Methodological Problems of Applying Mathematical Methods in Historical Research

Abstract

Intensive and purposeful use of mathematical methods in historical research, accompanied by logical- methodological analysis of the problems under study, has been practiced for over two decades in a number of countries, primarily the Soviet Union, the United States, France, Belgium, England, Sweden, and the Federal Republic of Germany. (1) The conditions have now appeared for drawing certain conclusions and determining some prospects. The present article makes an attempt to characterize these findings and perspectives and to evaluate them on the plane of analysis of significant methodological problems entailed in the application of mathematical methods in historical scholarship. We have in mind the significance and possible limits of application of the mathematical apparatus in historical studies, and also the interconnection between mathematical methods and the historical concepts used to explain various phenomena or structures. Many of these questions are answered differently in Marxist and bourgeois scholarship. Correspondingly, the Marxist and bourgeois methodologies of history ascribe different roles to the use of mathematical methods in historical research as this applies to the overall system of historical knowledge. Marxist historians regard the techniques of mathematical analysis of historical material as one of the supplemental means for deeper study of retrospective historical information. Use of mathematical methods in the works of Marxist historians is combined with traditional methods of historical analysis. (2) This testifies to further improvement in historical research and is totally in accord with Marxist views on history as a whole, particularly the idea of the historical process as the development of society in accordance with law. The use of mathematical methods in history accords with the requirement, characteristic of Marxist historical scholarship, that a problem-oriented approach be taken to the historical reality under study as well as to theoretical generalization from individual historical phenomena. The mathematical processing of historical information does not in any way signify a fundamentally new approach to the study of historical reality. (3)