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.

    This volume, the first comprehensive English-language translation of Halbwach's writings on the social construction of memory, fills a major gap in the literature on the sociology of knowledge.Halbwachs' primary thesis is that human memory can only function within a collective context. Collective memory, Halbwachs asserts, is always selective; various groups of people have different collective memories, which in turn give rise to different modes of behavior. Halbwachs shows, for example, how pilgrims to the Holy Land over the centuries evoked very different images of the events of Jesus' life; how wealthy old families in France have a memory of the past that diverges sharply from that of the nouveaux riches; and how working class construction of reality differ from those of their middle-class counterparts.With a detailed introduction by Lewis A. Coser, this translation will be an indispensable source for new research in historical sociology and cultural memory.Lewis A. Coser is Distinguished Professor of Sociology Emeritus at the State University of New York and Adjunct Professor of Sociology at Boston College.

    Frankfurt turns to what lies beyond them: the truth, a concept not as obvious as some might expect.Our culture's devotion to bullshit may seem much stronger than our apparently halfhearted attachment to truth. Some people (professional thinkers) won't even acknowledge "true" and "false" as meaningful categories, and even those who claim to love truth cause the rest of us to wonder whether they, too, aren't simply full of it. Practically speaking, many of us deploy the truth only when absolutely necessary, often finding alternatives to be more saleable, and yet somehow civilization seems to be muddling along. But where are we headed? Is our fast and easy way with the facts actually crippling us? Or is it "all good"? Really, what's the use of truth, anyway?With the same leavening wit and commonsense wisdom that animates his pathbreaking work "On Bullshit," Frankfurt encourages us to take another look at the truth: there may be something there that is perhaps too plain to notice but for which we have a mostly unacknowledged yet deep-seated passion. His book will have sentient beings across America asking, "The truth—why didn't I think of that?"

    As humans, we decipher the meaning of newspaper articles, books, legal matters, religious texts, political speeches, emails, and even dinner conversations every day . But how is knowledge mediated through these forms? What constitutes the process of interpretation? And how do we draw meaning from the world around us so that we might understand ourposition in it?In this Very Short Introduction Jens Zimmermann traces the history of hermeneutic theory, setting out its key elements, and demonstrating how they can be applied to a broad range of disciplines: theology; literature; law; and natural and social sciences. Demonstrating the longstanding and wide-ranging necessity of interpretation, Zimmermann reveals its significance in our current social and political landscape.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

    At an age when most babies are cooing "Mama, " Popo was speaking in complete sentences. He was reading college textbooks when he was still too young for nursery school. Popo may just be the smartest human being on Earth. And he spends all his time listening to the radio . . . to white noise that comes drifting down from the sky like stardust. Chill Bent is a two-time loser with a hair-trigger temper. After the death of Popo's mother, the ex-con assumes responsibility for his nephew, vowing to protect the boy from a government eager to strip away his African-American heritage and exploit his genius like a natural resource. Together, Popo and Chill are about to embark on an extraordinary journey into the farthest reaches of the mind and the soul . . . a journey you will never forget. In this stunning new speculative fiction short story by the bestselling author of Blue Light, part of an interconnected collection of stories called Futureland, a young African-American genius searches for God with the tools of cutting-edge science. Look for the complete volume of Futureland, available now.

    Showalter is one of the few scholars who can make her readers rush to their bookshelves to refute her point, or simply to experience again Jane Eyre, The Mill on the Floss, or the bitterly illuminating stories of Katherine Mansfield. Her chief innovation is to place the works of famous women writers beside those of the minor or forgotten, building a continuity of influence and inspiration as well as a more complete picture of the social conditions in which women's books have been produced. She has added a new introduction recounting, with justifiable pleasure, how daring and controversial her study seemed when it first appeared in 1977 (and how many enemies it made her). In an afterword, she touches on more recent developments in the women's novel in Britain, including the influence of the dazzling Angela Carter. --Regina Marler

    In her study of the state of modern humanity, Hannah Arendt considers humankind from the perspective of the actions of which it is capable. The problems Arendt identified then--diminishing human agency and political freedom; the paradox that as human powers increase through technological and humanistic inquiry, we are less equipped to control the consequences of our actions—continue to confront us today.

    Hailed by the New York Times as "one of the most influential texts in gender studies, men's studies and gay studies," this book uncovers the homosocial desire between men, from Restoration comedies to Tennyson's Princess.

    In January 1919, after being arrested for her involvement in a workers' uprising in Berlin, she was brutally murdered by a group of right-wing soldiers. Her body was recovered days later from a canal. Six years earlier she had published what was undoubtedly her finest achievement, The Accumulation of Capital - a book which remains one of the masterpieces of socialist literature. Taking Marx as her starting point, she offers an independent and fiercely critical explanation of the economic and political consequences of capitalism in the context of the turbulent times in which she lived, reinterpreting events in the United States, Europe, China, Russia and the British Empire. Many today believe there is no alternative to global capitalism. This book is a timely and forceful statement of an opposing view.

    But if we were to let go of this fond conviction, Bruno Latour asks, what would the world look like? His book, an anthropology of science, shows us how much of modernity is actually a matter of faith.What does it mean to be modern? What difference does the scientific method make? The difference, Latour explains, is in our careful distinctions between nature and society, between human and thing, distinctions that our benighted ancestors, in their world of alchemy, astrology, and phrenology, never made. But alongside this purifying practice that defines modernity, there exists another seemingly contrary one: the construction of systems that mix politics, science, technology, and nature. The ozone debate is such a hybrid, in Latour’s analysis, as are global warming, deforestation, even the idea of black holes. As these hybrids proliferate, the prospect of keeping nature and culture in their separate mental chambers becomes overwhelming—and rather than try, Latour suggests, we should rethink our distinctions, rethink the definition and constitution of modernity itself. His book offers a new explanation of science that finally recognizes the connections between nature and culture—and so, between our culture and others, past and present.Nothing short of a reworking of our mental landscape, We Have Never Been Modern blurs the boundaries among science, the humanities, and the social sciences to enhance understanding on all sides. A summation of the work of one of the most influential and provocative interpreters of science, it aims at saving what is good and valuable in modernity and replacing the rest with a broader, fairer, and finer sense of possibility.

    He analyzes previous contributions to a Marxist theory of literature from Marx himself to Lukacs, Althusser, and Goldmann, and develops his own approach by outlining a theory of cultural materialism' which integrates Marxist theories of language with Marxist theories of literature. Williams moves from a review of the growth of the concepts of literature and idealogy to a redefinition of determinism' and hegemony'. His incisive discussion of the 'social material process' of cultural activity culminates in a re-examination of the problems of alignment and commitment and of the creative practice in individual authors and wider social groups.

    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

    The exposition is simple and leads to the most complete direct means of solving problems in mechanics. The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted.

    According to the author, these trends sought to create a unified conceptual apparatus as a common basis for the whole of human knowledge.Because these new developments in logical thought tended to perfect and sharpen the deductive method, an indispensable tool in many fields for deriving conclusions from accepted assumptions, the author decided to widen the scope of the work. In subsequent editions he revised the book to make it also a text on which to base an elementary college course in logic and the methodology of deductive sciences. It is this revised edition that is reprinted here.Part One deals with elements of logic and the deductive method, including the use of variables, sentential calculus, theory of identity, theory of classes, theory of relations and the deductive method. The Second Part covers applications of logic and methodology in constructing mathematical theories, including laws of order for numbers, laws of addition and subtraction, methodological considerations on the constructed theory, foundations of arithmetic of real numbers, and more. The author has provided numerous exercises to help students assimilate the material, which not only provides a stimulating and thought-provoking introduction to the fundamentals of logical thought, but is the perfect adjunct to courses in logic and the foundation of mathematics.

    Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.