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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. Criticisms and Discussions of the Gödelian Argument.J. R. Lucas - manuscript
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  2. The Significance of Evidence-Based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences.Bhupinder Singh Anand - forthcoming
    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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  3. 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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  4. Magical Thinking: The Intersection of Quantum Entanglement and Self-Referential Recursion.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
    The superposition of magical thinking, quantum entanglement, and self-referential recursion explains the relationship between human and machine intelligence (universal intelligence).
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  5. Remarks on the Gödelian Anti-Mechanist Arguments.Panu Raatikainen - 2020 - Studia Semiotyczne 34 (1):267–278.
    Certain selected issues around the Gödelian anti-mechanist arguments which have received less attention are discussed.
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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. Gödel’s Disjunction: The Scope and Limits of Mathematical Knowledge. [REVIEW]Panu Raatikainen - 2018 - History and Philosophy of Logic 39 (4):401-403.
  14. Folk Psychology as Mental Simulation.Luca Barlassina & Robert M. Gordon - 2017 - 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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  15. Why We Shouldn't Reason Classically, and the Implications for Artificial Intelligence.Douglas Campbell - 2016 - In C. Vincent Müller (ed.), Computing and Philosophy: Selected Papers From Iacap 2014. Springer Verlag. pp. 151--165.
    In this paper I argue that human beings should reason, not in accordance with classical logic, but in accordance with a weaker ‘reticent logic’. I characterize reticent logic, and then show that arguments for the existence of fundamental Gödelian limitations on artificial intelligence are undermined by the idea that we should reason reticently, not classically.
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  16. A Theorem About Computationalism and “Absolute” Truth.Arthur Charlesworth - 2016 - Minds and Machines 26 (3):205-226.
    This article focuses on issues related to improving an argument about minds and machines given by Kurt Gödel in 1951, in a prominent lecture. Roughly, Gödel’s argument supported the conjecture that either the human mind is not algorithmic, or there is a particular arithmetical truth impossible for the human mind to master, or both. A well-known weakness in his argument is crucial reliance on the assumption that, if the deductive capability of the human mind is equivalent to that of a (...)
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  17. Kurt Gödel: Philosopher-Scientist.Gabriella Crocco & Eva-Maria Engelen (eds.) - 2016 - Marseille: Presses universitaires de Provence.
    This volume represents the beginning of a new stage of research in interpreting Kurt Gödel’s philosophy in relation to his scientific work. It is more than a collection of essays on Gödel. It is in fact the product of a long enduring international collaboration on Kurt Gödel’s Philosophical Notebooks (Max Phil). New and significant material has been made accessible to a group of experts, on which they rely for their articles. In addition to this, Gödel’s Nachlass is presented anew by (...)
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  18. Penrose on What Scientists Know.Rubén Herce - 2016 - Foundations of Science 21 (4):679-694.
    This paper presents an analysis and critique of Roger Penrose’s epistemological, methodological, and ontological positions. The analysis is relevant not only because Penrose is an influential scientist, but also because of the particular traits of his thought. These traits are directly connected with his background and approach to science: ontological and epistemological realism, mathematical Platonism, emphasis on the continuities of science, epistemological inclusiveness and essential openness of science, the role of common sense, emphasis on the connection between science, ethics, and (...)
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  19. Minds Vs. Machines. On Saka's Basic Blindspot Theorem.Laureano Luna - 2015 - Journal of Experimental and Theoretical Artificial Intelligence 27 (4):483-486.
    Under the name of ‘Basic Blindspot Theorem’, Paul Saka has proposed in the special issue on mind and paradox of this journal a Gödelian argument to the effect that no cognitive system can be complete and correct. We show that while the argument is successful as regards mechanical and formal systems, it may fail with respect to minds, so contributing to draw a boundary between the former and the latter. The existence of such a boundary may lend support to Saka’s (...)
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  20. A Machine That Knows Its Own Code.Samuel A. Alexander - 2014 - 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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  21. 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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  22. On Some Properties of Humanly Known and Humanly Knowable Mathematics.Jason L. Megill, Tim Melvin & Alex Beal - 2014 - Axiomathes 24 (1):81-88.
    We argue that the set of humanly known mathematical truths (at any given moment in human history) is finite and so recursive. But if so, then given various fundamental results in mathematical logic and the theory of computation (such as Craig’s in J Symb Log 18(1): 30–32(1953) theorem), the set of humanly known mathematical truths is axiomatizable. Furthermore, given Godel’s (Monash Math Phys 38: 173–198, 1931) First Incompleteness Theorem, then (at any given moment in human history) humanly known mathematics must (...)
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  23. Turingův test: filozofické aspekty umělé inteligence.Filip Tvrdý - 2014 - Prague: Togga.
    Kniha se zabývá problematikou připisování myšlení jiným entitám, a to pomocí imitační hry navržené v roce 1950 britským filozofem Alanem Turingem. Jeho kritérium, známé v dějinách filozofie jako Turingův test, je podrobeno detailní analýze. Kniha popisuje nejen původní námitky samotného Turinga, ale především pozdější diskuse v druhé polovině 20. století. Největší pozornost je věnována těmto kritikám: Lucasova matematická námitka využívající Gödelovu větu o neúplnosti, Searlův argument čínského pokoje konstatující nedostatečnost syntaxe pro sémantiku, Blockův návrh na použití brutální síly pro řešení (...)
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  24. This Sentence Does Not Contain the Symbol X.Samuel Alexander - 2013 - 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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  25. Hat Kurt Gödel Thomas von Aquins Kommentar zu Aristoteles' De anima rezipiert?Eva-Maria Engelen - 2013 - Philosophia Scientiae 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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  26. Gödel's Incompleteness Theorems.Panu Raatikainen - 2013 - The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), Edward N. Zalta (Ed.).
    Gödel's two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F. According to the second incompleteness theorem, such a formal system cannot (...)
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  27. Mind or Mechanism: Which Came First?Teed Rockwell - 2013 - In Liz Swan (ed.), Origins of Mind. pp. 243--258.
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  28. A Breath of Freedom: The Open-Air Anthologies of E.V. Lucas and Francis Meynell.Ian Rogerson - 2013 - Bulletin of the John Rylands Library 89 (2):177-202.
    Edward Verrall Lucas and Francis Meynell were men of letters in the old-fashioned sense. They were indefatigable both in creating text and bringing like matter together in new and meaningful forms. Lucas was a journalist, anthologist and publisher. Meynell was a printer, anthologist and publisher, and also a poet of considerable sensitivity and charm. Lucas did not write much poetry but was passionate about its merits, and sought, through his collections, to bring children into contact with the best of verse. (...)
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  29. Wybrane Elementy Krytyki Platonizmu Rogera Penrose’A.Krzysztof Śleziński - 2013 - Ruch Filozoficzny 70 (1).
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  30. The Lucas-Penrose Argument About Gödel's Theorem.Jason Megill - 2012 - In J. Feiser & B. Dowden (eds.), Internet Encyclopedia of Philosophy.
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  31. Towards an Actual Gödel Machine Implementation: A Lesson in Self-Reflective Systems.Bas R. Steunebrink & Jã¼Rgen Schmidhuber - 2012 - In Pei Wang & Ben Goertzel (eds.), Theoretical Foundations of Artificial General Intelligence. Springer. pp. 173--195.
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  32. Lionel Penrose and the Concept of Normal Variation in Human Intelligence.Sean A. Valles - 2012 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 43 (1):281-289.
  33. Eight Different Decagonal Tilings Derived From Rhombic Penrose Tiling.Kazuyuki Kato & Akiji Yamamoto - 2011 - Philosophical Magazine 91 (19-21):2579-2586.
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  34. The Cyclic Multiverse of Roger Penrose Hawking and Penrose, Two Alternative Models of Multi-Univrses.Javier Monserrat - 2011 - Pensamiento 67 (254):1147-1156.
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  35. 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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  36. The Godel Theorem and Human Nature.Hilary W. Putnam - 2011 - In Matthias Baaz (ed.), Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press. pp. 325.
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  37. Turingův test: filozofické aspekty umělé inteligence.Filip Tvrdý - 2011 - Dissertation, Palacky University
    Disertační práce se zabývá problematikou připisování myšlení jiným entitám, a to pomocí imitační hry navržené v roce 1950 britským filosofem Alanem Turingem. Jeho kritérium, známé v dějinách filosofie jako Turingův test, je podrobeno detailní analýze. Práce popisuje nejen původní námitky samotného Turinga, ale především pozdější diskuse v druhé polovině 20. století. Největší pozornost je věnována těmto kritikám: Lucasova matematická námitka využívající Gödelovu větu o neúplnosti, Searlův argument čínského pokoje konstatující nedostatečnost syntaxe pro sémantiku, Blockův návrh na použití brutální síly pro (...)
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  38. Are Turing Machines Platonists? Inferentialism and the Computational Theory of Mind.Jon Cogburn & Jason Megil - 2010 - 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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  39. Machines, Mechanism, and the Development of Mechanics: Contemporary Understandings.Douglas Jesseph - 2010 - Perspectives on Science 18 (1):pp. 98-112.
  40. Roger Penrose: Collected Works: Volume 2: 1968-1975.Roger Penrose - 2010 - Oxford University Press.
    Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Developing ideas sketched in the first volume, twistor theory is now applied to genuine issues of physics, and there are the beginnings of twistor diagram theory (an analogue (...)
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  41. Gödel, Nagel, Minds, and Machines.Solomon Feferman - 2009 - Journal of Philosophy 106 (4):201-219.
    Ernest Nagel Lecture, Columbia University, Sept. 27, 2007.
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  42. Roger Penrose's Quantization of the Mind.Wojciech P. Grygiel & Mateusz Hohol - 2009 - Filozofia Nauki 17 (3):5.
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  43. Rogera Penrose'a kwantowanie umysłu.Mateusz Hohol - 2009 - Filozofia Nauki 17 (3):67.
    The modeling of the human mind based on quantum effects has been gaining considerable interest due to the intriguing possibility of applying non-local interactions in the studies of consciousness. Inasmuch as the majority of the pertinent studies are restricted to the exclusive analysis of mental phenomena, the quantum model of mind proposed by Roger Penrose constitutes a part of a much larger scheme of the ultimate unification of physics. Penrose's efforts to find the 'missing science of consciousness' presuppose the non-algorithmic (...)
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  44. An Indian Solution to 'Incompleteness'.U. A. Vinaya Kumar - 2009 - AI and Society 24 (4):351-364.
    Kurt Gödel’s Incompleteness theorem is well known in Mathematics/Logic/Philosophy circles. Gödel was able to find a way for any given P (UTM), (read as, “P of UTM” for “Program of Universal Truth Machine”), actually to write down a complicated polynomial that has a solution iff (=if and only if), G is true, where G stands for a Gödel-sentence. So, if G’s truth is a necessary condition for the truth of a given polynomial, then P (UTM) has to answer first that (...)
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  45. An Indian Solution to 'Incompleteness'.Ua Vinaya Kumar - 2009 - AI and Society 24 (4):351-364.
  46. 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.
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  47. Roger Penrose's Quantization of the Mind (Rogera Penrose'a Kwantowanie Umyslu).Hohol Mateusz - 2009 - Filozofia Nauki 17 (3 (67)).
  48. Symmetry Properties of Penrose Type Tilings.N. Cotfas - 2008 - Philosophical Magazine 88 (13-15):2017-2023.
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  49. Consistency, Turing Computability and Gödel’s First Incompleteness Theorem.Robert F. Hadley - 2008 - Minds and Machines 18 (1):1-15.
    It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined with Gödel’s (...)
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  50. Penrose Matching Rules From Realistic Potentials in a Model System.S. Lim, M. Mihalkovič & C. L. Henley - 2008 - Philosophical Magazine 88 (13-15):1977-1984.
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