The work is predicated on the idea that studying mathematics can generate the same enthusiasm as playing a team sport - without necessarily being competitive.

    Walter Sinnott-Armstrong argues that God is not only not essential to morality, but that our moral behavior should be utterly independent of religion. He attacks several core ideas: that atheists are inherently immoral people; that any society will sink into chaos if it is becomes too secular; that without religion, we have no reason to be moral; that absolute moral standards require the existence of God; and that without religion, we simply couldn't know what is wrong and what is right.Sinnott-Armstrong brings to bear convincing examples and data, as well as a lucid, elegant, and easy to understand writing style. This book should fit well with the debates raging over issues like evolution and intelligent design, atheism, and religion and public life as an example of a pithy, tightly-constructed argument on an issue of great social importance.In his call for sincere dialogue with theists, Sinnott-Armstrong provides a welcome relief from the apoplectic excesses of Richard Dawkins and Christopher Hitchens, while also addressing objections to homosexuality and evolution frequently raised by evangelical Christians. --Publishers Weekly [I]t is accessible and lively, my hope is that it will be widely read, especially by theists.--Peter Lamal, The Humanist ... the clarity of this text successfully defuses many erroneous claims about religion and morality, both popular and academic; this volume certainly deserves a wide audience in this increasingly secular and skeptical world. -ChoiceMorality Without God? is an engaging, pithy book arguing against the necessity of God and religion for a robust morality. Walter Sinnott-Armstrong has distinguished himself as a leading philosopher in his work on metaethics and moral psychology, as well as books on moral and epistemological skepticism, and in Morality Without God? he commendably succeeds in writing a philosophically respectable introduction to the problems facing religious morality suitable for virtually any audience. --Philosophia Christi

    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.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Includes a new itineraries chapter for easy planning and "weekends to remember" suggestions throughout. of color photos. 128 maps.

    Scott's romantic image is however, far from the rogue which Nigel Tranter portrays in this classic work.