The main thesis of this paper is that, in their epistemological views, both Husserl and Ingarden accept two non-controversial theses that lead to logico-ontological problems. One of them is the conception of the intentionality of consciousness. The second is the conception of cognition as a synthesis of identification. The acceptance of both at the same time does not seem to be controversial at first glance. However, deeper investigation shows that one who accepts them both stands in the face of the logico-ontological problem of the identification of a kind of being with nothing in cognitional syntheses, or of the infinite identification of two intentional objects in every act of consciousness. Both consequences lead to the actual impossibility of active acts of cognition, even if we accept that most cognitional syntheses occur in the domain of passivity. The problem is shared by Husserl's conception of knowledge from his 'Logical Investigations' through the later writings, where he uses the concept of noema. There is a contemporary interpretation of the latter concept as identical to Ingarden's concept of intentional object. Therefore, the problem remains in Ingarden's theory of knowledge, which is based on Husserl's original theory of cognition as a synthesis of identification.