Existence Proofs and Computation

This refers, of course, to Duncan Foley's remarkably original and brilliant-- and unfortunately little acknowledged-- Yale doctoral dissertation of 1967 (Foley, 1967). In the by now vast orthodox literature on computable general equilibrium theory, and its applied off shoots, I have not been able to detect a single reference to what I may call Foley's Method (ibid, pp. 64-73), which could provide--as legitimately as Negishi's Method-- an alternative to the orthodox approach to `computing' Walrasian (Arrow-Debreu) equilibrium prices, using, for example, variants of Scarf's Method, (Scarf, 1973). Duncan Foleys many-faceted and outstanding contributions to macroeco-nomics, microeconomics, general equilibrium theory, the theory of taxation, history of economic thought, the magni\u85cent dynamics of classical economics, classical value theory, Bayesian statistics, formal dynamics and, most recently, fascinating forays into an interpretation of economic evolution from a variety of complexity theoretic viewpoints have all left and continue to leave signi\u85cant marks in the development and structure of economic theory. He belongs to the grand tradition of visionaries who theorise with imaginative audacity on the dy-namics, evolution and contradictions of capitalist economies a tradition that, perhaps, begins with Marx and Mill, continues with Keynes and Schumpeter, reaching new heights with the iconoclastic brilliancies of a Tsuru and a Good-win, a Chakravarty and a Nelson, and to which Duncan Foley adds a lustre of much value. In this contribution I return to mathematical themes broached in Foleys brilliant and pioneering Yale doctoral dissertation (Foley, 1967) and attempt to view them as a Computable Economist1 would.The intention is to suggest that algorithmic indeterminacies are intrinsic to the foundations of economic theory in the mathematical mode