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Author: Agustin Rayo
Publisher: MIT Press
ISBN: 0262039419
Category : Mathematics
Languages : en
Pages : 321
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Book Description
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: Agustin Rayo
Publisher: MIT Press
ISBN: 0262039419
Category : Mathematics
Languages : en
Pages : 321
Get Book Here
Book Description
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: David Pears
Publisher: Oxford University Press on Demand
ISBN: 0199247706
Category : Philosophy
Languages : en
Pages : 148
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Book Description
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Author: Wendy K. Smith
Publisher: Oxford University Press
ISBN: 0198754426
Category : Business & Economics
Languages : en
Pages : 625
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Book Description
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: Matthew C. Bagger
Publisher: Columbia University Press
ISBN: 023151185X
Category : Religion
Languages : en
Pages : 149
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Book Description
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: Poul Andersen
Publisher: BRILL
ISBN: 1684171040
Category : Religion
Languages : en
Pages : 370
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Book Description
The question of truth has never been more urgent than today, when the distortion of facts and the imposition of pseudo-realities in the service of the powerful have become the order of the day. In The Paradox of Being Poul Andersen addresses the concept of truth in Chinese Daoist philosophy and ritual. His approach is unapologetically universalist, and the book may be read as a call for a new way of studying Chinese culture, one that does not shy away from approaching “the other” in terms of an engagement with “our own” philosophical heritage. The basic Chinese word for truth is zhen, which means both true and real, and it bypasses the separation of the two ideas insisted on in much of the Western philosophical tradition. Through wide-ranging research into Daoist ritual, both in history and as it survives in the present day, Andersen shows that the concept of true reality that informs this tradition posits being as a paradox anchored in the inexistent Way (Dao). The preferred way of life suggested by this insight consists in seeking to be an exception to ordinary norms and rules of behavior which nonetheless engages what is common to us all.
Author: Dr Peter G Platt
Publisher: Ashgate Publishing, Ltd.
ISBN: 1409475158
Category : Drama
Languages : en
Pages : 270
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Book Description
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: Elizabeth Bradley
Publisher: Public Affairs
ISBN: 1610392094
Category : Political Science
Languages : en
Pages : 274
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Book Description
Considers why U.S. society is believed to be less healthy in spite of disproportionate spending on health care, identifying a lack of social services, outdated care allocations, and a resistance to government programs as the problem.
Author: Tim Maudlin
Publisher: Oxford University Press
ISBN: 0199247293
Category : Language Arts & Disciplines
Languages : en
Pages : 223
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Book Description
Consider the sentence 'This sentence is not true'. Certain notorious paradoxes like this have bedevilled philosophical theories of truth. Tim Maudlin presents an original account of logic and semantics which deals with these paradoxes, and allows him to set out a new theory of truth-values and the norms governing claims about truth.
Author: Roy Sorensen
Publisher: Oxford University Press
ISBN: 0199728577
Category : Philosophy
Languages : en
Pages : 413
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Book Description
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.
Author: Barry Schwartz
Publisher: Harper Collins
ISBN: 0061748994
Category : Psychology
Languages : en
Pages : 308
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Book Description
Whether we're buying a pair of jeans, ordering a cup of coffee, selecting a long-distance carrier, applying to college, choosing a doctor, or setting up a 401(k), everyday decisions—both big and small—have become increasingly complex due to the overwhelming abundance of choice with which we are presented. As Americans, we assume that more choice means better options and greater satisfaction. But beware of excessive choice: choice overload can make you question the decisions you make before you even make them, it can set you up for unrealistically high expectations, and it can make you blame yourself for any and all failures. In the long run, this can lead to decision-making paralysis, anxiety, and perpetual stress. And, in a culture that tells us that there is no excuse for falling short of perfection when your options are limitless, too much choice can lead to clinical depression. In The Paradox of Choice, Barry Schwartz explains at what point choice—the hallmark of individual freedom and self-determination that we so cherish—becomes detrimental to our psychological and emotional well-being. In accessible, engaging, and anecdotal prose, Schwartz shows how the dramatic explosion in choice—from the mundane to the profound challenges of balancing career, family, and individual needs—has paradoxically become a problem instead of a solution. Schwartz also shows how our obsession with choice encourages us to seek that which makes us feel worse. By synthesizing current research in the social sciences, Schwartz makes the counter intuitive case that eliminating choices can greatly reduce the stress, anxiety, and busyness of our lives. He offers eleven practical steps on how to limit choices to a manageable number, have the discipline to focus on those that are important and ignore the rest, and ultimately derive greater satisfaction from the choices you have to make.
