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)

James Griffin has considered a form of superiority in value that is weaker than lexical priority as a possible remedy to the Repugnant Conclusion. In this article, I demonstrate that, in a context where value is additive, this weaker form collapses into the stronger form of superiority. And in a context where value is non-additive, weak superiority does not amount to a radical value difference at all. These results are applied on one of Larry Temkin's cases against transitivity. I demonstrate (...) that Temkin appeals to two conflicting notions of aggregation. I then spell out the consequences of these results for different interpretations of Griffin's suggestion regarding population ethics. None of them comes out very successful, but perhaps they nevertheless retain some interest. (shrink)