Search results for 'Goedel's Incompleteness Theorems' (try it on Scholar)

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  1. Richard Zach (2005). Book Review: Michael Potter. Reason's Nearest Kin. Philosophies of Arithmetic From Kant to Carnap. [REVIEW] Notre Dame Journal of Formal Logic 46 (4):503-513.score: 432.0
  2. Geoffrey Hellman (1981). How to Goedel a Frege-Russell: Goedel's Incompleteness Theorem. Noûs 15:451-68.score: 379.5
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  3. H. Gaifman (2000). What Godel's Incompleteness Result Does and Does Not Show. Journal of Philosophy 97 (8):462-471.score: 324.0
    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 (...)
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  4. Aaron Sloman (1992). The Emperor's Real Mind -- Review of Roger Penrose's The Emperor's New Mind: Concerning Computers Minds and the Laws of Physics. Artificial Intelligence 56 (2-3):355-396.score: 286.5
    "The Emperor's New Mind" by Roger Penrose has received a great deal of both praise and criticism. This review discusses philosophical aspects of the book that form an attack on the "strong" AI thesis. Eight different versions of this thesis are distinguished, and sources of ambiguity diagnosed, including different requirements for relationships between program and behaviour. Excessively strong versions attacked by Penrose (and Searle) are not worth defending or attacking, whereas weaker versions remain problematic. Penrose (like Searle) regards the notion (...)
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  5. C. Chihara (1972). On Alleged Refutations of Mechanism Using Godel's Incompleteness Results. Journal of Philosophy 69 (September):507-26.score: 193.5
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  6. William E. Seager (2003). Yesterday's Algorithm: Penrose and the Godel Argument. Croatian Journal of Philosophy 3 (9):265-273.score: 172.0
    Roger Penrose is justly famous for his work in physics and mathematics but he is _notorious_ for his endorsement of the Gödel argument (see his 1989, 1994, 1997). This argument, first advanced by J. R. Lucas (in 1961), attempts to show that Gödel’s (first) incompleteness theorem can be seen to reveal that the human mind transcends all algorithmic models of it1. Penrose's version of the argument has been seen to fall victim to the original objections raised against Lucas (see (...)
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  7. Cezary Cieśliński & Rafal Urbaniak (2013). Gödelizing the Yablo Sequence. Journal of Philosophical Logic 42 (5):679-695.score: 171.0
    We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo (...)
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  8. Paolo Mancosu (2004). Book Review: Kurt G�Del. Collected Works , Volumes IV and V. [REVIEW] Notre Dame Journal of Formal Logic 45 (2):109-125.score: 171.0
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  9. Rafaele Di Giacomo, Jeffrey H. Schwartz & Bruno Maresca (2013). The Origin of Metazoa: An Algorithmic View of Life. Biological Theory 8 (3):221-231.score: 171.0
    We propose that the sudden emergence of metazoans during the Cambrian was due to the appearance of a complex genome architecture that was capable of computing. In turn, this made defining recursive functions possible. The underlying molecular changes that occurred in tandem were driven by the increased probability of maintaining duplicated DNA fragments in the metazoan genome. In our model, an increase in telomeric units, in conjunction with a telomerase-negative state and consequent telomere shortening, generated a reference point equivalent to (...)
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  10. Douglas S. Robertson (2000). Goedel's Theorem, the Theory of Everything, and the Future of Science and Mathematics. Complexity 5 (5):22-27.score: 146.5
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  11. Robert A. Schultz (1980). What Could Self-Reflexiveness Be? Or Goedel's Theorem Goes to Hollywood and Discovers That It's All Done with Mirrors. Semiotica 30 (1-2).score: 139.5
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  12. U. Fidelman (1999). Goedel's Theorem and Models of the Brain: Possible Hemispheric Basis for Kant's Psychological Ideas. Journal of Mind and Behavior 20 (1):43-56.score: 139.5
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  13. F. RivettiBarbo (1996). A Surreptitious Change in the Designation of a Term: The Foundation of Goedel's Theorem of the Non-Demonstrability of Non-Contradictoriness-A New Metalinguistic Exposition and Philosophical Considerations. Rivista di Filosofia Neo-Scolastica 88 (1):95-128.score: 139.5
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  14. I. Aimonetto (1993). Goedel Theorem of Incompleteness. Filosofia 44 (1):113-136.score: 129.0
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  15. Taner Edis (1998). How Godel's Theorem Supports the Possibility of Machine Intelligence. Minds and Machines 8 (2):251-262.score: 96.0
    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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  16. Heinz-Dieter Ebbinghaus (1996). Mathematical Logic. Springer.score: 84.0
    This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most (...)
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  17. Woosuk Park (2003). On the Motivations of Goedel's Ontological Proof. Modern Schoolman 80 (2):144-153.score: 81.0
  18. A. A. Zenkin & A. Linear (2002). Goedel's Numbering of Multi-Modal Texts. Bulletin of Symbolic Logic 8 (1):180.score: 81.0
     
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  19. I. J. Good (1969). Godel's Theorem is a Red Herring. British Journal for the Philosophy of Science 19 (February):357-8.score: 62.0
  20. Peter Slezak (1982). Godel's Theorem and the Mind. British Journal for the Philosophy of Science 33 (March):41-52.score: 62.0
  21. William H. Hanson (1971). Mechanism and Godel's Theorem. British Journal for the Philosophy of Science 22 (February):9-16.score: 62.0
  22. David Coder (1969). Godel's Theorem and Mechanism. Philosophy 44 (September):234-7.score: 62.0
  23. Graham Priest (1994). Godel's Theorem and the Mind... Again. In M. Michael & John O'Leary-Hawthorne (eds.), Philosophy in Mind: The Place of Philosophy in the Study of Mind. Kluwer. 41-52.score: 62.0
  24. John R. Lucas (1961). Minds, Machines and Godel. Philosophy 36 (April-July):112-127.score: 60.5
    Goedel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovable-in-the-system". If this formula were provable-in-the-system, we should have a contradiction: for if it were provablein-the-system, then it would not be unprovable-in-the-system, so that "This formula is unprovable-in-the-system" would be false: equally, if it were provable-in-the-system, then (...)
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  25. Philip Hugly & Charles Sayward (1989). Can There Be a Proof That an Unprovable Sentence of Arithmetic is True? Dialectica 43 (43):289-292.score: 54.0
    Various authors of logic texts are cited who either suggest or explicitly state that the Gödel incompleteness result shows that some unprovable sentence of arithmetic is true. Against this, the paper argues that the matter is one of philosophical controversy, that it is not a mathematical or logical issue.
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  26. Robert Kirk (1986). Mental Machinery and Godel. Synthese 66 (March):437-452.score: 48.0
  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.score: 48.0
  28. R. Michael Perry (2006). Consciousness as Computation: A Defense of Strong AI Based on Quantum-State Functionalism. In Charles Tandy (ed.), Death and Anti-Death, Volume 4: Twenty Years After De Beauvoir, Thirty Years After Heidegger. Palo Alto: Ria University Press.score: 48.0
  29. Luca Incurvati (2009). Does Truth Equal Provability in the Maximal Theory? Analysis 69 (2):233-239.score: 46.5
    According to the received view, formalism – interpreted as the thesis that mathematical truth does not outrun the consequences of our maximal mathematical theory – has been refuted by Goedel's theorem. In support of this claim, proponents of the received view usually invoke an informal argument for the truth of the Goedel sentence, an argument which is supposed to reconstruct our reasoning in seeing its truth. Against this, Field has argued in a series of papers that the principles involved (...)
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  30. Catherine Wilson (2000). Plenitude and Compossibility in Leibniz. The Leibniz Review 10:1-20.score: 46.5
    Leibniz entertained the idea that, as a set of “striving possibles” competes for existence, the largest and most perfect world comes into being. The paper proposes 8 criteria for a Leibniz-world. It argues that a) there is no algorithm e.g., one involving pairwise compossibility-testing that can produce even possible Leibniz-worlds; b) individual substances presuppose completed worlds; c) the uniqueness of the actual world is a matter of theological preference, not an outcome of the assembly-process; and d) Goedel’s theorem implies that (...)
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  31. Hans Moravec (1995). Roger Penrose's Gravitonic Brains: A Review of Shadows of the Mind by Roger Penrose. [REVIEW] Psyche 2 (1).score: 42.0
    Summarizing a surrounding 200 pages, pages 179 to 190 of Shadows of the Mind contain a future dialog between a human identified as "Albert Imperator" and an advanced robot, the "Mathematically Justified Cybersystem", allegedly Albert's creation. The two have been discussing a Gödel sentence for an algorithm by which a robot society named SMIRC certifies mathematical proofs. The sentence, referred to in mathematical notation as Omega(Q*), is to be precisely constructed from on a definition of SMIRC's algorithm. It can be (...)
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  32. Hung-Yul So (2008). Goedel, Nietzsche and Buddha. Proceedings of the Xxii World Congress of Philosophy 13:105-111.score: 42.0
    Hawking, in his book, A Brief History of Time, concludes with a conditional remark: If we find a complete theory to explain the physical world, then we will come to understand God’s mind. With Goedel in mind, we can raise questions about the completeness of our scientific understanding and the nature of our understanding with regard to God’s mind. We need to ask about the higher order of our understanding when we move to knowing God’s mind. We go onto develop (...)
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  33. John R. Lucas (1970). Mechanism: A Rejoinder. Philosophy 45 (April):149-51.score: 30.0
    PROFESSOR LEWIS 1 and Professor Coder 2 criticize my use of Gödel's theorem to refute Mechanism. 3 Their criticisms are valuable. In order to meet them I need to show more clearly both what the tactic of my argument is at one crucial point and the general aim of the whole manoeuvre.
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  34. John Burgess (2010). On the Outside Looking in : A Caution About Conservativeness. In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.score: 27.0
    My contribution to the symposium on Goedel’s philosophy of mathematics at the spring 2006 Association for Symbolic Logic meeting in Montreal. Provisional version: references remain to be added. To appear in an ASL volume of proceedings of the Goedel sessions at that meeting.
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  35. Mauro Dorato, Kant, Goedel and Relativity.score: 24.0
    Since the onset of logical positivism, the general wisdom of the philosophy of science has it that the kantian philosophy of (space and) time has been superseded by the theory of relativity, in the same sense in which the latter has replaced Newton’s theory of absolute space and time. On the wake of Cassirer and Gödel, in this paper I raise doubts on this commonplace by suggesting some conditions that are necessary to defend the ideality of time in the sense (...)
     
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  36. David Černý & Elisa Ferretti (2011). Gödelův důkaz Boží existence. Studia Neoaristotelica 8 (2):211-248.score: 24.0
    Dissertatio proposita circa “argumentum ontologicum” pro existentia Dei, quem K. Goedel construxit, versatur. In prima parte structuram logicam dicti argumenti exponimus, singulos gradus argumenti explicamus, “collapsumque modalitatum”, quo argumentum invalidari invenitur, examinamus. Sequenti parte recentiores quasdam confectiones argumenti pertractamus; et scil. praecipue formam eius, quae super conceptum mathematicum multitudinis seu “complexus elementorum terminatorum” fundatur, et formam “algebraicam”, quarum affinitates quasdam notabiles prae oculos ponimus. Ultima parte disceptationes, quae circa huiusce argumenti validitatem ac momentum respectu modernae theisticae philosophiae agebantur, describimus. Loco (...)
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  37. I. Aimonetto (1988). The Foundations of the Goedel Theorem-From Peano to Frege and Russell. Filosofia 39 (3):231-249.score: 24.0
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  38. Kordula Świętorzecka (2002). O stosowalności niektórych modalnych reguł inferencji w rozumowaniach pozalogicznych. Filozofia Nauki 1.score: 24.0
    The presented paper takes up the attempt to analyse and specify the suspicion that some modal rules of inference are paralogical in application to non-logical reasonings (s.c. modal fallacy). The considerations have been limited to modal prepositional calculi: K and S5, which are intended to be a formal base of these non-logical reasonings - proofs of so called specific thesis on the grounds of the particular specific theories. Pointing out the properties of being permitted, being valid and being derivable in (...)
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  39. Douglas Kutach (2013). Time Travel and Time Machines. In Adrian Bardon & Heather Dyke (eds.), A Companion to the Philosophy of Time. Blackwell.score: 18.0
    Thinking about time travel is an entertaining way to explore how to understand time and its location in the broad conceptual landscape that includes causation, fate, action, possibility, experience, and reality. It is uncontroversial that time travel towards the future exists, and time travel to the past is generally recognized as permitted by Einstein’s general theory of relativity, though no one knows yet whether nature truly allows it. Coherent time travel stories have added flair to traditional debates over the metaphysical (...)
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  40. William S. Robinson (1992). Penrose and Mathematical Ability. Analysis 52 (2):80-88.score: 18.0
  41. Gregory Landini (forthcoming). Russellian Facts About the Slingshot. Axiomathes:1-15.score: 18.0
    The so-called “Slingshot” argument purports to show that an ontology of facts is untenable. In this paper, we address a minimal slingshot restricted to an ontology of physical facts as truth-makers for empirical physical statements. Accepting that logical matters have no bearing on the physical facts that are truth-makers for empirical physical statements and that objects are themselves constituents of such facts, our minimal slingshot argument purportedly shows that any two physical statements with empirical content are made true by one (...)
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  42. Frank Stephan & Jason Teutsch (2008). Immunity and Hyperimmunity for Sets of Minimal Indices. Notre Dame Journal of Formal Logic 49 (2):107-125.score: 18.0
    We extend Meyer's 1972 investigation of sets of minimal indices. Blum showed that minimal index sets are immune, and we show that they are also immune against high levels of the arithmetic hierarchy. We give optimal immunity results for sets of minimal indices with respect to the arithmetic hierarchy, and we illustrate with an intuitive example that immunity is not simply a refinement of arithmetic complexity. Of particular note here are the fact that there are three minimal index sets located (...)
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  43. Albert E. Lyngzeidetson (1990). Massively Parallel Distributed Processing and a Computationalist Foundation for Cognitive Science. British Journal for the Philosophy of Science 41 (March):121-127.score: 16.0
    My purpose in this brief paper is to consider the implications of a radically different computer architecure to some fundamental problems in the foundations of Cognitive Science. More exactly, I wish to consider the ramifications of the 'Gödel-Minds-Machines' controversy of the late 1960s on a dynamically changing computer architecture which, I venture to suggest, is going to revolutionize which 'functions' of the human mind can and cannot be modelled by (non-human) computational automata. I will proceed on the presupposition that the (...)
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  44. Peter Slezak (1984). Minds, Machines and Self-Reference. Dialectica 38 (1):17-34.score: 16.0