The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

    More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.This Schaum's Outline gives you:Practice problems with full explanations that reinforce knowledgeCoverage of the most up-to-date developments in your course fieldIn-depth review of practices and applicationsFully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!Schaum's Outlines-Problem Solved.

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

    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.

    It will help students to think more clearly about how to form their moral beliefs in the wisest and most rational way. The basic approaches to metaethics and normative ethics are related to specific issues, particularly those of racism, education, and abortion. Written in a clear and concise way by an experienced textbook author, Ethics will also be of interest to the general reader.Unique features of the textbook: * boxed key ideas* Glossary of philosophical terms* Chapter summaries and study questions * Annotated further reading and Internet Web resourcesThere is an associated website for teachers and students at www.routledge.com/routledge/philosoph...

    It features writings from some of America's leading philosophers, including Martha Nussbaum, Charles Taliaferro, and J.P. Moreland. A first-of-its-kind collection of essays exploring those gems of philosophical wisdom runners contemplate when out for a run Topics considered include running and the philosophy of friendship; the freedom of the long distance runner; running as aesthetic experience, and "Could a Zombie Run a Marathon?" Contributing essayists include philosophers with athletic experience at the collegiate level, philosophers whose pasttime is running, and one philosopher who began running to test the ideas in his essay

    This question is central to all the great religions, Kreeft demonstrates, for striving toward holiness, moving toward perfect love, is the whole purpose of life.Kreeft admits that he is only a beginner on the climb to holiness, and it is to novices like him that he has written this engaging and encouraging book. Using the insights and experiences of saints and great spiritual writers throughout history, Kreeft shows what holiness is and how it can be achieved. He especially draws upon the spiritual classic Abandonment to Divine Providence by Jean-Pierre de Caussade, S.J. The core of Caussade's timeless gem is that God reveals himself to all of us through the daily events of our lives. The surest way toward spiritual growth, therefore, is by perceiving and accepting the merciful will of God in every situation.Kreeft stresses the simplicity of his approach to holiness, which focuses mainly on the virtue of love. Sanctity is love, he asserts, and only that can give us what we all long for—deep and lasting joy.

    From man's first act of counting to higher mathematics, from the smallest living creature to the dazzling reaches of outer space, Asimov is a master at "explaining complex material better than any other living person." (The New York Times) You'll learn: HOW to make a trillion seem small; WHY imaginary numbers are real; THE real size of the universe - in photons; WHY the zero isn't "good for nothing;" AND many other marvelous discoveries, in ASIMOV ON NUMBERS.

    In this treatise, he argues that the core intellectual errors of statism, socialism, protectionism, racism, irrationalism can be found in a revolt against economic logic and its special character. Epistemological Problems of Economics was original published in 1933, a period when the social sciences and economic policy were undergoing upheaval. The classical view of economics as a deductive science, along with the laissez-faire policies implied by that view, were being displaced by positivism and economic planning. Mises set out to put the classical view on a firmer foundation. In so doing, he examines a range of philosophical problems associated with economics. He goes further to delineate the scope of the general science of human action. This treatise, out of print for many years, is now brought back by the Mises Institute in a 3rd edition, with a comprehensive introduction by Jörg Guido Hülsmann, senior fellow of the Mises Institute. He observes that "the great majority of contemporary economists, sociologists, political scientists, and philosophers are either completely unaware of Mises's contributions to the epistemology of the social sciences or think they can safely neglect dealing with them. They are in error. One can ignore a thinker, but the fundamental problems of social analysis remain. There will be no progress in these disciplines before the mainstream has fully absorbed and digested Mises's ideas."

    For this and other reasons I chose to translate Toward the Creative Nothing by Renzo Novatore and publish several of his shorter pieces. Written shortly after World War I, as a revolution was occurring in Russia and uprisings were happening in Germany and Italy, this poetic text responds to the upheaval of its time with a call for a revolution that could truly move the human race beyond the spiritual impoverishment, the equality in baseness that democracy and socialism offered. Bourgeois society seemed to have reached its dusk, and Novatore saw the hope for a new dawn only in such a revolution-one that went beyond the mere economic demands of the socialists and communists--a revolution moved by great ideas and great passions that would break with the low values of bourgeois democratic civilization.

    Each chapter contains integrated worked examples and chapter tests. This edition has the ancillary ATLAST computer exercise guide and new MATLAB and Maple guides.

    In this entertaining and ingenious book, Blastland reveals how in our quest to make the world more understandable, we lose sight of how unexplainable it often is. The result - from GDP figures to medicine - is that experts know a lot less than they think. Filled with compelling stories from economics, genetics, business, and science, The Hidden Half is a warning that an explanation which works in one arena may not work in another. Entertaining and provocative, it will change how you view the world.

    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.

    Pure Mathematics 1 corresponds to unit P1. It covers quadratics, functions, coordinate geometry, circular measure, trigonometry, vectors, series, differentiation and integration.

    Hodgkinson offer you a wry look inside the mirrored palaces of high culture.Read this book and you'll never again mistake Hegel for Engels, you'll know when precisely to drop Foucault's name into a conversation and how to pronounce "Borgesian," and you'll learn many more essential pointers for the intellectual life.