Variations on the Theme of Conning in Mathematical Economics

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 infelicities. The attempt to extract these infelicities is in terms of three main examples: dynamics, policy and rational expectations and learning. The focus is on the role and reliance on standard xed point theorems in orthodox mathematical economics

A Computable Economist’s Perspective on Computational Complexity

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 unifications that emerged in the modern era was codified by means of the notions of efficiency of computations, non-deterministic computations, completeness, reducibility and verifiability - all three of the latter concepts had their origins on what may be called 'Post's Program of Research for Higher Recursion Theory'. Approximations, computations and constructions are also emphasised. The recent real model of computation as a basis for studying computational complexity in the domain of the reals is also presented and discussed, albeit critically. A brief sceptical section on algorithmic complexity theory is included in an appendix

Newcomb's Paradox: a Subversive Interpretation

A re-interpretation of the asymmetric roles assigned to the two agents in the genesis of Newcomb’s Paradox is suggested. The re-interpretation assigns a more active role for the 'rational' agent and a possible Turing Machine interpretation for the behaviour of the demon (alias 'being from another planet, with an advanced technology and science,..,etc.'). These modifications, while introducing new conundrums to an already diabolical interaction, do allow the 'rational' agent, as a computably behavioural agent, to make a clear decision, if any decision is possible at all. This latter caveat is necessary because in the Turing Machine formulation, the computably behavioural agent might have to face algorithmic undecidabilities

A Primer on the Tools and Concepts of Computable Economics

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, constructive mathematics should be one vision of computability theory. However, there are fundamental differences between computability theory and constructive mathematics: the Church-Turing thesis is a disciplining criterion in the former and not in the latter; and classical logic - particularly, the law of the excluded middle - is not accepted in the latter but freely invoked in the former, especially in proving universal negative propositions. In Computable Economic an eclectic approach is adopted where the main criterion is numerical content for economic entities. In this sense both the computable and the constructive traditions are freely and indiscriminately invoked and utilised in the formalization of economic entities. Some of the mathematical methods and concepts of computable economics are surveyed in a pedagogical mode. The context is that of a digital economy embedded in an information society

Using and producing ideas in computable endogenous growth

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 formally indeterminate in a precise and effective sense.endogenous growth,algorithmic ideas,computable growth

Negishi's Theorem and Method

Takashi Negishi's remarkable youthful contribution to welfare economics, general equilibrium theory and, with the benefit of hindsight, also to one strand of computable general equilibrium theory, all within the span of six pages in one article, has become one of the modern classics of general equilibrium theory and mathematical economics. Negishi's celebrated theorem and what has been called Negishi's Method have formed one foundation for computable general equilibrium theory. In this paper I investigate the computable and constructive aspects of the theorem and the methodComputable General Equilibrium, Fundamental Theorems of Welfare Economics, Negishi's Method

The foundations of computable general equilibrium theory

general equilibrium theory,CGE models,mathematical economics,computability,constructivity

The Phillips Machine, The Analogue Computing Traditoin in Economics and Computability

In this paper I try to argue for the desirability of analog computation in economics from a variety of perspectives, using the example of the Phillips Machine. Ultimately, a case is made for the underpinning of both analog and digital computing theory in constructive mathematics. Some conceptual confusion in the meaning of analog computing and its non-reliance on the theory of numerical analysis is also discussed. Digital computing has its mathematical foundations in (classical) recursion theory and constructive mathematics. The implicit, working, assumption of those who practice the noble art of analog computing may well be that the mathematical foundations of their subject is as sound as the foundations of the real analysis. That, in turn, implies a reliance on the soundness of set theory plus the axiom of choice. This is, surely, seriously disturbing from a computation point of view. Therefore, in this paper, I seek to locate a foundation for analog computing in exhibiting some tentative dualities with results that are analogous to those that are standard in computability theory. The main question, from the point of view of economics, is whether the Phillips Machine, as an analog computer, has universal computing properties. The conjectured answer is in the negative.Phillips Machine, Analogue Computation, Digital Computation, Computability, General Purpose Analogue Computer