The authors evaluate the search for the foundations of social theories within the framework of two projects, firstly, an ontological turn, and secondly, possible combination of methodological individualism and methodological institutionalism. The criticism of the two mentioned projects is made from the standpoint of the theory of conceptual transduction, headed by the principle of theoretical representation, according to which all scientific positions are presentations of scientific theories. It turns out that, contrary to the supporters of the ontological project, there is no need to isolate ontology from scientific theory, and it is present in the theory as a doctrine of subjects. The most meaningful characteristic of individuals and social groups is contained, again, not in the ontological project, but the theory of conceptual transduction. Individuals represent individual theories, and social groups represent group theories. Consideration of group theories from the standpoint of the individual should be complemented by an analysis of individual theories from the standpoint of groups. Accordingly, mutual complementarity also takes place in the case of a combination of methodological individualism and methodological institutionalism. Thus, the genuine foundations of the social sciences are the principle of theoretical representation and the methodology of conceptual transductions. The developed conception is used to characterize the nature of social psychology and social pedagogy. In the first case, an interdisciplinary connection of a certain scientific theory with sociology and psychology is realized, in the second with sociology and pedagogy.