Zenos Paradoxes

A reprint of the Bobbs-Merrill edition of 1970. These essays lead the reader through the land of the wonderful shrinking genie to the warehouse where the infinity machines are kept. By careful examination of a lamp that is switched on and off infinitely many times, or the workings of a machine that prints out an infinite decimal expansion of pi, we begin to understand how it is possible for Achilles to overtake the tortoise. The concepts that form the basis of modern science---space, time, motion, change, infinity---are examined and explored in this edition. Includes an updated bibliography..

The fascinating story of an ancient riddle and what it reveals about the nature of time and space Three millennia ago, the Greek philosopher Zeno constructed a series of logical paradoxes to prove that motion is impossible. Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno's Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs, but through it all, the paradox of motion remains..

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This revised and expanded edition provides a valuable and accessible introduction to paradoxes..

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Explores the higher-order thinking tools that are essential for students to become effective learners. It includes lessons that encourage students to understand and integrate information so that they can use what they know to solve problems and make decisions..

"His book...supplant[s] all others, even the immensely successful History of Western Philosophy by Bertrand Russell."—A. C. Grayling Already a classic in its first year of publication, this landmark study of Western thought takes a fresh look at the writings of the great thinkers of classic philosophy and questions many pieces of conventional wisdom. The book invites comparison with Bertrand Russell's monumental History of Western Philosophy, "but Gottlieb's book is less idiosyncratic and based on more recent scholarship" (Colin McGinn, Los Angeles Times). A New York Times Notable Book, a Los Angeles Times Best Book, and a Times Literary Supplement Best Book of 2001..

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company..

Oxford Studies in Ancient Philosophy is a volume of original articles on all aspects of ancient philosophy. The articles may be of substantial length, and include critical notices of major books. OSAP is now published twice yearly, in both hardback and paperback. "'Have you seen the latest OSAP?' is what scholars of ancient philosophy say to each other when they meet in corridors or on coffee breaks. Whether you work on Plato or Aristotle, on Presocratics or sophists, on Stoics, Epicureans, or Sceptics, on Roman philosophers or Greek Neoplatonists, you are liable to find OSAP articles now dominant in the bibliography of much serious published work in your particular subject: not safe to miss." - Malcolm Schofield, Cambridge University "OSAP was founded to provide a place for long pieces on major issues in ancient philosophy. In the years since, it has fulfilled this role with great success, over and over again publishing groundbreaking papers on what seemed to be familiar topics and others surveying new ground to break. It represents brilliantly the vigour - and the increasingly broad scope - of scholarship in ancient philosophy, and shows us all how the subject should flourish." - M.M. McCabe, King's College London.

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.”.

An enlightening introduction to the philosophy of time and space. J.B. Kennedy offers an introduction to one of the liveliest and most popular fields in philosophy - time and space - aimed specifically at a beginning readership with no background in philosophy or science. He goes to the philosophical heart of the issues without recourse to jargon, mathematics, or logical formulas and introduces Einstein's revolutionary ideas in a clear and simple way, as well as concepts and arguments of other relevant philosophers, both ancient and modern. Current debates in philosophy and physics are also handled with exemplary clarity and Kennedy is able to provide readers with a real sense of where we have come from and where we are going. The writing is engaging, lively, and entertaining and serves to introduce the subject to beginning students as well as providing a clear statement of the "state of the debate" for a popular science readership. Kennedy covers such topics as Einstein's special and general relativity, how to build an atom bomb, the four-dimensional universe, the possibility of time travel, the impossibility of motion, whether space curves, the big bang, black holes, and the idea of inflationary and accelerating universes..

This book entertainingly traces the history of physics from the observations of the earlyGreeks through the discoveries of Galileo and Newton to the dazzling theories of such scientists as Planck, Einstein, Bohr, and Bohm. This humanized view of science opens up the mind-stretching visions of how quantum mechanics, God, human thought, and will are related, and provides profound implications for our understanding of the nature of reality and our relationship to the cosmos..

“While my book attempts to reflect the full range of scholarly debate, I have also attempted to make it useful to anyone interested in Whitehead. To this end, I have introduced the Whiteheadian terms one by one, explaining each in the light of my interpretation, and I have used examples wherever possible. I try to show that Whitehead intended his philosophy have a place in our lives by reshaping our common conceptions, and that he did not intend it to be relegated to purely abstract or esoteric application.” — F. Bradford Wallack The twentieth century has seen the greatest innovations in philosophical cosmology since Newton and Descartes, and Alfred North Whitehead was the first and greatest of the philosophers to work out these innovations in systematic ways. In a book that will be controversial in the philosophical community, F. Bradford Wallack argues that interpretations widely accepted by Whiteheadians need revaluation because these interpretations are based on materialist and substantialist assumptions that Whitehead sought to replace. Specifically, she proposes a thorough revision of accepted interpretations of Whitehead’s concept of the actual entity. Wallack then elucidates Whitehead’s ideas in order of their increasing dependence upon other basic Whiteheadian terms to complete the study of Whiteheadian time and to clarify its purpose within the cosmology of Process and Reality. Whitehead’s philosophy then emerges as more intelligible and cohesive than is generally believed..

This new study of David Hume s philosophy of mathematics critically examines his objections to the concept of infinity, and his alternative phenomenalist theory of space and time as constituted by minima sensibilia or sensible extensionless indivisibles..

History of Psychology: The Making of a Science provides students with a comprehensive overview of the formulation of the field of psychological science. Starting with a chapter on 21st Century Psychology and then jumping to the dawn of civilization, author Edward P. Kardas is able to make connections between early understandings of human behavior with our current understandings and interpretations of psychological research. Through highlighting the zeitgeist of the era and making connections to the related fields of philosophy, computational science, biology, and social science, students will have a deeper understanding of how and why the field has formed in its current landscape and a sense for where it’s headed next..

This volume constitutes an attempt at bringing together philosophies of time—or more precisely, philosophies on time and, in a concomitant way, history—emerging from Christianity’s and Islam’s intellectual histories. Starting from the Neoplatonic heritage and the voice of classical philosophy, the volume enters the Byzantine and Arabic intellectual worlds up to Ibn Al-Arabi’s times. A conscious choice in this volume is not to engage with, perhaps, the most prominent figures of Christian and Arabic philosophy, i.e., Augustine on the one hand and Avicenna/Ibn Sina on the other, precisely because these have attracted so much attention due to their prominence in their respective traditions—and beyond. In a certain way, Maximus the Confessor and Ibn Al-Arabi—together with Al-Fārābi—emerge as alternative representatives of their two traditions in this volume, offering two axes for this endeavor. The synthesis of those approaches on time and history, their comparison rather than their mere co-existence, is left to the reader’s critical inquiry and philosophical investigation..