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Author: Rudy Rucker
Publisher: Princeton University Press
ISBN: 0691191255
Category : Mathematics
Languages : en
Pages :
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Book Description
A dynamic exploration of infinity In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the “Mindscape,” where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Using cartoons, puzzles, and quotations to enliven his text, Rucker acquaints us with staggeringly advanced levels of infinity, delves into the depths beneath daily awareness, and explains Kurt Gödel’s belief in the possibility of robot consciousness. In the realm of infinity, mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise, we gain profound insights into the human mind, its powers, and its limitations. This Princeton Science Library edition includes a new preface by the author.
Author: Rudy Rucker
Publisher: Princeton University Press
ISBN: 0691191255
Category : Mathematics
Languages : en
Pages :
Get Book
Book Description
A dynamic exploration of infinity In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the “Mindscape,” where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Using cartoons, puzzles, and quotations to enliven his text, Rucker acquaints us with staggeringly advanced levels of infinity, delves into the depths beneath daily awareness, and explains Kurt Gödel’s belief in the possibility of robot consciousness. In the realm of infinity, mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise, we gain profound insights into the human mind, its powers, and its limitations. This Princeton Science Library edition includes a new preface by the author.
Author: Shaughan Lavine
Publisher: Harvard University Press
ISBN: 0674265335
Category : Mathematics
Languages : en
Pages : 262
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Book Description
An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical commentary on, the modern notion of infinity as formalized in axiomatic set theory . . . An amazingly readable [book] given the difficult subject matter. Most of all, it is an eminently sensible book. Anyone who wants to explore the deep issues surrounding the concept of infinity . . . will get a great deal of pleasure from it.” —Ian Stewart, New Scientist “How, in a finite world, does one obtain any knowledge about the infinite? Lavine argues that intuitions about the infinite derive from facts about the finite mathematics of indefinitely large size . . . The issues are delicate, but the writing is crisp and exciting, the arguments original. This book should interest readers whether philosophically, historically, or mathematically inclined, and large parts are within the grasp of the general reader. Highly recommended.” —D. V. Feldman, Choice
Author: Joseph Warren Dauben
Publisher: Princeton University Press
ISBN: 9780691085838
Category : Infinite..
Languages : en
Pages : 422
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Book Description
One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula. Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.
Author: A.W. Moore
Publisher: Routledge
ISBN: 1351381253
Category : Philosophy
Languages : en
Pages : 361
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Book Description
We are all captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all-powerful God. In this acclaimed introduction to the infinite, A. W. Moore takes us on a journey back to early Greek thought about the infinite, from its inception to Aristotle. He then examines medieval and early modern conceptions of the infinite, including a brief history of the calculus, before turning to Kant and post-Kantian ideas. He also gives an account of Cantor’s remarkable discovery that some infinities are bigger than others. In the second part of the book, Moore develops his own views, drawing on technical advances in the mathematics of the infinite, including the celebrated theorems of Skolem and Gödel, and deriving inspiration from Wittgenstein. He concludes this part with a discussion of death and human finitude. For this third edition Moore has added a new part, ‘Infinity superseded’, which contains two new chapters refining his own ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. This new part is heavily influenced by the work of Deleuze. Also new for the third edition are: a technical appendix on still unresolved questions about different infinite sizes; an expanded glossary; and updated references and further reading. The Infinite, Third Edition is ideal reading for anyone interested in an engaging and historically informed account of this fascinating topic, whether from a philosophical point of view, a mathematical point of view, or a religious point of view.
Author: David Deutsch
Publisher: Penguin UK
ISBN: 0141969695
Category : Science
Languages : en
Pages : 571
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Book Description
'Science has never had an advocate quite like David Deutsch ... A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, Independent In our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely? In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility. 'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world ... I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement 'Bold ... profound ... provocative and persuasive' Economist 'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman
Author: Alva Noë
Publisher: Oxford University Press, USA
ISBN: 0190928182
Category : SPORTS & RECREATION
Languages : en
Pages : 209
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Book Description
"...Philosopher and baseball fan Alva Noë explores the many unexpected ways in which baseball is truly a philosophical kind of game. For example, he ponders how observers of baseball are less interested in what happens, than in who is responsible for what happens; every action receives praise or blame. To put it another way, in baseball - as in the law - we decide what happened based on who is responsible for what happened. Noe also explains the curious activity of keeping score: a score card is not merely a record of the game, like a video recording; it is an account of the game. Baseball requires that true fans try to tell the story of the game, in real time, as it unfolds, and thus actively participate in its creation. Some argue that baseball is fundamentally a game about numbers. Noe's wide-ranging, thoughtful observations show that, to the contrary, baseball is not only a window on language, culture, and the nature of human action, but is intertwined with deep and fundamental human truths."--Dust jacket flap.
Author: Ayon Maharaj
Publisher: Oxford University Press
ISBN: 0190868244
Category : Philosophy
Languages : en
Pages : 288
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Book Description
Sri Ramakrishna is widely known as a nineteenth-century Indian mystic who affirmed the harmony of all religions on the basis of his richly varied spiritual experiences and eclectic religious practices, both Hindu and non-Hindu. In Infinite Paths to Infinite Reality, Ayon Maharaj argues that Sri Ramakrishna was also a sophisticated philosopher of great contemporary relevance. Through a careful study of Sri Ramakrishna's recorded oral teachings in the original Bengali, Maharaj reconstructs his philosophical positions and analyzes them from a cross-cultural perspective. Sri Ramakrishna's spiritual journey culminated in the exalted state of "vijñana," his term for the "intimate knowledge" of God as the Infinite Reality that is both personal and impersonal, with and without form, immanent in the universe and beyond it. This expansive spiritual standpoint of vijñana, Maharaj contends, opens up a new paradigm for addressing central issues in cross-cultural philosophy of religion, including divine infinitude, religious pluralism, mystical experience, and the problem of evil. Sri Ramakrishna's vijñana-based religious pluralism--when grasped in all its subtlety--proves to have major philosophical advantages over dominant Western models. Moreover, his mystical testimony and teachings not only cut across long-standing debates about the nature of mystical experience but also bolster recent defenses of its epistemic value. Maharaj further demonstrates that Sri Ramakrishna's unique response to the problem of evil resonates strongly with Western "soul-making" theodicies and contemporary theories of skeptical theism. A pioneering interdisciplinary study of one of India's most important philosopher-mystics, Maharaj's book is essential reading for scholars and students in philosophy of religion, theology, religious studies, and Hindu studies.
Author: Michel Blay
Publisher: University of Chicago Press
ISBN: 9780226058351
Category : History
Languages : en
Pages : 230
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Book Description
Until the Scientific Revolution, the nature and motions of heavenly objects were mysterious and unpredictable. The Scientific Revolution was revolutionary in part because it saw the advent of many mathematical tools—chief among them the calculus—that natural philosophers could use to explain and predict these cosmic motions. Michel Blay traces the origins of this mathematization of the world, from Galileo to Newton and Laplace, and considers the profound philosophical consequences of submitting the infinite to rational analysis. "One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion."—Margaret Wertheim, New Scientist
Author: James Carse
Publisher: Simon and Schuster
ISBN: 1451657293
Category : Philosophy
Languages : en
Pages : 256
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Book Description
“There are at least two kinds of games,” states James Carse as he begins this extraordinary book. “One could be called finite; the other infinite.” Finite games are the familiar contests of everyday life; they are played in order to be won, which is when they end. But infinite games are more mysterious. Their object is not winning, but ensuring the continuation of play. The rules may change, the boundaries may change, even the participants may change—as long as the game is never allowed to come to an end. What are infinite games? How do they affect the ways we play our finite games? What are we doing when we play—finitely or infinitely? And how can infinite games affect the ways in which we live our lives? Carse explores these questions with stunning elegance, teasing out of his distinctions a universe of observation and insight, noting where and why and how we play, finitely and infinitely. He surveys our world—from the finite games of the playing field and playing board to the infinite games found in culture and religion—leaving all we think we know illuminated and transformed. Along the way, Carse finds new ways of understanding everything from how an actress portrays a role, to how we engage in sex, from the nature of evil, to the nature of science. Finite games, he shows, may offer wealth and status, power and glory. But infinite games offer something far more subtle and far grander. Carse has written a book rich in insight and aphorism. Already an international literary event, Finite and Infinite Games is certain to be argued about and celebrated for years to come. Reading it is the first step in learning to play the infinite game.
Author: Alain Badiou
Publisher: A&C Black
ISBN: 9780826479297
Category : Philosophy
Languages : en
Pages : 166
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Book Description
Alain Badiou is already regarded as one of the mostoriginal and powerful voices in contemporaryEuropean thought. Infinite Thought brings together arepresentative selection of the range of AlainBadiou's work, illustrating the power and diversity ofhis thought.
