Download or read book G del s Theorem A Very Short Introduction written by A. W. Moore and published by Oxford University Press. This book was released on 2022-11-10 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Short Introductions: Brilliant, Sharp, Inspiring Kurt Gödel first published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, nearly a century ago. The theorem challenged prevalent presuppositions about the nature of mathematics and was consequently of considerable mathematical interest, while also raising various deep philosophical questions. Gödel's Theorem has since established itself as a landmark intellectual achievement, having a profound impact on today's mathematical ideas. Gödel and his theorem have attracted something of a cult following, though his theorem is often misunderstood. This Very Short Introduction places the theorem in its intellectual and historical context, and explains the key concepts as well as common misunderstandings of what it actually states. A. W. Moore provides a clear statement of the theorem, presenting two proofs, each of which has something distinctive to teach about its content. Moore also discusses the most important philosophical implications of the theorem. In particular, Moore addresses the famous question of whether the theorem shows the human mind to have mathematical powers beyond those of any possible computer ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
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 Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Senses of the Future written by Gerard Delanty and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-03-04 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The future has become a problem for the present. Almost every critical issue is now understood and experienced through the prism of the future since this is the primary focus for the playing out of crises. Senses of the Future offers a wide-ranging discussion of theories of the future. It covers the main ideas of the future in modern thought and explores how we should view the future today in light of a plurality of very different and conflicting visions. The key contribution of this book is to bring together the different approaches with an account that is grounded in sociological and philosophical analysis as opposed to visions of the future that are inspired by extreme visions of catastrophe or approaches that see the future as only the continuation of the present. Given a revival of apocalyptical visions of the ‘end times’ and dystopian views of the future of human societies, there is urgent need for a new approach on how we should imagine the future. The author explores the future as a field of tensions that is revealed in narratives, utopian desires, hope, imaginaries, and social struggles concerning the potential possibilities of the present: the future does not just arrive; it has to be fought for. This book is an important contribution to a critical sociology of the future. It is both a work of reconstruction and critique grounded in a historical and philosophical hermeneutics of the future. Table of Contents Chapter One Introduction: Conflicting Visions of the Future Contested Visions of the Future Today Return to the Future Outline of the Chapters References Chapter Two When is the Future? The Problem of Time and the Human Condition Time in the Physical World: Lessons from Physics Has the Future already Begun? Time and History Time, Life, and the Human Condition: Biology, Evolution, and Culture Conclusion References Chapter Three Lessons from the Past: What Does the Past Tell Us about the Future? The Future in the Past Failed Societies and Civilizational Collapse Catastrophes and History Conclusion References Chapter Four Modernity and the Concept of the Future: Utopia, Progress, and Prophecy The Future as Expectation The Future as an Imaginary and the Emergence of Utopianism The Future as Possibility The Future as Experience Conclusion References Chapter Five Ideas of the Future in the Twentieth Century: Futurism, Modernism, Sociology, and Political Theory New Political Ideas of the Future after 1945 Responses to the Future: From Fear of the Future to Futurology Sociological Theory and the Future Conclusion: The New Sociology of the Future References Chapter Six Critical Theory and the Future: The Sources of Transcendence The Intellectual Origins of Critical Theory: A Brief Outline The Idea of the Future in the Critical Theory of the Early Frankfurt School Habermas and the Communication Paradigm The Responsibility Paradigm and Cosmopolitanism: Jonas and Apel Critical Cosmopolitanism and the Idea of the Future Conclusion: Cultural Models and the Future as Possibility References Chapter Seven Conclusion: In The Shadow of the Future Do We Need a Theory of the Future? Are we already in a New Historical Era? AI and a Posthuman Future Struggles for the Future References Index
Download or read book Learning from Our Mistakes written by William J. Talbott and published by Oxford University Press. This book was released on 2021-09-14 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Learning from Our Mistakes: Epistemology for the Real World, William J. Talbott provides a new framework for understanding the history of Western epistemology and uses it to propose a new way of understanding rational belief that can be applied to pressing social and political issues. Talbott's new model of rational belief is not a model of a theorem prover in mathematics It is a model of a good learner. Being a good learner requires sensitivity to clues, the imaginative ability to generate alternative explanatory narratives that fit the clues, and the ability to select the most coherent explanatory narrative. Sensitivity to clues requires sensitivity not only to evidence that supports one's own beliefs, but also to evidence that casts doubt on them. One of the most important characteristics of a good learner is the ability to correct mistakes. From this model, Talbott articulates nine principles that help to explain the difference between rational and irrational belief. Talbott contrasts his approach with the approach of historically important philosophers, including Socrates, Plato, Aristotle, Hume, Kant, Wittgenstein, and Kuhn, as well as with a range of contemporary approaches, including pragmatism, Bayesianism, and naturalism. On the basis of his model of rational belief, Talbott articulates a new theory of prejudice, which he uses to help diagnose the sources of inequity in the U.S. criminal justice system, as well as to provide insight into the proliferation of tribal and fascist epistemologies based on alt-facts and alt-truth. Learning from Our Mistakes offers a new lens through which to interpret the history of Western epistemology and analyze the complicated social and political phenomena facing us today.
Download or read book Reflections on Kurt G del written by Hao Wang and published by MIT Press. This book was released on 1990-03-14 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newton/Descartes. Einstein/Gödel. The seventeenth century had its scientific and philosophical geniuses. Why shouldn't ours have them as well? Kurt Gödel was indisputably one of the greatest thinkers of our time, and in this first extended treatment of his life and work, Hao Wang, who was in close contact with Gödel in his last years, brings out the full subtlety of Gödel's ideas and their connection with grand themes in the history of mathematics and philosophy. The subjects he covers include the completeness of elementary logic, the limits of formalization, the problem of evidence, the concept of set, the philosophy of mathematics, time, and relativity theory, metaphysics and religion, as well as general ideas on philosophy as a worldview. Wang, whose reflections on his colleague also serve to clarify his own philosophical thoughts, distinguishes his ideas from those of Gödel's and on points of agreement develops Gödel's views further. The book provides a generous array of information on and interpretation of the two main phases of Gödel's career - the years between 1924 and 1939 at the University of Vienna, which were marked by intense mathematical creativity, and the period from 1940 to his death in 1978, during which he was affiliated with the Institute for Advanced Studies in Princeton, a time in which Gödel's interests steadily shifted from questions of logic to metaphysics. And it also examines Gödel's relations with the Vienna Circle, his philosophical differences with Carnap and Wittgenstein, the intimate and mutually fruitful friendship with Einstein, and the periodic bouts of depression for which Gödel was hospitalized a number of times over the course of his life. A Bradford Book.
Download or read book A World Without Time written by Palle Yourgrau and published by Basic Books. This book was released on 2009-03-04 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a widely known but little considered fact that Albert Einstein and Kurt Godel were best friends for the last decade and a half of Einstein's life. The two walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German science in which they had grown up. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist . Einstein endorsed this result-reluctantly, since it decisively overthrew the classical world-view to which he was committed. But he could find no way to refute it, and in the half-century since then, neither has anyone else. Even more remarkable than this stunning discovery, however, was what happened afterward: nothing. Cosmologists and philosophers alike have proceeded with their work as if Godel's proof never existed -one of the greatest scandals of modern intellectual history. A World Without Time is a sweeping, ambitious book, and yet poignant and intimate. It tells the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue from undeserved obscurity the brilliant work they did together.
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 Godel s Proof written by Ernest Nagel and published by Routledge. This book was released on 2012-11-12 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to present a readable explanation of Godel's theorem to both scholars and non-specialists, this is a gripping combination of science and accessibility, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Download or read book Exact Thinking in Demented Times written by Karl Sigmund and published by Basic Books. This book was released on 2017-12-05 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: A dazzling group biography of the early twentieth-century thinkers who transformed the way the world thought about math and science Inspired by Albert Einstein's theory of relativity and Bertrand Russell and David Hilbert's pursuit of the fundamental rules of mathematics, some of the most brilliant minds of the generation came together in post-World War I Vienna to present the latest theories in mathematics, science, and philosophy and to build a strong foundation for scientific investigation. Composed of such luminaries as Kurt Gö and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science. Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.
Download or read book When Einstein Walked with G del written by Jim Holt and published by Farrar, Straus and Giroux. This book was released on 2018-05-15 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Jim Holt, the New York Times bestselling author of Why Does the World Exist?, comes an entertaining and accessible guide to the most profound scientific and mathematical ideas of recent centuries in When Einstein Walked with Gödel: Excursions to the Edge of Thought. Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction—and whether the universe truly has a future.
Download or read book Brave Men written by Ernie Pyle and published by Michael O'Mara Books. This book was released on 2016-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Ernie Pyle was a Pulitzer Prize-winning American journalist. This is his first hand account of life on the European front-line during World War II. Written with touching sympathy and humanism, Brave Men offers a poignant description of the everyday experiences of American foot soldiers; their courage, humanism and unshakeable camaraderie. A must-read war memoir.
Download or read book Lowside of the Road written by Barney Hoskyns and published by Crown. This book was released on 2010-05-11 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: With his trademark growl, carnival-madman persona, haunting music, and unforgettable lyrics, Tom Waits is one of the most revered and critically acclaimed singer-songwriters alive today. After beginning his career on the margins of the 1970s Los Angeles rock scene, Waits has spent the last thirty years carving out a place for himself among such greats as Bob Dylan and Neil Young. Like them, he is a chameleonic survivor who has achieved long-term success while retaining cult credibility and outsider mystique. But although his songs can seem deeply personal and somewhat autobiographical, fans still know very little about the man himself. Notoriously private, Waits has consistently and deliberately blurred the line between fact and fiction, public and private personas, until it has become impossible to delineate between truth and self-fabricated legend. Lowside of the Road is the first serious biography to cut through the myths and make sense of the life and career of this beloved icon. Barney Hoskyns has gained unprecedented access to Waits’s inner circle and also draws on interviews he has done with Waits over the years. Spanning his extraordinary forty-year career from Closing Time to Orphans, from his perilous “jazzbo” years in 1970s LA to such shape-shifting albums as Swordfishtrombones and Rain Dogs to the Grammy Award winners of recent years, this definitive biography charts Waits’s life and art step by step, album by album. Barney Hoskyns has written a rock biography—much like the subject himself—unlike any other. It is a unique take on one of rock’s great enigmas.
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: Peter Smith examines Gödel's Theorems, how they were established and why they matter.
Download or read book Introduction to Probability written by Joseph K. Blitzstein and published by CRC Press. This book was released on 2014-07-24 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.
Download or read book Unplugged written by Ryan G. Van Cleave and published by Health Communications, Inc.. This book was released on 2010-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: WARNING: THIS VIDEO GAME MAY IMPAIR YOUR JUDGMENT. IT MAY CAUSE SLEEP DEPRIVATION, ALIENATION OF FRIENDS AND FAMILY, WEIGHT LOSS OR GAIN, NEGLECT OF YOUR BASIC NEEDS AS WELL AS THE NEEDS OF LOVED ONES AND/OR DEPENDENTS, AND DECREASED PERFORMANCE ON THE JOB. THE DISTINCTION BETWEEN FANTASY AND REALITY MAY BECOME BLURRED. PLAY AT YOUR OWN RISK. NOT RESPONSIBLE FOR SUICIDE ATTEMPTS. No such warning was included on the latest and greatest release from the Warcraft series of massive multiplayer online role-playing games—World of Warcraft (WoW). So when Ryan Van Cleave—a college professor, husband, father, and one of the 11.5 million Warcraft subscribers worldwide—found himself teetering on the edge of the Arlington Memorial Bridge, he had no one to blame but himself. He had neglected his wife and children and had jeopardized his livelihood, all for the rush of living a life of high adventure in a virtual world. A fabulously written and gripping tale, Unplugged takes you on a journey through the author's semireclusive life with video games at the center of his experiences. Even when he was sexually molested by a young school teacher at age eleven, it was the promise of a new video game that had lured him to her house. As Ryan's life progresses, we witness the evolution of video games—from simple two-button consoles to today's multikey technology, brilliantly designed to keep the user actively participating. For Ryan, the virtual world was a siren-song he couldn't ignore, no matter the cost. As is the case with most recovering addicts, Ryan eventually hit rock bottom and shares with you his ongoing battle to control his impulses to play, providing prescriptive advice and resources for those caught in the grip of this very real addiction.
Download or read book The Sirens of Titan written by Kurt Vonnegut and published by . This book was released on 1964 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
