A genius who throughout his life solved complex mathematical calculations in his head, and a writer gifted with an inimitable style, Poincaré rose to the challenge of interpreting the philosophy of science to scientists and nonscientists alike. His lucid and welcoming prose made him the Carl Sagan of his time. This volume collects his three most important books: Science and Hypothesis (1903); The Value of Science (1905); and Science and Method (1908).

    His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.

    The result is a completely accessible introduction to the main themes of the philosophy of science. Intended for undergraduates and general readers with no prior background in philosophy, Theory and Reality covers logical positivism; the problems of induction and confirmation; Karl Popper's theory of science; Thomas Kuhn and "scientific revolutions"; the views of Imre Lakatos, Larry Laudan, and Paul Feyerabend; and challenges to the field from sociology of science, feminism, and science studies. The book then looks in more detail at some specific problems and theories, including scientific realism, the theory-ladeness of observation, scientific explanation, and Bayesianism. Finally, Godfrey-Smith defends a form of philosophical naturalism as the best way to solve the main problems in the field. Throughout the text he points out connections between philosophical debates and wider discussions about science in recent decades, such as the infamous "science wars." Examples and asides engage the beginning student; a glossary of terms explains key concepts; and suggestions for further reading are included at the end of each chapter. However, this is a textbook that doesn't feel like a textbook because it captures the historical drama of changes in how science has been conceived over the last one hundred years.Like no other text in this field, Theory and Reality combines a survey of recent history of the philosophy of science with current key debates in language that any beginning scholar or critical reader can follow.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    However, it is one of the basic principles of quantum theory, the most widely accepted explanation of the subatomic world - and one of the fascinating subjects dealt with in Equations of Eternity.

    It deals with one powerful obsession that preoccupied Escher: what he called "the regular division of the plane," the puzzlelike interlocking of birds, fish, lizards, and other natural forms in continuous patterns. Schattschneider asks, "How did he do it?" She answers the question by analyzing Escher's notebooks." Visions of Symmetry includes many of Escher's masterworks, as well as hundreds of lesser-known examples of his work. This new edition also features a foreward and an illustrated epilogue that reveals new information about Escher's inspiration and shows how his ideas of symmetry have influenced mathematicians, computer scientists, and contemporary artists.

    This new edition incorporates the striking developments that have taken place in neuroscience, cognitive science, and artificial intelligence and notes their expanding relevance to philosophical issues.Churchland organizes and clarifies the new theoretical and experimental results of the natural sciences for a wider philosophical audience, observing that this research bears directly on questions concerning the basic elements of cognitive activity and their implementation in real physical systems. (How is it, he asks, that living creatures perform some cognitive tasks so swiftly and easily, where computers do them only badly or not at all?) Most significant for philosophy, Churchland asserts, is the support these results tend to give to the reductive and the eliminative versions of materialism."A Bradford Book"

    

    A timeless introduction to the field and a landmark in symbolic logic, showing that classical logic can be treated algebraically.

    With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction--and whether the universe truly has a future.

    Explaining why the whole is sometimes smarter than the sum of its parts, Johnson presents surprising examples of feedback, self-organization, and adaptive learning. How does a lively neighborhood evolve out of a disconnected group of shopkeepers, bartenders, and real estate developers? How does a media event take on a life of its own? How will new software programs create an intelligent World Wide Web? In the coming years, the power of self-organization -- coupled with the connective technology of the Internet -- will usher in a revolution every bit as significant as the introduction of electricity. Provocative and engaging, Emergence puts you on the front lines of this exciting upheaval in science and thought.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.