Take the following propositions:
1. John is not in room A.
2. This table is not black.
Definition of nagative facts:
negative facts : The Blackwell Dictionary of Western Philosophy : Blackwell Reference Online
Accordingly, " Not in room A" and "Not black" are negative facts for proposition 1, and 2, respectively. According to one view, the reason why 1, and 2 is true is due to the existence of a complementary positive fact. For example, the reason why 1 is true is due to the fact that john is in room C, and the reason 2 is true is due to the fact that the table is red.
Take the proposition:
3. There is nothing.
Obviously, 3 is asserting the existence of a negative fact. We can use the same trick we did for 1, and 2. Suppose 3 is true, then there exist a positive fact that makes 3 true. Here is the problem, the exist of any positive fact would make 3 false. We have a contradiction. Either we reject 3, or we reject the problem of using a positive fact to make a negative fact true.