The progress towards mathematization or, in a broader context, towards an increased “objectivity” is one of the main trends in the development of biological systematics in the past century. It is commonplace to start the history of numerical taxonomy with the works of R. R. Sokal and P. H. A. Sneath that in the 1960s laid the foundations of this school of taxonomy. In this article, I discuss the earliest research program in this field, developed in the 1920s by the (...) Russian entomologist and biometrician Eugen (Evgeniy Sergeevich) Smirnov. The theoretical and methodological grounds of this program are considered based on the published works of Smirnov as well as some archival sources. The influence of Smirnov’s evolutionary (mechano-Lamarckian) convictions on the development of this project of “exact systematics” is analyzed as well as the author’s attempts to establish a novel concept of “mathematical essentialism” in animal taxonomy. The probable causes of the failure of Smirnov’s project are viewed from both externalist and internalist perspectives, including the opposition to the use of quantitative methods in biology by some of the Lysenkoist ideologists in the USSR. A brief comparison of Smirnov’s research program with that developed 40 years later by Sokal and Sneath is provided. (shrink)

The author elucidates the ontological basis of elementary mathematical theories and thereby assesses their certainty as a foundation for the more complex theories of modern mathematics, such as mathematical analysis and set theory. He adduces arguments in favor of the position of Frege, who held that geometry can provide a sufficiently broad and certain foundation for mathematics.

Small cities have a unique socio-economic and cultural potential for developing Russian regions, which is manifested in their unique features: com- pactness, historical heritage, the existence of rare industries and the local economy. At the same time, today in Russia the realization of their potential is primarily hindered by the existing system of politi- cal institutions and practices. The purpose of the work is to analyze the economic potential of small cities. The paper explores the potential for the devel- opment (...) of small cities in relation to the Russian context. So, the authors consider the features of small cities and highlight their economic, social and political problems. As illustrated by the successful ones, the potential of small cities in various sectors of the economy (primary, secondary and tertiary) is analyzed. The practical significance of the study lies in the possibility of using the studied experi- ence in developing the potential of small cities in various sectors of the economy in the practice of Russian management. As a result, it is concluded that small cities as such can be economically and socially efficient settlements, that is, they can be a completely competitive urbanized unit. However, the tools for the development of such territories should be focused on supporting the promising areas of development, providing an opportunity for independent and responsible development. (shrink)