Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations.

This book reflects the progress made in the forty years since the appearance of Robinson s revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained."

Is Economics an 'objective' or 'positive' science, independent of ethical and political positions? The financial crisis that began in 2007 gave rise to renewed doubts regarding the 'objectivity' of economics and brought into the public arena a debate that was previously confined to academia. A remarkable feature of the public debate on the value neutrality of economics since then was that it not only involved indictments of ideological biases in economic theory, but also the attribution of the crisis itself to the unethical orientation of economic agents, of economists acting as experts and of 'economic science' itself. The contributors to this volume believe that economists of all persuasions are once again compelled to probe the normative foundations of their discipline and give a public account of their doubts and conclusions.

In the light of questions about the state and responsibility in the wake of the financial crisis, the debate on value-neutrality and objectivity has again come to the fore. This volume brings together economists, sociologists and philosophers, to explore the key issues involved in this debate.

The collection explores three key issues:

• The role of values in economics at a time when the normative burden of economics is increasing- should we take values as subjective preferences or tastes, or rather as appropriate objects of rational inquiry and debate?
• Should economists still aspire to an objective point of view?
• The role of economists and the state of the profession.

Rather than simply revisiting past controversies, this collection responds to the perception that the old issue of value-freedom and objectivity in economics is re-emerging as an urgent topic.

The chapters consider these issues in innovative, thought-provoking and pluralistic ways, and constitute a significant contribution for a better understanding of the complexities and challenges economists face in their pursuit of objectivity.

This book reflects the progress made in the forty years since the appearance of Abraham Robinson 's revolutionary book Nonstandard Analysis in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.

This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.