Vague (in logic) [Lat, vagus, rambling, indefinite]: Ger. unbestimmt ; Fr. vague ; Ital. vago. Indeterminate in intention.
A proposition is vague when there are states of things concerning which it is intrinsically uncertain whether, had they been contemplated by the speaker, he would have regarded them as excluded or allowed by the proposition. By intrinsically uncertain we mean not uncertain in consequence of any ignorance of the interpreter, but because the speaker’s habits of language were indeterminate; so that one day he would regard the proposition as excluding, another as admitting, those states of things. Yet this must be under stood to have reference to what might be deduced from a perfect knowledge of his state of mind; for it is precisely because these questions never did, or did not frequently, present themselves that his habit remained indeterminate.
…an assertion is comprehensive in so far as it extends the person to whom it is addressed a certain latitude in the interpretation of it; it is vague in so far as it reserves to the utterer of it a similar latitude.
If a sign allows the utterer a certain latitude of choice as to what his meaning may be; so that he may perhaps defend its applicability in several ways […] then the sign may be said to be vague, or non-definite.
If a sign is apt to represent many things, the option as to what single thing it shall be taken to represent may be reserved by the utterer of it, to whom it naturally belongs; in which case it may be said to be used vaguely, or not definitely.
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. [—]
Perhaps a more scientific pair of definitions would be that anything is general in so far as the principle of excluded middle does not apply to it and is vague in so far as the principle of contradiction does not apply to it.