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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 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, (...)
  2. 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 (...)
  3. 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.
  4. 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.
  5. 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 (...)
  6. 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 (...)
  7. 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.
  8. 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.
  9. 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.
  10. 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 (...)
  11. added 2017-02-13
    The Emperor is Still Under-Dressed.David J. Buller, Jerry Fodor & Tessa L. Crume - 2005 - Trends in Cognitive Sciences 9 (11):508-510.
    Replies to Letters from Cosmides et al. (regarding cheater detection), Buss and Haselton (regarding sex differences in jealousy), and Daly and Wilson (regarding child abuse).
  12. 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.
  13. added 2017-02-13
    The Emperor's New Epistemology.Lissa Roberts & Michael E. Gorman - 1991 - Behavioral and Brain Sciences 14 (4):743-744.
  14. added 2017-02-13
    The Pretender's New Clothes.Tim Smithers - 1990 - Behavioral and Brain Sciences 13 (4):683-684.
  15. added 2017-02-13
    The Nonalgorithmic Mind.Roger Penrose - 1990 - Behavioral and Brain Sciences 13 (4):692-705.
  16. 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.
  17. added 2017-02-13
    The Emperor's Old Hat.Don Perlis - 1990 - Behavioral and Brain Sciences 13 (4):680-681.
  18. added 2017-02-13
    Mechanism at Two Thousand.John C. Marshall - 1984 - Behavioral and Brain Sciences 7 (4):637.
  19. added 2017-02-11
    Clusions From Gödel's Incompleteness Theorems, and Related Results From Mathematical Logic. Languages, Minds, and Machines Figure Prominently in the Discussion. Gödel's Theorems Surely Tell Us Something About These Important Matters. But What? A Descriptive Title for This Paper Would Be “Gödel, Lucas, Penrose, Tur”. [REVIEW]Diana Raffman Deutsch, George Schumm & Neil Tennant - 1998 - Bulletin of Symbolic Logic 4 (3).
  20. added 2017-02-09
    Gödel, Escher, Bach.V. Huber-Dyson - 1981 - Canadian Journal of Philosophy 11 (4):775-792.
  21. 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 (...)
  22. added 2017-02-08
    Leveling the Playing Field Between Mind and Machine.Daniel J. Velleman - 2000 - Journal of Philosophy 97 (8):456-461.
  23. added 2017-02-07
    Gödel, Turing, and K-Graph Machines.Wilfried Sieg & John Byrnes - unknown
  24. 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.
  25. added 2017-02-01
    Criticisms and Discussions of the Gödelian Argument.J. R. Lucas - manuscript
  26. 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.
  27. 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.
  28. added 2017-01-29
    J.R. Lucas, On Justice. [REVIEW]Jan Narveson - 1982 - Philosophy in Review 2:27-29.
  29. 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.
  30. added 2017-01-28
    Implication Et Engagement En Hommage À Philippe Lucas.Philippe Fritsch & Lucas - 2000
  31. added 2017-01-28
    LUCAS, J. R. Responsibility. [REVIEW]T. S. Champlin - 1994 - Philosophy 69:254.
  32. added 2017-01-28
    LUCAS, J. R. The Future. [REVIEW]C. J. F. Williams - 1991 - Philosophy 66:124.
  33. added 2017-01-28
    Philosophical Consequences Of Godel's Theorem.Stanislaw Krajewski - 1983 - Bulletin of the Section of Logic 12 (4):157-161.
  34. added 2017-01-28
    Sex, Equality and Mr Lucas: Discussion.Andrew Belsey - 1980 - Philosophy 55 (213):386-391.
  35. added 2017-01-28
    LUCAS, J. R. - "The Freedom of the Will". [REVIEW]G. Robinson - 1973 - Mind 82:306.
  36. added 2017-01-28
    LUCAS, J. R.-"The Freedom of the Will". [REVIEW]D. M. Mackay - 1972 - Philosophy 47:180.
  37. added 2017-01-28
    LUCAS, J. R. - "The Concept of Probability". [REVIEW]L. J. Cohen - 1972 - Mind 81:625.
  38. added 2017-01-28
    LUCAS, J. R.-"The Principles of Politics". [REVIEW]Alan Ryan - 1968 - Philosophy 43:300.
  39. added 2017-01-28
    DOUGLAS, A. C. - The Physical Mechanism of the Human Mind. [REVIEW]W. J. H. Sprott - 1934 - Mind 43:225.
  40. added 2017-01-28
    The Physical Mechanism of the Human Mind. [REVIEW]A. H. Martin - 1933 - Australasian Journal of Philosophy 11 (3):233.
  41. added 2017-01-27
    Review of Roger Penrose's Shadows of the Mind. [REVIEW]W. S. Robinson - 1996 - Philosophical Psychology 9:119-121.
  42. added 2017-01-27
    A Note on Gödel's Ontological Argument.Francesco Orilia - 1994 - European Review of Philosophy 1:125-131.
  43. added 2017-01-27
    The World Machine. The First Phase: The Cosmic Mechanism.Carl Snyder - 1908 - Philosophical Review 17 (4):446-448.
  44. added 2017-01-27
    Consistency, Mechanicalness and Incompleteness.Qiuen Yu - unknown
    Submitted to the Faculty of Graduate Studies and Research in partial fulfilment of the requirements for the degree of Master of Arts, Department of Philosophy.
  45. added 2017-01-26
    Mind or Mechanism: Which Came First?Teed Rockwell - 2013 - In Liz Swan (ed.), Origins of Mind. pp. 243--258.
  46. added 2017-01-26
    Roger Penrose's Quantization of the Mind.Wojciech P. Grygiel & Mateusz Hohol - 2009 - Filozofia Nauki 17 (3):5.
  47. added 2017-01-26
    Sarah Lucas's Toilets and the Transmogrification of the Body.Elisabeth Vigée Le Brun’S. & Mary Cassatt’S. - 2009 - In Olga Gershenson Barbara Penner (ed.), Ladies and Gents.
  48. added 2017-01-26
    Roger Penrose's Quantization of the Mind (Rogera Penrose'a Kwantowanie Umyslu).Hohol Mateusz - 2009 - Filozofia Nauki 17 (3 (67)).
  49. added 2017-01-26
    An Indian Solution to 'Incompleteness'.Ua Vinaya Kumar - 2009 - AI and Society 24 (4):351-364.
  50. added 2017-01-26
    Roger Penrose, The Large, the Small and the Human Mind. [REVIEW]B. Josephson - 1997 - Journal of Consciousness Studies 4:271-273.
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