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)

In the article, we undertook an analysis of the prospects described in the research literature in connection with overcoming the linear interpretations of time and the transition to the concept of multiple times. We argue that it is possible to link two relatively autonomous objects on the basis of which they are discussed: the sphere of historical knowledge and the theme of memory. We argue that, overcome at the level of theories of the historical process, the linear idea of time (...) is preserved at the level of the creation of national histories and finds its expression in ethnocentrism or methodological individualism. Overcoming ethnocentrism should be associated not so much with the search for a more balanced attitude to specific interpretations of the historical past, associated with the inclusion of injustice shown in relation to other peoples in their own national histories, but with the development of alternative concepts of time that constitute the very formats of writing stories. We believe that the prospects for overcoming linear interpretations of time are associated with the development of the theory of multiple times. We argue that the constructivist approach should be considered the most heuristic theoretical and methodological basis for its implementation. We believe that modern interpretations of the heterogeneity of time imply the recognition of the mobility of time boundaries between the past, present, and future. We put forward the thesis that the criterion for distinguishing the modes of time should be considered the difference in the formats of the organization of knowledge. Correspondingly, we offer an interpretation of the historical past in the format of historical experience. As one of the consequences of this thesis, we affirm the need to revise ideas about the forms of influence of the past on the present. We argue that the recognition of the theory of the heterogeneity of time gives rise to relativism in determining the significance of different time streams in different social groups and cultures. We believe that the recognition of the theory of the diversity of temporal flows for different social and cultural groups presupposes the implementation of a procedure for synchronizing the data of temporal flows, which, on the one hand, makes it possible to overcome relativism, and, on the other hand, allochronism. Furthermore, we emphasize that synchronization should be based on the concept of modernity, which in turn is built on the basis of the project of the future and thus allows for the selection of various ideas about time. (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.