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.
The role of conventions has been an area of increasing interest to writers in the post-Keynesian tradition, particularly over the last thirty years. This has arisen from the reexamination of John Maynard Keynes’s notion of convention in the context of radical uncertainty along with the status of rationality in the face of uncertainty. This chapter discusses some of the principal tenets of Henri Poincaré’s analysis of conventions and relates them to the post-Keynesian methodological agenda, more specifically to provide a Poincaréan defense of the role of conventions in rational decision-making. It argues that this provides an innovative and more adequate philosophical defense of nonergodicity in economic theory, which has become a central axiom of post-Keynesian economics. The chapter first provides an overview of the post-Keynesian literature on uncertainty and conventions arising from Keynes’s employment of the concept. It then outlines the emergence of conventions and conventionalism in philosophy, examines Poincaré’s conventionalism and its relationship with rationality, and considers the implications of Poincaré’s conventionalism for post-Keynesian economics.
This paper revisits Kaldor's methodological critique of orthodox economics. The main target of his critique was the theory of general equilibrium as expounded in the work of Debreu and others. Kaldor deemed this theory to be seriously flawed as an empirically adequate description of real-world economies. According to Kaldor, scientific progress was not possible in economics without a major act of demolition, by which he meant the destruction of the basic conceptual framework of the theory of general equilibrium. We extend Kaldor's critique by recourse to major developments in 20 th century philosophy of mathematics, and then go on to demonstrate that Debreu's work, based as it is on Bourbakist formalism and in particular Cantorian set theory, is conceptually incompatible with Kaldor's requirements for an empirical science. This aspect of Kaldor's critique has not been explored, and as a consequence a major source of substantiating his critique has remained undeveloped.3
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