Roman Ingarden devoted many of his philosophical works to the question of purely intentional objects. According to him, works of art are such objects. He investigated their ontological and epistemological aspects. Taking inspiration from his remarks on the cognition of purely intentional objects, and referring to Edmund Husserl's investigations, this paper sketches a general scheme of the cognition of such objects. The cognition of primarily intentional and secondarily intentional objects is described separately.