Incompleteness The Proof and Paradox of Kurt G del Great Discoveries

Incompleteness  The Proof and Paradox of Kurt G  del  Great Discoveries Author Rebecca Goldstein
ISBN-10 9780393327601
Release 2006-02-17
Pages 296
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A portrait of the eminent twentieth-century mathematician discusses his theorem of incompleteness, relationships with such contemporaries as Albert Einstein, and untimely death as a result of mental instability and self-starvation.



Kurt G del Collected Works Volume I

Kurt G  del  Collected Works  Volume I Author Kurt Gödel
ISBN-10 0195039645
Release 1986
Pages 490
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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to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass.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.



Kurt G del Collected Works Volume III

Kurt G  del  Collected Works  Volume III Author Kurt Gödel
ISBN-10 0195072553
Release 1995-05-25
Pages 532
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"Anyone interested in the life and work of Kurt Gödel, or in the history of mathematical logic in this century, is indebted to all of the contributors to this volume for the care with which they have presented Gödel's work. They have succeeded in using their own expertise to elucidate both the nature and significance of what Gödel and, in turn, mathematical logic have accomplished." --Isis (on volume I). The third volume brings togetherGödels unpublished essays and lectures.



Godel

Godel Author John L. Casti
ISBN-10 0786747609
Release 2009-04-21
Pages 224
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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.



Simply G del

Simply G  del Author Richard Tieszen
ISBN-10 9781943657148
Release 2017-04-11
Pages 164
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Kurt Gödel (1906–1978) was born in Austria-Hungary (now the Czech Republic) and grew up in an ethnic German family. As a student, he excelled in languages and mathematics, mastering university-level math while still in high school. He received his doctorate from the University of Vienna at the age of 24 and, a year later, published the pioneering theorems on which his fame rests. In 1939, with the rise of Nazism, Gödel and his wife settled in the U.S., where he continued his groundbreaking work at the Institute for Advanced Study (IAS) in Princeton and became a close friend of Albert Einstein’s. In Simply Gödel, Richard Tieszen traces Gödel’s life and career, from his early years in tumultuous, culturally rich Vienna to his many brilliant achievements as a member of IAS, as well as his repeated battles with mental illness. In discussing Gödel’s ideas, Tieszen not only provides an accessible explanation of the incompleteness theorems, but explores some of his lesser-known writings, including his thoughts on time travel and his proof of the existence of God. With clarity and sympathy, Simply Gödel brings to life Gödel’s fascinating personal and intellectual journey and conveys the lasting impact of his work on our modern world.



Reflections on Kurt G del

Reflections on Kurt G  del Author Hao Wang
ISBN-10 0262730871
Release 1990-03-14
Pages 336
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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.



Godel s Theorem in Focus

Godel s Theorem in Focus Author S.G. Shanker
ISBN-10 9781134947973
Release 2012-08-21
Pages 272
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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.



Kurt G del

Kurt G  del Author Kurt Gödel
ISBN-10 3764353104
Release 1995-12-01
Pages 235
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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).



G del Escher Bach

G  del  Escher  Bach Author Douglas R. Hofstadter
ISBN-10 0140179976
Release 1979
Pages 777
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G del Escher Bach has been writing in one form or another for most of life. You can find so many inspiration from G del Escher Bach also informative, and entertaining. Click DOWNLOAD or Read Online button to get full G del Escher Bach book for free.



Kurt G del

Kurt G  del Author Solomon Feferman
ISBN-10 9781139487757
Release 2010-04-19
Pages
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Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.



Interpreting Godel

Interpreting Godel Author Juliette Kennedy
ISBN-10 9781107002661
Release 2014-08-21
Pages 288
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In this groundbreaking volume, leading philosophers and mathematicians explore Kurt Gödel's work on the foundations and philosophy of mathematics.



An Introduction to G del s Theorems

An Introduction to G  del s Theorems Author Peter Smith
ISBN-10 9781107328488
Release 2013-02-21
Pages
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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.



Kurt G del Collected Works

Kurt G  del  Collected Works Author Kurt Gödel
ISBN-10 9780191003776
Release 2014-01-09
Pages 692
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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. 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
Release 1967
Pages 664
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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 and the Foundations of Mathematics

Kurt G  del and the Foundations of Mathematics Author Matthias Baaz
ISBN-10 9781139498432
Release 2011-06-06
Pages
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This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.



Kurt G del Collected Works Volume II

Kurt G  del  Collected Works  Volume II Author Kurt G?del
ISBN-10 0195039726
Release 2003
Pages 407
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This second volume of a comprehensive edition of Kurt Godel's works collects the remainder of his published work, covering the period 1938-1974. (Volume I included all of his publications from 1929-1936). Each article or closely related group of articles is preceded by an introductory note that elucidates it and places it in historical context.



Godel s Incompleteness Theorems

Godel s Incompleteness Theorems Author Raymond M. Smullyan
ISBN-10 9780195364378
Release 1992-08-20
Pages 160
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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.