Axiomatization and formalism in economics

In this paper we address a number of issues in the historiography and methodology of the formalization of economics in the twentieth century. We argue that Debreu's approach to formalism pursuing his Bourbakist programme was based on Hilbert's version of finitism. The latter project attempted to retain its place in Cantor's 'paradise' and in so doing bequeathed serious methodological consequences. There was, however, at the turn of the twentieth century an alternative version of finitism available, that provided by Poincaré, which if adopted by economics would have led to a radically different approach to economic theorizing and modelling. We argue that these reflections must be embedded in an alternative larger methodological framework.