The process of objectification is interpreted as a transition from internality (endo) to externality (exo). Both perspectives can be relevant to both facts (in the sense of Descartes' res extensa) and models (in the sense of Descartes' res cogitans). The internal perspective is fundamentally distinction-free, i.e., no object can be distinguished from anything else. The associated cognitive modes are denoted as participation and imagination. The external perspective allows one to distinguish between objects, subjects, and their environment. Corresponding distinctions are required for the processes of observation and description. The two basic methodologies of traditional science, Baconian empiricism and Cartesian rationalism, can be classified accordingly.In a subsequent step a specific formal relationship between the endo/exodichotomy on the levels of facts and models and the concepts of space and time is suggested. The four possible regimes of endofacts, exofacts, endomodels, and exomodels are associated with real (concrete) and imaginary (abstract) concepts of space and time. The significance of these concepts results from theoretical arguments. They provide a general framework for (i) questions of spatial and temporal nonlocality, (ii) a formulation of criteria for operational access, (iii) a particular way to define the concept of wholeness, (iv) a clarification of the historical confusion about the notion of time, and (v) an interesting link to a classification of basic cognitive modes.