What people usually mean when they say this is that it is impossible to prove a global proposition about the real world. I don't know when the irrelevant word "negative" was added (after all, every "positive" statement can be trivially re-written in a "negative" form), but it's become very popular for some reason.

For example: "There are no orange swans" is equivalent to "All swans are either colorless or colored other than orange." Similar techniques can be applied to all statements.