Taming The Incomputable, Reconstructing The Nonconstructive And Deciding The Undecidable In Mathematical Economics
The emergence of non-constructivities in economics is entirely due to the unnecessary and inappropriate formalization of economics by means of 'classical' mathematics. I have made similar claims for the emergence of uncomputabilities and undecidabilities in economics in earlier writings. Here, on the other hand, I want to suggest a way of confronting uncomputabilities, and remedying non-constructivities, in economics, and turning them into a positive force for modeling, for example, endogenous growth, as suggested by Stefano Zambelli. 107,108 In between, a case is made for economics to take seriously the kind of mathematical methodology fostered by Feynman and Dirac, in particular the way they developed the path integral and the δ-function, respectively. A sketch of a "research program" in mathematical economics, analogous to the way Gödel thought incompleteness and its perplexities should be interpreted and resolved, is also outlined, albeit briefly, in the concluding section.
Volume (Year): 08 (2012)
Issue (Month): 01 ()
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"The computation of equilibrium prices: An exposition,"
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in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 21, pages 1007-1061
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