Journey To The Edge Of Reason The Life Of Kurt G Del

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.

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

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.

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.

"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

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.

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.