A Logical Journey

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Publisher : MIT Press
ISBN 13 : 9780262261258
Total Pages : 420 pages
Book Rating : 4.51/5 ( download)

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Book Synopsis A Logical Journey by : Hao Wang

Download or read book A Logical Journey written by Hao Wang and published by MIT Press. This book was released on 1997-02-03 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.

A Logical Journey

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Author :
Publisher : Bradford Books
ISBN 13 : 9780262231893
Total Pages : 391 pages
Book Rating : 4.91/5 ( download)

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Book Synopsis A Logical Journey by : Hao Wang

Download or read book A Logical Journey written by Hao Wang and published by Bradford Books. This book was released on 1996 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Experts in mathematical logic will find this book of engrossing interest. For mere philosphers it will have a different fascination: in seeing how the achievements of a genius can seem to him to provide a firm foundation for a species of Platonism and the conviction of the superiority of minds over computers, and at the same time can encourage him to favour a quasi-Leibnizian speculative metaphysics and theology. Hao Wang records and assesses the whole with an expert and balanced reasonableness." -- Sir Peter F. Strawson, Magdalen College, Oxford Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gö del. "A Logical Journey" is a continuation of Wang's "Reflections on Gö del" and also elaborates on discussions contained in "From Mathematics to Philosophy." A decade in preparation, it contains important and unfamiliar insights into Gö del's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gö del's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gö del's other major contributions to logic and philosophy. They reveal that there is much more in Gö del's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structuredconversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gö del's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gö del's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gö del's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gö del's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gö del's outlook.

Reflections on Kurt Gödel

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Author :
Publisher : MIT Press
ISBN 13 : 9780262730877
Total Pages : 366 pages
Book Rating : 4.71/5 ( download)

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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.

From Mathematics to Philosophy (Routledge Revivals)

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Publisher : Routledge
ISBN 13 : 1134884338
Total Pages : 445 pages
Book Rating : 4.39/5 ( download)

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Book Synopsis From Mathematics to Philosophy (Routledge Revivals) by : Hao Wang

Download or read book From Mathematics to Philosophy (Routledge Revivals) written by Hao Wang and published by Routledge. This book was released on 2016-06-10 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge.

Godel

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Publisher :
ISBN 13 : 0786747609
Total Pages : 222 pages
Book Rating : 4.03/5 ( download)

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Book Synopsis Godel by : John L. Casti

Download or read book Godel written by John L. Casti and published by . This book was released on 2009-04-21 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Shattering hopes that logic would, in the end, allow us a complete understanding of the universe, Gödel's theorem also raised many provocative questions: What are the limits of rational thought? Can we ever fully understand the machines we build? Or the inner workings of our own minds? How should mathematicians proceed in the absence of complete certainty about their results? Equally legendary were Gödel's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first book for a general audience on this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life.

1089 and All that

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Publisher : Oxford University Press, USA
ISBN 13 : 9780198516231
Total Pages : 200 pages
Book Rating : 4.31/5 ( download)

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Book Synopsis 1089 and All that by : D. J. Acheson

Download or read book 1089 and All that written by D. J. Acheson and published by Oxford University Press, USA. This book was released on 2002 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famouscartoonists. This unusual book is one of the most readable explanations of mathematics available.

Developmental Journey

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Publisher :
ISBN 13 :
Total Pages : 298 pages
Book Rating : 4.51/5 ( download)

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Book Synopsis Developmental Journey by : Mary M. Wilcox

Download or read book Developmental Journey written by Mary M. Wilcox and published by . This book was released on 1979 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Incompleteness

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Publisher : W. W. Norton & Company
ISBN 13 : 0393327604
Total Pages : 299 pages
Book Rating : 4.01/5 ( download)

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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.

A First Journey Through Logic

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Publisher :
ISBN 13 : 9781470454074
Total Pages : pages
Book Rating : 4.76/5 ( download)

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Book Synopsis A First Journey Through Logic by : Martin Hils

Download or read book A First Journey Through Logic written by Martin Hils and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present mathematical logic to students who are interested in what this field is but have no intention of specializing in it. The point of view is to treat logic on an equal footing to any other topic in the mathematical curriculum. The book starts with a presentation of naive set theory, the theory of sets that mathematicians use on a daily basis. Each subsequent chapter presents one of the main areas of mathematical logic: first order logic and formal proofs, model theory, recursion theory, Gödel's incompleteness theorem, and, finally, the axiomatic set theory. Each.

Journey to the Edge of Reason

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Publisher : Oxford University Press
ISBN 13 : 0192636138
Total Pages : 384 pages
Book Rating : 4.33/5 ( download)

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Book Synopsis Journey to the Edge of Reason by : Stephen Budiansky

Download or read book Journey to the Edge of Reason written by Stephen Budiansky and published by Oxford University Press. This book was released on 2021-05-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A remarkable account of Kurt Gödel, weaving together creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval. At age 24, a brilliant Austrian-born mathematician published a mathematical result that shook the world. Nearly a hundred years after Kurt Gödel's famous 1931 paper "On Formally Undecidable Propositions" appeared, his proof that every mathematical system must contain propositions that are true - yet never provable within that system - continues to pose profound questions for mathematics, philosophy, computer science, and artificial intelligence. His close friend Albert Einstein, with whom he would walk home every day from Princeton's famous Institute for Advanced Study, called him "the greatest logician since Aristotle." He was also a man who felt profoundly out of place in his time, rejecting the entire current of 20th century philosophical thought in his belief that mathematical truths existed independent of the human mind, and beset by personal demons of anxiety and paranoid delusions that would ultimately lead to his tragic end from self-starvation. Drawing on previously unpublished letters, diaries, and medical records, Journey to the Edge of Reason offers the most complete portrait yet of the life of one of the 20th century's greatest thinkers. Stephen Budiansky's account brings to life the remarkable world of philosophical and mathematical creativity of pre-war Vienna, and documents how it was barbarically extinguished by the Nazis. He charts Gödel's own hair's-breadth escape from Nazi Germany to the scholarly idyll of Princeton; and the complex, gently humorous, sensitive, and tormented inner life of this iconic but previously enigmatic giant of modern science. Weaving together Gödel's public and private lives, this is a tale of creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval.