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 Essays on G del s Reception of Leibniz Husserl and Brouwer written by Mark van Atten and published by Springer. This book was released on 2016-09-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism. The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not. The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.
Download or read book A Logical Journey written by Hao Wang and published by MIT Press. This book was released on 1997-02-03 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.
Download or read book Wooden Eyes written by Carlo Ginzburg and published by Columbia University Press. This book was released on 2001 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ginzburg, "the preeminent Italian historian of his generation [who] helped create the genre of microhistory" ("New York Times"), ruminates on how perspective affects what we see and understand. 26 illustrations.
Download or read book G del Escher Bach written by Douglas R. Hofstadter and published by Penguin Group(CA). This book was released on 2000 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'What is a self and how can a self come out of inanimate matter?' This is the riddle that drove Douglas Hofstadter to write this extraordinary book. In order to impart his original and personal view on the core mystery of human existence - our intangible sensation of 'I'-ness - Hofstadter defines the playful yet seemingly paradoxical notion of 'strange loop', and explicates this idea using analogies from many disciplines.
Download or read book Hendrik Petrus Berlage written by Hendrik Petrus Berlage and published by Getty Publications. This book was released on 1996-01-01 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hendrik Petrus Berlage, the Dutch architect and architectural philosopher, created a series of buildings and a body of writings from 1886 to 1909 that were among the first efforts to probe the problems and possibilities of modernism. Although his Amsterdam Stock Exchange, with its rational mastery of materials and space, has long been celebrated for its seminal influence on the architecture of the 20th century, Berlage's writings are highlighted here. Bringing together Berlage's most important texts, among them "Thoughts on Style in Architecture", "Architecture's Place in Modern Aesthetics", and "Art and Society", this volume presents a chapter in the history of European modernism. In his introduction, Iain Boyd Whyte demonstrates that the substantial contribution of Berlage's designs to modern architecture cannot be fully appreciated without an understanding of the aesthetic principles first laid out in his writings.
Download or read book A Man Without a Country written by Kurt Vonnegut and published by Dial Press. This book was released on 2017-06-20 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: NEW YORK TIMES BESTSELLER • “For all those who have lived with Vonnegut in their imaginations . . . this is what he is like in person.”–USA Today In a volume that is penetrating, introspective, incisive, and laugh-out-loud funny, one of the great men of letters of this age–or any age–holds forth on life, art, sex, politics, and the state of America’s soul. From his coming of age in America, to his formative war experiences, to his life as an artist, this is Vonnegut doing what he does best: Being himself. Whimsically illustrated by the author, A Man Without a Country is intimate, tender, and brimming with the scope of Kurt Vonnegut’s passions. Praise for A Man Without a Country “[This] may be as close as Vonnegut ever comes to a memoir.”–Los Angeles Times “Like [that of] his literary ancestor Mark Twain, [Kurt Vonnegut’s] crankiness is good-humored and sharp-witted. . . . [Reading A Man Without a Country is] like sitting down on the couch for a long chat with an old friend.”–The New York Times Book Review “Filled with [Vonnegut’s] usual contradictory mix of joy and sorrow, hope and despair, humor and gravity.”–Chicago Tribune “Fans will linger on every word . . . as once again [Vonnegut] captures the complexity of the human condition with stunning calligraphic simplicity.”–The Australian “Thank God, Kurt Vonnegut has broken his promise that he will never write another book. In this wondrous assemblage of mini-memoirs, we discover his family’s legacy and his obstinate, unfashionable humanism.”–Studs Terkel
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 Godel s Incompleteness Theorems written by Raymond M. Smullyan and published by Oxford University Press. This book was released on 1992-08-20 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
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 There s Something About G del written by Francesco Berto and published by John Wiley & Sons. This book was released on 2011-09-13 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments. Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chapters Discusses interpretations of the Theorem made by celebrated contemporary thinkers Sheds light on the wider extra-mathematical and philosophical implications of Gödel's theories Written in an accessible, non-technical style
Download or read book Vision Reflection and Desire in Western Painting written by David Summers and published by UNC Press Books. This book was released on 2015-12-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spanning more than 2,500 years in the history of art, Vision, Reflection, and Desire in Western Painting demonstrates how the rise and diffusion of the science of optics in ancient Greece and the Mediterranean world correlated to pictorial illusion in the development of Western painting from Hellenistic Greece to the present. Using examples from the late Middle Ages and the Renaissance, David Summers argues that scene-painting (architectural backdrops) and shadow-painting (in which forms are modeled or shown as if in relation to a source of light) not only evolved in close association with geometric optics toward the end of the fifth century B.C.E., but also contributed substantially to the foundations of the new science. The spread of understanding of how light is transmitted, reflected, and refracted is evident in the works of artists such as Brunelleschi, van Eyck, Alberti, and Leonardo. The interplay between optics and painting that influenced the course of Western art, Summers says, persisted as a framework for the realism of Caravaggio, Rembrandt, and Goya and continues today in modern photography and film.
Download or read book Anatomy of the Soul written by Curt Thompson and published by Tyndale House Publishers, Inc.. This book was released on 2010 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do you want to improve your relationships and experience lasting personal change? Join Curt Thompson, M.D., on an amazing journey to discover the surprising pathways for transformation hidden inside your own mind. Integrating new findings in neuroscience and attachment with Christian spirituality, Dr. Thompson reveals how it is possible to rewire your mind, altering your brain patterns and literally making you more like the person God intended you to be. Explaining discoveries about the brain in layman’s terms, he shows how you can be mentally transformed through spiritual practices, interaction with Scripture, and connections with other people. He also provides practical exercises to help you experience healing in areas where you’ve been struggling. Insightful and challenging, "Anatomy of the Soul" illustrates how learning about one of God’s most miraculous creations—your brain—can enrich your life, your relationships, and your impact on the world around you.
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 From Dedekind to G del written by Jaakko Hintikka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.
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 385 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 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.
