Godel

Godel Author John L. Casti
ISBN-10 0786747609
Year 2009-04-21
Pages 224
Language en
Publisher Basic Books
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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.

Kurt G del Collected Works Volume I

Kurt G  del  Collected Works  Volume I Author Kurt Gödel
ISBN-10 0195039645
Year 1986
Pages 490
Language en
Publisher Oxford University Press
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Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. L All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.

From Frege to G del

From Frege to G  del Author Jean Van Heijenoort
ISBN-10 0674324498
Year 1967
Pages 664
Language en
Publisher Harvard University Press
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Gathered together in this book are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege's "Begriffsschrift"--which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory--begins the volume. The texts that follow depict the emergence of set theory and foundations of mathematics, two new fields on the borders of logic, mathematics, and philosophy. Essays trace the trends that led to "Principia mathematica," the appearance of modern paradoxes, and topics including proof theory, the theory of types, axiomatic set theory, and Lowenheim's theorem. The volume concludes with papers by Herbrand and by Godel, including the latter's famous incompleteness paper."

Kurt G del

Kurt G  del Author Kurt Gödel
ISBN-10 3764353104
Year 1995-12-01
Pages 235
Language en
Publisher Springer Science & Business Media
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Kurt Gödel, together with Bertrand Russell, is the most important name in logic, and in the foundations and philosophy of mathematics of this century. However, unlike Russel, Gödel the mathematician published very little apart from his well-known writings in logic, metamathematics and set theory. Fortunately, Gödel the philosopher, who devoted more years of his life to philosophy than to technical investigation, wrote hundreds of pages on the philosophy of mathematics, as well as on other fields of philosophy. It was only possible to learn more about his philosophical works after the opening of his literary estate at Princeton a decade ago. The goal of this book is to make available to the scholarly public solid reconstructions and editions of two of the most important essays which Gödel wrote on the philosophy of mathematics. The book is divided into two parts. The first provides the reader with an incisive historico-philosophical introduction to Gödel's technical results and philosophical ideas. Written by the Editor, this introductory apparatus is not only devoted to the manuscripts themselves but also to the philosophical context in which they were written. The second contains two of Gödel's most important and fascinating unpublished essays: 1) the Gibbs Lecture ("Some basic theorems on the foundations of mathematics and their philosophical implications", 1951); and 2) two of the six versions of the essay which Gödel wrote for the Carnap volume of the Schilpp series The Library of Living Philosophers ("Is mathematics syntax of language?", 1953-1959).

Godel s Theorem in Focus

Godel s Theorem in Focus Author S.G. Shanker
ISBN-10 9781134947973
Year 2012-08-21
Pages 272
Language en
Publisher Routledge
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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.

G del Escher Bach

G  del  Escher  Bach Author Douglas R. Hofstadter
ISBN-10 0140289208
Year 2000
Pages 832
Language en
Publisher Penguin Group(CA)
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'What is a self and how can a self come out of inanimate matter?' This is the riddle that drove Douglas Hofstadter to write this extraordinary book. In order to impart his original and personal view on the core mystery of human existence - our intangible sensation of 'I'-ness - Hofstadter defines the playful yet seemingly paradoxical notion of 'strange loop', and explicates this idea using analogies from many disciplines.

Godel s Proof

Godel s Proof Author Ernest Nagel
ISBN-10 9780814758014
Year 2001-10-01
Pages 160
Language en
Publisher NYU Press
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In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times." However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. Marking the 50th anniversary of the original publication of Gödel's Proof, New York University Press is proud to publish this special anniversary edition of one of its bestselling and most frequently translated books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

A World Without Time

A World Without Time Author Palle Yourgrau
ISBN-10 9780786737000
Year 2009-03-04
Pages 224
Language en
Publisher Basic Books
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In 1942, the logician Kurt Godel and Albert Einstein became close friends; they walked to and from their offices every day, exchanging ideas about science, philosophy, politics, and the lost world of German science. 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 but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

An Introduction to G del s Theorems

An Introduction to G  del s Theorems Author Peter Smith
ISBN-10 9781107328488
Year 2013-02-21
Pages
Language en
Publisher Cambridge University Press
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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 - extensively rewritten for its second edition - 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.

Reflections on Kurt G del

Reflections on Kurt G  del Author Hao Wang
ISBN-10 0262730871
Year 1990-03-14
Pages 336
Language en
Publisher MIT Press
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Newton/Descartes. Einstein/Gödel. The seventeenth century had its scientific andphilosophical geniuses. Why shouldn't ours have them as well? Kurt Gödel was indisputably one of thegreatest 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 ideasand their connection with grand themes in the history of mathematics and philosophy.The subjects hecovers include the completeness of elementary logic, the limits of formalization, the problem ofevidence, 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, whosereflections on his colleague also serve to clarify his own philosophical thoughts, distinguishes hisideas from those of Gödel's and on points of agreement develops Gödel's views further.The bookprovides a generous array of information on and interpretation of the two main phases of Gödel'scareer - the years between 1924 and 1939 at the University of Vienna, which were marked by intensemathematical creativity, and the period from 1940 to his death in 1978, during which he wasaffiliated with the Institute for Advanced Studies in Princeton, a time in which Gödel's interestssteadily shifted from questions of logic to metaphysics. And it also examines Gödel's relations withthe Vienna Circle, his philosophical differences with Carnap and Wittgenstein, the intimate andmutually fruitful friendship with Einstein, and the periodic bouts of depression for which Gödel washospitalized a number of times over the course of his life.Hao Wang is Professor of Logic at TheRockefeller University and author of scores of articles and several books on logic, computers, andphilosophy, including From Mathematics to Philosophy (extensively discussed with Gödel andcontaining contributions by him) and Beyond Analytic Philosophy: Doing Justice to What We Know (MITPress Bradford Books). He is currently preparing a companion volume, Conversations with Kurt Gödelwhich will concentrate on Gödel's unpublished ideas. A Bradford Book.

On G del

On G  del Author Jaakko Hintikka
ISBN-10 0534575951
Year 2000
Pages 74
Language en
Publisher Wadsworth Publishing Company
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This brief text assists students in understanding Godel's philosophy and thinking so that they can more fully engage in useful, intelligent class dialogue and improve their understanding of course content. Part of the "Wadsworth Philosophers Series," (which will eventually consist of approximately 100 titles, each focusing on a single "thinker" from ancient times to the present), ON G -DEL is written by a philosopher deeply versed in the philosophy of this key thinker. Like other books in the series, this concise book offers sufficient insight into the thinking of a notable philosopher better enabling students to engage in the reading and to discuss the material in class and on paper.

Godel s Incompleteness Theorems

Godel s Incompleteness Theorems Author Raymond M. Smullyan
ISBN-10 9780195364378
Year 1992-08-20
Pages 160
Language en
Publisher Oxford University Press
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Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.