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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