The paper shows the path from the cultural-activity approach, represented by the names of L.S. Vygotsky, A.N. Leontiev, O.K. Tikhomirov, to the ontology of personal meanings and to the psychological mechanisms of generation of such meanings. It is argued that O.K. Tikhomirov’s personal meanings theory of thinking has exceeded the non-classical notions of sense formation and can therefore be considered as a part of the theoretical and methodological basis of cognitive science, dealing with the ideals of post-nonclassical rationality. Siberian scientists developed systematic anthropological psychology in its development is based on the O.K. Tikhomirov ideas about the ontological nature of operational meaning and tries to determine the possibility of cultural psychology in the activity of new (post-nonclassical) conditions. However, it relies on the notion of complementarity (selective and directed) as a mechanism of interaction of meaning. It is suggested that a complimentary interaction manifests itself at different levels of organization of matter, thus ensuring the stability of the universe as self-developing system.