Recent activities in virtually all fields engaged in consciousness studies indicate early signs of a structural turn, where verbal descriptions or simple formalisations of conscious experiences are replaced by structural tools, most notably mathematical spaces. My goal here is to offer three comments that, in my opinion, are essential to avoid misunderstandings in these developments early on. These comments concern metaphysical premises of structural approaches, the viability of structure-preserving mappings, and the question of what a structure of conscious experience is (...) in the first place. I will also explain what, in my opinion, are the great promises of structural methodologies and how they might impact consciousness science at large. (shrink)

In consciousness science, several promising approaches have been developed for how to represent conscious experience in terms of mathematical spaces and structures. What is missing, however, is an explicit definition of what a 'mathematical structure of conscious experience' is. Here, we propose such a definition. This definition provides a link between the abstract formal entities of mathematics and the concreta of conscious experience; it complements recent approaches that study quality spaces, qualia spaces or phenomenal spaces; it provides a general method (...) to identify and investigate structures of conscious experience; and it may serve as a framework to unify the various approaches from different fields. We hope that ultimately this work provides a basis for developing a common formal language to study consciousness. (shrink)