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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.

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.

'Grayling brings satisfying order to daunting subjects' Steven Pinker 'An enthusiastic thinker who embraces humour, common sense and lucidity' Independent _______________ From the eminent philosopher, an authoritative exploration of the great questions of how to live 'There is a question everyone has to ask and answer - in fact, has to keep on asking and keep on answering. It is, 'How should I live my life?' meaning, 'What values shall I live by? 'What sort of person should I be? What shall I aim for?' The great majority of people do not ask this question, they merely answer it unthinkingly, by adopting conventional views of life and what matters in it...' From Stoics to existentialists, in philosophy and literature, discussion of the philosophy of life -- of love and death, of courage, fortitude and wisdom -- challenges us all to think about what kinds of life are truly worth living. In this summation of a lifetime thinking and writing about this great question, A. C. Grayling explores with clarity and depth the ideas that each of us must use in answering it for ourselves. Drawing on the lives, experiences and works of a fantastically eclectic range of thinkers -- taking in not only philosophers such as Confucius, Seneca and Nietzsche, but also authors from Shakespeare to Ursula LeGuin, and modern thinkers such as Martha Nussbaum and Bernard Williams - Philosophy and Life brings together wisdom from across eras and continents in a tour de force on the philosophy of being human in a complicated world.

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

Kurt Gödel (1906-1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory and stronger systems, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, the foundations of computation theory, unusual cosmological models, and for the strong individuality of his writings on the philosophy of mathematics. The Collected Works is a landmark resource that draws together a lifetime of creative accomplishment. The first two volumes were devoted to Gödel's publications in full (both in the original and translation). This third volume features a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass, documents that enlarge considerably our appreciation of his scientific and philosophical thought and add a great deal to our understanding of his motivations. Continuing the format of the earlier volumes, the present volume includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, English translations of material originally written in German (some transcribed from Gabelsberger shorthand), and a complete bibliography. A succeeding volume is to contain a comprehensive selection of Gödel's scientific correspondence and a complete inventory of his Nachlass. The books are designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science.

Called by many France's foremost philosopher, Gilles Deleuze is one of the leading thinkers in the Western World. His acclaimed works and celebrated collaborations with Félix Guattari have established him as a seminal figure in the fields of literary criticism and philosophy. The long-awaited publication of What Is Philosophy? in English marks the culmination of Deleuze's career.Deleuze and Guattari differentiate between philosophy, science, and the arts, seeing as means of confronting chaos, and challenge the common view that philosophy is an extension of logic. The authors also discuss the similarities and distinctions between creative and philosophical writing. Fresh anecdotes from the history of philosophy illuminate the book, along with engaging discussions of composers, painters, writers, and architects.A milestone in Deleuze's collaboration with Guattari, What Is Philosophy? brings a new perspective to Deleuze's studies of cinema, painting, and music, while setting a brilliant capstone upon his work.

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.

Voltaire's Philosophical Dictionary, first published in 1764, is a series of short, radical essays - alphabetically arranged - that form a brilliant and bitter analysis of the social and religious conventions that then dominated eighteenth-century French thought. One of the masterpieces of the Enlightenment, this enormously influential work of sardonic wit - more a collection of essays arranged alphabetically, than a conventional dictionary - considers such diverse subjects as Abraham and Atheism, Faith and Freedom of Thought, Miracles and Moses. Repeatedly condemned by civil and religious authorities, Voltaire's work argues passionately for the cause of reason and justice, and criticizes Christian theology and contemporary attitudes towards war and society - and claims, as he regards the world around him: 'common sense is not so common'.

When is it right to go to war? The most persuasive answer to this question has always been 'in self-defense'. In a penetrating new analysis, bringing together moral philosophy, political science, and law, David Rodin shows what's wrong with this answer. He proposes a comprehensive new theory of the right of self-defense which resolves many of the perplexing questions that have dogged both jurists and moral philosophers. By applying the theory of self-defense to international relations, Rodin produces a far-reaching critique of the canonical Just War theory. The simple analogy between self-defense and national defense - between the individual and the state - needs to be fundamentally rethought, and with it many of the basic elements of international law and the ethics of international relations.