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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.

Product Description 'I'll stop doing it as soon as I understand what I'm doing.' Somewhere between a historical account and work of philosophy, Socrates' Defence details the final plea of Plato's beloved mentor. Introducing Little Black Classics: 80 books for Penguin's 80th birthday. Little Black Classics celebrate the huge range and diversity of Penguin Classics, with books from around the world and across many centuries. They take us from a balloon ride over Victorian London to a garden of blossom in Japan, from Tierra del Fuego to 16th-century California and the Russian steppe. Here are stories lyrical and savage; poems epic and intimate; essays satirical and inspirational; and ideas that have shaped the lives of millions. Plato (474 BC-347 BC). Plato's works available in Penguin Classics are Republic, The Last Days of Socrates, The Laws, Phaedrus, Protagoras and Meno, Timaeus and Critias, Theaetetus, Early Socratic Dialogues, The Symposium and Gorgias. About the Author Plato (474 BC-347 BC). Plato's works available in Penguin Classics are Republic, The Last Days of Socrates, The Laws, Phaedrus, Protagoras and Meno, Timaeus and Critias, Theaetetus, Early Socratic Dialogues, The Symposium and Gorgias.

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. The Father of Existentialism, Kierkegaard transformed philosophy with his conviction that we must all create our own nature; in this great work of religious anxiety, he argues that a true understanding of God can only be attained by making a personal 'leap of faith'.

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.

There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations.Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics.Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach―that is, to incorporate prior knowledge when reasoning with incomplete information―in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data―and how to fix it.

A profoundly beautiful and uniquely insightful description of the universe, Benedict de Spinoza's Ethics is one of the masterpieces of Enlightenment-era philosophy.Published shortly after his death, the Ethics is undoubtedly Spinoza's greatest work - an elegant, fully cohesive cosmology derived from first principles, providing a coherent picture of reality, and a guide to the meaning of an ethical life. Following a logical step-by-step format, it defines in turn the nature of God, the mind, the emotions, human bondage to the emotions, and the power of understanding - moving from a consideration of the eternal, to speculate upon humanity's place in the natural order, the nature of freedom and the path to attainable happiness. A powerful work of elegant simplicity, the Ethics is a brilliantly insightful consideration of the possibility of redemption through intense thought and philosophical reflection. The Ethics is presented in the standard translation of the work by Edwin Curley. This edition also includes an introduction by Stuart Hampshire, outlining Spinoza's philosophy and placing it in context.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.

This book, one of the first full-length studies of the modalities to emerge from the debate to which Saul Kripke, David Lewis, Ruth Marcus, and others are contributing, is an exploration and defense of the notion of modality de re, the idea that objects have both essential and accidental properties. Plantinga develops his argument by means of the notion of possible worlds and ranges over such key problems as the nature of essence, transworld identity, negative existential propositions, and the existence of unactual objects in other possible worlds. He also applies his logical theories to the elucidation of two problems in the philosophy of religion: the problem of evil and the ontological argument.

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.

Written over the last 18 months of his life and inspired by his interest in G. E. Moore's defense of common sense, this much discussed volume collects Wittgenstein's reflections on knowledge and certainty, on what it is to know a proposition for sure.

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.