The unreasonable ineffectiveness of mathematics in economics

Abstract

Stimulating comments and constructive criticisms made at the presentation and by an anonymous referee helped reduce ambiguities and some of the harsher, critical, tones in the original version. I am, in particular, indebted to Professor Deidre McCloskey for her extremely perceptive comments on existence problems as framed and presented in the earlier version. I am also indebted to general supportive reactions and clarifying comments from Tom Boylan, Francisco Doria, Duncan Foley and Marcelo Tsuji. Alas, the remaining errors and ambiguities are entirely my own responsibility.

The uncertainty of systemic risk

“…However, the intention here is to explain relevance and discuss fecundity not to argue proofs (Di Maggio, 1995;Sutton and Staw, 1995;Wacker, 1998), as evident in its use of simple logical notation to formally outline definitions, and its elementary mathematical expressions derived from the juxtaposition of insights from different disciplines in a useful new context. Indeed, there is a growing consensus within the mathematics discipline that: '… the common practice [in economics] of axiomatic encapsulation and compression of unrealistic fundamentals into precise mathematical theorems suggesting proof is shown to be misleading and irrelevant, because it cannot explain the proven mathematical intractability, insolvability and undecidability of solutions capable of experimentally demonstrating the true dynamical and complex nature of observed economic phenomena', (Velupillai, 2005).…”

The Rhetoric of Failure: A Hyper-Dialog About Method in Economics and How to Get Things Going

“…Quite the contrary, the plain fact that products of pure deductive reasoning correspond in numerous cases admirably to the objects and processes of reality has puzzled physicists, philosophers, and the mathematicians themselves since the ancient Greeks (Wigner, 1979), (Kline, 1982, pp. 328-354), (Feynman, 1992, p. 171), (Velupillai, 2005), (Penrose, 2007, pp. 613-614).…”

Ordering infinite utility streams comes at the cost of a non-Ramsey set

“…For a thorough discussion of constructivism and its modifications, we refer to Beeson (1988); for a discussion of constructivism in economic theory, to Velupillai (2005); and for the history of The Axiom of Choice and its relation to the Zermelo-Fraenkel axioms of set theory, to Moore (1982) and Jech (1973, 1978.…”