The Uses Of Paradox

Author : Agustin Rayo
Publisher : MIT Press
ISBN 13 : 0262039419
Total Pages : 321 pages
Book Rating : 4.13/5 ( download)

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Download or read book On the Brink of Paradox written by Agustin Rayo and published by MIT Press. This book was released on 2019-04-02 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

Author : Margaret Cuonzo
Publisher : MIT Press
ISBN 13 : 0262525496
Total Pages : 240 pages
Book Rating : 4.97/5 ( download)

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Download or read book Paradox written by Margaret Cuonzo and published by MIT Press. This book was released on 2014-02-14 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to paradoxes showing that they are more than mere puzzles but can prompt new ways of thinking. Thinkers have been fascinated by paradox since long before Aristotle grappled with Zeno's. In this volume in The MIT Press Essential Knowledge series, Margaret Cuonzo explores paradoxes and the strategies used to solve them. She finds that paradoxes are more than mere puzzles but can prompt new ways of thinking. A paradox can be defined as a set of mutually inconsistent claims, each of which seems true. Paradoxes emerge not just in salons and ivory towers but in everyday life. (An Internet search for “paradox” brings forth a picture of an ashtray with a “no smoking” symbol inscribed on it.) Proposing solutions, Cuonzo writes, is a natural response to paradoxes. She invites us to rethink paradoxes by focusing on strategies for solving them, arguing that there is much to be learned from this, regardless of whether any of the more powerful paradoxes is even capable of solution. Cuonzo offers a catalog of paradox-solving strategies—including the Preemptive-Strike (questioning the paradox itself), the Odd-Guy-Out (calling one of the assumptions into question), and the You-Can't-Get-There-from-Here (denying the validity of the reasoning). She argues that certain types of solutions work better in some contexts than others, and that as paradoxicality increases, the success of certain strategies grows more unlikely. Cuonzo shows that the processes of paradox generation and solution proposal are interesting and important ones. Discovering a paradox leads to advances in knowledge: new science often stems from attempts to solve paradoxes, and the concepts used in the new sciences lead to new paradoxes. As Niels Bohr wrote, “How wonderful that we have met with a paradox. Now we have some hope of making progress.”

Author : Stan Wagon
Publisher : Cambridge University Press
ISBN 13 : 9780521457040
Total Pages : 276 pages
Book Rating : 4.41/5 ( download)

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Download or read book The Banach-Tarski Paradox written by Stan Wagon and published by Cambridge University Press. This book was released on 1993-09-24 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asserting that a solid ball may be taken apart into many pieces that can be rearranged to form a ball twice as large as the original, the Banach-Tarski paradox is examined in relationship to measure and group theory, geometry and logic.

Author : Dr Peter G Platt
Publisher : Ashgate Publishing, Ltd.
ISBN 13 : 1409475158
Total Pages : 270 pages
Book Rating : 4.56/5 ( download)

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Download or read book Shakespeare and the Culture of Paradox written by Dr Peter G Platt and published by Ashgate Publishing, Ltd.. This book was released on 2013-04-28 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Shakespeare's intellectual interest in placing both characters and audiences in a state of uncertainty, mystery, and doubt, this book interrogates the use of paradox in Shakespeare's plays and in performance. By adopting this discourse-one in which opposites can co-exist and perspectives can be altered, and one that asks accepted opinions, beliefs, and truths to be reconsidered-Shakespeare used paradox to question love, gender, knowledge, and truth from multiple perspectives. Committed to situating literature within the larger culture, Peter Platt begins by examining the Renaissance culture of paradox in both the classical and Christian traditions. He then looks at selected plays in terms of paradox, including the geographical site of Venice in Othello and The Merchant of Venice, and equity law in The Comedy of Errors, Merchant, and Measure for Measure. Platt also considers the paradoxes of theater and live performance that were central to Shakespearean drama, such as the duality of the player, the boy-actor and gender, and the play/audience relationship in the Henriad, Hamlet, As You Like It, Twelfth Night, Antony and Cleopatra, The Winter's Tale, and The Tempest. In showing that Shakespeare's plays create and are created by a culture of paradox, Platt offers an exciting and innovative investigation of Shakespeare's cognitive and affective power over his audience.

Author : Yakir Aharonov
Publisher : John Wiley & Sons
ISBN 13 : 3527619127
Total Pages : 299 pages
Book Rating : 4.22/5 ( download)

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Download or read book Quantum Paradoxes written by Yakir Aharonov and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Guide through the Mysteries of Quantum Physics! Yakir Aharonov is one of the pioneers in measuring theory, the nature of quantum correlations, superselection rules, and geometric phases and has been awarded numerous scientific honors. The author has contributed monumental concepts to theoretical physics, especially the Aharonov-Bohm effect and the Aharonov-Casher effect. Together with Daniel Rohrlich, Israel, he has written a pioneering work on the remaining mysteries of quantum mechanics. From the perspective of a preeminent researcher in the fundamental aspects of quantum mechanics, the text combines mathematical rigor with penetrating and concise language. More than 200 exercises introduce readers to the concepts and implications of quantum mechanics that have arisen from the experimental results of the recent two decades. With students as well as researchers in mind, the authors give an insight into that part of the field, which led Feynman to declare that "nobody understands quantum mechanics". * Free solutions manual available for lecturers at www.wiley-vch.de/supplements/

Author : J. Labbe
Publisher : Springer
ISBN 13 : 0230596762
Total Pages : 211 pages
Book Rating : 4.64/5 ( download)

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Download or read book The Romantic Paradox written by J. Labbe and published by Springer. This book was released on 2000-06-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why are there so few 'happily ever afters' in the Romantic-period verse romance? Why do so many poets utilise the romance and its parts to such devastating effect? Why is gender so often the first victim? The Romantic Paradox investigates the prevalence of death in the poetic romances of the Della Cruscans, Coleridge, Keats, Mary Robinson, Felicia Hemans, Letitia Landon, and Byron, and posits that understanding the romance and its violent tendencies is vital to understanding Romanticism itself.

Author : Matthew C. Bagger
Publisher : Columbia University Press
ISBN 13 : 0231140827
Total Pages : 150 pages
Book Rating : 4.29/5 ( download)

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Download or read book The Uses of Paradox written by Matthew C. Bagger and published by Columbia University Press. This book was released on 2007 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this groundbreaking comparative study, Matthew Bagger investigates the role of paradox in Western and Asian religious discourse. Drawing on both philosophy and social scientific theory, he offers a naturalistic explanation of religion's oft-noted propensity to sublime paradox and argues that religious thinkers employ intractable paradoxes as the basis for various techniques of self-transformation. Considering the writings of Kierkegaard, Pseudo-Dionysus, St. John of the Cross, N'g'rjuna, and Chuang-tzu, among others, Bagger identifies two religious uses of paradox: cognitive asceticism, which wields the psychological discomfort of paradox as an instrument of self-transformation, and mysticism, which seeks to transform the self through an alleged extraordinary cognition that ineffably comprehends paradox. Bagger contrasts these techniques of self-transformation with skepticism, which cultivates the appearance of contradiction in order to divest a person of beliefs altogether. Bagger further contends that a thinker's social attitudes determine his or her response to paradox. Attitudes concerning crossing the boundary of a social group prefigure attitudes concerning supposed truths that lie beyond the boundaries of understanding. Individuals who fear crossing the boundary of their social group and would prohibit them tend to use paradox ascetically, while individuals who find the controlled incorporation of outsiders enriching commonly find paradox revelatory. Although scholars have long noted that religious discourse seems to cultivate and perpetuate paradox, their scholarship tends to ratify religious attitudes toward paradox instead of explaining the unusual reaction paradox provokes. A vital contribution to discussions of mystical experience, The Uses of Paradox reveals how much this experience relies on social attitudes and cosmological speculation.

Author : Wendy K. Smith
Publisher : Oxford University Press
ISBN 13 : 019106937X
Total Pages : 528 pages
Book Rating : 4.76/5 ( download)

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Download or read book The Oxford Handbook of Organizational Paradox written by Wendy K. Smith and published by Oxford University Press. This book was released on 2017-09-07 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of paradox dates back to ancient philosophy, yet only recently have scholars started to explore this idea in organizational phenomena. Two decades ago, a handful of provocative theorists urged researchers to take seriously the study of paradox, and thereby deepen our understanding of plurality, tensions, and contradictions in organizational life. Studies of organizational paradox have grown exponentially over the past two decades, canvassing varied phenomena, methods, and levels of analysis. These studies have explored such tensions as today and tomorrow, global integration and local distinctions, collaboration and competition, self and others, mission and markets. Yet even with both the depth and breadth of interest in organizational paradoxes, key issues around definitions and application remain. This handbook seeks to aid, engage, and fuel the expanding interest in organizational paradox. Contributions to this volume depict how paradox studies inform, and are informed, by other theoretical perspectives, while creating a resource that enables scholars to learn about and apply this lens across varied organizational phenomena. The increasing complexity, volatility, and ambiguity in our world continually surfaces paradoxical dynamics. Thus, this handbook offers insights to scholars across organizational theory.

Author : Patricia Spadaro
Publisher : SCB Distributors
ISBN 13 : 0981603319
Total Pages : 176 pages
Book Rating : 4.15/5 ( download)

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Download or read book Honor Yourself written by Patricia Spadaro and published by SCB Distributors. This book was released on 2020-04-28 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Patricia Spadaro is a marvelous guide through the inner realms of the heart. I always feel uplifted by her words." —Marianne Williamson, #1 New York Times bestselling author of A Return to Love Honor Yourself: The Inner Art of Giving and Receiving (winner of two national book awards) skillfully guides us through one of the key stressors and paradoxes of our time—how to balance what others need with what we need, how to give and to receive. Should I sacrifice for others or take time to care for myself? Be generous or draw boundaries? Stay in a relationship or say goodbye? When I give to others, do I really need to give up myself? Tensions like these are not only a natural part of life, they are life. But rather than focusing on how to pamper ourselves, Honor Yourself goes to the heart of the problem so you can find real solutions. While modern society is ill-equipped to bring us back into balance, the sages of East and West are experts, and Honor Yourself explores their practical, and surprising, advice. Combining wisdom from around the world with real-life stories and a treasury of tools, it exposes the most potent myths about giving that can sabotage your relationships, career, finances, even your health, without you knowing it. With candor and compassion, it shows how to move beyond the myths to the magic of honoring yourself so you can live a life filled with possibility and passion and give your greatest gifts to your loved ones, your community, and the world. We are called to master the delicate dance of giving and receiving in virtually every area of our lives, and this beautiful work offers empowering and heartfelt ways to do it. It will free you to celebrate your own gifts and greatness as you explore the dynamics behind setting boundaries, being honest about unhealthy people in your life, honoring endings, using feelings to stay true to yourself, finding your own voice, giving with the heart rather than the head, and much more. Just as importantly, Honor Yourself will teach you the steps for staying in balance. For when you learn the steps, you can perform the dance—and that's when the magic begins.

Author : Roy Sorensen
Publisher : Oxford University Press
ISBN 13 : 0190289317
Total Pages : 416 pages
Book Rating : 4.17/5 ( download)

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Download or read book A Brief History of the Paradox written by Roy Sorensen and published by Oxford University Press. This book was released on 2003-12-04 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor.