A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of Princeton’s Institute for Advanced Study, where Gödel and Einstein both worked.Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.

    Astronomer John Barrow takes an intriguing look at the limits of science, who argues that there are things that are ultimately unknowable, undoable, or unreachable.

    In Mind and World, based on the 1991 John Locke Lectures, one of the most distinguished philosophers writing today offers his diagnosis of this difficulty and points to a cure. In doing so, he delivers the most complete and ambitious statement to date of his own views, a statement that no one concerned with the future of philosophy can afford to ignore.John McDowell amply illustrates a major problem of modern philosophy--the insidious persistence of dualism--in his discussion of empirical thought. Much as we would like to conceive empirical thought as rationally grounded in experience, pitfalls await anyone who tries to articulate this position, and McDowell exposes these traps by exploiting the work of contemporary philosophers from Wilfrid Sellars to Donald Davidson. These difficulties, he contends, reflect an understandable--but surmountable--failure to see how we might integrate what Sellars calls the logical space of reasons" into the natural world. What underlies this impasse is a conception of nature that has certain attractions for the modern age, a conception that McDowell proposes to put aside, thus circumventing these philosophical difficulties. By returning to a pre-modern conception of nature but retaining the intellectual advance of modernity that has mistakenly been viewed as dislodging it, he makes room for a fully satisfying conception of experience as a rational openness to independent reality. This approach also overcomes other obstacles that impede a generally satisfying understanding of how we are placed in the world.

    This volume brings together some of the most influential contributions to the topic of free will during the past 50 years, as well as some notable recent work.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    These noteworthy accounts of the lives of David Hilbert and Richard Courant are closely related: Courant's story is, in many ways, seen as the sequel to the story of Hilbert. Originally published to great acclaim, both books explore the dramatic scientific history expressed in the lives of these two great scientists and described in the lively, nontechnical writing style of Contance Reid.

    In this book Saul Kripke brings his powerful philosophic intelligence to bear on Wittgenstein's analysis of the notion of following a rule.

    Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

    A brilliantly clear and penetrating exposition of developments in physical science and mathematics brought about by the advent of non-Euclidean geometries, including in-depth coverage of the foundations of geometry, the theory of time, Einstein's theory of relativity and its consequences, other key topics.

    Unlike party puzzles or brain teasers, many paradoxes are serious in that they raise serious philosophical problems, and are associated with crises of thought and revolutionary advances. To grapple with them is not merely to engage in an intellectual game, but to come to grips with issues of real import. The second, revised edition of this intriguing book expands and updates the text to take account of new work on the subject. It provides a valuable and accessible introduction to a range of paradoxes and their possible solutions, with questions designed to engage the reader with the arguments and full bibliographical references to both classic and current literature on the topic.

    A fun and fascinating look at great scientific paradoxes.   Throughout history, scientists have come up with theories and ideas that just don't seem to make sense.  These we call paradoxes.  The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.  For example, how can a cat be both dead and alive at the same time?  Why will Achilles never beat a tortoise in a race, no matter how fast he runs?  And how can a person be ten years older than his twin?   With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.  Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic.  In doing so, he brings to life a select group of the most exciting concepts in human knowledge.  Paradox is mind-expanding fun.

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    More than anything else, he argues, it is the neglect of consciousness that results in so much barrenness and sterility in psychology, the philosophy of mind, and cognitive science: there can be no study of mind that leaves out consciousness. What is going on in the brain is neurophysiological processes and consciousness and nothing more -- no rule following, no mental information processing or mental models, no language of thought, and no universal grammar. Mental events are themselves features of the brain, "like liquidity is a feature of water."Beginning with a spirited discussion of what's wrong with the philosophy of mind, Searle characterizes and refutes the philosophical tradition of materialism. But he does not embrace dualism. All these "isms" are mistaken, he insists. Once you start counting types of substance you are on the wrong track, whether you stop at one or two. In four chapters that constitute the heart of his argument, Searle elaborates a theory of consciousness and its relation to our overall scientific world view and to unconscious mental phenomena. He concludes with a criticism of cognitive science and a proposal for an approach to studying the mind that emphasizes the centrality of consciousness to any account of mental functioning.In his characteristically direct style, punctuated with persuasive examples, Searle identifies the very terminology of the field as the main source of truth. He observes that it is a mistake to suppose that the ontology of the mental is objective and to suppose that the methodology of a science of the mind must concern itself only with objectively observable behavior; that it is also a mistake to suppose that we know of the existence of mental phenomena in others only by observing their behavior; that behavior or causal relations to behavior are not essential to the existence of mental phenomena; and that it is inconsistent with what we know about the universe and our place in it to suppose that everything is knowable by us.

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