Incompleteness The Proof And Paradox Of Kurt G Del Great Discoveries
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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.
G Del S Proof
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Author : Ernest Nagel
language : en
Publisher: Psychology Press
Release Date : 1989
G Del S Proof written by Ernest Nagel and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Gödel's theorem categories.
In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proofby Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Journey To The Edge Of Reason
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Author : Stephen Budiansky
language : en
Publisher: Oxford University Press
Release Date : 2021
Journey To The Edge Of Reason written by Stephen Budiansky 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 2021 with Biography & Autobiography categories.
A remarkable account of the brilliant, troubled mathematician and philosopher Kurt Gödel. From his famous Incompleteness Theorem, which shook the foundations of mathematical truth, to his perilous escape from Nazi Vienna, this book weaves together his creative genius, mental illness, and idealism in the face of adversity.
Principia Mathematica
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Author : Alfred North Whitehead
language : en
Publisher: Cambridge University Press
Release Date : 1927
Principia Mathematica written by Alfred North Whitehead 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 1927 with Mathematics categories.
The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.
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
Infinity And The Mind
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Author : Rudy Rucker
language : en
Publisher: Bantam Books
Release Date : 1983-01-01
Infinity And The Mind written by Rudy Rucker and has been published by Bantam Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Philosophy categories.
The book contains popular expositions (accessible to readers with no more than a high school mathematics background) on the mathematical theory of infinity, and a number of related topics. These include G?del's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt G?del.An appendix contains one of the few popular expositions on set theory research on what are known as "strong axioms of infinity."
Philosophy In Reality
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Author : Joseph E. Brenner
language : en
Publisher: Springer Nature
Release Date : 2020-11-30
Philosophy In Reality written by Joseph E. Brenner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-30 with Science categories.
Philosophy in Reality offers a new vision of the relation between science and philosophy in the framework of a non-propositional logic of real processes, grounded in the physics of the real world. This logical system is based on the work of the Franco-Romanian thinker Stéphane Lupasco (1900-1988), previously presented by Joseph Brenner in the book Logic in Reality (Springer, 2008). The present book was inspired in part by the ancient Chinese Book of Changes (I Ching) and its scientific-philosophical discussion of change. The emphasis in Philosophy in Reality is on the recovery of dialectics and semantics from reductionist applications and their incorporation into a new synthetic paradigm for knowledge. Through an original re-interpretation of both classical and modern Western thought, this book addresses philosophical issues in scientific fields as well as long-standing conceptual problems such as the origin, nature and role of meaning, the unity of knowledge and the origin of morality. In a rigorous transdisciplinary manner, it discusses foundational and current issues in the physical sciences - mathematics, information, communication and systems theory and their implications for philosophy. The same framework is applied to problems of the origins of society, the transformation of reality by human subjects, and the emergence of a global, sustainable information society. In summary, Philosophy in Reality provides a wealth of new perspectives and references, supporting research by both philosophers and physical and social scientists concerned with the many facets of reality.
On Formally Undecidable Propositions Of Principia Mathematica And Related Systems
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Author : Kurt Gödel
language : en
Publisher: Courier Corporation
Release Date : 1992-01-01
On Formally Undecidable Propositions Of Principia Mathematica And Related Systems written by Kurt Gödel and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument. This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.
From Mathematics To Philosophy Routledge Revivals
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Author : Hao Wang
language : en
Publisher: Routledge
Release Date : 2016-06-10
From Mathematics To Philosophy Routledge Revivals written by Hao Wang and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-10 with Philosophy categories.
First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge.