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A Logical Journey
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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 These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy.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.
Book Synopsis Reflections on Kurt Gödel by : Hao Wang
Download or read book Reflections on Kurt Gödel 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.
Book Synopsis Incompleteness by : Rebecca Goldstein
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 written by John L. Casti and published by . This book was released on 2009-04-21 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Shattering hopes that logic would, in the end, allow us a complete understanding of the universe, Gödel's theorem also raised many provocative questions: What are the limits of rational thought? Can we ever fully understand the machines we build? Or the inner workings of our own minds? How should mathematicians proceed in the absence of complete certainty about their results? Equally legendary were Gödel's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first book for a general audience on this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life.
Book Synopsis Popular Lectures on Mathematical Logic by : Hao Wang
Download or read book Popular Lectures on Mathematical Logic written by Hao Wang and published by Courier Corporation. This book was released on 2014-09-22 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.
Book Synopsis From Mathematics to Philosophy (Routledge Revivals) by : Hao Wang
Download or read book From Mathematics to Philosophy (Routledge Revivals) written by Hao Wang and published by Routledge. This book was released on 2016-06-10 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge.
Book Synopsis Journey to the Edge of Reason by : Stephen Budiansky
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 Mathematics and Logic written by Mark Kac and published by Courier Corporation. This book was released on 1992-01-01 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."
Book Synopsis Developmental Journey by : Mary M. Wilcox
Download or read book Developmental Journey written by Mary M. Wilcox and published by . This book was released on 1979 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis My Best Mathematical and Logic Puzzles by : Martin Gardner
Download or read book My Best Mathematical and Logic Puzzles written by Martin Gardner and published by Courier Corporation. This book was released on 2013-04-10 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The noted expert selects 70 of his favorite "short" puzzles, including such mind-bogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, and dozens more involving logic and basic math. Solutions included.
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 Good Math written by Mark C. Chu-Carroll and published by Pragmatic Bookshelf. This book was released on 2013-07-18 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you. Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird. Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing. If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.
Book Synopsis I Know This Much Is True by : Wally Lamb
Download or read book I Know This Much Is True written by Wally Lamb and published by Cambridge University Press. This book was released on 1998-06-03 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt: With his stunning debut novel, She's Come Undone, Wally Lamb won the adulation of critics and readers with his mesmerizing tale of one woman's painful yet triumphant journey of self-discovery. Now, this brilliantly talented writer returns with I Know This Much Is True, a heartbreaking and poignant multigenerational saga of the reproductive bonds of destruction and the powerful force of forgiveness. A masterpiece that breathtakingly tells a story of alienation and connection, power and abuse, devastation and renewal--this novel is a contemporary retelling of an ancient Hindu myth. A proud king must confront his demons to achieve salvation. Change yourself, the myth instructs, and you will inhabit a renovated world. When you're the same brother of a schizophrenic identical twin, the tricky thing about saving yourself is the blood it leaves on your bands--the little inconvenience of the look-alike corpse at your feet. And if you're into both survival of the fittest and being your brother's keeper--if you've promised your dying mother--then say so long to sleep and hello to the middle of the night. Grab a book or a beer. Get used to Letterman's gap-toothed smile of the absurd, or the view of the bedroom ceiling, or the influence of random selection. Take it from a godless insomniac. Take it from the uncrazy twin--the guy who beat the biochemical rap. Dominick Birdsey's entire life has been compromised and constricted by anger and fear, by the paranoid schizophrenic twin brother he both deeply loves and resents, and by the past they shared with their adoptive father, Ray, a spit-and-polish ex-Navy man (the five-foot-six-inch sleeping giant who snoozed upstairs weekdays in the spare room and built submarines at night), and their long-suffering mother, Concettina, a timid woman with a harelip that made her shy and self-conscious: She holds a loose fist to her face to cover her defective mouth--her perpetual apology to the world for a birth defect over which she'd had no control. Born in the waning moments of 1949 and the opening minutes of 1950, the twins are physical mirror images who grow into separate yet connected entities: the seemingly strong and protective yet fearful Dominick, his mother's watchful "monkey"; and the seemingly weak and sweet yet noble Thomas, his mother's gentle "bunny." From childhood, Dominick fights for both separation and wholeness--and ultimately self-protection--in a house of fear dominated by Ray, a bully who abuses his power over these stepsons whose biological father is a mystery. I was still afraid of his anger but saw how he punished weakness--pounced on it. Out of self-preservation I hid my fear, Dominick confesses. As for Thomas, he just never knew how to play defense. He just didn't get it. But Dominick's talent for survival comes at an enormous cost, including the breakup of his marriage to the warm, beautiful Dessa, whom he still loves. And it will be put to the ultimate test when Thomas, a Bible-spouting zealot, commits an unthinkable act that threatens the tenuous balance of both his and Dominick's lives. To save himself, Dominick must confront not only the pain of his past but the dark secrets he has locked deep within himself, and the sins of his ancestors--a quest that will lead him beyond the confines of his blue-collar New England town to the volcanic foothills of Sicily 's Mount Etna, where his ambitious and vengefully proud grandfather and a namesake Domenico Tempesta, the sostegno del famiglia, was born. Each of the stories Ma told us about Papa reinforced the message that he was the boss, that he ruled the roost, that what he said went. Searching for answers, Dominick turns to the whispers of the dead, to the pages of his grandfather's handwritten memoir, The History of Domenico Onofrio Tempesta, a Great Man from Humble Beginnings. Rendered with touches of magic realism, Domenico's fablelike tale--in which monkeys enchant and religious statues weep--becomes the old man's confession--an unwitting legacy of contrition that reveals the truth's of Domenico's life, Dominick learns that power, wrongly used, defeats the oppressor as well as the oppressed, and now, picking through the humble shards of his deconstructed life, he will search for the courage and love to forgive, to expiate his and his ancestors' transgressions, and finally to rebuild himself beyond the haunted shadow of his twin. Set against the vivid panoply of twentieth-century America and filled with richly drawn, memorable characters, this deeply moving and thoroughly satisfying novel brings to light humanity's deepest needs and fears, our aloneness, our desire for love and acceptance, our struggle to survive at all costs. Joyous, mystical, and exquisitely written, I Know This Much Is True is an extraordinary reading experience that will leave no reader untouched.
Download or read book The Logical Book written by Laura Shenton and published by Wymer UK. This book was released on 2023-10-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Endearingly, the differences between Rick Davies and Roger Hodgson were key ingredients in what would become the musical and writing chemistry of Supertramp - a band that made a fascinating and diverse contribution to music. From their first commercial breakthrough in 1974 with Crime Of The Century, they exceeded their own expectations with the colossal success of Breakfast In America in 1979. But it was never a smooth journey. With ups and downs financially, commercially and in terms of their working relationship, Supertramp lived the highs and lows of the music business. From local gigs to many highly demanding tours, this book documents it all. As Roger Hodgson once said, "The music always came pretty easily. Both the music and the lyrics come from the same place. For me, composing is literally losing myself in the music. I let the inspiration just come naturally. It is a very magical process. When I start hearing melodies, then I just start singing and the words start coming. The words will have something to do with what I am going through in my life, or what's in my heart at the time. I will have an idea of what the song's about and then work with the melody."
Book Synopsis Gödel, Escher, Bach by : Douglas R. Hofstadter
Download or read book Gödel, 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.
Book Synopsis A First Journey Through Logic by : Martin Hils
Download or read book A First Journey Through Logic written by Martin Hils and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present mathematical logic to students who are interested in what this field is but have no intention of specializing in it. The point of view is to treat logic on an equal footing to any other topic in the mathematical curriculum. The book starts with a presentation of naive set theory, the theory of sets that mathematicians use on a daily basis. Each subsequent chapter presents one of the main areas of mathematical logic: first order logic and formal proofs, model theory, recursion theory, Gödel's incompleteness theorem, and, finally, the axiomatic set theory. Each.
Book Synopsis Journey Through Genius by : William Dunham
Download or read book Journey Through Genius written by William Dunham and published by Penguin Books. This book was released on 1991-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve. Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity. “It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov
