2 - The use of mathematics in theoretical modeling

Summary

The previous chapter developed a pragmatic account of scientific modeling, and with it a new standard for assessing the merits of a scientific modeling exercise. Specifically, it argued that for a modeling exercise to be successful, the model has to be an apt representation of the target. And that, in turn, means that the model narrative generated in the modeling exercise must also be possible in respect of the target.

This chapter uses that standard to assess the modeling process commonly followed by economists. As noted, this modeling process centers on mathematics. Mathematical models are not the only conceivable way one might choose to represent economic activity; one might construct a physical model, for example, or a narrative in ordinary language. But economics today is unquestionably a mathematical-model-based science, and this has been the case since at least the mid-twentieth century. Broken into its component parts, this process involves (a) the use of mathematical models (b) to represent social phenomena (c) for the purpose of illuminating aspects of the latter (d) through the production of inferences about the latter.

I will argue that this process rests on a crucial presupposition: that the social phenomena under study can be adequately represented in the language of mathematics. More specifically, it presupposes that mathematical models can be used as metaphors for human social activity. This chapter will defend the characterization of economists' use of mathematical models as metaphorical, and consider the implications of that characterization for economics. Its purview will be limited in one respect. In the interests of clarity, only theoretical modeling exercises – i.e. those that do not include empirical testing – will be explored at present. Empirical modeling exercises – i.e. those that engage directly with data – will be discussed in the next chapter.

As argued in the previous chapter, scientific modeling embodies a general representational ideal of the modeling process, which is to illuminate a given target in a manner that addresses the motivating question of the given exercise. In economics, the models in question are typically mathematical, and the manner in which the motivating question is addressed is generally through the production of inferences that are at least in principle testable (though as we saw, this is not always the case).