Kurt Gödel and the Foundations of Mathematics
Kurt Gödel and the Foundations of Mathematics

Author: Matthias Baaz

Publisher: Cambridge University Press

Published: 2011-06-06

Total Pages: 541

ISBN-13: 1139498436

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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 Gödel and the Foundations of Mathematics
Kurt Gödel and the Foundations of Mathematics

Author: Matthias Baaz

Publisher:

Published: 2011

Total Pages: 515

ISBN-13: 9781139077378

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"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"--

After Gödel
After Gödel

Author: Richard L. Tieszen

Publisher: Oxford University Press

Published: 2011-05-05

Total Pages: 258

ISBN-13: 019960620X

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Richard Tieszen analyzes, develops, and defends the writings of Kurt Gödel (1906-1978) on the philosophy and foundations of mathematics and logic. Gödel's relation to the work of Plato, Leibniz, Husserl, and Kant is examined, and a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is proposed.

Kurt Gödel: Collected Works: Volume III
Kurt Gödel: Collected Works: Volume III

Author: Kurt Gödel

Publisher: Oxford University Press, USA

Published: 1986

Total Pages: 558

ISBN-13: 0195072553

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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.

Incompleteness
Incompleteness

Author: Rebecca Goldstein

Publisher: W. W. Norton & Company

Published: 2006-01-31

Total Pages: 299

ISBN-13: 0393327604

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

Kurt Godel and the Foundations of Mathematics
Kurt Godel and the Foundations of Mathematics

Author: Matthias Baaz

Publisher:

Published: 2011

Total Pages: 540

ISBN-13:

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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.

Kurt Gödel
Kurt Gödel

Author: Solomon Feferman

Publisher: Cambridge University Press

Published: 2010-04-19

Total Pages: 384

ISBN-13: 1139487752

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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.

Incompleteness: The Proof and Paradox of Kurt Gödel (Great Discoveries)
Incompleteness: The Proof and Paradox of Kurt Gödel (Great Discoveries)

Author: Rebecca Goldstein

Publisher: W. W. Norton & Company

Published: 2006-02-17

Total Pages: 299

ISBN-13: 0393242455

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"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.