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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.

Decision-Theoretic Foundations.- From Prior Information to Prior Distributions.- Bayesian Point Estimation.- Tests and Confidence Regions.- Bayesian Calculations.- Model Choice.- Admissibility and Complete Classes.- Invariance, Haar Measures, and Equivariant Estimators.- Hierarchical and Empirical Bayes Extensions.- A Defense of the Bayesian Choice.

'a Cerebrally Enjoyable Survey, Written With Great Clarity And Touches Of Wit . . . The Non-western Section Throws Up Some Fascinating Revelations' Sunday Times 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 There Has Been No Comprehensive And Entertaining, Single-volume History Of This Great Intellectual Journey Since 1945. 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.

Classical Philosophy is the first of a series of books in which Peter Adamson aims ultimately to present a complete history of philosophy, more thoroughly but also more enjoyably than ever before. In short, lively chapters, based on the popular History of Philosophy podcast, he offers an accessible, humorous, and detailed look at the emergence of philosophy with the Presocratics, the probing questions of Socrates, and the first full flowering of philosophy with the dialogues of Plato and the treatises of Aristotle. The story is told 'without any gaps', discussing not only such major figures but also less commonly discussed topics like the Hippocratic Corpus, the Platonic Academy, and the role of women in ancient philosophy. Within the thought of Plato and Aristotle, the reader will find in-depth introductions to major works, such as the Republic and the Nicomachean Ethics, which are treated in detail that is unusual in an introduction to ancient philosophy. Adamson looks at fascinating but less frequently read Platonic dialogues like the Charmides and Cratylus, and Aristotle's ideas in zoology and poetics. This full coverage allows him to tackle ancient discussions in all areas of philosophy, including epistemology, metaphysics, philosophy of language, philosophy of science, ethics and politics. Attention is also given to the historical and literary context of classical philosophy, with exploration of how early Greek cosmology responded to the poets Homer and Hesiod, how Socrates was presented by the comic playwright Aristophanes and the historian Xenophon, and how events in Greek history may have influenced Plato's thought. This is a new kind of history which will bring philosophy to life for all readers, including those coming to the subject for the first time.

"[Mythologies] illustrates the beautiful generosity of Barthes's progressive interest in the meaning (his word is signification) of practically everything around him, not only the books and paintings of high art, but also the slogans, trivia, toys, food, and popular rituals (cruises, striptease, eating, wrestling matches) of contemporary life . . . For Barthes, words and objects have in common the organized capacity to say something; at the same time, since they are signs, words and objects have the bad faith always to appear natural to their consumer, as if what they say is eternal, true, necessary, instead of arbitrary, made, contingent. Mythologies finds Barthes revealing the fashioned systems of ideas that make it possible, for example, for 'Einstein's brain' to stand for, be the myth of, 'a genius so lacking in magic that one speaks about his thought as a functional labor analogous to the mechanical making of sausages.' Each of the little essays in this book wrenches a definition out of a common but constructed object, making the object speak its hidden, but ever-so-present, reservoir of manufactured sense."--Edward W. Said

Who ought to govern? Why should I obey the law? How should conflict be controlled? What is the proper education for a citizen and a statesman? These questions probe some of the deepest and most enduring problems that every society confronts, regardless of time and place. Today we ask the same crucial questions about law, authority, justice, and freedom that Plato, Aristotle, Machiavelli, Hobbes, Locke, Rousseau, and Tocqueville faced in previous centuries.In this lively and enlightening book, Professor Steven B. Smith introduces the wide terrain of political philosophy through the classic texts of the discipline. Works by the greatest thinkers illuminate the permanent problems of political life, Smith shows, and while we may not accept all their conclusions, it would be a mistake to overlook the relevance of their insights.

'...every page shows evidence of great mastery of the subject.' Trans. Faraday Society 'this book is destined to play a major part in the future education of theoretical physicists.' Proceedings of the Physical Society This edition has been completely revised to include some 20% of new material. Important recent developments such as the theory of Regge poles are now included. Many problems with solutions have been added to those already contained in the book.

This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.

In this invaluable book, Tim Lewens shows in a clear and accessible manner how important Darwin is for philosophy and how his work has shaped and challenged the very nature of the subject. Beginning with an overview of Darwin's life and work, the subsequent chapters discuss the full range of fundamental philosophical topics from a Darwinian perspective. These include natural selection; the origin and nature of species; the role of evidence in scientific enquiry; the theory of Intelligent Design; evolutionary approaches to the human mind; the implications of Darwin's work for ethics and epistemology; and the question of how social and political thought needs to be updated in the light of a Darwinian understanding of human nature. A concluding chapter assesses the philosophical legacy of Darwin's thought. Darwin is essential reading for anyone in the humanities, social sciences and sciences seeking a philosophical introduction to Darwin, or anyone simply seeking a philosophical companion to Darwin's own writings.

Philosophy of education has an honored place in the history of Western philosophical thought. Its questions are as vital now, both philosophically and practically, as they have ever been. In recent decades, however, philosophical thinking about education has largely fallen off the philosophical radar screen. Philosophy of education has lost intimate contact with the parent discipline to a regrettably large extent--to the detriment of both. The Oxford Handbook of Philosophy of Education is intended to serve as a general introduction to key issues in the field, to further the philosophical pursuit of those issues, and to bring philosophy of education back into closer contact with general philosophy. Distinguished philosophers and philosophers of education, most of whom have made important contributions to core areas of philosophy, turn their attention in these 28 essays to a broad range of philosophical questions concerning education. The chapters are accessible to readers with no prior exposure to philosophy of education, and provide both surveys of the general domain they address, and advance the discussion in those domains in original and fruitful ways. Together their authors constitute a new wave of general philosophers taking up fundamental philosophical questions about education--the first such cohort of outstanding general philosophers to do so (in English) in a generation.