This article is about the hypothesis of a generalized cultural script that permeates all aspects of personal and social life. A generalized cultural script is culture-speciёc and is formed in the human consciousness during socialization and enculturation. It happens when special cultural event scripts are condensed and generalized in the person’s consciousness. The article studies a cultural context for the functioning of a generalized cultural script, or a sociocultural system consisting of different types of artefacts and presenting, generally, a system of intentions. The generalized cultural script itself is seen as an intentional artefact system that transforms a human into an intentional personality. It sets the problem of the relation between intentionality of the human world and freedom of will.