Godel S Incompleteness Theorems
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Godel S Incompleteness Theorems
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Author : Raymond M. Smullyan
language : en
Publisher: Oxford University Press
Release Date : 1992-08-20
Godel S Incompleteness Theorems written by Raymond M. Smullyan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-20 with Mathematics categories.
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.
G Del S Theorem
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Author : Torkel Franzén
language : en
Publisher: CRC Press
Release Date : 2005-06-06
G Del S Theorem written by Torkel Franzén and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-06 with Mathematics categories.
"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
Godel S Proof
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Author : Ernest Nagel
language : en
Publisher: Lulu.com
Release Date : 2018-09-14
Godel S Proof written by Ernest Nagel and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-14 with Gödel's theorem categories.
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.
Incompleteness The Proof And Paradox Of Kurt G Del Great Discoveries
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Author : Rebecca Goldstein
language : en
Publisher: W. W. Norton & Company
Release Date : 2006-02-17
Incompleteness The Proof And Paradox Of Kurt G Del Great Discoveries written by Rebecca Goldstein and has been published by W. W. Norton & Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-17 with Biography & Autobiography categories.
"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.
Incompleteness The Proof And Paradox Of Kurt G Del Great Discoveries
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Author : Rebecca Goldstein
language : en
Publisher: W. W. Norton & Company
Release Date : 2006-02-17
Incompleteness The Proof And Paradox Of Kurt G Del Great Discoveries written by Rebecca Goldstein and has been published by W. W. Norton & Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-17 with Biography & Autobiography categories.
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.
Godel S Theorem In Focus
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Author : S.G. Shanker
language : en
Publisher: Taylor & Francis
Release Date : 2012-08-21
Godel S Theorem In Focus written by S.G. Shanker and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-21 with Philosophy categories.
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 S Incompleteness Theorems
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Author : Juliette Kennedy
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-31
G Del S Incompleteness Theorems written by Juliette Kennedy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Philosophy categories.
This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a. It considers the main ingredients of Gödel's proof: arithmetization, strong representability, and the Fixed Point Theorem in a layered fashion, returning to their various aspects: semantic, syntactic, computational, philosophical and mathematical, as the topic arises. It samples some of the most important proofs of the Incompleteness Theorems, e.g. due to Kuratowski, Smullyan and Robinson, as well as newer proofs, also of other independent statements, due to H. Friedman, Weiermann and Paris-Harrington. It examines the question whether the incompleteness of e.g. Peano Arithmetic gives immediately the undecidability of the Entscheidungsproblem, as Kripke has recently argued. It considers set-theoretical incompleteness, and finally considers some of the philosophical consequences considered in the literature.
Recursive Functions And Metamathematics
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Author : Roman Murawski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Recursive Functions And Metamathematics written by Roman Murawski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Philosophy categories.
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
An Introduction To G Del S Theorems
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Author : Peter Smith
language : en
Publisher: Cambridge University Press
Release Date : 2007-07-26
An Introduction To G Del S Theorems written by Peter Smith and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-26 with Mathematics categories.
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
Metamathematics Machines And G Del S Proof
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Author : N. Shankar
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-30
Metamathematics Machines And G Del S Proof written by N. Shankar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-30 with Computers categories.
Describes the use of computer programs to check several proofs in the foundations of mathematics.