On the foundations of mathematical economics (Q2873497)

This paper revisits the arguments of \textit{K. V. Velupillai} [ibid. 8, No. 1, 5--51 (2012; Zbl 1306.91039)] in which this author starts with J. Barkley Rosser sen.'s extension of Gödel's incompleteness theorem. Velupillai finds that Rosser sens.'s proof of the existence of the undecidability of a statement that can be rephrased as ``For every proof of me, there is a shorter proof of my negation'' (Wikipedia entry on J. Barkley Rosser) provides the definitive ground for claiming that only the strongest version of constructivism (i.e. á la Bishop) can be the foundations of mathematics. From then on Velupillai goes on to show ways of making constructive some fundamental claims for mathematical economics and decrying all other approaches to the field. NEWLINENEWLINENEWLINEIn this paper, Barkley Rosser jun. revisits his father's legacy (both in published work and the recollections of conversations with him) to state that he was far from being an extreme constructivist. Furthermore, that he was closer to be a pluralist, seen in the way in which he supported the development of nonstandard analysis, an approach that in many ways can be seen as being in the antipodes of constructivism, but nevertheless can be made consistent with intuitionism.