The article dwells upon the issue of a subject intrinsic to the art of the 70s and 80s of the 20th century, it elicits the reasons determining the problematization of “the Self” category inherent in the aesthetic program of the Moscow Conceptualism, preeminently with regards to the works of Dmitry Prigov. “The crisis of the language describing ‘the Self’” has been considered as discrediting the dominant discursive models, disabling the possibility of individual expressing. Within the first part of the article we problematize “the Self” category inherent in the aesthetic program of the Moscow Conceptualism, examine the dominant discursive models and denote the crisis of the language describing “the Self.” The second part is devoted to the issue of “the personal consciousness” coming into being within the aesthetic program of Moscow Conceptualism. The Self is considered as a “category of categories” in dichotomy between “the collective” and “individual” ones. Finally, the third part represents the analysis of a subject of the aesthetic activity. “An imaginary personality” intrinsic to the works of Dmitry Prigov is considered as a subject of “a gnoseological game.”