Download or read book Kurt G del and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to G del s Theorems written by Peter Smith and published by Cambridge University Press. This book was released on 2007-07-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
Download or read book G del s Proof written by Ernest Nagel and published by Psychology Press. This book was released on 1989 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Godel s Theorem in Focus written by S.G. Shanker and published by Routledge. This book was released on 2012-08-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Incompleteness written by Rebecca Goldstein and published by W. W. Norton & Company. This book was released on 2006-01-31 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Download or read book Journey to the Edge of Reason written by Stephen Budiansky and published by Oxford University Press. This book was released on 2021-05-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A remarkable account of Kurt Gödel, weaving together creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval. At age 24, a brilliant Austrian-born mathematician published a mathematical result that shook the world. Nearly a hundred years after Kurt Gödel's famous 1931 paper "On Formally Undecidable Propositions" appeared, his proof that every mathematical system must contain propositions that are true - yet never provable within that system - continues to pose profound questions for mathematics, philosophy, computer science, and artificial intelligence. His close friend Albert Einstein, with whom he would walk home every day from Princeton's famous Institute for Advanced Study, called him "the greatest logician since Aristotle." He was also a man who felt profoundly out of place in his time, rejecting the entire current of 20th century philosophical thought in his belief that mathematical truths existed independent of the human mind, and beset by personal demons of anxiety and paranoid delusions that would ultimately lead to his tragic end from self-starvation. Drawing on previously unpublished letters, diaries, and medical records, Journey to the Edge of Reason offers the most complete portrait yet of the life of one of the 20th century's greatest thinkers. Stephen Budiansky's account brings to life the remarkable world of philosophical and mathematical creativity of pre-war Vienna, and documents how it was barbarically extinguished by the Nazis. He charts Gödel's own hair's-breadth escape from Nazi Germany to the scholarly idyll of Princeton; and the complex, gently humorous, sensitive, and tormented inner life of this iconic but previously enigmatic giant of modern science. Weaving together Gödel's public and private lives, this is a tale of creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval.
Download or read book Kurt G del Philosopher Scientist written by Collectif and published by Presses universitaires de Provence. This book was released on 2021-10-15 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the essays that are collected in this volume are the outcome of talks given at the international conference Kurt Gödel Philosopher: From Logic to Cosmology that was held in Aix-en-Provence (France) in summer 2013. In addition many of the authors belong to a group of scientists who have contributed to a project with the same title under the direction of Gabriella Crocco, to a larger or lesser degree.For this reason the volume represents more than just a collection of essays on Gödel. It is in fact the product of a long and enduring international collaboration. There was a group in France that worked on the transcriptions of the Max Phil and its interpretations. It consisted of: Mark van Atten, Eric Audureau, Julien Bertrand, Paola Cantù, Gabriella Crocco, Eva-Maria Engelen, Amélie Mertens and Robin Rollinger. And then there was a group of experts in Gödel studies and logic to whom the results of this ongoing research were presented and with whom they were discussed every now and then. This group consisted of: John W. Dawson Jr. and Cheryl Dawson, Akihiro Kanamori, Per Martin-Löf, Göran Sundholm and Richard Tieszen. For the conference the group of experts was enlarged by Eberhard Knobloch and Massimo Mugnai as authorities on Leibniz – to whom Gödel refers quite often – and by several Gödel-enthusiasts who gave us great pleasure by reacting to our call for papers. The transcriptions of notebooks IX, X, XI, and XII were only made accessible to the experts for their lectures at the conference even though not all of the transcriptions are yet ready for circulation or for publication.
Download or read book Computability written by B. Jack Copeland and published by MIT Press. This book was released on 2013-06-07 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.ContributorsScott 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
Download or read book The Evolutionary Foundations of Economics written by Kurt Dopfer and published by Cambridge University Press. This book was released on 2005-05-23 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is widely recognised that mainstream economics has failed to translate micro consistently into macro economics and to provide endogenous explanations for the continual changes in the economic system. Since the early 1980s, a growing number of economists have been trying to provide answers to these two key questions by applying an evolutionary approach. This new departure has yielded a rich literature with enormous variety, but the unifying principles connecting the various ideas and views presented are, as yet, not apparent. This 2005 volume brings together fifteen original articles from scholars - each of whom has made a significant contribution to the field - in their common effort to reconstruct economics as an evolutionary science. Using meso economics as an analytical entity to bridge micro and macro economics as well as static and dynamic realms, a unified economic theory emerges.
Download or read book On Formally Undecidable Propositions of Principia Mathematica and Related Systems written by Kurt Gödel and published by Courier Corporation. This book was released on 2012-05-24 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Download or read book The Foundations of Computability Theory written by Borut Robič and published by Springer Nature. This book was released on 2020-11-13 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism. In Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability. In Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.
Download or read book Philosophical Approaches to the Foundations of Logic and Mathematics written by Marcin Trepczyński and published by BRILL. This book was released on 2021-01-25 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophical Approaches to the Foundations of Logic and Mathematics consists of eleven articles addressing various aspects of the "roots" of logic and mathematics, their basic concepts and the mechanisms that work in the practice of their use.
Download or read book The Behavioral Foundations of Public Policy written by Eldar Shafir and published by Princeton University Press. This book was released on 2013-01-10 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: An interdisciplinary look at the behavioral roots of public policy from the field's leading experts In recent years, remarkable progress has been made in behavioral research on a wide variety of topics, from behavioral finance, labor contracts, philanthropy, and the analysis of savings and poverty, to eyewitness identification and sentencing decisions, racism, sexism, health behaviors, and voting. Research findings have often been strikingly counterintuitive, with serious implications for public policymaking. In this book, leading experts in psychology, decision research, policy analysis, economics, political science, law, medicine, and philosophy explore major trends, principles, and general insights about human behavior in policy-relevant settings. Their work provides a deeper understanding of the many drivers—cognitive, social, perceptual, motivational, and emotional—that guide behaviors in everyday settings. They give depth and insight into the methods of behavioral research, and highlight how this knowledge might influence the implementation of public policy for the improvement of society. This collection examines the policy relevance of behavioral science to our social and political lives, to issues ranging from health, environment, and nutrition, to dispute resolution, implicit racism, and false convictions. The book illuminates the relationship between behavioral findings and economic analyses, and calls attention to what policymakers might learn from this vast body of groundbreaking work. Wide-ranging investigation into people's motivations, abilities, attitudes, and perceptions finds that they differ in profound ways from what is typically assumed. The result is that public policy acquires even greater significance, since rather than merely facilitating the conduct of human affairs, policy actually shapes their trajectory. The first interdisciplinary look at behaviorally informed policymaking Leading behavioral experts across the social sciences consider important policy problems A compendium of behavioral findings and their application to relevant policy domains
Download or read book Logical Dilemmas written by John Dawson and published by A K Peters/CRC Press. This book was released on 2005-06-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative biography of Kurt Goedel relates the life of this most important logician of our time to the development of the field. Goedel's seminal achievements that changed the perception and foundations of mathematics are explained in the context of his life from the turn of the century Austria to the Institute for Advanced Study in Princeton.
Download or read book The Michigan Business School Annual Report written by University of Michigan. School of Business Administration and published by . This book was released on 1990 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Agricultural Trade Negotiations written by Mary E. Lassanyi and published by . This book was released on 1988 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
