Correlation of Theoretical and Empirical Knowledge when Using Mathematical Methods in Sociological Research


Tolstova Yu.N.

Dr. Sci. (Sociol.), Prof., National Research University «Higher School of Economics»; Chief Researcher, Institute of Sociology, Federal Center of Theoretical and Applied Sociology, Russian Academy of Sciences, Moscow, Russia untolstova@mail.ru

DOI: 10.31857/S013216250003164-3
ID of the Article: 7458


For citation:

Tolstova Yu.N. Correlation of Theoretical and Empirical Knowledge when Using Mathematical Methods in Sociological Research. Sotsiologicheskie issledovaniya [Sociological Studies]. 2018. No 12. P. 39-48




Abstract

In our time, few argue that the theoretical and empirical knowledge of the sociologist should closely interact with each other in the process of solving any sociological problem: empirical knowledge must confirm the correctness of the theoretical, theoretical – provide a basis for obtaining the empirical. However, no constructive rules for the practical organization of such interaction have yet been developed. In this article, such rules are proposed for a situation where new empirical knowledge is obtained through the use of mathematical methods in traditional ways for sociology. Namely, it is shown that for the effective interaction of the theoretical and empirical stages of research it is required that the process of applying the mathematical apparatus boils down to the construction of a series of such mathematical models of social reality that can be considered carriers of the sociologist’s theoretical knowledge of the phenomenon being studied. This can be facilitated by: (a) the introduction into scientific use of a specific view of mathematics, according to which it is understood in two ways: not only traditionally, as a rigorous formal science, but also as a scientific branch aimed at developing rules for constructing a model of the reality being studied, written in mathematical language; (b) the consideration of all models embodied in mathematical methods as results of a generalized measurement, ensuring that the interpretation of the above models corresponds to the a priori theoretical views of the sociologist; (c) use of methodological principles of application in the sociology of the mathematical apparatus developed, in particular, by (1) well-known American methodologist P.F. Lazarsfeld; (2) Russian mathematician A.A. Chuprov; (3) creators of the data analysis; (4) the author of this article. According to the author’s intention, the article should show that the possibility of successful application of theoretical knowledge for obtaining empirical and back is not accidental arises precisely on the basis of using a mathematical apparatus, since such use requires a clear formulation of ideas about both types of knowledge.


Keywords
mathematical methods; mathematical modeling; theoretical knowledge; empirical knowledge

References

Adler Yu. (1982) Science and the Art of Data Analysis. In: Mosteller F., Tukey J. Data Analysis and Regression. Мoscow: Financy i Statistica: 5–13. (In Russ.)

Blum А., Mespoulet М. (2008) L'Anarchie Bureaucratique: Statistique et pouvoir sous Staline. Мoscow: ROSSPEN. (In Russ.)

Chuprov A.A. (1910) Essays on the Theory of Statistics. Saint Petersburg: M. i S. Sabashnikovy. (In Russ.)

Chuprov A.A. (1960) Problems of Statistics. Moscow: Gosstatizdat TsSU SSSR. (In Russ.)

Lazarsfeld P.F. (1972) Measurement. In: Parsons T. (ed.) American Sociology. Perspectives, Problems, Methods. Мoscow: Progress: 134–149. (In Russ.)

Lazarsfeld P.F. (1958) Problems in Methodology. In: Merton R.K., Broom L., Cottrell L.S. jr. (eds) Sociology Today. New York: Basic Books: 39–78.

Seneta E. (1985) A Sketch of the History of Survey Sampling in Russia. Journal of the Royal Statistical Society. Series A (General). Vol. 148. No. 2: 118–125.

Stevens S.S. (1946) On the Theory of Scales of Measurement. Science. Vol. 103. No. 2684: 677–680.

Suppes P., Zinnes J.L. (1967) Foundation of Theory of Measurement. In: Luce R.D., Bush R.R., Galanter E. Handbook of Mathematical Psychology. Vol. 1. Мoscow: Mir: 9–110. (In Russ.)

Tolstova Yu.N. (2000a) Analysis of Sociological Data. Мoscow: Nauchnyj mir. (In Russ.)

Tolstova Yu.N. (2009) Measurement in Sociology. Мoscow: Knizhnyj dom «Universitet». (In Russ.)

Tolstova Yu.N. (2000b) Ought Sociology «Talk» the Math’s Language? Sotsiologicheskie issledovaniya [Sociological Studies]. No. 5: 107–116. (In Russ.)

Tolstova Yu.N., Mazina E.E. (2007) On the History of Sociology and Mathematics Relations: Russia in Period of the Middle of the XVII – the Beginning of the XX Case. Sotsiologiya: metodologiya, metody, matematicheskoe modelirovanie (4М) [Sociology: Methodology, Methods, Mathematical Modeling (4М)]. No. 24: 28–59. (In Russ.)

Tolstova Yu.N., Voronina N.D. (2012) On the Necessity to Widen the Notion of Sociological Measurement. Sotsiologicheskie issledovaniya [Sociological Studies]. No. 7: 67–77. (In Russ.)

Typology and Classification in Social Reseach. (1982) Мoscow: Nauka. (In Russ.)

Content No 12, 2018