I first encountered Peirce’s dimensions of generality and vagueness — two measures of determinacy on sign relations describing the extent to which objects are determined by signs and interpretant signs — while exploring the closely related subjects of definition and determination.
Lately I’ve noticed Peirce’s treatment of objectively indeterminate signs has a bearing on my approach to Category Theory through the Logic of Relatives, so it looks worth paying attention to their potential relationships. To get things rolling, here’s a good entry point:
A sign (under which designation I place every kind of thought, and not alone external signs), that is in any respect objectively indeterminate (i.e., whose object is undetermined by the sign itself) is objectively general in so far as it extends to the interpreter the privilege of carrying its determination further.
Example: “Man is mortal.” To the question, What man? the reply is that the proposition explicitly leaves it to you to apply its assertion to what man or men you will.
A sign that is objectively indeterminate in any respect is objectively vague in so far as it reserves further determination to be made in some other conceivable sign, or at least does not appoint the interpreter as its deputy in this office.
Example: “A man whom I could mention seems to be a little conceited.” The suggestion here is that the man in view is the person addressed; but the utterer does not authorize such an interpretation or any other application of what she says. She can still say, if she likes, that she does not mean the person addressed.
Every utterance naturally leaves the right of further exposition in the utterer; and therefore, in so far as a sign is indeterminate, it is vague, unless it is expressly or by a well-understood convention rendered general.
C.S. Peirce, Collected Papers, CP 5.447