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

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.

Frege's logicism

In this paper, I provide an interpretation of Frege's logicist project, drawing a connection between it and his idiosyncratic view of truth

Reconstructions of science

'In vier Rekonstruktionen wird versucht, die natur- und sozialwissenschaftliche Diskussion der Basiskonzepte von Raum und Zeit zu vereinen. Dazu bedarf es einer neuen Diskursform, die bereits in Alfred North Whiteheads Naturphilosophie anklingt. Auf sozial-wissenschaftlicher Seite besinnen wir uns grundlegender Themen von Sozialphänomenologie, Strukturalismus und Interaktionismus. Fragestellungen von PrähistorikerInnen, ÄgyptologInnen und EthnomathematikerInnen werden wichtig, wo wir zeigen, daß unsere Konzepte von Raum und Zeit kulturelle Institutionen der Bedeutung sind, die ihrerseits Gesellschaft konstituieren und konstanter Rekonstruktion bedürfen. Die vierte Rekonstruktion greift die Frage der theoretischen Physik auf und stützt sich auf das integrative Instrument der Theorie der geometrischen Clifford Algebren. Wir leiten ab, daß und wie die inneren Symmetrien der Materie mit den äußeren Symmetrien der Raum-Zeit verbunden sind und daß die Metapher vom 'achtfachen Pfad', die Gell-Mann für einen Teil des Standardmodells verwendete, entgegen seiner Auffassung nicht als Witz zu verstehen ist. Der Faktor (D4)m in der Dirac-Gruppe jeder geometrischen Clifford Algebra C/p,q bildet eine Grundstruktur von Orientierung und Logik ab und korrespondiert daher mit einem Interface zwischen Geist und Materie.' (Autorenreferat)'In four reconstructions it is attempted to lead the natural and social science debate of the basis concepts of space and time in common. For this we need a new mode of science discourse which has already been initiated in Alfred North Whitehead's philosophy of nature. In social science we reconsider the basis themes of social phenomenology, structuralism and interactionism as far as those contribute to a space-time topic. Investigations of prehistorians, egyptologists and ethno-mathematicians are of importance where we demonstrate that our concepts of space and time represent cultural institutions of meaning which on their part constitute society and require that we constantly reconstruct them. The fourth reconstruction deals with the space-time of postmodern theoretical physics and is founded on the integrative instrument of the theory of geometric Clifford algebras. We show that and how the inner symmetrics of matter are connected with the outer symmetries of space-time and that Gell-Mann's metaphor of the 'eightfold path' that he used to denote part of the standard model of physics cannot be interpreted as quirk, in opposition to his own intention. The factor (D4)m in the Dirac group of any geometric Clifford Algebra C/p,q represents a ground template (or archetypal structure) for both orientation and logic and corresponds therefore with an interface between matter and mind.' (author's abstract)

Computation in Economics

This is an attempt at a succinct survey, from methodological and epistemological perspectives, of the burgeoning, apparently unstructured, field of what is often – misleadingly – referred to as computational economics. We identify and characterise four frontier research fields, encompassing both micro and macro aspects of economic theory, where machine computation play crucial roles in formal modelling exercises: algorithmic behavioural economics, computable general equilibrium theory, agent based computational economics and computable economics. In some senses these four research frontiers raise, without resolving, many interesting methodological and epistemological issues in economic theorising in (alternative) mathematical modesClassical Behavioural Economics, Computable General Equilibrium theory, Agent Based Economics, Computable Economics, Computability, Constructivity, Numerical Analysis

The Role of Ignorance about Keynes’s Inexact, Approximation Approach to Measurement in the A Treatise on Probability in the Keynes-Tinbergen Exchanges of 1938-1940 in the Economic Journal

J.Tinbergen and J. M. Keynes held diametrically opposed positions on measurement. Tinbergen’s physics background led him to deploy an exact approach to measurement based on the specification of probability distributions, like the normal and log normal, with exact and precisely probabilities that were linear, additive and definite. All probabilities for Tinbergen were assumed to be well defined, precise, exact, determinate, definite, additive, linear, independent single number answers, whether the field was physics or economics. Keynes’s approach was an inexact one. Probabilities for Keynes were, with a few exceptions, partially defined, imprecise, inexact, indefinite, indeterminate ,non additive, non linear, and dependent. Probability estimates for Keynes required two numbers to specify the probability within a lower and upper bound (limit), and not one single number like Tinbergen’s approach. Keynes called this approach Approximation. Keynesian probabilities are interval valued.The problem, from Keynes’s perspective, was that Tinbergen was trying to apply to economic data techniques which were only sound when applied in physics ,where laboratory controlled environments with detailed experimental design could generate data and replicate/duplicate the experiments. Keynes had always argued that economics was not a physical or life science like physics, engineering, biology or chemistry and that it could never be like physics