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.
Unraveling the Ancient Mystery Behind the Science of Space and Time
Author: Joseph Mazur
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.
Author: Wesley C. Salmon
Publisher: Hackett Publishing
This book is about my own personal favourite puzzles and conundrums in science, all of which have famously been referred to as paradoxes, but which turn out not to be paradoxes at all when considered carefully and viewed from the right angle. A true paradox is a statement that leads to a circular and self-contradictory argument, or one that describes a logically impossible situation. Our subject is 'perceived paradoxes' - questions or thought-experiments that on first encounter seem impossible to answer, but which science has been able to solve. Our tour of these mind-expanding puzzles will take us through some of the greatest hits of science - from Einstein's theories about space and time, to the latest ideas of how the quantum world works. Some of our paradoxes may be familiar, such as Schrödinger's famous cat, which is seemingly alive and dead at the same time; or the Grandfather Paradox - if you travelled back in time and killed your grandfather you would not have been born and would not therefore have killed your grandfather. Other paradoxes will be new to you, but no less bizarre and fascinating. We will ask such questions as: how does the fact that it gets dark at night prove the Universe must have started with a big bang? Where are all the aliens? And why does the length of a piece of string vary depending on how fast it is moving? In resolving our paradoxes we will have to travel to the furthest reaches of the Universe and explore the very essence of space and time. Hold on tight.
The Nine Greatest Enigmas in Physics
Author: Jim Al-Khalili
Publisher: Random House
This revised and expanded edition provides a valuable and accessible introduction to paradoxes.
Author: R. M. Sainsbury
Publisher: Cambridge University Press
Brian Skyrms presents a set of influential essays which deploy formal methods to address epistemological and metaphysical questions. The first part of the book focuses on quantity; the second on degrees of belief, belief revision, and coherence; the third on aspects of inductive reasoning.
Essays on Quantity, Coherence, and Induction
Author: Brian Skyrms
Publisher: Oxford University Press
Antiphon was a fifth-century Athenian intellectual (ca. 480-411 BCE) who created the profession of speechwriting while serving as an influential and highly sought-out adviser to litigants in the Athenian courts. Three of his speeches are preserved, together with three sets of Tetralogies (four hypothetical paired speeches), whose authenticity is sometimes doubted. Fragments also survive of intellectual treatises on subjects including justice, law, and nature (physis), which are often attributed to a separate Antiphon the Sophist. Were these two Antiphons really one and the same individual, endowed with a wide-ranging mind ready to tackle most of the diverse intellectual interests of his day? Through an analysis of all these writings, this book convincingly argues that they were composed by a single individual, Antiphon the Athenian. Michael Gagarin sets close readings of individual works within a wider discussion of the fifth-century Athenian intellectual climate and the philosophical ferment known as the sophistic movement. This enables him to demonstrate the overall coherence of Antiphon's interests and writings and to show how he was a pivotal figure between the sophists and the Attic orators of the fourth century. In addition, Gagarin's argument allows us to reassess the work of the sophists as a whole, so that they can now be seen as primarily interested in logos (speech, argument) and as precursors of fourth-century rhetoric, rather than in their usual role as foils for Plato.
Oratory, Law, and Justice in the Age of the Sophists
Author: Michael Gagarin
Publisher: University of Texas Press
Ein Mann, der die Gletscher so sehr liebt, dass er an ihrem Sterben verzweifelt: Zeno hat sein Leben als Glaziologe einem Alpengletscher gewidmet. Als das Sterben seines Gletschers nicht mehr aufzuhalten ist, heuert er auf einem Kreuzfahrtschiff an, um Touristen die Wunder der Antarktis zu erklären. Doch auf seiner Reise verzweifelt er an der Ignoranz der Urlauber, der mangelnden Achtung vor der fremden Welt und der fortschreitenden Schmelze des Eises. Ilija Trojanows neuer Roman erzählt mit gewaltiger Wortkunst vom Drama eines jungen Mannes, von der Verletzlichkeit der Natur und des Klimas und von ihrer absoluten Schönheit. „EisTau“ ist ein aufrüttelnder Gesang auf das, was unsere Welt ausmacht und sie zerstört.
Author: Ilija Trojanow
Publisher: Carl Hanser Verlag GmbH Co KG
Author: Richard M. Sainsbury
Author: Johann v. Neumann
Author: Jorge Luis Borges
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.
Philosophy and the Labyrinths of the Mind
Author: Roy Sorensen
Publisher: Oxford University Press
In choosing between moral alternatives -- choosing between various forms of ethical action -- we typically make calculations of the following kind: A is better than B; B is better than C; therefore A is better than C. These inferences use the principle of transitivity and are fundamental to many forms of practical and theoretical theorizing, not just in moral and ethical theory but in economics. Indeed they are so common as to be almost invisible. What Larry Temkin's book shows is that, shockingly, if we want to continue making plausible judgments, we cannot continue to make these assumptions. Temkin shows that we are committed to various moral ideals that are, surprisingly, fundamentally incompatible with the idea that "better than" can be transitive. His book develops many examples where value judgments that we accept and find attractive, are incompatible with transitivity. While this might seem to leave two options -- reject transitivity, or reject some of our normative commitments in order to keep it -- Temkin is neutral on which path to follow, only making the case that a choice is necessary, and that the cost either way will be high. Temkin's book is a very original and deeply unsettling work of skeptical philosophy that mounts an important new challenge to contemporary ethics.
Moral Ideals and the Nature of Practical Reasoning
Author: Larry S. Temkin
Publisher: Oxford University Press
Platon: Menon Entstanden etwa zwischen 393 und 388 v. Chr. Erstdruck (in lateinischer Übersetzung durch Marsilio Ficino) in: Opera, Florenz o. J. (ca. 1482/84). Erstdruck des griechischen Originals in: Hapanta ta tu Platônos, herausgegeben von M. Musoros, Venedig 1513. Erste deutsche Übersetzung durch Friedrich Gedike in: Vier Dialogen des Platon, Berlin 1780. Der Text folgt der Übersetzung durch Ludwig von Georgii von 1860. Vollständige Neuausgabe mit einer Biographie des Autors. Herausgegeben von Karl-Maria Guth. Berlin 2016. Textgrundlage ist die Ausgabe: Platon: Sämtliche Werke. Berlin: Lambert Schneider, . Die Paginierung obiger Ausgabe wird in dieser Neuausgabe als Marginalie zeilengenau mitgeführt. Umschlaggestaltung von Thomas Schultz-Overhage unter Verwendung des Bildes: Raffael, Die Schule von Athen (Detail). Gesetzt aus der Minion Pro, 11 pt.
Publisher: BoD – Books on Demand
This is a philosophical introduction to Aristotle, and Professor Lear starts where Aristotle himself started. He introduces us to the essence of Aristotle's philosophy and guides us through all the central Aristotelian texts--selected from the Physics, Metaphysics, Ethics, Politics and the biological and logical works. The book is written in a direct, lucid style that engages the reader with the themes in an active and participatory manner. It will prove a stimulating introduction for all students of Greek philosophy and for a wide range of others interested in Aristotle as a giant figure in Western intellectual history.
The Desire to Understand
Author: Jonathan Lear
Publisher: Cambridge University Press
An Episodic History of Mathematics will acquaint students and readers with mathematical language, thought, and mathematical life by means of historically important mathematical vignettes. It will also serve to help prospective teachers become more familiar with important ideas of in the history of mathematicsboth classical and modern.Contained within are wonderful and engaging stories and anecdotes about Pythagoras and Galois and Cantor and Poincar, which let readers indulge themselves in whimsy, gossip, and learning. The mathematicians treated here were complex individuals who led colorful and fascinating lives, and did fascinating mathematics. They remain interesting to us as people and as scientists.This history of mathematics is also an opportunity to have some fun because the focus in this text is also on the practicalgetting involved with the mathematics and solving problems. This book is unabashedly mathematical. In the course of reading this book, the neophyte will become involved with mathematics by working on the same problems that, for instance, Zeno and Pythagoras and Descartes and Fermat and Riemann worked on.This is a book to be read, therefore, with pencil and paper in hand, and a calculator or computer close by. All will want to experiment; to try things; and become a part of the mathematical process.
Mathematical Culture Through Problem Solving
Author: Steven G. Krantz