Results for 'Gödel'

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  1.  83
    Do Goedel's Incompleteness Theorems Set Absolute Limits on the Ability of the Brain to Express and Communicate Mental Concepts Verifiably?Bhupinder Singh Anand - 2004 - Neuroquantology 2:60-100.
    Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...)
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  2.  40
    Goedel's Other Legacy And The Imperative Of A Self­Reflective Science.Vasileios Basios - 2006 - Goedel Society Collegium Logicum 9:pg. 1-5.
    The Goedelian approach is discussed as a prime example of a science towards the origins. While mere self­referential objectification locks in to its own by­products, self­releasing objectification informs the formation of objects at hand and their different levels of interconnection. Guided by the spirit of Goedel's work a self­reflective science can open the road where old tenets see only blocked paths. “This is, as it were, an analysis of the analysis itself, but if that is done it forms the fundamental (...)
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  3. The Significance of Evidence-Based Reasoning in Mathematics, Mathematics Education, Philosophy, and the Natural Sciences.Bhupinder Singh Anand - 2020 - Mumbai: DBA Publishing (First Edition).
    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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  4. The Truth Assignments That Differentiate Human Reasoning From Mechanistic Reasoning: The Evidence-Based Argument for Lucas' Goedelian Thesis.Bhupinder Singh Anand - 2016 - Cognitive Systems Research 40:35-45.
    We consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary evidence-based definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways: (1) in terms of classical algorithmic verifiabilty; and (2) in terms of finitary algorithmic computability. We then show that the two definitions correspond to two distinctly different assignments of satisfaction and truth (...)
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  5.  48
    The Dialectica Categories.Valeria Correa Vaz De Paiva - 1990 - Dissertation, University of Cambridge, UK
    This thesis describes two classes of Dialectica categories. Chapter one introduces dialectica categories based on Goedel's Dialectica interpretation and shows that they constitute a model of Girard's Intuitionistic Linear Logic. Chapter two shows that, with extra assumptions, we can provide a comonad that interprets Girard's !-course modality. Chapter three presents the second class of Dialectica categories, a simplification suggested by Girard, that models (classical) Linear Logic and chapter four shows how to provide modalities ! and ? for this second class (...)
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  6. Time Travel and Time Machines.Douglas Kutach - 2013 - In Adrian Bardon & Heather Dyke (eds.), A Companion to the Philosophy of Time. Blackwell.
    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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  7. Wissenschaft, Religion und die deutungsoffenen Grundfragen der Biologie.Alfred Gierer - 2009 - In Preprint series Max Planck Institute for the History of Science. Berlin: mpi history of science. pp. preprint 388.
    The full text of this essay is available in an English translation (also in philpapers) under: Alfred Gierer, Science, religion, and basic biological issues that are open to interpretation. Der Artikel bildet das Schlusskapitel des Buches " Alfred Gierer: Wissenschaftliches Denken, das Rätsel Bewusstsein und pro-religiöse Ideen", Königshausen&Neumann, Würzburg 2019. Reichweite und Grenzen naturwissenschaftlicher Erklärungen ergeben sich zum einen aus der universellen Gültigkeit physikalischer Gesetze, zum anderen aus prinzipiellen, intrinsischen Grenzen der Bestimmbarkeit und Berechenbarkeit, zumal bei selbstbezüglichen Fragestellungen. In diesem (...)
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  8.  53
    Indeterminism and Undecidability.Klaas Landsman - forthcoming - In Undecidability, Uncomputability, and Unpredictability. Cham: Springer Nature.
    The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Goedel's (first) incompleteness theorem. In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (i.e. uncorrelated measurement (...)
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  9. In the Beginning Was the Verb: The Emergence and Evolution of Language Problem in the Light of the Big Bang Epistemological Paradigm.Edward G. Belaga - 2008 - Cognitive Philology 1 (1).
    The enigma of the Emergence of Natural Languages, coupled or not with the closely related problem of their Evolution is perceived today as one of the most important scientific problems. The purpose of the present study is actually to outline such a solution to our problem which is epistemologically consonant with the Big Bang solution of the problem of the Emergence of the Universe}. Such an outline, however, becomes articulable, understandable, and workable only in a drastically extended epistemic and scientific (...)
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  10. Retrieving the Mathematical Mission of the Continuum Concept From the Transfinitely Reductionist Debris of Cantor’s Paradise. Extended Abstract.Edward G. Belaga - forthcoming - International Journal of Pure and Applied Mathematics.
    What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock of (...)
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  11. Justifying and Exploring Realistic Monism.Paul Budnik - manuscript
    The foundations of mathematics and physics no longer start with fundamental entities and their properties like spatial extension, points, lines or the billiard ball like particles of Newtonian physics. Mathematics has abolished these from its foundations in set theory by making all assumptions explicit and structural. Particle physics has become completely mathematical, connecting to physical reality only through experimental technique. Applying the principles guiding the foundations of mathematics and physics to philosophical analysis underscores that only conscious experience has an intrinsic (...)
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  12.  66
    From the Closed Classical Algorithmic Universe to an Open World of Algorithmic Constellations.Mark Burgin & Gordana Dodig-Crnkovic - 2013 - In Gordana Dodig-Crnkovic Raffaela Giovagnoli (ed.), Computing Nature. pp. 241--253.
    In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the conventional approach to computation. Then we explain how new models of algorithms turned the classical closed algorithmic universe into the open world of algorithmic constellations, allowing higher flexibility and expressive power, supporting constructivism and creativity in mathematical modeling. As Goedels undecidability theorems demonstrate, the closed algorithmic universe restricts (...)
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  13. What is Mathematical Logic?John Corcoran & Stewart Shapiro - 1978 - Philosophia 8 (1):79-94.
    This review concludes that if the authors know what mathematical logic is they have not shared their knowledge with the readers. This highly praised book is replete with errors and incoherency.
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  14. Consciousness as Computation: A Defense of Strong AI Based on Quantum-State Functionalism.R. Michael Perry - 2006 - In Charles Tandy (ed.), Death and Anti-Death, Volume 4: Twenty Years After De Beauvoir, Thirty Years After Heidegger. Palo Alto: Ria University Press.
    The viewpoint that consciousness, including feeling, could be fully expressed by a computational device is known as strong artificial intelligence or strong AI. Here I offer a defense of strong AI based on machine-state functionalism at the quantum level, or quantum-state functionalism. I consider arguments against strong AI, then summarize some counterarguments I find compelling, including Torkel Franzén’s work which challenges Roger Penrose’s claim, based on Gödel incompleteness, that mathematicians have nonalgorithmic levels of “certainty.” Some consequences of strong AI (...)
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  15. Science, Religion and Basic Biological Issues That Are Open to Interpretation.Alfred Gierer - 2009 - English Translation Of: Preprint 388, Mpi for History of Science.
    This is an English translation of my essay: Alfred Gierer Wissenschaft, Religion und die deutungsoffenen Grundfragen der Biologie. Mpi for the History of Science, preprint 388, 1-21, also in philpapers. Range and limits of science are given by the universal validity of physical laws, and by intrinsic limitations, especially in self-referential contexts. In particular, neurobiology should not be expected to provide a full understanding of consciousness and the mind. Science cannot provide, by itself, an unambiguous interpretation of the natural order (...)
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  16. Three Dogmas of First-Order Logic and Some Evidence-Based Consequences for Constructive Mathematics of Differentiating Between Hilbertian Theism, Brouwerian Atheism and Finitary Agnosticism.Bhupinder Singh Anand - manuscript
    We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...)
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