The ideas of human-dimensional scientific knowledge originated more than 100 years ago in the thoughts of the cosmists of М. Umov, V. Vernadsky, K. Tsiolkovsky, O. Chizhevsky, who wrote about the cosmic origin of man, the influence of his creative activity on cosmic processes are represented in the introduction. At the end of the XXth-at the beginning of the XXIst cc., they were developed by natural scientists who are investigating the origin of the universe and living conditions in it with the help of modern high technologies. It actualizes the philosophical conception of the correlation of the anthropological orientation of scientific cosmism and postnonclassical science. Hence the task of the article is to identify the connections between the philosophy of cosmism (its scientific direction) of the end of the XIXth and early XXth centuries and post-nonclassical science in the aspect of their anthropological dimension. For this purpose, philosophical-anthropological, cultural-historical and comparative methodological approaches and research methods of cultural-semantic analysis and interdisciplinary research are used. On the basis of the study and comparison of the anthropocosmic ideas of the native cosmists of the conditions for the origin of man in the cosmos and the influence of space processes on man's life, of the possibility of transformation of the biosphere into the noosphere in the process of human activity, the author of the article within research results substantiates the position of the relationship of these ideas with the scientific concepts of representatives of postclassical science. In these concepts, man himself is scientifically proven to become one of the factors of further evolution of nature in the part of the universe inhabited by him. And the laws of nonequilibrium thermodynamics, discovered by a scientific school under the direction of I. Prygozhin, confirm the hypotheses of cosmic scientists about the possibilities of the origin of life in the cosmos through the birth of living from nonliving and further - the higher forms of organization of living matter in the universe because of the emergence of instability in extremely unbalanced conditions. The discussion analyzes the results of the research of anthropological ideas of cosmic scientists and contemporary natural scientists, carried out by M. Wallerstein, V. Kazyutinsky, M. Moiseyev, I. Mochalov, V. Onoprienko, N. Popkova, V. Stepin, S. Yahodzinskyi and others. These researchers are shown in the article not to aim to compare the anthropological views of representatives of cosmism and postnonclassical science. The conclusions prove that the leading idea of anthropocosmism is to understand man as an integral part of the cosmos, his role and place in the world evolutionary processes - has become quite promising for the science of the late XXth - early XXIth centuries, has generated a large number of new hypotheses regarding the origin, formation and development of the universe, the planet Earth and man as a special species of living organisms. It discovers the laws of functioning of self-organized systems that represent non-linear, stochastic, cooperative, and other properties of such systems, which are all components of the space process, including the social world and man himself.