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Godel's Proof

New York, NY, USA: Routledge. Edited by James Roy Newman (1958)

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  1. Nature, Science, Bayes 'Theorem, and the Whole of Reality‖.Moorad Alexanian - manuscript
    A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of each model or hypothesis. Thomas Bayes’ Theorem relates the data and prior information to posterior probabilities associated with differing models or hypotheses and thus is useful in identifying the roles played by the known data and the assumed prior information when making inferences. (...)
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  • Formalization and the Meaning of “Theory” in the Inexact Biological Sciences.James Griesemer - 2013 - Biological Theory 7 (4):298-310.
    Exact sciences are described as sciences whose theories are formalized. These are contrasted to inexact sciences, whose theories are not formalized. Formalization is described as a broader category than mathematization, involving any form/content distinction allowing forms, e.g., as represented in theoretical models, to be studied independently of the empirical content of a subject-matter domain. Exactness is a practice depending on the use of theories to control subject-matter domains and to align theoretical with empirical models and not merely a state of (...)
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  • Quantum hypercomputation.Tien D. Kieu - 2002 - Minds and Machines 12 (4):541-561.
    We explore the possibility of using quantum mechanical principles for hypercomputation through the consideration of a quantum algorithm for computing the Turing halting problem. The mathematical noncomputability is compensated by the measurability of the values of quantum observables and of the probability distributions for these values. Some previous no-go claims against quantum hypercomputation are then reviewed in the light of this new positive proposal.
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  • Are perceptual fields quantum fields?Brian Flanagan - 2003 - Neuroquantology 3:334-364.
    I argue that our sensory fields are photon fields. The philosophical foundation here is informed by mind/brain identity theory, such as we find in Russell, Feigl, Lockwood and Chalmers. In brief, given Dyson's observation that all material things consist of quantum fields, and given an identity of mind and brain, our sensory fields are then most plausibly photon fields.
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  • Artificial intelligence and consciousness.Drew McDermott - 2007 - In Morris Moscovitch, Philip Zelazo & Evan Thompson (eds.), Cambridge Handbook of Consciousness. New York: Cambridge University Press. pp. 117--150.
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  • On the Anti-Mechanist Arguments Based on Gödel’s Theorem.Stanisław Krajewski - 2020 - Studia Semiotyczne 34 (1):9-56.
    The alleged proof of the non-mechanical, or non-computational, character of the human mind based on Gödel’s incompleteness theorem is revisited. Its history is reviewed. The proof, also known as the Lucas argument and the Penrose argument, is refuted. It is claimed, following Gödel himself and other leading logicians, that antimechanism is not implied by Gödel’s theorems alone. The present paper sets out this refutation in its strongest form, demonstrating general theorems implying the inconsistency of Lucas’s arithmetic and the semantic inadequacy (...)
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  • The Anti-Mechanist Argument Based on Gödel’s Incompleteness Theorems, Indescribability of the Concept of Natural Number and Deviant Encodings.Paula Quinon - 2020 - Studia Semiotyczne 34 (1):243-266.
    This paper reassesses the criticism of the Lucas-Penrose anti-mechanist argument, based on Gödel’s incompleteness theorems, as formulated by Krajewski : this argument only works with the additional extra-formal assumption that “the human mind is consistent”. Krajewski argues that this assumption cannot be formalized, and therefore that the anti-mechanist argument – which requires the formalization of the whole reasoning process – fails to establish that the human mind is not mechanistic. A similar situation occurs with a corollary to the argument, that (...)
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  • (1 other version)Introduction. Le projet de Mario Bunge.François Maurice - 2020 - Mεtascience: Discours Général Scientifique 1:15-27.
    Ce premier numéro de Mεtascience rend un hommage posthume à Mario Bunge, décédé en février 2020. Ce n’est pas la première fois, et certainement pas la dernière, que des penseurs rendent hommage à Mario Bunge ou que son oeuvre fait l’objet d’une étude, à juste titre d’ailleurs, car l’homme est un humaniste et l’oeuvre digne héritière des Lumières. Bunge a contribué de façon significative à un très grand nombre de disciplines : physique, philosophie, sociologie, psychologie, sciences cognitives. Ce numéro est (...)
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  • Squaring the Circle: In Quest for Sustainability.Gennady Shkliarevsky - 2015 - Systems Research and Behavioral Science 32 (6):629-49.
    Development has been themain strategy in addressing the problemof sustainability since at least the mid-1980s. The results of this strategy have been mixed, if not disappointing. In their objections to this approach, critics frequently invoke constraints imposed by physical reality of which the most important one is entropy production. They question the belief that technological innovations are capable of solving the problem of sustainability. Is development the right response to this problem and is the current course capable of attaining sustainability? (...)
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  • Is our Universe Deterministic? Some Philosophical and Theological Reflections on an Elusive Topic.Taede A. Smedes - 2003 - Zygon 38 (4):955-979.
    . The question of whether or not our universe is deterministic remains of interest to both scientists and theologians. In this essay I argue that this question can be solved only by metaphysical decision and that no scientific evidence for either determinism or indeterminism will ever be conclusive. No finite being, no matter how powerful its cognitive abilities, will ever be able to establish the deterministic nature of the universe. The only being that would be capable of doing so would (...)
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  • Hertz and Wittgenstein's philosophy of science.Peter C. Kjaergaard - 2002 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 33 (1):121-149.
    The German physicist Heinrich Hertz played a decisive role for Wittgenstein's use of a unique philosophical method. Wittgenstein applied this method successfully to critical problems in logic and mathematics throughout his life. Logical paradoxes and foundational problems including those of mathematics were seen as pseudo-problems requiring clarity instead of solution. In effect, Wittgenstein's controversial response to David Hilbert and Kurt Gödel was deeply influenced by Hertz and can only be fully understood when seen in this context. To comprehend the arguments (...)
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  • Gödel’s Incompleteness Theorem and the Anti-Mechanist Argument: Revisited.Yong Cheng - 2020 - Studia Semiotyczne 34 (1):159-182.
    This is a paper for a special issue of Semiotic Studies devoted to Stanislaw Krajewski’s paper. This paper gives some supplementary notes to Krajewski’s on the Anti-Mechanist Arguments based on Gödel’s incompleteness theorem. In Section 3, we give some additional explanations to Section 4–6 in Krajewski’s and classify some misunderstandings of Gödel’s incompleteness theorem related to AntiMechanist Arguments. In Section 4 and 5, we give a more detailed discussion of Gödel’s Disjunctive Thesis, Gödel’s Undemonstrability of Consistency Thesis and the definability (...)
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  • On the necessary philosophical premises of the Goedelian arguments.Fano Vincenzo & Graziani Pierluigi - unknown
    Lucas-Penrose type arguments have been the focus of many papers in the literature. In the present paper we attempt to evaluate the consequences of Gödel’s incompleteness theorems for the philosophy of the mind. We argue that the best answer to this question was given by Gödel already in 1951 when he realized that either our intellectual capability is not representable by a Turing Machine, or we can never know with mathematical certainty what such a machine is. But his considerations became (...)
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  • A physical approach to the construction of cognition and to cognitive evolution.Olaf Diettrich - 2001 - Foundations of Science 6 (4):273-341.
    It is shown that the method of operationaldefinition of theoretical terms applied inphysics may well support constructivist ideasin cognitive sciences when extended toobservational terms. This leads to unexpectedresults for the notion of reality, inductionand for the problem why mathematics is sosuccessful in physics.A theory of cognitive operators is proposedwhich are implemented somewhere in our brainand which transform certain states of oursensory apparatus into what we call perceptionsin the same sense as measurement devicestransform the interaction with the object intomeasurement results. Then, (...)
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  • An Application of Single-Valued Neutrosophic Sets in Medical Diagnosis.G. Shahzadi, M. Akram & A. B. Saeid - 2017 - Neutrosophic Sets and Systems 18:80-88.
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  • Idealization and exemplification as tools of philosophy.Tommi Lehtonen - 2012 - E-Logos 19 (1):1-15.
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  • Myślenie za pomocą reprezentacji zewnętrznych.David Kirsh - 2014 - Avant: Trends in Interdisciplinary Studies 5 (1):94-125.
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  • Gödel’s metaphor.Michael R. Jackson - 1994 - Semiotica 98 (1-2):5-48.
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  • Historical development of the foundations of mathematics: Course description.Robert L. Brabenec - 1994 - Science & Education 3 (3):295-309.
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