Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...) in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body. (shrink)

The grand and sweeping claims of many relativists might seem to amount to the argument that everything is relative--except the thesis of relativism. In this book, Steven Hales defends relativism, but in a more circumscribed form that applies specifically to philosophical propositions. His claim is that philosophical propositions are relatively true--true in some perspectives and false in others. Hales defends this argument first by examining rational intuition as the method by which philosophers come to have the beliefs they do. Analytic (...) rationalism, he claims, has a foundational reliance on rational intuition as a method of acquiring basic beliefs. He then argues that there are other methods that people use to gain beliefs about philosophical topics that are strikingly analogous to rational intuition and examines two of these: Christian revelation and the ritual use of hallucinogens. Hales argues that rational intuition is not epistemically superior to either of these alternative methods. There are only three possible outcomes: we have no philosophical knowledge ; there are no philosophical propositions ; or there are knowable philosophical propositions, but our knowledge of them is relative to doxastic perspective. Hales defends relativism against the charge that it is self-refuting and answers a variety of objections to this account of relativism. Finally, he examines the most sweeping objection to relativism: that philosophical propositions are not merely relatively true, because there are no philosophical propositions--all propositions are ultimately empirical, as the naturalists contend. Hales's somewhat disturbing conclusion--that intuition-driven philosophy does produce knowledge, but not absolute knowledge--is sure to inspire debate among philosophers. (shrink)