Along with F. A. Hayek, Milton Friedman forms the "Twin Towers" of defenders of conservative neo-classical economics. Friedman died in 2006 and Hayek in 1992, so they were both alive when Alain Lewis published his demolition of neo-classical economics' choice theories:
On effectively computable realizations of choice functions: Dedicated to Professors Kenneth J. Arrow and Anil Nerode
Alain A. Lewis
Department of Mathematics, Cornell University, Ithaca, NY 14850, U.S.A.
Received 31 August 1984. Revised 26 November 1984.
Mathematical Social Sciences, Volume 10, Issue 1, August 1985, Pages 43–80
Here's Lewis' devastating conclusion:
The point we are trying to make with Theorem 3.1 is simply this. The theorem of representable choice functions in the neoclassical setting, and thus consequently the theory of neoclassical demand correspondences and the theory of SDF-derived social welfare functions, when defined on families of compact subsets of Rn, presumes the possibility of a mathematical correspondence that, even in principle, cannot be performed or realized in effectively computable terms under the weakest, and therefore best, possible circumstances of recursive approximation. As we have mentioned previously, but do not mind stating yet once more, this appears to have serious consequences for the foundations of neoclassical mathematical economics.
And here is Theorem 3.1:
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