Results for 'Gödel'

14 found
Order:
  1.  23
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  2.  59
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  41
    Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic Via Linear Nested Sequents.Tim Lyon - 2020 - In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science. Cham: pp. 156-176.
    This paper employs the linear nested sequent framework to design a new cut-free calculus (LNIF) for intuitionistic fuzzy logic---the first-order Goedel logic characterized by linear relational frames with constant domains. Linear nested sequents---which are nested sequents restricted to linear structures---prove to be a well-suited proof-theoretic formalism for intuitionistic fuzzy logic. We show that the calculus LNIF possesses highly desirable proof-theoretic properties such as invertibility of all rules, admissibility of structural rules, and syntactic cut-elimination.
    Download  
     
    Export citation  
     
    Bookmark  
  4.  70
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  5.  88
    The Significance of Evidence-Based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences.Bhupinder Singh Anand - manuscript
    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. (...)
    Download  
     
    Export citation  
     
    Bookmark  
  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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  7. 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.
    Download  
     
    Export citation  
     
    Bookmark  
  8. 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 (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  9.  81
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  10. 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  11. 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  12. 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 (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  13. 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  14. 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 (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark