“First-order” science is an account of events in the physical world. It is not concerned with analyzing theory and methodology, nor the state of mind of the scientist. Such considerations are generally left to philosophers and historians of science. This restriction serves to keep science within currently defined bounds, and is responsible for much of its success. Yet it also represents a limit on the kind and terms of reflection that may be undertaken. One symptom of this limit is the tendency to recycle a domain of description to serve as its own rationale, which I call “the problem of cognitive domains.” This dilemma results from attempting to use a conceptual framework that does not accommodate reflexivity in a world in which reflexivity is an everyday, unavoidable, and essential aspect. Another symptom is the inability of first-order science to question its own assumptions and methods—for example, the focus on isolated systems and linear equations. Of course, in order to fully understand the results of experiment or observation, the physics of the apparatus—and of intervening physical processes involved in observation—may be considered along with the physics of the defined system under study. But any other kind of role that thought might play in shaping scientific results is not discussed. Despite reference to “observers” one remains within the bounds of first-order description, which focuses on what the observer sees rather than on what the observer brings to observation. For good reasons, the Scientific Revolution served above all to redefine natural philosophy as first-order science: a science whose exclusive focus is the external world, not its own process. The nature of the scientist’s participation is excluded from discussion. The very existence of consciousness, therefore, poses a problem for first-order science, which deals strictly in objectivist accounts. The ability of cosmology now to consider the universe as a whole poses a similar problem. For there is no longer a place outside the system for the observer to stand.