Varieties of Mathematics in Economics- A Partial View

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 seems to be ubiquitous in research, teaching and learning. At least three other varieties of mathematics, each underpinned by its own mathematical logic, have come to be used in the formalization of mathematics in more recent years. To set theory, model theory, proof theory and recursion theory correspond, roughly speaking, real analysis, non-standard analysis, constructive analysis and computable analysis. These other varieties, we claim, are more consistent with the intrinsic nature and ontology of economic concepts. In this paper we discuss aspects of the way real analysis dominates the mathematical formalization of economic theory and the prospects for overcoming this dominance.

Mathematics and Microeconomics

The article deals a number of issues regarding the use of mathematics in economics&nbsp

KONSEP-KONSEP DASAR MATEMATIKA DALAM EKONOMI

The basic concepts of mathematics in economics are important materials in learning economics mathematics. This study aims to examine the basic concepts of mathematics in economics as a support and reference in learning activities. The method used in the study used a literature review study. Based on the studies carried out there are six subjects of basic mathematical concepts in economics, namely: 1) variables, constants, coefficients, and parameters, 2) equations and inequalities, 3) set concepts and theory, 4) real number systems, 5) rules exponents, roots, factoring, and 6) fractions, decimals and percentages

An Inquiry into the Metaphysical Foundations of Mathematics in Economics

Economics is supposed to fall somewhere between a hard science and a social science. During the last half century, economics has become highly mathematical trying to mimic physics. The purpose of this study is to look at the metaphysical statements linked to mathematical models, specifically, Game Theory. In doing so, it will be demonstrated that Game Theory, as part of neoclassical economics, engages in analysis which can be categorized as metaphysical, with real metaphysical implications. In categorizing the metaphysical assumptions of neoclassical economists/game theorists we will see how much of their analysis is consists in a reductive, implausible metaphysical view. Problems that arise from this view are hardly taken into consideration most economists. This lack of consideration has nontrivial consequences for economics as a discipline and for its methodology

What’s Wrong with Contemporary Economics?

It is argued that in educating economists we should sacrifice some of the more technical aspects of economics (which can be learned later), in favour of the compulsory inclusion of (a) philosophy, (b) political science and (c) economic history. Three reasons for interdisciplinary studies are given. In the discussion of the place of mathematics in economics fuzziness enters when the symbols a, b, c are identified with individuals, firms, or farms. The identification of the precise symbol with the often ambiguous and fuzzy reality, invites lack of precision and blurs the concepts. If the social sciences, including economics, are regarded as a “soft” technology compared with the “hard” technology of the natural sciences, development studies have been regarded as the soft underbelly of “economic science”. In development economics the important question is: what are the springs of development? We must confess that we cannot answer this question, that we do not know what causes successful development.

What Economists can learn from physics and finance

Some economists (Mirowski, 2002) have asserted that the neoclassical economic model was motivated by Newtonian mechanics. This viewpoint encourages confusion. Theoretical mechanics is firmly grounded in reproducible empirical observations and experiments, and provides a very accurate description of macroscopic motions to within high decimal precision. In stark contrast, neo-classical economics, or ‘rational expectations’ (ratex), is a merely postulated model that cannot be used to describe any real market or economy, even to zeroth order in perturbation theory. In mechanics we study both chaotic and complex dynamics whereas ratex restricts itself to equilibrium. Wigner (1967) has isolated the reasons for what he called ‘the unreasonable effectiveness of mathematics in physics’. In this article we isolate the reason for what Velupillai (2005), who was motivated by Wigner (1960), has called the ineffectiveness of mathematics in economics. I propose a remedy, namely, that economic theory should strive for the same degree of empirical success in modeling markets and economies as is exhibited by finance theory.Nonequilibrium; empirically based modelling; stochastic processes; complexity

Criticizing the critique. Some methodological insights into the debate on the state of economic theory in the face of the post 2008 crisis

The aim of this paper is to investigate the current debate on the state of economics from a methodological perspective. We claim that the majority of contributions criticizing modern economics are not based on clear methodological principles and thus many of them are not correct. We show this with respect to such issues as the problem of realisticness of models and their assumptions, the role of mathematics in economics, the way we conceptualize the relation between economics (theory) and economy (empiria), as well as the general problem of comparing theories. In doing so we use the research apparatus taken form the philosophy of science and also we benefit a lot from recent developments in the philosophy of economics. Finally, we show one of the paradoxes of that debate, namely that many critics of economics accuse economists of using the wrong language (mathematics) while they do not use proper language themselves while criticizing economics, namely the apparatus taken from the philosophy of science.methodology of economics, mathematization, assumptions, theories of explanation, global economic crisis