ABSTRACT
This chapter discusses a brief account of the development of axiomatic systems from Euclid to Hilbert. It outlines the formalist school's philosophy of axiomatisation and how that philosophy impinges on the process of the mathematisation of a scientific domain. The chapter argues Debreu's definitive summing up of the theory of competitive equilibrium is constructed in accordance with the formalist school's model for the mathematisation of a scientific theory which, for reasons of rigour, replaced the older Euclidean model. It reflects on how the formalist's purely syntactical understanding of mathematical form impacts on the interpretation of Debreu's mathematical model. The chapter introduces the reader to how the commitment to the formalist philosophy of mathematical form, as distinct from the commitment to a semanticist philosophy of mathematical form, can inform one' methodological defence of neo-Walrasian theorising. It concludes with a brief analysis of what Debreu sees as the assets of his philosophy of economic analysis.
