No reality, please. We’re economists!

26 Nov, 2013 at 18:22 | Posted in Theory of Science & Methodology | 4 Comments

Ever since the Enlightenment various economists had been seeking to mathematise the study of the economy. In this, at least prior to the early years of the twentieth century, economists keen to mathematise their discipline felt constrained in numerous ways, and not least by pressures by (non-social) natural scientists and influential peers to conform to the ‘standards’ and procedures of (non-social) natural science, and thereby abandon any idea of constructing an autonomous tradition of mathematical economics. Especially influential, in due course, was the classical reductionist programme, the idea that all mathematical disciplines should be reduced to or based on the model of physics, in particular on the strictly deterministic approach of mechanics, with its emphasis on methods of infinitesimal calculus …

However, in the early part of the twentieth century changes occurred in the inter-pretation of the very nature of mathe-matics, changes that caused the classical reductionist programme itself to fall into disarray. With the development of relativity theory and especially quantum theory, the image of nature as continuous came to be re-examined in particular, and the role of infinitesimal calculus, which had previously been regarded as having almost ubiquitous relevance within physics, came to be re-examined even within that domain.

The outcome, in effect, was a switch away from the long-standing emphasis on mathematics as an attempt to apply the physics model, and specifically the mechanics metaphor, to an emphasis on mathematics for its own sake.

Mathematics, especially through the work of David Hilbert, became increasingly viewed as a discipline properly concerned with providing a pool of frameworks for possible realities. No longer was mathematics seen as the language of (non-social) nature, abstracted from the study of the latter. Rather, it was conceived as a practice concerned with formulating systems comprising sets of axioms and their deductive consequences, with these systems in effect taking on a life of their own. The task of finding applications was henceforth regarded as being of secondary importance at best, and not of immediate concern.

This emergence of the axiomatic method removed at a stroke various hitherto insurmountable constraints facing those who would mathematise the discipline of economics. Researchers involved with mathematical projects in economics could, for the time being at least, postpone the day of interpreting their preferred axioms and assumptions. There was no longer any need to seek the blessing of mathematicians and physicists or of other economists who might insist that the relevance of metaphors and analogies be established at the outset. In particular it was no longer regarded as necessary, or even relevant, to economic model construction to consider the nature of social reality, at least for the time being. Nor, it seemed, was it possible for anyone to insist with any legitimacy that the formulations of economists conform to any specific model already found to be successful elsewhere (such as the mechanics model in physics). Indeed, the very idea of fixed metaphors or even interpretations, came to be rejected by some economic ‘modellers’ (albeit never in any really plausible manner).

The result was that in due course deductivism in economics, through morphing into mathematical deductivism on the back of developments within the discipline of mathematics, came to acquire a new lease of life, with practitioners (once more) potentially oblivious to any inconsistency between the ontological presuppositions of adopting a mathematical modelling emphasis and the nature of social reality. The consequent rise of mathematical deductivism has culminated in the situation we find today.

Tony Lawson