Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    Magnificent collection of Mark Twain's topical writings, mainly and most eloquently concerned with the themes of social justice, the American Civilization

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    This predicament seems inevitable, but in fact it's quite new. In medieval Europe, God's calling was a grounding force. In ancient Greece, a whole pantheon of shining gods stood ready to draw an appropriate action out of you. Like an athlete in “the zone,” you were called to a harmonious attunement with the world, so absorbed in it that you couldn’t make a “wrong” choice. If our culture no longer takes for granted a belief in God, can we nevertheless get in touch with the Homeric moods of wonder and gratitude, and be guided by the meanings they reveal?All Things Shining says we can. Hubert Dreyfus and Sean Dorrance Kelly illuminate some of the greatest works of the West to reveal how we have lost our passionate engagement with and responsiveness to the world. Their journey takes us from the wonder and openness of Homer’s polytheism to the monotheism of Dante; from the autonomy of Kant to the multiple worlds of Melville; and, finally, to the spiritual difficulties evoked by modern authors such as David Foster Wallace and Elizabeth Gilbert.Dreyfus, a philosopher at the University of California, Berkeley, for forty years, is an original thinker who finds in the classic texts of our culture a new relevance for people’s everyday lives. His lively, thought-provoking lectures have earned him a podcast audience that often reaches the iTunesU Top 40. Kelly, chair of the philosophy department at Harvard University, is an eloquent new voice whose sensitivity to the sadness of the culture— and to what remains of the wonder and gratitude that could chase it away—captures a generation adrift.Re-envisioning modern spiritual life through their examination of literature, philosophy, and religious testimony, Dreyfus and Kelly unearth ancient sources of meaning, and teach us how to rediscover the sacred, shining things that surround us every day. This book will change the way we understand our culture, our history, our sacred practices, and ourselves. It offers a new—and very old—way to celebrate and be grateful for our existence in the modern world.

    This modern section has been overhauled to reflect the diversity of American writing since 1945. A section on 19th-century women's writing is included.

    This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

    Of these, gravity may the most obvious, but it is also the most mysterious. Newton managed to predict the force of gravity but couldn't explain how it worked at a distance. Einstein picked up on the simple premise that gravity and acceleration are interchangeable to devise his mind-bending general relativity, showing how matter warps space and time. Not only did this explain how gravity worked – and how apparently simple gravitation has four separate components – but it predicted everything from black holes to gravity's effect on time. Whether it's the reality of anti-gravity or the unexpected discovery that a ball and a laser beam drop at the same rate, gravity is the force that fascinates.

    Written in the author's early forties in the last years of the fourth century A.D. and during his first years as a bishop, they reflect on his life and on the activity of remembering and interpreting a life. Books I-IV are concerned with infancy and learning to talk, schooldays, sexual desire and adolescent rebellion, intense friendships and intellectual exploration. Augustine evolves and analyses his past with all the resources of the reading which shaped his mind: Virgil and Cicero, Neoplatonism and the Bible. This volume, which aims to be usable by students who are new to Augustine, alerts readers to the verbal echoes and allusions of Augustine's brilliant and varied Latin, and explains his theological and philosophical questioning of what God is and what it is to be human. The edition is intended for use by students and scholars of Latin literature, theology and Church history.

    Inspired by and expanding on a series of lectures presented by Leonard Peikoff, David Harriman presents a fascinating answer to the problem of induction-the epistemological question of how we can know the truth of inductive generalizations.Ayn Rand presented her revolutionary theory of concepts in her book Introduction to Objectivist Epistemology. As Dr. Peikoff subsequently explored the concept of induction, he sought out David Harriman, a physicist who had taught philosophy, for his expert knowledge of the scientific discovery process.Here, Harriman presents the result of a collaboration between scientist and philosopher. Beginning with a detailed discussion of the role of mathematics and experimentation in validating generalizations in physics-looking closely at the reasoning of scientists such as Galileo, Kepler, Newton, Lavoisier, and Maxwell-Harriman skillfully argues that the inductive method used in philosophy is in principle indistinguishable from the method used in physics.

    Combine this with thoughtful and thorough apparatus, and Philosophy of Science: The Central Issues is the most flexible and comprehensive collection ever created for undergraduate courses.

    This Penguin Classics edition is translated with an introduction by Betty Radice.A prominent lawyer and administrator, Pliny was also a prolific letter-writer, who numbered among his correspondents such eminent figures as Tacitus, Suetonius and the Emperor Trajan, as well as a wide circle of friends and family. His lively and very personal letters address an astonishing range of topics, from a deeply moving account of his uncle's death in the eruption that engulfed Pompeii, to observations on the early Christians - 'a desperate sort of cult carried to extravagant lengths' - from descriptions of everyday life in Rome, with its scandals and court cases, to Pliny's life in the country.Betty Radice's definitive edition was the forst complete modern translation of Pliny's letters. In her introduction she examines the shrewd, tolerant and occasionally pompous man who emerges from these letters.Gaius Plinius Caecilius Secundus (c. 61-113), better known as Pliny the Younger, and nephew of Pliny the Elder, was born in Como, Italy. Beginning his career at the bar when he was eighteen, Pliny managed to emerge unscathed from Domitian's 'reign of terror', even being appointed an official at the treasury. In 103 he was awarded a priesthood in recognition of his distinguished public service, and was prominent in several major prosecutions. His nine books of personal letters were selected by Pliny himself and published during his lifetime, while his official correspondence with Trajan was published as a tenth book after his death and contains a celebrated exchange of letters on the early Christians.If you enjoyed The Letters of the Younger Pliny, you might like Tacitus' The Annals of Imperial Rome, also available in Penguin Classics.

    It defines our experience of the world; it echoes through our every waking hour. Time is the very foundation of conscious experience. Yet as familiar as it is, time is also deeply mysterious. We cannot see, hear, smell, taste, or touch it. Yet we do "feel" it--or at least we "think" we feel it. No wonder poets, writers, philosophers, and scientists have grappled with time for centuries.In his latest book, award-winning science writer Dan Falk chronicles the story of how humans have come to understand time over the millennia, and by drawing from the latest research in physics, psychology, and other fields, Falk shows how that understanding continues to evolve. "In Search of Time" begins with our earliest ancestors' perception of time and the discoveries that led--with much effort--to the Gregorian calendar, atomic clocks, and "leap seconds." Falk examines the workings of memory, the brain's remarkable "bridge across time," and asks whether humans are unique in their ability to recall the past and imagine the future. He explores the possibility of time travel, and the paradoxes it seems to entail. Falk looks at the quest to comprehend the beginning of time and how time--and the universe--may end. Finally, he examines the puzzle of time's "flow," and the remarkable possibility that the passage of time may be an illusion.Entertaining, illuminating, and ultimately thought provoking, "In Search of Time "reveals what some of our most insightful thinkers have had to say about time, from Aristotle to Kant, from Newton to Einstein, and continuing with the brightest minds of today.

    Wolke, professor emeritus of chemistry at the University of Pittsburgh and acclaimed author of What Einstein Didn't Know, understands the need to...well, understand. Now he provides more amusing explanations of such everyday phenomena as gravity (If you're in a falling elevator, will jumping at the last instant save your life?) and acoustics (Why does a whip make such a loud cracking noise?), along with amazing facts, belly-up-to-the-bar bets, and mind-blowing reality bites all with his trademark wit and wisdom.If you shoot a bullet into the air, can it kill somebody when it comes down? You can find out about all this and more in an astonishing compendium of the proverbial mind-boggling mysteries of the physical world we inhabit.Arranged in a question-and-answer format and grouped by subject for browsing ease, WHAT EINSTEIN TOLD HIS BARBER is for anyone who ever pondered such things as why colors fade in sunlight, what happens to the rubber from worn-out tires, what makes red-hot objects glow red, and other scientific curiosities. Perfect for fans of Newton's Apple, Jeopardy!, and The Discovery Channel, WHAT EINSTEIN TOLD HIS BARBER also includes a glossary of important scientific buzz words and a comprehensive index. -->

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.