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Belief And Incompleteness
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Book Synopsis Incompleteness by : Rebecca Goldstein
Download or read book Incompleteness written by Rebecca Goldstein and published by W. W. Norton & Company. This book was released on 2006-01-31 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Book Synopsis Belief and Incompleteness by : Kurt Konolige
Download or read book Belief and Incompleteness written by Kurt Konolige and published by . This book was released on 1984 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both agents are state-of-theart constructions, incorporating the latest Al research in chess playing, natural-language understanding, planning, etc. But because of the overwhelming combinatorics of' chess, neither they nor the fastest foreseeable computers would be able to search the entire game tree to find out whether White has a forced win. Why then do they come to such an odd conclusion about their own knowledge of the game? The chess scenario is an anecdotal example of the way inaccurate cognitive models can lead to behavior that is less than intelligent in artificial agents. In this case, the agents' model of belief is not correct. They make the assumption that an agent actually knows all the consequences of his beliefs. S1 knows that chess is a finite game, and thus reasons that, in principle, knowing the rules of chess is all that is required to figure out whether White has a forced ini%ial win. Mter learning that S2 does indeed know the rules of chess he comes to the erroneous conclusion that S2 also knows this particular consequence of the rules. And S2 himself, reflecting on his own knowledge in the same manner, arrives at the same conclusion, even though in actual fact he could never carry out the computations necessary to demonstrate it.
Download or read book Gödel's Theorem written by Torkel Franzén and published by CRC Press. This book was released on 2005-06-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
Book Synopsis Reflections on Kurt Gödel by : Hao Wang
Download or read book Reflections on Kurt Gödel written by Hao Wang and published by MIT Press. This book was released on 1990-03-14 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newton/Descartes. Einstein/Gödel. The seventeenth century had its scientific and philosophical geniuses. Why shouldn't ours have them as well? Kurt Gödel was indisputably one of the greatest thinkers of our time, and in this first extended treatment of his life and work, Hao Wang, who was in close contact with Gödel in his last years, brings out the full subtlety of Gödel's ideas and their connection with grand themes in the history of mathematics and philosophy. The subjects he covers include the completeness of elementary logic, the limits of formalization, the problem of evidence, the concept of set, the philosophy of mathematics, time, and relativity theory, metaphysics and religion, as well as general ideas on philosophy as a worldview. Wang, whose reflections on his colleague also serve to clarify his own philosophical thoughts, distinguishes his ideas from those of Gödel's and on points of agreement develops Gödel's views further. The book provides a generous array of information on and interpretation of the two main phases of Gödel's career - the years between 1924 and 1939 at the University of Vienna, which were marked by intense mathematical creativity, and the period from 1940 to his death in 1978, during which he was affiliated with the Institute for Advanced Studies in Princeton, a time in which Gödel's interests steadily shifted from questions of logic to metaphysics. And it also examines Gödel's relations with the Vienna Circle, his philosophical differences with Carnap and Wittgenstein, the intimate and mutually fruitful friendship with Einstein, and the periodic bouts of depression for which Gödel was hospitalized a number of times over the course of his life. A Bradford Book.
Book Synopsis An Introduction to Gödel's Theorems by : Peter Smith
Download or read book An Introduction to Gödel's Theorems written by Peter Smith and published by Cambridge University Press. This book was released on 2007-07-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
Book Synopsis A World Without Time by : Palle Yourgrau
Download or read book A World Without Time written by Palle Yourgrau and published by Basic Books. This book was released on 2009-03-04 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a widely known but little considered fact that Albert Einstein and Kurt Godel were best friends for the last decade and a half of Einstein's life. The two walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German science in which they had grown up. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist . Einstein endorsed this result-reluctantly, since it decisively overthrew the classical world-view to which he was committed. But he could find no way to refute it, and in the half-century since then, neither has anyone else. Even more remarkable than this stunning discovery, however, was what happened afterward: nothing. Cosmologists and philosophers alike have proceeded with their work as if Godel's proof never existed -one of the greatest scandals of modern intellectual history. A World Without Time is a sweeping, ambitious book, and yet poignant and intimate. It tells the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue from undeserved obscurity the brilliant work they did together.
Download or read book On Belief written by Slavoj Zizek and published by Routledge. This book was released on 2003-09-02 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the basis of belief in an era when globalization, multiculturalism and big business are the new religion? Slavoj Zizek, renowned philosopher and irrepressible cultural critic takes on all comers in this compelling and breathless new book. From 'cyberspace reason' to the paradox that is 'Western Buddhism', On Belief gets behind the contours of the way we normally think about belief, in particular Judaism and Christianity. Holding up the so-called authenticity of religious belief to critical light, Zizek draws on psychoanalysis, film and philosophy to reveal in startling fashion that nothing could be worse for believers than their beliefs turning out to be true.
Book Synopsis Incomplete Information and Heterogeneous Beliefs in Continuous-time Finance by : Alexandre C. Ziegler
Download or read book Incomplete Information and Heterogeneous Beliefs in Continuous-time Finance written by Alexandre C. Ziegler and published by Springer Science & Business Media. This book was released on 2012-11-02 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: After a brief review of the existing incomplete information literature, the effect of incomplete information on investors' exptected utility, risky asset prices, and interest rates is described. It is demonstrated that increasing the quality of investors' information need not increase their expected utility and the prices of risky assets. The impact of other factors is discussed in detail. It is also demonstrated that financial markets in general do not aggregate information efficiently, a fact that can explain the equity premium puzzle.
Book Synopsis The Blind Spot by : Jean-Yves Girard
Download or read book The Blind Spot written by Jean-Yves Girard and published by European Mathematical Society. This book was released on 2011 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic. The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is ``more equal than the other'': one thus discovers essentialist blind spots. Starting with Godel's paradox (1931)--so to speak, the incompleteness of answers with respect to questions--the book proceeds with paradigms inherited from Gentzen's cut-elimination (1935). Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction (GoI), all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra. Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect (perennial) and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity. This highly original course on logic by one of the world's leading proof theorists challenges mathematicians, computer scientists, physicists, and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way.
Book Synopsis Righteous Religion by : Kathleen Ritter
Download or read book Righteous Religion written by Kathleen Ritter and published by Psychology Press. This book was released on 1996 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stories of 17 women who have struggled for human rights throughout the world during the 20th century but have been largely overlooked by the conventional literature. They are depicted confronting authoritarian governments, struggling with race and ethnicity, seeking environmental justice, upholding women's rights as human rights, and making the world safe for children. Paper edition (unseen), $18.95. Annotation copyright by Book News, Inc., Portland, OR
Book Synopsis Godel's Theorem in Focus by : S.G. Shanker
Download or read book Godel's Theorem in Focus written by S.G. Shanker and published by Taylor & Francis. This book was released on 2012-08-21 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
Book Synopsis Predicative Arithmetic. (MN-32) by : Edward Nelson
Download or read book Predicative Arithmetic. (MN-32) written by Edward Nelson and published by Princeton University Press. This book was released on 2014-07-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Preferences and Decisions under Incomplete Knowledge by : Janos Fodor
Download or read book Preferences and Decisions under Incomplete Knowledge written by Janos Fodor and published by Physica. This book was released on 2013-11-11 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, decision problems are pervaded with incomplete knowledge, i.e., imprecision and/or uncertain information, both in the problem description and in the preferential information. In this volume leading scientists in the field address various theoretical and practical aspects related to the handling of this incompleteness. The problems discussed are taken from multi-objective linear programming, rationality considerations in preference modelling, non-probabilistic utility theory, data fusion, group decision making and multicriteria decision aid. The book is oriented towards researchers, graduate and postgraduate students in decision analysis, fuzzy sets and fuzzy logic, and operations research/management science.
Book Synopsis The Incomplete Universe by : Patrick Grim
Download or read book The Incomplete Universe written by Patrick Grim and published by MIT Press. This book was released on 1991 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central claim of this powerful philosophical exploration is that within any logic we have, there can be no coherent notion of all truth or of total knowledge. Grim examines a series of logical paradoxes and related formal results to reveal their implications for contemporary epistemology, metaphysics, and the philosophy of religion. He reaches the provocative conclusion that, if the universe is thought of in terms of its truths, it is essentially open and incomplete. The Incomplete Universe includes detailed work on the liar paradox and recent attempts at solution, Kaplan and Montague's paradox of the knower, the Gödel theorems and related incompleteness phenomena, and new forms of Cantorian argument. The emphasis throughout is philosophical rather than formal, with an eye to connection's with possible worlds, the notion of omniscience, and the opening lines of the Tractatus: "The world is all that is the case. "
Book Synopsis ECAI 2010 by : European Coordinating Committee for Artificial Intelligence
Download or read book ECAI 2010 written by European Coordinating Committee for Artificial Intelligence and published by IOS Press. This book was released on 2010 with total page 1184 pages. Available in PDF, EPUB and Kindle. Book excerpt: LC copy bound in 2 v.: v. 1, p. 1-509; v. 2, p. [509]-1153.
Book Synopsis The Incomplete Fear by : Gurusrinivas G
Download or read book The Incomplete Fear written by Gurusrinivas G and published by Griffin Publications . This book was released on 2023-08-03 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ultimate goal of this book is to show away to live a contentful life throughout the journey between life and death and be in the present moment for most of the time without any fearful anxieties and recover from mental disturbance in the shortest time; this book will act as a framework to fallback in case we have disturbance in focusing on the present. This book will lead you toward self-realization and teach you to devote time to self-care and progress by focusing on the present moment rather than living in fear thinking about the uncertainties of the future. The pages of the book will lead us to embrace peace and calmness and thus pave the way to make society peaceful.
Download or read book Christian Science Sentinel written by and published by . This book was released on 1904 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt:
