Consciousness and topologically structured phenomenal spaces

There are strong reasons to believe that our conscious inner life is structured, suggested both by introspection as well as scientific psychology. One of the most salient structural characteristics of conscious experiences is known as unity of consciousness. In this contribution, we wish to demonstrate how features of experience that pertain to the unity of consciousness could be made precise in terms of mathematical relations that hold between phenomenal objects. Based on phenomenological considerations, we first outline three such features. These are (i) environmental embedding, (ii) the mutual constraint between local and global representations, and (iii) a top-down process of object formation in consciousness. We then introduce a formal model based on the notion of phenomenal space, defined in terms of a set of quasi-elementary and extended entities. We describe the structure of phenomenal space by appealing to mereological and topological concepts, and we outline a projector-based calculus to account for the idea that the structure of phenomenal space is ultimately dynamical. Using the above concepts, one could approach the mind-matter problem by relating environmentally embedded agents to topologically well-defined objects that result from decompositions of phenomenal space. We conclude our discussion by putting it into the context of some recent conceptual questions that appear in cognitive science and consciousness studies. We opt for the possibility to regard the phenomenon of consciousness not in terms of a singular transition that happens between "brain" and "mind" but rather in terms of a series of transitions between structured layers of experience.