The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic...

A computable economist's view of the world of computational complexity theory is described. This means the model of computation underpinning theories of computational complexity plays a central role. The emergence of computational complexity theories from diverse traditions is emphasised. The...

Computability theory came into being as a result of Hilbert?s attempts to meet Brouwer?s challenges, from an intuitionistc and constructive standpoint, to formalism as a foundation for mathematical practice. Viewed this way, con- structive mathematics should be one vision of computability...

Real analysis, founded on the Zermelo-Fraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this dominance is not inevitable, especially in an age when the digital computer...

It is shown that for a `complex economy', characterised in terms of a formal dynamical system capable of computation universality, it is impossible to devise an effective theory of policy.

Michio Morishima's nonlinear model of the trade cycle (Morishima, 1958) is simplified and generalized to show, by means of the Andronov-Hopf bifurcation theorem, the existence of a periodic orbit. In addition, an attempt is made to place Morishima's contribution in the broader tradition of the...

In this paper I try to substantiate the thesis that Jevons may have been too harsh on the vices of induction and generously optimistic about the virtues of deduction, as discussed, primarily, in his magnum opus, The Principles of Science [6]. With this aim in mind the paper attempts to suggest...

A nonlinear disequilibrium macrodynamic model of ?uctuations in the labour and product markets, mediated by variations in factor shares, is developed and the exis- tence of a periodic orbit is proved using the Hopf bifurcation theore

It is shown that Paul Romer's suggestion to model algorithmically the use and production of ideas in an endogenous growth model is formally feasible. Such a modelling exercise imparts a natural evolutionary flavour to growth models. However, it is also shown that the policy implications are...

In this paper I attempt to show that mathematical economics is unreasonably ineffective. Unreasonable, because the mathematical assumptions are economically unwarranted; ineffective because the mathematical formalizations imply nonconstructive and uncomputable structures. A reasonable and...