What is Integrated Information Theory a Theory Of?

In the first instance, IIT is formulated as a theory of the physical basis of the 'degree' or ‘level’ or ‘amount’ of consciousness in a system. I raise a series of questions about the central explanatory target, the 'degree' or ‘level’ or ‘amount’ of consciousness. I suggest it is not at all clear what scientists and philosophers are talking about when they talk about consciousness as gradable. This point is developed in more detail in my paper "What Is the Integrated Information Theory of Consciousness?"Journal of Consciousness Studies 26 (1-2):1-2 (2019)