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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, in 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. Samuel Alexander (2013). This Sentence Does Not Contain the Symbol X. The Reasoner 7 (9):108.
    A suprise may occur if we use a similar strategy to the Liar's paradox to mathematically formalize "This sentence does not contain the symbol X".
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  2. Samuel A. Alexander (2014). A Machine That Knows Its Own Code. Studia Logica 102 (3):567-576.
    We construct a machine that knows its own code, at the price of not knowing its own factivity.
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  3. Paul Benacerraf (1967). God, the Devil, and Godel. The Monist 51 (January):9-32.
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  4. Damjan Bojadziev (1997). Mind Versus Godel. In Matjaz Gams & M. Wu Paprzycki (eds.), Mind Versus Computer. IOS Press. 202-210.
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  5. G. Lee Bowie (1982). Lucas' Number is Finally Up. Journal of Philosophical Logic 11 (3):279-85.
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  6. David L. Boyer (1983). R. Lucas, Kurt Godel, and Fred Astaire. Philosophical Quarterly 33 (April):147-59.
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  7. Selmer Bringsjord, A Refutation of Penrose's Godelian Case Against Artificial Intelligence.
    Having, as it is generally agreed, failed to destroy the computational conception of mind with the G\"{o}delian attack he articulated in his {\em The Emperor's New Mind}, Penrose has returned, armed with a more elaborate and more fastidious G\"{o}delian case, expressed in and 3 of his {\em Shadows of the Mind}. The core argument in these chapters is enthymematic, and when formalized, a remarkable number of technical glitches come to light. Over and above these defects, the argument, at best, is (...)
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  8. Selmer Bringsjord & H. Xiao (2000). A Refutation of Penrose's New Godelian Case Against the Computational Conception of Mind. Journal of Experimental and Theoretical Artificial Intelligence 12.
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  9. Donald E. Broadbent (ed.) (1993). The Simulation of Human Intelligence. Blackwell.
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  10. Peter Carruthers & Peter K. Smith (eds.) (1996). Theories of Theories of Mind. Cambridge University Press.
    Theories of Theories of Mind brings together contributions by a distinguished international team of philosophers, psychologists, and primatologists, who between them address such questions as: what is it to understand the thoughts, feelings, and intentions of other people? How does such an understanding develop in the normal child? Why, unusually, does it fail to develop? And is any such mentalistic understanding shared by members of other species? The volume's four parts together offer a state of the art survey of the (...)
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  11. David J. Chalmers (1996). Minds, Machines, and Mathematics. Psyche 2:11-20.
    In his stimulating book SHADOWS OF THE MIND, Roger Penrose presents arguments, based on Gödel's theorem, for the conclusion that human thought is uncomputable. There are actually two separate arguments in Penrose's book. The second has been widely ignored, but seems to me to be much more interesting and novel than the first. I will address both forms of the argument in some detail. Toward the end, I will also comment on Penrose's proposals for a "new science of consciousness".
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  12. C. T. K. Chari (1963). Further Comments on Minds, Machines and Godel. Philosophy 38 (April):175-8.
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  13. C. Chihara (1972). On Alleged Refutations of Mechanism Using Godel's Incompleteness Results. Journal of Philosophy 69 (September):507-26.
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  14. David Coder (1969). Godel's Theorem and Mechanism. Philosophy 44 (September):234-7.
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  15. Jon Cogburn & Jason Megill (2010). Are Turing Machines Platonists? Inferentialism and the Computational Theory of Mind. Minds and Machines 20 (3):423-439.
    We first discuss Michael Dummett’s philosophy of mathematics and Robert Brandom’s philosophy of language to demonstrate that inferentialism entails the falsity of Church’s Thesis and, as a consequence, the Computational Theory of Mind. This amounts to an entirely novel critique of mechanism in the philosophy of mind, one we show to have tremendous advantages over the traditional Lucas-Penrose argument.
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  16. A. G. Cohn & J. R. Thomas (eds.) (1986). Artificial Intelligence and Its Applications. John Wiley and Sons.
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  17. Jack Copeland (1998). Turing's o-Machines, Searle, Penrose, and the Brain. Analysis 58 (2):128-138.
    In his PhD thesis (1938) Turing introduced what he described as 'a new kind of machine'. He called these 'O-machines'. The present paper employs Turing's concept against a number of currently fashionable positions in the philosophy of mind.
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  18. Daniel C. Dennett (1989). Murmurs in the Cathedral: Review of R. Penrose, The Emperor's New Mind. [REVIEW] Times Literary Supplement (September) 29.
    The idea that a computer could be conscious--or equivalently, that human consciousness is the effect of some complex computation mechanically performed by our brains--strikes some scientists and philosophers as a beautiful idea. They find it initially surprising and unsettling, as all beautiful ideas are, but the inevitable culmination of the scientific advances that have gradually demystified and unified the material world. The ideologues of Artificial Intelligence (AI) have been its most articulate supporters. To others, this idea is deeply repellent: philistine, (...)
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  19. Daniel C. Dennett (1978). Brainstorms. MIT Press.
    This collection of 17 essays by the author offers a comprehensive theory of mind, encompassing traditional issues of consciousness and free will.
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  20. Daniel C. Dennett (1978). The Abilities of Men and Machines. In Brainstorms. MIT Press.
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  21. Taner Edis (1998). How Godel's Theorem Supports the Possibility of Machine Intelligence. Minds and Machines 8 (2):251-262.
    Gödel's Theorem is often used in arguments against machine intelligence, suggesting humans are not bound by the rules of any formal system. However, Gödelian arguments can be used to support AI, provided we extend our notion of computation to include devices incorporating random number generators. A complete description scheme can be given for integer functions, by which nonalgorithmic functions are shown to be partly random. Not being restricted to algorithms can be accounted for by the availability of an arbitrary random (...)
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  22. Eva-Maria Engelen (2013). Hat Kurt Gödel Thomas von Aquins Kommentar zu Aristoteles' De anima rezipiert? Philosophia Scientiæ. Travaux d'Histoire Et de Philosophie des Sciences 17 (17-1):167-188.
    La recherche d’une réponse à la question qui constitue le titre a conduit à des éclaircissements concernant la réception critique d’œuvres philosophiques majeures par Kurt Gödel. Cela illustre la manière dont il utilise des argumentations philosophiques d’auteurs classiques et les change en des aspects nouveaux pour sa propre argumentation philosophique. Dans le cas qui nous concerne, Gödel emploie un argument classique d’Aristote pour l’immatérialité de l’âme afin d’ajouter certains éléments à son propre raisonnement concernant l’inexhaustibilité des mathématiques, le problème corps-esprit, (...)
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  23. S. Feferman (1996). Penrose's Godelian Argument. Psyche 2:21-32.
    In his book Shadows of the Mind: A search for the missing science of con- sciousness [SM below], Roger Penrose has turned in another bravura perfor- mance, the kind we have come to expect ever since The Emperor’s New Mind [ENM ] appeared. In the service of advancing his deep convictions and daring conjectures about the nature of human thought and consciousness, Penrose has once more drawn a wide swath through such topics as logic, computa- tion, artificial intelligence, quantum physics (...)
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  24. H. Gaifman (2000). What Godel's Incompleteness Result Does and Does Not Show. Journal of Philosophy 97 (8):462-471.
    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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  25. Matjaz Gams (ed.) (1997). Mind Versus Computer: Were Dreyfus and Winograd Right? Amsterdam: IOS Press.
  26. Jay L. Garfield (1990). Foundations of Cognitive Science: The Essential Readings. New York: Paragon House.
  27. A. George & Daniel J. Velleman (2000). Leveling the Playing Field Between Mind and Machine: A Reply to McCall. Journal of Philosophy 97 (8):456-452.
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  28. F. H. George (1962). Minds, Machines and Godel: Another Reply to Mr. Lucas. Philosophy 37 (January):62-63.
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  29. Brie Gertler (2004). Simulation Theory on Conceptual Grounds. Protosociology 20:261-284.
    I will present a conceptual argument for a simulationist answer to (2). Given that our conception of mental states is employed in attributing mental states to others, a simulationist answer to (2) supports a simulationist answer to (1). I will not address question (3). Answers to (1) and (2) do not yield an answer to (3), since (1) and (2) concern only our actual practices and concepts. For instance, an error theory about (1) and (2) would say that our practices (...)
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  30. I. J. Good (1969). Godel's Theorem is a Red Herring. British Journal for the Philosophy of Science 19 (February):357-8.
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  31. I. J. Good (1967). Human and Machine Logic. British Journal for the Philosophy of Science 18 (August):145-6.
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  32. Robert M. Gordon, Folk Psychology As Mental Simulation. Stanford Encyclopedia of Philosophy.
    by, or is otherwise relevant to the seminar "Folk Psychology vs. Mental Simulation: How Minds Understand Minds," a National.
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  33. Rick Grush & P. Churchland (1995). Gaps in Penrose's Toiling. In Thomas Metzinger (ed.), Conscious Experience. Ferdinand Schoningh. 10-29.
    Using the Gödel 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 Gödel 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 (...)
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  34. Robert F. Hadley (1987). Godel, Lucas, and Mechanical Models of Mind. Computational Intelligence 3:57-63.
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  35. William H. Hanson (1971). Mechanism and Godel's Theorem. British Journal for the Philosophy of Science 22 (February):9-16.
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  36. Douglas R. Hofstadter (1979). Godel, Escher, Bach: An Eternal Golden Braid. Basic Books.
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  37. A. Hutton (1976). This Godel is Killing Me. Philosophia 3 (March):135-44.
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  38. Andrew D. Irvine (1983). Lucas, Lewis, and Mechanism -- One More Time. Analysis 43 (March):94-98.
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  39. Dale Jacquette (1987). Metamathematical Criteria for Minds and Machines. Erkenntnis 27 (July):1-16.
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  40. Jeffrey Ketland & Panu Raatikainen, Truth and Provability Again.
    Lucas and Redhead ([2007]) announce that they will defend the views of Redhead ([2004]) against the argument by Panu Raatikainen ([2005]). They certainly re-state the main claims of Redhead ([2004]), but they do not give any real arguments in their favour, and do not provide anything that would save Redhead’s argument from the serious problems pointed out in (Raatikainen [2005]). Instead, Lucas and Redhead make a number of seemingly irrelevant points, perhaps indicating a failure to understand the logico-mathematical points at (...)
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  41. D. King (1996). Is the Human Mind a Turing Machine? Synthese 108 (3):379-89.
    In this paper I discuss the topics of mechanism and algorithmicity. I emphasise that a characterisation of algorithmicity such as the Turing machine is iterative; and I argue that if the human mind can solve problems that no Turing machine can, the mind must depend on some non-iterative principle — in fact, Cantor's second principle of generation, a principle of the actual infinite rather than the potential infinite of Turing machines. But as there has been theorisation that all physical systems (...)
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  42. Robert Kirk (1986). Mental Machinery and Godel. Synthese 66 (March):437-452.
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  43. Geoffrey Laforte, Pat Hayes & Kenneth M. Ford (1998). Why Godel's Theorem Cannot Refute Computationalism: A Reply to Penrose. Artificial Intelligence 104.
  44. Alan M. Leslie, Shaun Nichols, Stephen P. Stich & David B. Klein (1996). Varieties of Off-Line Simulation. In P. Carruthers & P. Smith (eds.), Theories of Theories of Mind. Cambridge University Press. 39-74.
    In the last few years, off-line simulation has become an increasingly important alternative to standard explanations in cognitive science. The contemporary debate began with Gordon (1986) and Goldman's (1989) off-line simulation account of our capacity to predict behavior. On their view, in predicting people's behavior we take our own decision making system `off line' and supply it with the `pretend' beliefs and desires of the person whose behavior we are trying to predict; we then let the decision maker reach a (...)
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  45. David Lewis (1979). Lucas Against Mechanism II. Canadian Journal of Philosophy 9 (June):373-6.
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  46. David Lewis (1969). Lucas Against Mechanism. Philosophy 44 (June):231-3.
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  47. Per Lindstrom (2006). Remarks on Penrose's New Argument. Journal of Philosophical Logic 35 (3):231-237.
    It is commonly agreed that the well-known Lucas-Penrose arguments and even Penrose's 'new argument' in [Penrose, R. (1994): Shadows of the Mind, Oxford University Press] are inconclusive. It is, perhaps, less clear exactly why at least the latter is inconclusive. This note continues the discussion in [Lindström, P. (2001): Penrose's new argument, J. Philos. Logic 30, 241-250; Shapiro, S.(2003): Mechanism, truth, and Penrose's new argument, J. Philos. Logic 32, 19-42] and elsewhere of this question.
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  48. John R. Lucas, The Implications of Godel's Theorem.
    In 1931 Kurt Gödel proved two theorems about the completeness and consistency of first-order arithmetic. Their implications for philosophy are profound. Many fashionable tenets are shown to be untenable: many traditional intuitions are vindicated by incontrovertible arguments.
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  49. John R. Lucas, The Godelian Argument: Turn Over the Page.
    I have no quarrel with the first two sentences: but the third, though charitable and courteous, is quite untrue. Although there are criticisms which can be levelled against the Gödelian argument, most of the critics have not read either of my, or either of Penrose's, expositions carefully, and seek to refute arguments we never put forward, or else propose as a fatal objection one that had already been considered and countered in our expositions of the argument. Hence my title. The (...)
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  50. John R. Lucas (1996). Mind, Machines and Godel: A Retrospect. In Peter Millican & A. Clark (eds.), Machines and Thought. Oxford University Press. 103.
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