In the attempt to construct a scientific approach to consciousness, it has been proposed that transcendental phenomenology or phenomenological psychology be introduced into the framework of cognitive neuroscience. In this article, the consequences of such an approach in terms of basic assumptions, methods for the collection of data, and evaluation of the collected data are discussed. Especially, the proposed notions of "mutual constraint" and "the second perso" are discussed. It is concluded that even though naturalising of phenomenology might not prove impossible, the "projec" has not yet found a coherent basic ground.