Just to go along with those last comments of mine, the following quote is be useful.
The logic of relatives furnishes the solution, by showing that propositions usually have several subjects, that one of these subjects is the so-called Universe of Discourse, that as a general rule a proposition refers to several Universes of Discourse, the chief of which are Singulars, and that all propositions whatsoever refer to one common universe,— the Universal Universe or aggregate of all Singulars , which in ordinary language we denominate the Truth. The analysis of the logic of relations shows that such is the fact, and by the aid of the categories we can easily see why it should be so. A proposition is a symbol which separately INDICATES its object, and the representation in the proposition of that object is called the subject of the proposition. Now to INDICATE is to represent in the manner in which an index represents. But an index is a representamen which is such by virtue of standing in a genuine reaction with its object; while a singular is nothing but a genuine reacting object. It does not follow that the subject of a proposition must literally be an index, although it indicates the object of the representamen in a manner like the mode of representation of an index. It may be a precept by following which a singular could be found. (“The Categories Defended” EP 2:168)
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