15
    The Comprehensibility Theorem and the Foundations of Artificial Intelligence.Arthur Charlesworth - 2014 - Minds and Machines 24 (4):439-476.
    Problem-solving software that is not-necessarily infallible is central to AI. Such software whose correctness and incorrectness properties are deducible by agents is an issue at the foundations of AI. The Comprehensibility Theorem, which appeared in a journal for specialists in formal mathematical logic, might provide a limitation concerning this issue and might be applicable to any agents, regardless of whether the agents are artificial or natural. The present article, aimed at researchers interested in the foundations of AI, addresses many questions (...)
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  20. added 2017-02-14
    FYSE 1211 Gödel, Escher, Bach 27. October 2008 The Mind Behind the Swarm Evolution has Accomplished Some Spectacular Things in the Time Since Simple Organic. [REVIEW]Mike Papadakis - forthcoming - Mind.
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  21. added 2017-02-14
    Lucas Van Leyden S Dance Around the Gowen Calf· the Orthern Triptych in the Age of The.Jennifer R. Pease - 2006 - Inquiry: The University of Arkansas Undergraduate Research Journal 7.
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  22. added 2017-02-14
    The Essential Incompleteness of All Science,".Kari R. Popper & Scientific Reduction - 1974 - In F. Ayala & T. Dobzhansky (eds.), Studies in the Philosophy of Biology. University of California Press.
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  23. added 2017-02-13
    Godel, the Mind, and the Laws of Physics.Roger Penrose - 2011 - In Matthias Baaz (ed.), Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press. pp. 339.
    Gödel appears to have believed strongly that the human mind cannot be explained in terms of any kind of computational physics, but he remained cautious in formulating this belief as a rigorous consequence of his incompleteness theorems. In this chapter, I discuss a modification of standard Gödel-type logical arguments, these appearing to strengthen Gödel’s conclusions, and attempt to provide a persuasive case in support of his standpoint that the actions of the mind must transcend computation. It appears that Gödel did (...)
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  24. added 2017-02-13
    Goedel's Theorem, the Theory of Everything, and the Future of Science and Mathematics.Douglas S. Robertson - 2000 - Complexity 5 (5):22-27.
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  25. added 2017-02-13
    The Emperor's New Epistemology.Lissa Roberts & Michael E. Gorman - 1991 - Behavioral and Brain Sciences 14 (4):743-744.
  26. added 2017-02-13
    The Nonalgorithmic Mind.Roger Penrose - 1990 - Behavioral and Brain Sciences 13 (4):692-705.
  27. added 2017-02-13
    Where is the Material of the Emperor's Mind?David L. Gilden & Joseph S. Lappin - 1990 - Behavioral and Brain Sciences 13 (4):665-666.
  28. added 2017-02-13
    The Pretender's New Clothes.Tim Smithers - 1990 - Behavioral and Brain Sciences 13 (4):683-684.
  29. added 2017-02-13
    The Emperor's Old Hat.Don Perlis - 1990 - Behavioral and Brain Sciences 13 (4):680-681.
  30. added 2017-02-13
    Mechanism at Two Thousand.John C. Marshall - 1984 - Behavioral and Brain Sciences 7 (4):637.
  31. added 2017-02-09
    Gödel, Escher, Bach.V. Huber-Dyson - 1981 - Canadian Journal of Philosophy 11 (4):775-792.
  32. added 2017-02-08
    Fellow of Merton College, Oxford.J. R. Lucas - unknown
    I must start with an apologia. My original paper, ``Minds, Machines and Gödel'', was written in the wake of Turing's 1950 paper in Mind, and was intended to show that minds were not Turing machines. Why, then, didn't I couch the argument in terms of Turing's theorem, which is easyish to prove and applies directly to Turing machines, instead of Gödel's theorem, which is horrendously difficult to prove, and doesn't so naturally or obviously apply to machines? The reason was that (...)
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  33. added 2017-02-07
    Gödel, Turing, and K-Graph Machines.Wilfried Sieg & John Byrnes - unknown
    Wilfried Sieg and John Byrnes. Gödel, Turing, and K-Graph Machines.
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  34. added 2017-02-02
    The Large, the Small and the Human Mind by Roger Penrose. Cambridge University Press, 1997, XVIII + 185 Pp. £14.95. [REVIEW]Peter Lipton - 1998 - Philosophy 73 (1):125-139.
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  35. added 2017-02-01
    Criticisms and Discussions of the Gödelian Argument.J. R. Lucas - manuscript
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  36. added 2017-02-01
    Review of G. Lakoff and R. E. Núñez, Where Mathematics Comes From[REVIEW]Gary M. Shute - 2005 - Minds and Machines 15 (1):118-123.
  37. added 2017-01-29
    EBB, J. C.: "Mechanism, Mentalism and Metamathematics". [REVIEW]J. R. Lucas - 1982 - British Journal for the Philosophy of Science 33:441.
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  38. added 2017-01-29
    J.R. Lucas, On Justice. [REVIEW]Jan Narveson - 1982 - Philosophy in Review 2:27-29.
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  39. added 2017-01-29
    LUCAS, J. R. "The Freedom of the Will". [REVIEW]I. J. Good - 1971 - British Journal for the Philosophy of Science 22:382.
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  40. added 2017-01-28
    Implication Et Engagement En Hommage À Philippe Lucas.Philippe Fritsch & Lucas - 2000
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  41. added 2017-01-28
    LUCAS, J. R. Responsibility. [REVIEW]T. S. Champlin - 1994 - Philosophy 69:254.
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  42. added 2017-01-28
    LUCAS, J. R. The Future. [REVIEW]C. J. F. Williams - 1991 - Philosophy 66:124.
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  43. added 2017-01-28
    Philosophical Consequences Of Godel's Theorem.Stanislaw Krajewski - 1983 - Bulletin of the Section of Logic 12 (4):157-161.
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  44. added 2017-01-28
    Sex, Equality and Mr Lucas: Discussion.Andrew Belsey - 1980 - Philosophy 55 (213):386-391.
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  45. added 2017-01-28
    LUCAS, J. R. - "The Freedom of the Will". [REVIEW]G. Robinson - 1973 - Mind 82:306.
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  46. added 2017-01-28
    LUCAS, J. R. - "The Concept of Probability". [REVIEW]L. J. Cohen - 1972 - Mind 81:625.
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  47. added 2017-01-28
    LUCAS, J. R.-"The Freedom of the Will". [REVIEW]D. M. Mackay - 1972 - Philosophy 47:180.
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  48. added 2017-01-28
    LUCAS, J. R.-"The Principles of Politics". [REVIEW]Alan Ryan - 1968 - Philosophy 43:300.
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  49. added 2017-01-28
    DOUGLAS, A. C. - The Physical Mechanism of the Human Mind. [REVIEW]W. J. H. Sprott - 1934 - Mind 43:225.
  50. added 2017-01-28
    The Physical Mechanism of the Human Mind. [REVIEW]A. H. Martin - 1933 - Australasian Journal of Philosophy 11 (3):233.
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1 — 50 / 266