Thinking About Godel And Turing
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Thinking About Godel And Turing
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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 2007
Thinking About Godel And Turing 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 2007 with Computers categories.
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as GAdel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of GAdel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity."
Thinking About G Del And Turing
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Author : Gregory J. Chaitin
language : en
Publisher: World Scientific
Release Date : 2007
Thinking About G Del And Turing 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 2007 with Mathematics categories.
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable ê number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gdel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of Gdel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity.
Thinking About Godel And Turing Essays On Complexity 1970 2007
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Author : Gregory J Chaitin
language : en
Publisher: World Scientific
Release Date : 2007-08-06
Thinking About Godel And Turing Essays On Complexity 1970 2007 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 2007-08-06 with Computers categories.
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable Ω number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gödel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of Gödel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity.
Thinking On The Web
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Author : H. Peter Alesso
language : en
Publisher: Wiley-Interscience
Release Date : 2006-09-12
Thinking On The Web written by H. Peter Alesso and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-12 with Computers categories.
What Is Thinking? What is Turing's Test? What is Gödel's Undecidability Theorem? How is Berners-Lee's Semantic Web logic going to overcome paradoxes and complexity to produce machine processing on the Web? Thinking on the Web draws from the contributions of Tim Berners-Lee (What is solvable on the Web?), Kurt Gödel (What is decidable?), and Alan Turing (What is machine intelligence?) to evaluate how much "intelligence" can be projected onto the Web. The authors offer both abstract and practical perspectives to delineate the opportunities and challenges of a "smarter" Web through a threaded series of vignettes and a thorough review of Semantic Web development.
Thinking On The Web
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Author : H. Peter Alesso
language : en
Publisher: Wiley-Interscience
Release Date : 2008-12-03
Thinking On The Web written by H. Peter Alesso and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-03 with Computers categories.
What Is Thinking? What is Turing's Test? What is Gödel's Undecidability Theorem? How is Berners-Lee's Semantic Web logic going to overcome paradoxes and complexity to produce machine processing on the Web? Thinking on the Web draws from the contributions of Tim Berners-Lee (What is solvable on the Web?), Kurt Gödel (What is decidable?), and Alan Turing (What is machine intelligence?) to evaluate how much "intelligence" can be projected onto the Web. The authors offer both abstract and practical perspectives to delineate the opportunities and challenges of a "smarter" Web through a threaded series of vignettes and a thorough review of Semantic Web development.
Computability
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Author : B. Jack Copeland
language : en
Publisher: MIT Press
Release Date : 2015-01-30
Computability written by B. Jack Copeland and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-30 with Computers categories.
Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics. Contributors Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani
Thinking
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Author : Corinne Brumbaugh
language : en
Publisher: Xlibris Corporation
Release Date : 2010-10-30
Thinking written by Corinne Brumbaugh and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-30 with Religion categories.
The Prehistory Of Mathematical Structuralism
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Author : Erich H. Reck
language : en
Publisher: Oxford University Press
Release Date : 2020
The Prehistory Of Mathematical Structuralism written by Erich H. Reck 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 2020 with Mathematics categories.
This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism.
Kurt G Del And The Foundations Of Mathematics
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Author : Matthias Baaz
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-06
Kurt G Del And The Foundations Of Mathematics written by Matthias Baaz 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 2011-06-06 with Mathematics categories.
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.
Limits Of Mathematical Modeling In The Social Sciences The The Significance Of Godel S Incompleteness Phenomenon
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Author : Francisco Antonio Doria
language : en
Publisher: World Scientific
Release Date : 2017-05-30
Limits Of Mathematical Modeling In The Social Sciences The The Significance Of Godel S Incompleteness Phenomenon written by Francisco Antonio Doria and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-30 with Social Science categories.
Current mathematical models are notoriously unreliable in describing the time evolution of unexpected social phenomena, from financial crashes to revolution. Can such events be forecast? Can we compute probabilities about them? Can we model them? This book investigates and attempts to answer these questions through Gödel's two incompleteness theorems, and in doing so demonstrates how influential Gödel is in modern logical and mathematical thinking. Many mathematical models are applied to economics and social theory, while Gödel's theorems are able to predict their limitations for more accurate analysis and understanding of national and international events.This unique discussion is written for graduate level mathematicians applying their research to the social sciences, including economics, social studies and philosophy, and also for formal logicians and philosophers of science.