The paper is dedicated to the reconstruction of Alexander Piatigorsky’s observational philosophy within the context of the confrontation between two versions of the transcendental project of man-in-the-world. The first project accentuates the invariant functional organization of cognitive systems by abstracting from bodily, affective and phenomenological realization of this organization. On the contrary, the second project emphasizes the phenomenological perspective of the experience of givenness, always already dependent on whose experience this is and how the cognitive system living this experience is organized. The first project can be called functionalist, and the second – phenomenological. Ontological and epistemological positions of these projects are specified in the problem of the observer, its status in the world and cognitive practice. The observational philosophy possesses an intermediate position between these two programs since, aiming to disclose the invariant structure of observation, it proceeds from the factual experience of the embodied subject placed into the situation of self-observation and observation of the other subject. It is concluded that Piatigorsky’s philosophy borrows from the functionalist project the commitment to self-objectivation (observation of thinking is always the observation of the other thinking) and rejection from the spatiotemporal localization of cognitive activity (thinking is always “none’s” and does not belong to any kind of individual). With the phenomenological project of enactivism Piatigorsky shares the aspiration to disclose the invariant cognitive structures during the empirical observation of the real enactment of cognitive agency (the organization of cognitive systems is the same while its structural realizations are multiple), abandonment of substantialization of the self (“none’s” thinking is considered as the emergent effect of interaction among two or several observers – the autopoietic systems) as well as the refusal from theoretical formulation of the problem of consciousness (observational philosophy develops metatheoretical prolegomena to theory of consciousness, which in turn is considered as lived and essentially practical in phenomenology).