But there is one big, fat problem with all this. Among professional logicians, guess how many think that you can’t prove a negative? That’s right: zero. Yes, Virginia, you can prove a negative, and it’s easy, too.Excerpts here, also.
Proving a negative is not necessarily any harder than proving a positive. I can prove that there is no elephant in my room, because it would have to be big enough for me to see, and there is no place to hide. Proof of impossibility dates back to 500 BC, when it was proved that no rational number could be the diagonal of a unit square.
Sometimes the phrase "proving a negative" is invoked in connection with some untestable hypothesis, such as how many angels can dance on the head of a pin. But the problem there is the lack of an empirical hypothesis, not any negativity.