E. Moore, and Ludwig Wittgenstein in the four decades around the turn of the twentieth century, analytic philosophy established itself in various forms in the 1930s. After the Second World War, it developed further in North America, in the rest of Europe, and is now growing in influence as the dominant philosophical tradition right across the world, from Latin America to East Asia.In this Very Short Introduction Michael Beaney introduces some of the key ideas of the founders of analytic philosophy by exploring certain fundamental philosophical questions and showing how those ideas can be used in offering answers. Considering the work of Susan Stebbing, he also explores the application of analytic philosophy to critical thinking, and emphasizes the conceptual creativity that lies at the heart of fruitful analysis. Throughout, Beaney illustrates why clarity of thinking, precision of expression, and rigour of argumentation are rightly seen as virtues of analytic philosophy.

    Austin was one of the leading philosophers of the twentieth century. The William James Lectures presented Austin's conclusions in the field to which he directed his main efforts on a wide variety of philosophical problems. These talks became the classic How to Do Things with Words.For this second edition, the editors have returned to Austin's original lecture notes, amending the printed text where it seemed necessary. Students will find the new text clearer, and, at the same time, more faithful to the actual lectures. An appendix contains literal transcriptions of a number of marginal notes made by Austin but not included in the text. Comparison of the text with these annotations provides new dimensions to the study of Austin's work.

    Monk's life of Wittgenstein is such a one."--"The Christian Science Monitor."

    Taking examples from sources as diverse as Plato and Steven Spielberg, author Julian Baggini presents abstract philosophical issues in concrete terms, suggesting possible solutions while encouraging readers to draw their own conclusions: Lively, clever, and thought-provoking, The Pig That Wants to Be Eaten is a portable feast for the mind that is sure to satisfy any intellectual appetite.

    Magee does a great job of balancing the various aspects of the history of philosophy that may be of interest to different readers. Each philosopher is covered in a section of a few pages outlining the thinker's major ideas, but also containing sidebars with famous quotes, major works, related topics and historical notes. The book is organized chronologically and philosophers are grouped into intellectual movements, introduced and expanded by insets. This format allows the book to be used as a point reference on a single thinker or school of thought, but also reads well from cover to cover as the "story of thought". If you are looking for a good introduction to philosophy, it would be hard to find a more complete, accessible, and universally appealing resource.

    It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn...In The Calculus Story David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, he demonstrates how to start doing calculus, from the very beginning.

    Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

    Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.-- "Notices of the American Mathematical Society"

    Combine this with thoughtful and thorough apparatus, and Philosophy of Science: The Central Issues is the most flexible and comprehensive collection ever created for undergraduate courses.

    How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book--a model of clarity, succinctness, and a humor bordering at times on the sardonic.

    But it was C. P. Snow's Rede lecture of 1959 that brought it to prominence and began a public debate that is still raging in the media today. This 50th anniversary printing of The Two Cultures and its successor piece, A Second Look (in which Snow responded to the controversy four years later) features an introduction by Stefan Collini, charting the history and context of the debate, its implications and its afterlife. The importance of science and technology in policy run largely by non-scientists, the future for education and research, and the problem of fragmentation threatening hopes for a common culture are just some of the subjects discussed.

    Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge--from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool--the general principle--from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

    Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives—from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century.Many of the greatest names in intellectual history—Pythagoras, Plato, Archimedes, Euclid— were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions—his famed Coxeter groups and Coxeter diagrams—have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational.Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.