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An accessible and fascinating exploration of how Alan Turing’s mathematical theory gave rise to modern computer science and applications—from the desktops to cell phonesIn 1936, when he was just 24 years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing’s Vision, Chris Bernhardt explains the theory for the general reader, beginning with its foundations and systematically building to its surprising conclusions. He also views Turing’s theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing’s later work, and the birth of the modern computer.Turing wanted to show that there were problems that were beyond any computer’s ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing’s ideas, Bernhardt examines 3 well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing’s problem concerning computable numbers.

Throughout history, some books have changed the world. They have transformed the way we see ourselves - and each other. They have inspired debate, dissent, war and revolution. They have enlightened, outraged, provoked and comforted. They have enriched lives - and destroyed them. Now Penguin brings you the works of the great thinkers, pioneers, radicals and visionaries whose ideas shook civilization and helped make us who we are. Plato's retelling of the discourses between Socrates and his friends on such subjects as love and desire, truth and illusion, spiritual transcendence and the qualities of a good ruler, profoundly affected the ways in which we view human relationships, society and leadership - and shaped the whole tradition of Western philosophy.

This handsome new edition of Stanley Cavell's landmark text, first published 20 years ago, provides a new preface that discusses the reception and influence of his work, which occupies a unique niche between philosophy and literary studies.

Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.“It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov

Friedrich Nietzsche's most accessible and influential philosophical work, misquoted, misrepresented, brilliantly original and enormously influentialNietzsche was one of the most revolutionary and subversive thinkers in Western philosophy, and Thus Spoke Zarathustra remains his most famous and influential work. It describes how the ancient Persian prophet Zarathustra descends from his solitude in the mountains to tell the world that God is dead and that the Superman, the human embodiment of divinity, is his successor. Nietzsche's utterance 'God is dead', his insistence that the meaning of life is to be found in purely human terms, and his doctrine of the Superman and the will to power were all later seized upon and unrecognisably twisted by, among others, Nazi intellectuals. With blazing intensity and poetic brilliance, Nietzsche argues that the meaning of existence is not to be found in religious pieties or meek submission to authority, but in an all-powerful life force: passionate, chaotic and free.For more than seventy years, Penguin has been the leading publisher of classic literature in the English-speaking world. With more than 1,700 titles, Penguin Classics represents a global bookshelf of the best works throughout history and across genres and disciplines. Readers trust the series to provide authoritative texts enhanced by introductions and notes by distinguished scholars and contemporary authors, as well as up-to-date translations by award-winning translators.

In a single work of colossal scope one of the world’s greatest scientists has given us a complete and unrivalled guide to the glories of the universe.The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader — for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book.Roger Penrose’s purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. Rarely less than challenging, the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams.The Road to Reality was a Sunday Times top-ten bestseller in the hardcover edition, with over 40,000 copies sold.

Widely recognized as the finest definition of existentialist philosophy ever written, this book introduced existentialism to America in 1958. Barrett speaks eloquently and directly to concerns of the 1990s: a period when the irrational and the absurd are no better integrated than before and when humankind is in even greater danger of destroying its existence without ever understanding the meaning of its existence.Irrational Man begins by discussing the roots of existentialism in the art and thinking of Augustine, Aquinas, Pascal, Baudelaire, Blake, Dostoevski, Tolstoy, Hemingway, Picasso, Joyce, and Beckett. The heart of the book explains the views of the foremost existentialists—Kierkegaard, Nietzsche, Heidegger, and Sartre. The result is a marvelously lucid definition of existentialism and a brilliant interpretation of its impact.

"Great philosophical biographies can be counted on one hand. Monk's life of Wittgenstein is such a one."—The Christian Science Monitor.

Now in its fifth edition, this historically organized introductory text treats philosophy as a dramatic and continuous story--a conversation about humankind's deepest and most persistent concerns. Tracing the exchange of ideas between history's key philosophers, The Great Conversation: A Historical Introduction to Philosophy, Fifth Edition, demonstrates that while constructing an argument or making a claim, one philosopher almost always has others in mind. The book addresses the fundamental questions of human life: Who are we? What can we know? How should we live? and What sort of reality do we inhabit?The fifth edition retains the distinctive feature of previous editions: author Norman Melchert provides a generous selection of excerpts from major philosophical works and makes them more easily understandable to students with his lucid and engaging explanations. Ranging from the Pre-Socratics to Derrida and Quine, the selections are organized historically and include four complete works: Plato's Euthyphro, Apology, and Crito, and Descartes' Meditations on First Philosophy. The author's commentary offers a rich intellectual and cultural context for the philosophical ideas conveyed in the excerpts. Extensive cross-referencing shows students how philosophers respond appreciatively or critically to the thoughts of other philosophers. The text is enhanced by two types of exercises--"Basic Questions" and "For Further Thought"--and more than sixty illustrations.New to the Fifth Edition:* A new chapter (25) on Simone de Beauvoir and her contributions to philosophy* New material on Buddhist, Muslim, and Jewish thinkers, including profiles of the Buddha, Avicenna (Ibn Sina), Averroës (Ibn Rushd), and Maimonides (Moses ben Maimon)* A new profile of Jean-Jacques Rousseau* Improved translations of several of Plato's works, including Protagoras, Gorgias, Phaedo, Symposium,Meno, and the Republic* Review questions that are now dispersed throughout the chapters (instead of at chapter ends) to follow relevant passages and facilitate classroom discussion* Thirteen new images, including seven explanatory cartoons that help students understand key concepts* A revised Instructor's Manual and Test Bank--available both on CD and in a printed version--containing essential points, teaching suggestions, and multiple-choice, short-answer, and essay exam questionsThe Great Conversation, Fifth Edition, is also available in two paperback volumes to suit your course needs. Volume I: Pre-Socratics through Descartes includes chapters 1-13 of the combined volume, while Volume II: Descartes through Derrida and Quine includes chapters 12-26.

The story of philosophy is an epic tale: an exploration of the ideas, views and teachings of some of the most creative minds known to humanity. But since the long-popular classic Bertrand Russell's History of Western Philosophy, first published in 1945, there has been no comprehensive and entertaining, single-volume history of this great intellectual journey.With his characteristic clarity and elegance A. C. Grayling takes the reader from the world-views and moralities before the age of the Buddha, Confucius and Socrates, through Christianity's dominance of the European mind to the Renaissance and Enlightenment, and on to Mill, Nietzsche, Sartre, and philosophy today. And, since the story of philosophy is incomplete without mention of the great philosophical traditions of India, China and the Persian-Arabic world, he gives a comparative survey of them too.Intelligible for students and eye-opening for philosophy readers, he covers epistemology, metaphysics, ethics, aesthetics, logic, the philosophy of mind, the philosophy of language, political philosophy and the history of debates in these areas of enquiry, through the ideas of the celebrated philosophers as well as less well-known influential thinkers. He also asks what we have learnt from this body of thought, and what progress is still to be made.The first authoritative and accessible single-volume history of philosophy for decades, remarkable for its range and clarity, this is a landmark work.