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
"Scolnicov’s aim is to provide a new translation of Plato’s Parmenides, with a commentary designed to show that the arguments of the second half of the dialogue, the purpose of which has long been a matter of scholarly dispute, make sense as an attempt to establish the necessary logical and epistemological conditions for Plato’s own theory of forms and participation. In particular, Scolnicov attempts to show that the otherwise bewildering concatenation of arguments and hypotheses answers to a style of argument paralleled in other dialogues. Scolnicov also argues that the dialogue is intended as a serious rebuttal of Parmenides’ monist philosophy. Scolnicov’s thesis is thus diametrically opposed to those who think that the dialogue is intended as a successful critique of Plato’s own theory in the light of arguments adapted from Parmenides."—Denis O’Brien, author of Etudes sur Parménide; Empedocles' Cosmic Cycle: A Reconstruction from the Fragments and Secondary Sources "Scolnicov’s introduction presents a very clear account of Parmenides’ method and the contrast that Plato’s use of hypothesis presents to it as early as the Meno. Scolnicov then offers a clear account of Plato’s method and the way it establishes an idea of philosophical method in general: not a reasoning from first principles but a disclosing of the principles at the foundation of one’s prior convictions in order to test those principles. He subsequently takes up the principle of noncontradiction in particular before tackling the questions Parmenidean philosophy might raise about the doctrine of participation. An immensely clear and interesting introduction and way into the Parmenides."—Georgia Warnke, author of Justice and Interpretation: Studies in Contemporary German Social Thought
Publisher: Univ of California Press
The Three Paradoxes is an intricate and complex autobiographical comic by one of the most talented and innovative young cartoonists today. The story begins with a story inside the story: the cartoon character Paul Hornschemeier is trying to finish a story called "Paul and the Magic Pencil." Paul has been granted a magical implement, a pencil, and is trying to figure out what exactly it can do. He isn't coming up with much, but then we zoom out of this story to the creator, Paul, whose father is about to go on a walk to turn off the lights in his law office in the center of the small town. Abandoning the comic strip temporarily, Paul leaves with his camera, in order to fulfill a promise to his girlfriend that he would take pictures of the places that affected him as a child. Each "chapter" of the story is drawn in a completely different style, with strikingly unique production and color themes, and yet, somehow, despite (or perhaps because of) this non-linear progression, it all comes together as one story: a story questioning change, progress, and worth within the author's life.
Author: Paul Hornschemeier
Publisher: Fantagraphics Books
Category: Comics & Graphic Novels
When an arrogant hare thinks he�s the best around, who could possibly bring him down? One determined tortoise is about to try! Readers will delight in this beautiful retelling of one of Aesop�s most beloved fables. Clean, simple language makes the story accessible, while adorable illustrations draw in even reluctant readers. As they follow the epic race between hare and tortoise, readers will see how boastfulness can catch up to even the fastest runner, and how a good work ethic can carry anyone to victory. This classic tale introduces readers to important values such as commitment, humility, and sportsmanship in a fun way, making it a valuable addition to any library.
Publisher: The Rosen Publishing Group, Inc
Category: Juvenile Fiction
This book is about OC diamondOCO, a logic of paradox. In diamond, a statement can be true yet false; an OC imaginaryOCO state, midway between being and non-being. Diamond''s imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. Diamond is a new way to solve the dilemmas of higher mathematics. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book consists of two sections: Elementary; which covers the classic paradoxes of mathematical logic and shows how they can be resolved in this new system; and Advanced, which relates diamond to Boolean logic, three-valued logic, GAdelian meta-mathematics and dilemma games."
A Paradox Logic
Author: Nathaniel S. Hellerstein
Publisher: World Scientific
This sharply intelligent, consistently provocative book takes the reader on an astonishing, thought-provoking voyage into the realm of delightful uncertainty--a world of paradox in which logical argument leads to contradiction and common sense is seemingly rendered irrelevant. From the Trade Paperback edition.
Paradox, Puzzles, and the Frailty of Knowledge
Author: William Poundstone
A fun and fascinating look at great scientific paradoxes. Throughout history, scientists have come up with theories and ideas that just don't seem to make sense. These we call paradoxes. The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds. For example, how can a cat be both dead and alive at the same time? Why will Achilles never beat a tortoise in a race, no matter how fast he runs? And how can a person be ten years older than his twin? With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle. Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic. In doing so, he brings to life a select group of the most exciting concepts in human knowledge. Paradox is mind-expanding fun.
The Nine Greatest Enigmas in Physics
Author: Jim Al-Khalili
Publisher: Broadway Books
While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.
A Short History of Mathematical Notation and Its Hidden Powers
Author: Joseph Mazur
Publisher: Princeton University Press
In this book Saul Kripke brings his powerful philosophical intelligence to bear on Wittgenstein's analysis of the notion of following a rule.
An Elementary Exposition
Author: Saul A. Kripke
Publisher: Harvard University Press
This book is about "delta", a paradox logic. In delta, a statement can be true yet false; it is an "imaginary" state, midway between being and non-being. Delta's imaginary value solves many logical dilemmas unsolvable in two-valued Boolean logic. Delta resolves these paradoxes -- Russell's, Cantor's, Betty's and Zeno's. Delta has two parts: inner delta logic, or "Kleenean logic", which resolves the classic paradoxes of mathematical logic; and outer delta logic, which relates delta to Z mod 3, conjugate logics, cyclic distribution, and the voter' paradox.
A Paradox Logic
Author: Nathaniel Hellerstein
Publisher: World Scientific
This eponymous comic became an instant hit when it went live on The Oatmeal.com and was liked on Facebook by 700,000 fans. Now fans will have a keepsake book of this comic to give and to keep. In My Dog: The Paradox, Inman discusses the canine penchant for rolling in horse droppings, chasing large animals four times their size, and acting recklessly enthusiastic through the entirety of their impulsive, lovable lives. Hilarious and heartfelt, My Dog: The Paradox eloquently illustrates the complicated relationship between man and dog. We will never know why dogs fear hair dryers, or being baited into staring contests with cats, but as Inman explains, perhaps we love dogs so much “because their lives aren’t lengthy, logical, or deliberate, but an explosive paradox composed of fur, teeth, and enthusiasm.”
A Lovable Discourse about Man's Best Friend
Author: The Oatmeal,Matthew Inman
Publisher: Andrews McMeel Publishing
A paradox can be defined as an unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Many paradoxes raise serious philosophical problems, and they are associated with crises of thought and revolutionary advances. The expanded and revised third edition of this intriguing book considers a range of knotty paradoxes including Zeno's paradoxical claim that the runner can never overtake the tortoise, a new chapter on paradoxes about morals, paradoxes about belief, and hardest of all, paradoxes about truth. The discussion uses a minimum of technicality but also grapples with complicated and difficult considerations, and is accompanied by helpful questions designed to engage the reader with the arguments. The result is not only an explanation of paradoxes but also an excellent introduction to philosophical thinking.
Author: R. M. Sainsbury
Publisher: Cambridge University Press
Originally published in 1936, this book presents the ancient Greek text of the paraphrases and quotations of Zeno's philosophical arguments, together with a facing-page English translation and editorial commentary. Detailed notes are incorporated throughout and a bibliography is also included. This book will be of value to anyone with an interest in Zeno and ancient philosophy.
Author: H. D. P. Lee
Publisher: Cambridge University Press
On Location is the first book in English exclusively devoted to a highly significant doctrine in the history of philosophy and science--Aristotle's account of place in the Physics. The central question which Aristotle aims to answer is: What is it for something to be somewhere? Ben Morison examines how Aristotle works from simple observations about replacement to a definition of the notion of the place of a body--the inner limit of that body's surroundings. Thisdefinition lies at the heart of what we say about places, for instance when we say that we cannot be in two places at once, or that two bodies cannot be in the same place at the same time. Morison also assesses Aristotle's brilliant, though often obscure, criticisms of rival theories.This authoritative exposition and defence of Aristotle's account of place not only allows it to be properly understood in the wider context of the Physics, but also demonstrates that it is of enduring philosophical interest and value.
Aristotle's Concept of Place
Author: Benjamin Morison
Publisher: Oxford University Press on Demand
Reference book on mathematics.
From Abracadabra to Zeno's Paradoxes
Author: David Darling
Publisher: John Wiley & Sons
This book is an attempt to bring the full range of relativity theory within reach of advanced undergraduates, while containing enough new material and simplifications of old arguments so as not to bore the expert teacher. Roughly equal coverage is given tospecial relativity, general relativity, and cosmology. With many judicious omissions it can be taught in one semester, but it would better serve as the basis of a year's work. It is my hope, anyway, that its level and style of presentation may appeal also to wider c1asses of readers unrestricted by credit considerations. General relativity, the modern theory of gravitation in which free particles move along "straightest possible" lines in curved spacetime, and cosmology, with its dynamics for the whole possibly curved uni verse, not only seem necessary for a scientist's balanced view of the world, but offer some of the greatest intellectual thrills of modern physics. Nevertheless, considered luxuries, they are usu ally squeezed out of the graduate curriculum by the pressure of specialization. Special relativity escapes this tag with a ven geance, and tends to be taught as a pure service discipline, with too little emphasis on its startling ideas. What better time, there fore, to enjoy these subjects for their own sake than as an und- v vi PREFACE graduate? In spite of its forbidding mathematical reputation, even general relativity is accessible at that stage.
Special, General, and Cosmological
Author: W. Rindler
Review of the original edition: This is an inspiring textbook for students who know the theory of functions of real and complex variables and wish further knowledge of mathematical analysis. There are no problems displayed and labelled ``problems,'' but one who follows all of the arguments and calculations of the text will find use for his ingenuity and pencil. The book deals with interesting and important problems and topics in many fields of mathematical analysis, to an extent very much greater than that indicated by the titles of the chapters. It is, of course, an indispensable handbook for those interested in divergent series. It assembles a considerable part of the theory of divergent series, which has previously existed only in periodical literature. Hardy has greatly simplified and improved many theories, theorems and proofs. In addition, numerous acknowledgements show that the book incorporates many previously unpublished results and improvements of old results, communicated to Hardy by his colleagues and by others interested in the book. --Mathematical Reviews
Author: Godfrey Harold Hardy
Publisher: American Mathematical Soc.