The computable alternative in the formalization of economics: A counterfactual essay

The mathematization of economics has, almost without exception, proceeded along pathways delineated by the Formalists and the Bourbakians. The methodological underpinnings have been provided by deductivism. Recent developments in logic, the foundations of mathematics and the philosophy of science suggest new possibilities for the formalization of economics along recursion theoretic and inductive lines. In this essay 1 explore, counterfactually, alternative paths for the mathematization of economics on the basis of these new visions. By choosing particular nodes in an imaginary decision tree depicting the development of mathematical economics, I ask whether a recursion theoretic formalism of economics could have led to alternative, more interesting and interdisciplinary, histories. My conclusion is unambiguously positive in at least one important sense: often, at such crucial nodes, economic concepts have been forced to conform to a narrow mathematical and methodological formalism simply because the appropriate alternatives have been absent; or, when present, unknown to the practitioners. A broader awareness of theoretical technologies and a deeper understanding of the development of mathematical economics is not only necessary; it is also eminently feasible when viewed in this particular counterfactual mode, Examples from core areas in economic theory - consumer and production theory, games and existence proofs - are harnessed to extract the above messages.