Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science.Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.

    Each chapter, or unit, is divided into easily comprehended small "bites" that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics. For individuals interested in the formal study of logic.

    

    The meeting -- which lasted ten minutes -- did not go well. Their loud and aggressive confrontation became the stuff of instant legend, but precisely what happened during that brief confrontation remained for decades the subject of intense disagreement.An engaging mix of philosophy, history, biography, and literary detection, Wittgenstein's Poker explores, through the Popper/Wittgenstein confrontation, the history of philosophy in the twentieth century. It evokes the tumult of fin-de-siécle Vienna, Wittgentein's and Popper's birthplace; the tragedy of the Nazi takeover of Austria; and postwar Cambridge University, with its eccentric set of philosophy dons, including Bertrand Russell. At the center of the story stand the two giants of philosophy themselves -- proud, irascible, larger than life -- and spoiling for a fight.

    Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack ofadvanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicatedwith the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

    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.

    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.

    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.

    Philosopher Paul Churchland explains these scientific developments in a simple, authoritative fashion. He not only opens the door into the ongoing research of the neurobiological and connectionist communities but goes further, probing the social and moral dimensions of recent experimental results that assign consciousness to all but the very simplest forms of animals.

    It is an area that continues to attract and fascinate many people, even though it is generally thought to be highly complex and abstract. For some it is associated with the mystical or religious. For others it is known through the metaphysical poets who talk of love and spirituality. This Very Short Introduction goes right to the heart of the matter, getting to the basic and most important questions of metaphysical thought in order to understand the theory: What are objects? Do colors and shapes have some form of independent existence? Is the whole just a sum of the parts? What is it for one thing to cause another rather than just being associated with it? What is possible? Does time pass? By using simple questions to initiate thought about the basic issues around substance, properties, changes, causes, possibilities, time, personal identity, nothingness, and consciousness, Stephen Mumford provides a clear and down-to-earth path through this analytical tradition at the core of philosophical thought.

    An astonishing synthesis of literary criticism, philosophy, theology, the theory of law and classical scholarship, it is undoubtedly one of the most important texts in twentieth century philosophy. Looking behind the self-consciousness of science, he discusses the tense relationship between truth and methodology. In examining the different experiences of truth, he aims to "present the hermeneutic phenomenon in its fullest extent."

    An attempt to formulate common laws that apply to virtually every scientific field, this conceptual approach has had a profound impact on such widely diverse disciplines as biology, economics, psychology, and demography.

    Contemporary research in the empirical neurosciences and recent research in the philosophy of mind and the philosophy of science are used to illuminate fundamental questions concerning the relation between abstract cognitive theory and substantive neuroscience.

    What makes this work so important is that it returned the body to the forefront of philosophy for the first time since Plato.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.