Online research in philosophy

The New Economic Windows Series, derived from Massimo Salzano's ideas and work, incorporates material from textbooks, monographs and conference proceedings that deals with both the theoretical and applied aspects of various sub-disciplines ...

Kumaraswamy Vela Velupillai [74] presents a constructivist perspective on the foundations of mathematical economics, praising the views of Feynman in developing path integrals and Dirac in developing the delta function. He sees their approach as consistent with the Bishop constructive mathematics and considers its view on the Bolzano-Weierstrass, Hahn-Banach, and intermediate value theorems, and then the implications of these arguments for such “crown jewels” of mathematical economics as the existence of general equilibrium and the second welfare theorem. He (...) also relates these ideas to the weakening of certain assumptions to allow for more general results as shown by Rosser [51] in his extension of Gödel’s incompleteness theorem in his opening section. This paper considers these arguments in reverse order, moving from the matters of economics applications to the broader issue of constructivist mathematics, concluding by considering the views of Rosser on these matters, drawing both on his writings and on personal conversations with him. (shrink)

“The ‘fallacy of composition’ that drives a felicitous wedge between micro and macro, between the individual and the aggregate, and gives rise to emergent phenomena in economics, non-algorithmic ways – as conjectured originally by John Stuart Mill…, George Herbert Lewes … , and codified by Lloyd Morgan … in his popular Gifford Lectures - may yet be tamed by unconventional models of computation.” --K. Vela Velupillai (2008, p. 21).

The claim in this paper is that Sraffa employed a rigorous logic of mathematical reasoning in his book, Production of Commodities by Means of Commodities (PCC), in such a way that the existence proofs were constructive. This is the kind of mathematics that was prevalent at the beginning of the nineteenth century, which was dominated by the concrete, the constructive and the algorithmic. It is, therefore, completely consistent with the economics of the nineteenth century, which was the fulcrum around which (...) the economics of PCC was conceived. (shrink)