Traces the epic history of Greek philosopher Zeno's yet-unsolved paradox of motion, citing the contributions of top minds to the scientific community's understanding of the elusive basic structure of time and space.

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.

Of all Plato’s dialogues, the Parmenides is notoriously the most difficult to interpret. Scholars of all periods have disagreed about its aims and subject matter. The interpretations have ranged from reading the dialogue as an introduction to the whole of Platonic metaphysics to seeing it as a collection of sophisticated tricks, or even as an elaborate joke. This work presents an illuminating new translation of the dialogue together with an extensive introduction and running commentary, giving a unified explanation of the Parmenides and integrating it firmly within the context of Plato's metaphysics and methodology. Scolnicov shows that in the Parmenides Plato addresses the most serious challenge to his own philosophy: the monism of Parmenides and the Eleatics. In addition to providing a serious rebuttal to Parmenides, Plato here re-formulates his own theory of forms and participation, arguments that are central to the whole of Platonic thought, and provides these concepts with a rigorous logical and philosophical foundation. In Scolnicov's analysis, the Parmenides emerges as an extension of ideas from Plato's middle dialogues and as an opening to the later dialogues. Scolnicov’s analysis is crisp and lucid, offering a persuasive approach to a complicated dialogue. This translation follows the Greek closely, and the commentary affords the Greekless reader a clear understanding of how Scolnicov’s interpretation emerges from the text. This volume will provide a valuable introduction and framework for understanding a dialogue that continues to generate lively discussion today.

This book examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.

'This sentence is false'. Is it? If a hotel with an infinite number of rooms is fully occupied, can it still accommodate a new guest? How can we have emotional responses to fiction, when we know that the objects of our emotions do not exist?

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.