The article presents the experience of building an epistemological space of communication of the concepts of the philosophy of science. Based on his experience of teaching philosophy of science at three universities, the author raises the question of the conditions for building such a space. One condition is the analysis of different approaches to constructing the concepts of science. The second is the correction of one’s own approach and understanding of science, which would take into account other approaches to the study of science and the results obtained in them. The concepts of K. Popper, T. Kuhn, S. Toulmin, I. Lakatos are chosen for correction. In addition, the author’s concept of science is presented, carried out within the framework of the cultural-historical approach and general methodology. The author distinguishes two start-ups of science - the ancient one, where the ‘genome of science’ is formed, and the new European one, in which science and its genome function as an ‘institution of modernity’ are presented. He shows that in the construction of the theory of science, an important role is played by problems arising in culture, their resolution with the help of schemes, the construction of ideal objects based on schemes and logic requirements, which allow building a theoretical discourse, solving problems within its framework, comprehending empirical material. The methodological analysis made it possible to state that the development of science is not only a law-like process, due to the change of cultures, personality traits of scientists and forms of understanding science (“conceptualization” of science), but also a singular process in which each historical step in the development of science brings unique features with it. (they can be described, but cannot be subsumed under the concepts of ‘law’ or ‘regularity’). These provisions correspond to the ideas about science by Popper, Kuhn, Toulmin and Lakatos. At the same time, the author shows that they set themselves the task of explaining scientific revolutions or the historical development of science, but they took modern natural science as the ideal of science, often referred to the situation of the formation of modern science to illustrate these processes, and replaced the historical study of science by constructing it as a constant mechanism.