What exactly do you mean by "positive knowledge" or "negative knowledge?"
Negative knowledge is: there is not an instance of x (where not existing is not a predicate of x)
It's not just the word "not" it's an odd number of nots (double negatives and all that).
It is a statement about an abstraction, not existence. Like saying "the cup is above the table" is a statement about the existence of the "above-ness with respect to the table" of the cup. One needn't survey all of reality to know if it is possible for some abstraction to exist. It need only be consistent with the rest of your language, so that's all you need to survey.