Document Type : علمی - پژوهشی
Author
Mohammad Ali Farahani Fard (Researcher of the Research Center of the Higher Institute of Fiqh and Islamic Sciences, Qom, Iran
Abstract
Mathematics is a science that discusses numbers or topics that have a quantitative and quantitative aspect. The subject of mathematical knowledge is a kind of quantitative order, and the extension of mathematics to economics is the extension of this quantitative order to economic studies.
The main issue in mathematical economics is not mathematical realization at the level of customs offices and general economic statistics; rather, the main problem is the realization of economic theories with mathematical dimensions that have a theoretical analysis of raw economic realities. Mathematics has various applications in economics. These applications include a wide range of economic indicators and geometric explanations.
Mathematics in economics sometimes plays the role of the language of expressing theories, which is summarized in the geometric and algebraic representation of theories, and sometimes it is used as a theoretical tool of economics. In the second role, mathematics explains functional relationships between economic variables and tests theories by econometrics, measures the simple and theoretical quantities, and extracts the statistical values of economic variables using statistical techniques. Based on this, mathematical applications in economics include 1. Units of measurement; 2. Explaining the relationships of various economic variables; 3. Statistical calculations; 4. Econometrics; 5. Geometric representations of economic theories.
Mathematical economics has several developments in the history of economics, and to explain these changes, it is necessary to explain its theoretical and Individual-social factors in conventional economics. Individual-Social factors explain the individual and social conditions and contexts of mathematics in economics, and theoretical factors include ontological, epistemological, and methodological foundations, philosophy of mathematics, compatibility of economic concepts with mathematics, and availability of mathematical theories required for economic mathematical analysis.
Some theorists have only focused on the theoretical factors of mathematics in economics, and some have only focused on its social factors. It seems that focusing on single-factor analysis has led to a limited and out-of-context view of mathematics in economics. Also, proper logical analysis of the combination of these factors has not been considered. Paying attention to the comprehensive analysis as well as the logical combination of these factors leads to the recognition of different types of mathematics throughout the history of economics under the shadow of different combinations between theoretical foundations and different social conditions.
Therefore, the present article seeks to comprehensively review these factors based on the logical historical analytical method.
This article uses a logical analysis method to identify the titles of these factors.
The method of historical analysis deals with the historical study of these factors in the history of economics and economic facts to intercept the mentioned factors in the history of economic theories and economic facts.
The logical combination of theoretical factors and objective factors can significantly help to understand the developments of mathematics in economics.
The findings of the research show that mathematics in economics follows the logical combination of the ontological, epistemological, and methodological foundations, main concepts, theories of mathematical philosophy, required mathematical theories, and social factors.
Based on the explanation of these factors, the ontological foundations determine the core study of economics, and after that, the epistemology and theorizing methods are determined. By clarifying the theorizing method, the main concepts of this science are formed. Concepts that have a quantitative ability in turn determine the fate of using mathematics in economics; but other steps, such as the theory of mathematical philosophy accepting the flow of mathematics, as well as the realization of appropriate mathematical theories in mathematics and the formation of appropriate social conditions, are necessary for the realization of mathematical analysis in economics.
Based on the analysis of the mentioned combination of the theoretical and social factors, seven periods can be recognized in economics.
The pre-mathematical era of economics (from Siva's writings about money in 1711 to Cournot in 1838): this era includes the works of the era of mercantilists, physiocrats, and classics;
Early beginning (Cournot's theory of partial equilibrium): This period is related to the works and theories of August Cournot;
The marginalist revolution (Jones 1871 and Walras 1874 and Perto 1906): This period is related to the neoclassical school when the marginalist revolution was achieved by the economists of this school;
The opposite view of the historical school (the time of Marshall and his followers): This period includes the works of Marshall, Keynes, etc., which were influenced by the historical school. Non-mainstream schools such as interpretative and critical approaches can be considered as the continuation of the historical school in a new form in the matter of opposition to mathematics;
The maturity of mathematical economic theory in classical econometrics: the era of the Coles Foundation (1938), economic journals, and the Nobel Prize: since the 1930s, mathematical expression occupied an increasing proportion of the pages of important economic journals;
The era of the emergence of mathematics in macroeconomic theories: Keynes's followers in macroeconomics after him, based on the naturalism of economic society, by mathematizing his discussions, presented a new field of mathematical research to economists;
Separation of mathematics from economic theory (pragmatism: 1944): In this era, with the spread of the pragmatic theories of John Van Neumann, econometrics changed its direction to modern econometrics, and economic theories were marginalized.
Based on this, mathematics in economics reached its peak when various ontological developments in naturalism included the quantitative nature of economic relations, decisions of economic agents, economic behavior, and economic society, and based on that, various epistemological and methodological tools were used for mathematical analysis. These methods created quantitative concepts in economics, which led to the mathematical modeling of all economic theories in the shadow of mathematical philosophy's agreement with their quantification and the realization of the required mathematical theories, and then by removing the economic theory, led to the simple analysis of mathematical trends.
The main challenge of the mainstream is the dominance of mathematical content over economic theories. Although the mainstream of economics is not satisfied with the removal of economic theory in the shadow of this extreme mathematics and emphasizes the importance of economic theory in this field, with the increasing need for complex economic analysis, only the estimated analysis of mathematical trends remains available to some econometrics. This issue has provoked many discussions among economic methodologists.
The mentioned results indicate that any change in the current state of mathematics in economics will also be subject to the mentioned factors.
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