Holding up the so-called authenticity of religious belief to critical light, Zizek draws on psychoanalysis, film and philosophy to reveal in startling fashion that nothing could be worse for believers than their beliefs turning out to be true.

    With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

    Danto argues that recent developments in the art world, in particular the production of works of art that cannot be told from ordinary things, make urgent the need for a new theory of art and make plain the factors such a theory can and cannot involve. In the course of constructing such a theory, he seeks to demonstrate the relationship between philosophy and art, as well as the connections that hold between art and social institutions and art history.The book distinguishes what belongs to artistic theory from what has traditionally been confused with it, namely aesthetic theory and offers as well a systematic account of metaphor, expression, and style, together with an original account of artistic representation. A wealth of examples, drawn especially from recent and contemporary art, illuminate the argument.

    This work represents the views of a mathematician on the analogies between computing machines and the living human brain.

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    A superb work on the nature of human action, it features influential discussions of numerous topics. These include the freedom to act; weakness of the will; thelogical form of talk about actions, intentions, and causality; the logic of practical reasoning; Hume's theory of the indirect passions; and the nature and limits of decision theory.

    In 1935, aged 22, he developed the mathematical theory upon which all subsequent stored-program digital computers are modeled.At the outbreak of hostilities with Germany in September 1939, he joined the Government Codebreaking team at Bletchley Park, Buckinghamshire and played a crucial role in deciphering Engima, the code used by the German armed forces to protect their radio communications. Turing's work on the versionof Enigma used by the German navy was vital to the battle for supremacy in the North Atlantic. He also contributed to the attack on the cyphers known as Fish, which were used by the German High Command for the encryption of signals during the latter part of the war. His contribution helped toshorten the war in Europe by an estimated two years.After the war, his theoretical work led to the development of Britain's first computers at the National Physical Laboratory and the Royal Society Computing Machine Laboratory at Manchester University.Turing was also a founding father of modern cognitive science, theorizing that the cortex at birth is an unorganized machine which through training becomes organized into a universal machine or something like it. He went on to develop the use of computers to model biological growth, launchingthe discipline now referred to as Artificial Life.The papers in this book are the key works for understanding Turing's phenomenal contribution across all these fields. The collection includes Turing's declassified wartime Treatise on the Enigma; letters from Turing to Churchill and to codebreakers; lectures, papers, and broadcasts which opened upthe concept of AI and its implications; and the paper which formed the genesis of the investigation of Artifical Life.

    Sipser's candid, crystal-clear style allows students at every level to understand and enjoy this field. His innovative "proof idea" sections explain profound concepts in plain English. The new edition incorporates many improvements students and professors have suggested over the years, and offers updated, classroom-tested problem sets at the end of each chapter.

    It now has 600,000 to a million page hits daily. Every now and then, Munroe would get emails asking him to arbitrate a science debate. 'My friend and I were arguing about what would happen if a bullet got struck by lightning, and we agreed that you should resolve it . . . ' He liked these questions so much that he started up What If. If your cells suddenly lost the power to divide, how long would you survive? How dangerous is it, really, to be in a swimming pool in a thunderstorm? If we hooked turbines to people exercising in gyms, how much power could we produce? What if everyone only had one soulmate?When (if ever) did the sun go down on the British empire? How fast can you hit a speed bump while driving and live?What would happen if the moon went away?In pursuit of answers, Munroe runs computer simulations, pores over stacks of declassified military research memos, solves differential equations, and consults with nuclear reactor operators. His responses are masterpieces of clarity and hilarity, studded with memorable cartoons and infographics. They often predict the complete annihilation of humankind, or at least a really big explosion. Far more than a book for geeks, WHAT IF: Serious Scientific Answers to Absurd Hypothetical Questions explains the laws of science in operation in a way that every intelligent reader will enjoy and feel much the smarter for having read.

    How do we reconcile these two standpoints--intellectually, morally, and practically? To what extent are they irreconcilable and to what extent can they be integrated? Thomas Nagel's ambitious and lively book tackles this fundamental issue, arguing that our divided nature is the root of a whole range of philosophical problems, touching, as it does, every aspect of human life. He deals with its manifestations in such fields of philosophy as: the mind-body problem, personal identity, knowledge and skepticism, thought and reality, free will, ethics, the relation between moral and other values, the meaning of life, and death. Excessive objectification has been a malady of recent analytic philosophy, claims Nagel, it has led to implausible forms of reductionism in the philosophy of mind and elsewhere. The solution is not to inhibit the objectifying impulse, but to insist that it learn to live alongside the internal perspectives that cannot be either discarded or objectified. Reconciliation between the two standpoints, in the end, is not always possible.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems.

    This is the initial volume of a four-book set in which Kenny will unfold a magisterial new history of Western philosophy, the first major single-author history of philosophy to appear in decades.Ancient Philosophy spans over a thousand years and brings to life the great minds of the past, from Thales, Pythagoras, and Parmenides, to Socrates, Epictetus, Marcus Aurelius, and Augustine. The book's great virtue is that it is written by one of the world's leading authorities on the subject. Instead of an uncritical, straightforward recitation of known facts—Plato and his cave of shadows, Aristotle's ethics, Augustine's City of God—we see the major philosophers through the eyes of a man who has spent a lifetime contemplating their work. Thus we do not simply get an overview of Aristotle, for example, but a penetrating and insightful critique of his thought. Kenny offers an illuminating account of the various schools of thought, from the Pre-Socratics to the Epicureans. He examines the development of logic and reason, ancient ideas about physics ("how things happen"), metaphysics and ethics, and the earliest thinking about the soul and god.Vividly written, but serious and deep enough to offer a genuine understanding of the great philosophers, Kenny's lucid and stimulating history will become the definitive work for anyone interested in the people and ideas that shaped the course of Western thought.Sir Anthony Kenny is one of Britain's most distinguished academic figures. He has been Pro-Vice-Chancellor of the University of Oxford, Master of Balliol College, Chairman of the Board of the British Library, and President of the British Academy. He has published more than forty books on philosophy and history.

    "Is my death possible?" How is this question to be understood? How and by whom can it be asked, can it be quoted, can it be an appropriate question, and can it be asked in the appropriate moment, the moment of "my death"? One of the anoretic experiences touched upon in this seminal essay is the impossible, yet unavoidable experience that "my death" can never be subject to an experience that would be properly mine, that I can have and account for, yet that there is, at the same time, nothing closer to me and more properly mine than "my death."

    Entering into The Dhammapada with Osho is to enter into a deep friendship of enlightened masters. These sutras were compiled by Buddha's disciples to contain the essence of all his teachings.This was the last turning of the Wheel of Dharma, 2,500 years ago. Osho's commentaries on these sutras set the Wheel of Dharma in motion again.Osho also answers questions from disciples and other seekers in alternate discourses all generously sprinkled with stories, personal anecdotes and, of course, a multitude of jokes. Visually this boxed set is stunning, without doubt a collector's piece and twelve volumes to dive into for years to come."Now that religion has become just a formality, and the burning messages of the buddhas who have been on earth degraded to mere formal faith, the message of Osho who has reached to such dazzling heights of human consciousness through his own experience, is incomparable in its strength to pierce the beauty within our hearts."Talks given from 21/06/79 am to 30/04/80 am