Kurt Gödel And The Foundations Of Mathematics

Author : Matthias Baaz,Christos H. Papadimitriou,Hilary W. Putnam,Dana S. Scott,Charles L. Harper, Jr
Publisher : Cambridge University Press
Page : 541 pages
File Size : 49,8 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9781139498432

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Kurt Gödel and the Foundations of Mathematics by Matthias Baaz,Christos H. Papadimitriou,Hilary W. Putnam,Dana S. Scott,Charles L. Harper, Jr Pdf

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.

Author : Jack John Bulloff,Thomas Campell Holyoke,S.W. Hahn
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642867453

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Foundations of Mathematics by Jack John Bulloff,Thomas Campell Holyoke,S.W. Hahn Pdf

Dr. KURT GODEL'S sixtieth birthday (April 28, 1966) and the thirty fifth anniversary of the publication of his theorems on undecidability were celebrated during the 75th Anniversary Meeting of the Ohio Ac ademy of Science at The Ohio State University, Columbus, on April 22, 1966. The celebration took the form of a Festschrift Symposium on a theme supported by the late Director of The Institute for Advanced Study at Princeton, New Jersey, Dr. J. ROBERT OPPENHEIMER: "Logic, and Its Relations to Mathematics, Natural Science, and Philosophy." The symposium also celebrated the founding of Section L (Mathematical Sciences) of the Ohio Academy of Science. Salutations to Dr. GODEL were followed by the reading of papers by S. F. BARKER, H. B. CURRY, H. RUBIN, G. E. SACKS, and G. TAKEUTI, and by the announcement of in-absentia papers contributed in honor of Dr. GODEL by A. LEVY, B. MELTZER, R. M. SOLOVAY, and E. WETTE. A short discussion of "The II Beyond Godel's I" concluded the session.

Author : Matthias Baaz,Christos H. Papadimitriou,Hilary W. Putnam,Dana S. Scott
Publisher : Unknown
Page : 515 pages
File Size : 44,7 Mb
Release : 2011
Category : Gödel's theorem
ISBN : 1139077376

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Kurt Gödel and the Foundations of Mathematics by Matthias Baaz,Christos H. Papadimitriou,Hilary W. Putnam,Dana S. Scott Pdf

"This volume commemorates the life, work, and foundational views of Kurt Gödel (1906-1978), 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"--

Author : Maria Hämeen-Anttila,Jan von Plato
Publisher : Springer Nature
Page : 327 pages
File Size : 48,9 Mb
Release : 2023-08-18
Category : Mathematics
ISBN : 9783031378751

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Kurt Gödel: Results on Foundations by Maria Hämeen-Anttila,Jan von Plato Pdf

Kurt Gödel (1906-1978) gained world-wide fame by his incompleteness theorem of 1931. Later, he set as his aim to solve what are known as Hilbert's first and second problems, namely Cantor's continuum hypothesis about the cardinality of real numbers, and secondly the consistency of the theory of real numbers and functions. By 1940, he was halfway through the first problem, in what was his last published result in logic and foundations. His intense attempts thereafter at solving these two problems have remained behind the veil of a forgotten German shorthand he used in all of his writing. Results on Foundations is a set of four shorthand notebooks written in 1940-42 that collect results Gödel considered finished. Its main topic is set theory in which Gödel anticipated several decades of development. Secondly, Gödel completed his 1933 program of establishing the connections between intuitionistic and modal logic, by methods and results that today are at the same time new and 80 years old. The present edition of Gödel's four notebooks encompasses the 368 numbered pages and 126 numbered theorems of the Results on Foundations, together with a list of 74 problems on set theory Gödel prepared in 1946, and a list of an unknown date titled "The grand program of my research in ca. hundred questions.''

Author : Matthias Baaz
Publisher : Unknown
Page : 540 pages
File Size : 53,9 Mb
Release : 2011
Category : Electronic
ISBN : OCLC:1137347356

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Kurt Godel and the Foundations of Mathematics by Matthias Baaz Pdf

This volume commemorates the life, work and foundational views of Kurt Gödel (1906-1978), 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.

Author : Petr Hájek
Publisher : Cambridge University Press
Page : 331 pages
File Size : 52,5 Mb
Release : 2017-03-02
Category : Mathematics
ISBN : 9781107168022

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Gödel '96 by Petr Hájek Pdf

The proceedings of the conference 'Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Gödel's Legacy', held in Brno, Czech Republic, on the 90th anniversary of Gödel's birth. The papers in this volume cover the wide range of topics Gödel's work touched, and affirm its continuing importance.

Author : Solomon Feferman,Charles Parsons,Stephen G. Simpson
Publisher : Cambridge University Press
Page : 384 pages
File Size : 53,9 Mb
Release : 2010-04-19
Category : Mathematics
ISBN : 9781139487757

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Kurt Gödel by Solomon Feferman,Charles Parsons,Stephen G. Simpson Pdf

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.

Author : Rebecca Goldstein
Publisher : W. W. Norton & Company
Page : 224 pages
File Size : 45,9 Mb
Release : 2006-02-17
Category : Biography & Autobiography
ISBN : 9780393242454

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Incompleteness: The Proof and Paradox of Kurt Gödel (Great Discoveries) by Rebecca Goldstein Pdf

"A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven Pinker Probing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

Author : Rebecca Goldstein
Publisher : W. W. Norton & Company
Page : 299 pages
File Size : 52,9 Mb
Release : 2006-01-31
Category : Biography & Autobiography
ISBN : 9780393327601

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Incompleteness by Rebecca Goldstein Pdf

"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

Author : Jan von Plato
Publisher : Springer Nature
Page : 221 pages
File Size : 47,5 Mb
Release : 2022-05-06
Category : Mathematics
ISBN : 9783030971342

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Chapters from Gödel’s Unfinished Book on Foundational Research in Mathematics by Jan von Plato Pdf

This volume contains English translations of Gödel's chapters on logicism and the antinomies and on the calculi of pure logic, as well as outlines for a chapter on metamathematics. It also comprises most of his reading notes. This book is a testimony to Gödel's understanding of the situation of foundational research in mathematics after his great discovery, the incompleteness theorem of 1931. It is also a source for his views on his logical predecessors, from Leibniz, Frege, and Russell to his own times. Gödel's "own book on foundations," as he called it, is essential reading for logicians and philosophers interested in foundations. Furthermore, it opens a new chapter to the life and achievement of one of the icons of 20th century science and philosophy.

Author : S.G. Shanker
Publisher : Routledge
Page : 272 pages
File Size : 48,8 Mb
Release : 2012-08-21
Category : Philosophy
ISBN : 9781134947973

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Godel's Theorem in Focus by S.G. Shanker Pdf

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.

Author : Hao Wang
Publisher : MIT Press
Page : 366 pages
File Size : 48,8 Mb
Release : 1990-03-14
Category : Philosophy
ISBN : 0262730871

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Reflections on Kurt Gödel by Hao Wang Pdf

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.

Author : Ludwig Wittgenstein
Publisher : Unknown
Page : 204 pages
File Size : 43,6 Mb
Release : 1972
Category : Mathematics
ISBN : 0262730170

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Bemerkungen Über Die Grundlagen Der Mathematik by Ludwig Wittgenstein Pdf

Author : Ernest Nagel,James R. Newman
Publisher : Lulu.com
Page : 132 pages
File Size : 44,7 Mb
Release : 2018-09-14
Category : Gödel's theorem
ISBN : 9780359079261

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Godel's Proof by Ernest Nagel,James R. Newman Pdf

In 1931 Kurt Gödel published his paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Gödel’s paper challenged certain basic assumptions underlying much research in mathematics and logic. However, few scholars were unable to understand Gödel’s ideas. Ernest Nagel and James Newman provide a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery.

Author : Petr Hájek
Publisher : A K Peters/CRC Press
Page : 336 pages
File Size : 45,9 Mb
Release : 2001-03-26
Category : Mathematics
ISBN : 1568811535

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Gödel 96: Logical Foundations of Mathematics, Computer Science, and Physics by Petr Hájek Pdf

This volume contains the proceedings of the conference Logical Foundations of Mathematics, Computer Science, and Physics-Kurt Gödel's Legacy, held in Brno, Czech Republic on the 90th anniversary of his birth. The wide and continuing importance of Gödel s work in the logical foundations of mathematics, computer science, and physics is confirmed by the broad range of speakers who participated in making this gathering a scientific event.