C.S. Peirce defines the symbol in general as a sign whose particular definition is in terms of how said sign will be interpreted irrespectively of reaction or resemblance with its object. This interpretant is not all the interpretant(s) which might be expected to arise on a given occasion -- it is more a habitual interpretant, or a habitual part of various interpretants on various occasions.
Thus the symbol in general seems to be defined by something like its comprehension or intension.
Insofar as the comprehension or intension consists in the qualities or properties themselves comprehended or intended, it might be more appropriate to say that the symbol in general is defined by a relation to its comprehension or intension. This is not unlike as an index is defined not by its reactive object but by its reaction with its object, and also not unlike as an icon is defined not by the quality of the icon's object but by the icon's likeness (in respect of 'ground,' the quality's pure abstraction) to its object.
I'm not sure what to call this. "Intensionality" means "state of having an intension," whereas what seems desirable here is a word signifying the relation itself, rather than just the fact of having it. I could make up a word like "intendency" or "intensure" but for the time being I'll just stretch the meaning of "intensionality" a bit in order to adapt it for the momentary purpose, which is to ask this question:
Q: Is there any reason not to hold that the symbol in general is a sign defined by its intensionality or intensional relation, in the sense sketched out above?
Another question: Do I have something extra extending up my sleeve? Yes.