"Lyric's task is to mediate between particularity and totality in the representation of persons." It is less important to me to decide whether this is Adorno's or Stewart's or Mlinko's axiom than it is to connect it to my own axiomatic.
The first task for the pangrammarian is to construct a provisional transposition of this insight in philosophical terms. I think we can keep "task" and "mediate" and "representation", which are grammatically equivalent for poetry and philosophy.
We automatically replace "person" with "thing" and carry out a simple dialectical inversion of "particularity" into "universality" (the particular is to poetry what the universal is to philosophy and vice versa). The same reasoning can be applied to the replacement of "totality" with "elementarity".
I take it "lyric" just means "poetry", which would allow us to substitute "philosophy", but I would prefer to find a word for philosophy that is to it what "lyric" is to "poetry". Perhaps I'll come up with something later (logic is taken). In any case,
Philosophy's task is to mediate between universality and elementarity in the representation of things.
This is a perfectly respectable suggestion, its means of construction notwithstanding.
Notice that we can here replace "lyric" with "emotional notation" salva veritate.
The task of emotional notation is to mediate between particularity and totality in the representation of persons.
This suggests that it is the noted emotion that carries out the requisite mediation. It must, of course, be accomplished immediately (or we would ask what mediates the mediation), and while the concept is available immediately in intuition for philosophy, the emotion is available to poetry only in institution. (Indeed, concepts and emotions are what make things and people respectively available to knowledge and power respectively in, respectively, intuition and institution.)
So everything works out very nicely. Poetry presents the institutional ground of the representation of persons, and the institution is nothing other than the immediacy of the mediation of a particular person ("I") and its totality (history). Homologously, philosophy presents the intuitive ground of the representation of things, and the intuition is nothing other than the immediacy of the mediation of a universal thing (the world) and its elmentarity ("it").
I wonder if that helps.