The author explores origins of the tradition of positivism in the Russian military-philosophical thought. The subjects of comparative analysis are some elements of A. Comte's philosophy and theoretical assumptions of G.A. Leer's theory of strategy as a type of positive social science of war. The author pays attention to the historical method as the basis of the methodology of social sciences and the science of war in particular, to the role of research in theoretical constructions of laws and principles, and to the relationship between science and art, knowledge and activity. The author concludes about the impact of ideas of classical positivism over the formation of G.A. Leer's theory of strategy. In addition, the article identifies the main shortcomings of G.A. Leer's theory of war, such as the inclusion of the subject area and the content of the science of war into the subject area of the theory of strategy, i.e., reduction of the first to the status of the philosophy of martial arts, as well as the incompleteness of truly positive social science of war due to the lack of the necessary scientific sociological basis in the late XIX century. The author defines subsequent direction of the study of positivism in the domestic military-philosophical thought in the works of Russian emigrant thinkers, Soviet military theorists and philosophers.