Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics

It is natural to claim, as I do in this paper, that the emergence of non-constructivities in economics is entirely due to the 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 uncomputabilites, and remedying non-constructivities, in economics, and turning them into a positive force for modelling, 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 delta-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 in the concluding section.