Mathematics, Metaphors and Economic Visualisability

In the nineteenth century, scholars trained in both mathematics and political economy began to construct economic theory in mathematical form. Over the course of the next half century, mathematical analysis gradually came to be applied, sometimes implicitly and often relegated to appendices and footnotes, in more and more parts of economic theory. Then, quite suddenly, in the years immediately following the Second World War, the mathematization of economic theory gathered pace. So forceful and all-encompassing was the subsequent transformation in the way in which economic theory was constructed that a mere three decades later it would be difficult to find a branch of economic theory untouched by mathematical analysis. Despite the pervasiveness of mathematics in economic theory, many important methodological issues relevant to the deployment of mathematics in economics remain untouched in the economics literature. Part of the reason for this is that debate over the utilization of mathematics in economics has been narrowly focused on the appropriateness of the deductive method—the proof of many theorems that logically flow from a few axioms. As a consequence of this narrow focus, the nature and role of mathematics in the development of economic science and knowledge has not received the attention that it deserves. Important fundamental questions have gone unanswered. What does mathematical economics mean? What is its nature? Can it help solve any economic problem? Does it do more harm than good? Despite Samuelson's (1952) declaration that "Mathematics is language," there have been only a few attempts to explore such questions using the tools of linguistic theory and cognitive psychology. In this paper, it is shown how linguistic theory and the closely related investigations of cognitive psychologists illuminate the path that must be taken to generate answers to the questions that the utilization of mathematics in economics has posed for economists. Mathematical models in economic theory, like all models