Towards a Mathematical Structure of Global Phenomenal Consciousness

Recent work in the structural approach to consciousness has shown great promise as a research paradigm for the formal and empirical study of the phenomenal qualities of experience, i.e., qualia. In this paradigm, qualia are characterized by modeling the internal organization of parts within an experience, or by modeling external relations between instances of experience. A major next step for the structural approach is to integrate these two perspectives into an account of phenomenally unified global experience. In this paper, we describe these two types of structural models and how their category-theoretic formalizations contribute to the task of identifying the physical bases of phenomenal consciousness. We then propose a sheaf-theoretic framework that integrates these two approaches by mapping mereological parts of experience to empirical measures of their qualia. Through an application to the experience of visual space, we demonstrate that this framework enables a formal description of the structure of experience and conditions for phenomenal unity. We discuss how this integrative approach supports an empirical research program for investigating the relationship between local and global phenomenal qualities, and outline directions for future work toward a structural characterization of global phenomenal consciousness.