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Author: Agustin Rayo Publisher: MIT Press ISBN: 0262039419 Category : Mathematics Languages : en Pages : 321
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
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: James E. von der Heydt Publisher: University of Iowa Press ISBN: 1587297736 Category : Literary Criticism Languages : en Pages : 263
Book Description
From popular culture to politics to classic novels, quintessentially American texts take their inspiration from the idea of infinity. In the extraordinary literary century inaugurated by Ralph Waldo Emerson, the lyric too seemed to encounter possibilities as limitless as the U.S. imagination. This raises the question: What happens when boundlessness is more than just a figure of speech? Exploring new horizons is one thing, but actually looking at the horizon itself is something altogether different. In this carefully crafted analysis, James von der Heydt shines a new light on the lyric craft of Emily Dickinson, Robert Frost, Elizabeth Bishop, and James Merrill and considers how their seascape-vision redefines poetry's purpose. Emerson famously freed U.S. literature from its past and opened it up to vastness; in the following century, a succession of brilliant, rigorous poets took the philosophical challenges of such freedom all too seriously. Facing the unmarked horizon, Emersonian poets capture—and are captured by—a stark, astringent version of human beauty. Their uncompromising visions of limitlessness reclaim infinity's proper legacy—and give American poetry its edge. Von der Heydt's book recovers the mystery of their world.
Author: Michael Bruce Publisher: John Wiley & Sons ISBN: 1444336371 Category : Philosophy Languages : en Pages : 435
Book Description
Does the existence of evil call into doubt the existence of God? Show me the argument. Philosophy starts with questions, but attempts at answers are just as important, and these answers require reasoned argument. Cutting through dense philosophical prose, 100 famous and influential arguments are presented in their essence, with premises, conclusions and logical form plainly identified. Key quotations provide a sense of style and approach. Just the Arguments is an invaluable one-stop argument shop. A concise, formally structured summation of 100 of the most important arguments in Western philosophy The first book of its kind to present the most important and influential philosophical arguments in a clear premise/conclusion format, the language that philosophers use and students are expected to know Offers succinct expositions of key philosophical arguments without bogging them down in commentary Translates difficult texts to core arguments Designed to provides a quick and compact reference to everything from Aquinas’ “Five Ways” to prove the existence of God, to the metaphysical possibilities of a zombie world
Author: Michael J. Loux Publisher: Cornell University Press ISBN: 9780801491788 Category : First philosophy Languages : en Pages : 340
Book Description
This well-chosen collection of fifteen important essays in the fields of philosophical logic and metaphysics addresses questions relating to the nature and status of possible worlds.
Author: Stanley B. Sprague Publisher: McFarland ISBN: 1476641706 Category : History Languages : en Pages : 286
Book Description
This concise and balanced account details Pakistan's turbulent 73-year history of civil war, military coups, political assassinations, wars with India, cooperation with the U.S. during the Afghan-Soviet war, and events following 9/11. An unpredictable nuclear nation, Pakistan has been variously described as the center of international terrorism, the world's biggest nuclear weapons proliferator, the most dangerous place in the world and, some experts predict, the most likely site of the world's first nuclear war.
Author: Parker J. Palmer Publisher: Berrett-Koehler Publishers ISBN: 152309544X Category : Philosophy Languages : en Pages : 217
Book Description
Aging as a passage of discovery and engagement From bestselling author Parker J. Palmer comes a brave and beautiful book for all who want to age reflectively, seeking new insights and life-giving ways to engage in the world. “Age itself,” he says, “is no excuse to wade in the shallows. It's a reason to dive deep and take creative risks.” Looking back on eight decades of life—and on his work as a writer, teacher, and activist—Palmer explores what he's learning about self and world, inviting readers to explore their own experience. In prose and poetry—and three downloadable songs written for the book by the gifted Carrie Newcomer—he meditates on the meanings of life, past, present, and future. “The laws of nature that dictate sundown dictate our demise. But how we travel the arc toward the sunset of our lives is ours to choose: will it be denial, defiance, or collaboration?” With compassion and chutzpah, gravitas and levity, Palmer writes about cultivating a vital inner and outer life, finding meaning in suffering and joy, and forming friendships across the generations that bring new life to young and old alike.
Author: Cory Seibel Publisher: Wipf and Stock Publishers ISBN: 1532681828 Category : Religion Languages : en Pages : 221
Book Description
Virtually all churches aim to invest meaningfully in the faith development of the younger generations who have been entrusted into their care. Some churches have a longstanding track record of faithfulness in living out this commitment. Some lose sight of this priority over time and allow their intentionality to fade. This book makes a distinctive contribution to our understanding of children's, youth, and young adult ministries by appropriating Erik Erikson's concept of generativity ("the interest in establishing and guiding the next generation") as a way of exploring congregational life. Eleven accomplished authors representing five different countries provide diverse theological and cultural perspectives on key aspects of what it means for churches to invest intentionally in the faith development of the members of emerging generations. Their chapters challenge us to think about the intergenerational dynamics of our churches, the crucial partnership between church and parents, and what it means to involve young people meaningfully in the life of the church. The intriguing topics explored by this group of authors--and the diverse contexts from which they write--promise to broaden and enrich our thinking about caring for children, youth, and young adults as a vital responsibility shared by the entire congregation.
Author: Dr Oliver D Crisp Publisher: Ashgate Publishing, Ltd. ISBN: 1409481549 Category : Religion Languages : en Pages : 172
Book Description
Constructive contemporary theology requires serious engagement with the theologians of the past. This book offers a series of studies in the Christology of key representatives in the Reformed tradition engaging their thought for contemporary dogmatics. Thinkers from each of the five centuries in which Reformed theology has flourished are represented - John Calvin; John Owen; Jonathan Edwards; William Shedd; Donald Baillie; and Kathryn Tanner - each of whom in different ways challenge conventional accounts of Christology. The book is organized thematically, linking historic and contemporary discussions of Christology in theology and philosophy by engaging the thinking of these theologians in a collegial way, using their work as means of promoting constructive systematic theology today. Oliver Crisp presents an important contribution to broadening our understanding of Reformed theology by showing how important theologians have taken views often at odds with 'textbook' accounts of the tradition. Written in an accessible style, this book will appeal to a wide range of readers, including upper-level undergraduates, graduate students and scholars of Christian theology, philosophy and religious studies.
Author: Oliver D. Crisp Publisher: Routledge ISBN: 1317063635 Category : Religion Languages : en Pages : 183
Book Description
Constructive contemporary theology requires serious engagement with the theologians of the past. This book offers a series of studies in the Christology of key representatives in the Reformed tradition engaging their thought for contemporary dogmatics. Thinkers from each of the five centuries in which Reformed theology has flourished are represented - John Calvin; John Owen; Jonathan Edwards; William Shedd; Donald Baillie; and Kathryn Tanner - each of whom in different ways challenge conventional accounts of Christology. The book is organized thematically, linking historic and contemporary discussions of Christology in theology and philosophy by engaging the thinking of these theologians in a collegial way, using their work as means of promoting constructive systematic theology today. Oliver Crisp presents an important contribution to broadening our understanding of Reformed theology by showing how important theologians have taken views often at odds with 'textbook' accounts of the tradition. Written in an accessible style, this book will appeal to a wide range of readers, including upper-level undergraduates, graduate students and scholars of Christian theology, philosophy and religious studies.
Author: Agustin Rayo
Author: Agustin Rayo
Author: James E. von der Heydt
Author: Michael Tooley
Author: Michael Bruce
Author: Michael J. Loux
Author: Stanley B. Sprague
Author: Parker J. Palmer
Author: Cory Seibel
Author: Dr Oliver D Crisp
Author: Oliver D. Crisp