ABSTRACT
This chapter explores the general philosophy of mathematics by bringing two well-known critiques of the Hilbert formalist philosophy of mathematics to bear on the orthodox commitments to both rationality and equilibrium. It argues furnish methodologists with a range of insights and themes into both the analysis and the critical evaluation of these orthodox commitments. The chapter presents a methodological case for the thesis that Debreu's general equilibrium explanation of prices is rendered economically vacuous by its recourse to algorithmetically undecidable theorems. In light of the philosophy of mathematics the chapter argues that a prima facie methodological case can be made for limiting mathematical resources to computable mathematics in economic theorising. The chapter distinguishes between strict and pragmatic intuitionism. It focuses on Bourbaki because of the manner in which he identifies the Achilles' heel in Brouwerian intuitionism. The chapter focuses on one strand in Dummett's many-layered philosophical argument for this radical conclusion.
