> term ‘aspect’ denotes an instantiated phenomenal property or quale. The set of aspects A(e),
> then, comprises the phenomenal properties or qualia which are instantiated in the experience e,
> also called the phenomenal states of the experience e. Our question, then, is what it means
> that “any set of phenomenal states of a subject at a time is phenomenally unified”
> [...]
> A promising answer is the
> so-called subsumptive unity thesis, developed in [5]:
> “For any set of phenomenal states of a subject at a time, the subject has a
> phenomenal state that subsumes each of the states in that set.” [5, p. 20]
> According to this thesis, what underlies the experience of the unity of a conscious experience
> is that for any set X of phenomenal states in the conscious experience, there is a further
> phenomenal state that subsumes each of the states in X. This phenomenal state characterizes
> what it is like to be in all of the states of X at once [5, p. 20].
> [...]
> Phenomenal unity gives rise to a mathematical structure of conscious experience.
When I try to state this in natural language I come to something like "Conscious states consist of qualities, or contain qualia. And they are unified _in_ consciousness, meaning that our experience is whole. The mathematical structure is this: For any set of experiencing qualities there is a(n additional) state integrating them all into one state."
When I studied philosophy in the 2000s we discussed such kinds of solutions already in a seminar and found them lacking on two grounds.
First: there is no clear notion of non-conscious qualia, and Ockham help us here to keep it so. But if this is true, each of the integrated states already presupposes the whole (because it is already conscious, consciousness is more the medium of qualia), which then cannot come after them to unify them. Unless one wants to assume that a lot of conscious splintered experiences are integrated into a whole later. That would be even more questionable, because who experiences them?
Second: The integrating state needs another integrating state to integrate it into the whole of conscious experience etc. ad inf. Unless it is a state that integrates itself into the whole as well, which would just be a sleigh of hand - because exactly that is the riddle that a mathematical structure must overcome to be about consciousness. The self-reference, the self-presentation of consciousness. Apologies for lacking the proper terminology here.
edit: formatting