Ken’s comment made me realize that the notation is probably not the best. It tends to mislead us into thinking we already have in hand, in other words, that we already have perfect information about and are merely abstracting as some derivative of it. But that is not the sort of situation we are concerned with here.
It might be better to say that is all the information we have at a given moment of investigation and abstracts the portion of that has to do with That might lead us to notate it as This brings to mind the way we speak of observables in physics, as operators on the wave function that represents the total state of the system observed.
If I had to concoct an informal linguistic example — which I’d do solely by way of rough analogy to the formal mathematical cases we’d have much hope of resolving in our lifetimes — I’d say the sorts of we’re facing are what used to be called definite descriptions like “Desdemona’s infidelity” or “Manafort’s guilt on the 10 mistried counts”.
In those sorts of situations, discussed to death in years gone by, what a modicum of pragmatic-semiotic insight adds to the mix is that all descriptions are indefinite to some degree, all syntax lax to some extent.
Not too surprisingly, we find foresights of that insight throughout Peirce’s work. And that is what I’ll be getting around to presently.