Incompleteness
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Incompleteness
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Author : Rebecca Goldstein
language : en
Publisher: W. W. Norton & Company
Release Date : 2006-01-31
Incompleteness 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 2006-01-31 with Biography & Autobiography categories.
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
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
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Author : Rebecca Goldstein
language : en
Publisher: W. W. Norton & Company
Release Date : 2005
Incompleteness 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 2005 with Biography & Autobiography categories.
Considered the 20th century's greatest mathematician, Kurt Godel is the subject of this lucid and accessible study, which explains the significance of his theorems and the remarkable vision behind them, while bringing this eccentric, tortured genius and his world to life.
Introduction To Incompleteness
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Author : Serafim Batzoglou
language : en
Publisher: Springer Nature
Release Date : 2024-08-30
Introduction To Incompleteness written by Serafim Batzoglou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-30 with Mathematics categories.
Incompleteness is a fascinating phenomenon at the intersection of mathematical foundations, computer science, and epistemology that places a limit on what is provable. However, despite its importance, it is often overlooked in the mathematics curricula because it is difficult to teach. This book aims to help bridge this pedagogical gap by providing a complete and accessible technical exposition of incompleteness for a wide audience. The author accomplishes this by making conceptually difficult proofs more approachable by providing intuitive explanations of the main ideas. Care is taken to emphasize the different layers of the mathematical argument – the layer within and the metalayer about an axiomatic system. Structurally, the book efficiently examines key results and arrives at some of the most interesting concepts as quickly as possible. It begins with Gödel's incompleteness theorems before continuing on to challenging concepts in the arithmetized completeness theorem, the Paris-Harrington theorem, and the independence of the continuum hypothesis. Other topics covered include the Lucas-Penrose arguments, ordinals and cardinals, and axiomatic set theory. Additionally, the author’s coverage of forcing is a notable addition to the existing literature. Introduction to Incompleteness will be of interest to researchers, students, and instructors looking for a resource to teach this topic. It may also be suitable for self-study. Knowledge of undergraduate-level theoretical mathematics or computer science is required, as well as a familiarity with abstract proofs.
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 Incompleteness Theorems
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Author : Dirk W. Hoffmann
language : en
Publisher: Springer Nature
Release Date : 2024-08-30
G Del S Incompleteness Theorems written by Dirk W. Hoffmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-30 with Mathematics categories.
In 1931, the mysterious-sounding article "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I" shook the mathematical world. In this article, Kurt Gödel proved two incompleteness theorems that have fundamentally changed our view of mathematics. Gödel's theorems manifest that the concept of truth and the concept of provability cannot coincide. Since their discovery, the incompleteness theorems have attracted much attention, and a flood of articles and books have been devoted to their striking consequences. For good reasons, however, hardly any work deals with Gödel's article in its original form: His complex lines of thought described with meticulous precision, the many definitions and theorems, and the now largely outdated notation turn Gödel's historical masterpiece into a difficult read. This book explores Gödel's original proof in detail. All individual steps are carefully explained and illustrated with numerous examples. However, this book is more than just an annotated version of the historical article, as the proper understanding of Gödel's work requires a solid grasp of history. Thus, numerous excursions take the reader back to the beginning of the twentieth century. It was the time when mathematics experienced one of its greatest crises, when type theory and axiomatic set theory were taking shape, and Hilbert's formalistic logic and Brouwer's intuitionistic mathematics were openly confronting each other. This book is the revised translation of the second edition of the author's German language book "Die Gödel'schen Unvollständigkeitssätze".
The Incompleteness Phenomenon
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Author : Martin Goldstern
language : en
Publisher: CRC Press
Release Date : 2018-10-08
The Incompleteness Phenomenon written by Martin Goldstern and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Mathematics categories.
This introduction to mathematical logic takes Gödel's incompleteness theorem as a starting point. It goes beyond a standard text book and should interest everyone from mathematicians to philosophers and general readers who wish to understand the foundations and limitations of modern mathematics.
Information Theoretic Incompleteness
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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 1992
Information Theoretic Incompleteness written by Gregory J. Chaitin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computers categories.
In this mathematical autobiography, Gregory Chaitin presents a technical survey of his work and a nontechnical discussion of its significance. The volume is an essential companion to the earlier collection of Chaitin's papers Information, Randomness and Incompleteness, also published by World Scientific.The technical survey contains many new results, including a detailed discussion of LISP program size and new versions of Chaitin's most fundamental information-theoretic incompleteness theorems. The nontechnical part includes the lecture given by Chaitin in G?del's classroom at the University of Vienna, a transcript of a BBC TV interview, and articles from New Scientist, La Recherche, and the Mathematical Intelligencer.
Incompleteness Mobility And Conviviality
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Author : Francis Nyamnjoh
language : en
Publisher: African Books Collective
Release Date : 2023-12-05
Incompleteness Mobility And Conviviality written by Francis Nyamnjoh and has been published by African Books Collective this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-05 with Social Science categories.
Central to the Jensen Memorial Lectures 2023 is an invitation to take incompleteness seriously in how we imagine, relate to and seek to understand a world in perpetual motion. Despite our instinct for and obsession with completeness, we are constantly reminded that the sooner one recognises and provides for incompleteness and the conviviality it inspires as the normal way of being, the better we are for it. Fluidity, compositeness and the capacity to be present in multiple places and forms simultaneously in whole or in fragments are core characteristics of reality and ontology of incompleteness. How would we frame our curiosities and conversations about processes, relationships and phenomena with an understanding of the universality of incompleteness and mobility? West and Central Africa, for example, are regions where it is commonplace to embrace and celebrate incompleteness in nature, the suprasensory, human beings, human actions, human inventions and human achievements. The lectures indicate how we could draw inspiration in this regard to inform current clamours for decolonisation and the growing ambivalence about rapid advances in digital technologies (artificial intelligence (AI) in particular), as well as with twenty-first century concerns about migrants and strangers knocking at the doors of opportunities we feel more entitled to as bona fide citizens and insiders. The lectures draw on the writings of Amos Tutuola as well as from popular ideas of personhood and agency in Africa, to make a case for sidestepped and silenced traditions of knowledge. They highlight Africa’s possibilities, prospects and emergent capacities for being and becoming in tune with the continent’s creativity and imagination. They speak to the nimble-footed flexible-minded frontier African at the crossroads and junctions of myriad encounters, facilitating creative conversations and challenging regressive logics of exclusionary claims and articulation of identities and achievements. The traditions of knowledge discussed in these lectures do not only speak to Africans, but to the world, as the philosophies explored have universal application. “The crucial anthropological question of relationality and othering is at the heart of this original and enlightening book. Nyamnjoh cautions the missionaries of decoloniality against the risk of substituting one illusion of completeness with another. For him, incompleteness is the basis of any healthy exchange. He therefore recommends embracing the universality of incompleteness in motion and taking seriously an ancestral tradition of self-extension through creative imagination in this anxious age of artificial intelligence. Forcefully argued and abundantly substantiated – with finesse and laughter that run through it – this book will be a milestone by making us rediscover the demands and the magic of fieldwork.” Prof. Dr. Mamadou Diawara, Goethe University, Frankfurt/Main Frobenius-Institut, Frankfurt/Main Point Sud, Bamako, Mali
Incompleteness At Every Turn
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Author : Rishabh Bhatt
language : en
Publisher: Rishabh Bhatt
Release Date : 2024-02-13
Incompleteness At Every Turn written by Rishabh Bhatt and has been published by Rishabh Bhatt this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-13 with Architecture categories.
"Incompleteness At Every Turn" This book is a journey of incompleteness in which every story is wandering somewhere in search of its completeness. Ask yourself the answer to each story and see what answer your heart gives. I believe you will always get a positive answer. Whenever negativity develops inside us, our desires overpower us at that moment. We are not able to understand the difference between right and wrong. But in the meantime, if we find a small pitiful scene, then the unit of positivity within us gets awakened. Believe me, this unit of positivity is the identity of this human life. We have to fight the incompleteness within us and become thirsty and search for the well. If we reach near this well, our thirst will be quenched for a few moments by the water of that well. Life also has the same relation with incompleteness. We try to complete what we know is incomplete. After it is complete, some more incompleteness become visible. Just like drinking water from a well once quenches thirst only for a few moments. After some time, we feel thirsty again and we need water again. This same cycle continues in our lives between incompleteness and life. Therefore, we should always keep moving forward while fighting this.