ABSTRACT
In previous chapters, but particularly in Chapters 7 and 8, we have seen that mathematics has a very important role to play in the strategies of theory development which are followed in the debate. The present chapter is devoted to a more explicit examination of the way in which mathematics operates in the debate, and perhaps in economics in general, and of the ways economists think it operates. I will start by giving four traditional views that seem to be quite widely held. These views share the idea that mathematics is a neutral instrument which is entirely subservient to economic analysis. Then I shall describe a different conception of the role of mathematics in economic analysis, one which parts with the neutrality idea. Next, another set of case studies will be presented, the first of which discusses one more defence against the criticism on neoclassical production models, an article by Lowell Gallaway and Vishwa Shukla. This article demonstrates very clearly how a particular application of mathematical methods may go wrong. Also included are the descriptions of two reactions to this article, by Kazuo Sato and Pierangelo Garegnani, both of whom have a very different style of using mathematics. The chapter ends with some conclusions that are based on my analysis of the debate.
