Why can't you prove a negative?
http://grammar.about.com/od/c/g/claimterm.htm
Claims of fact assert that something is true or not true.
In rational arguments, all three types of claims must be supported by facts.
For example, my wife claims I did not do the dishes.
She then sends me a picture of our sink full of dishes.
She just proved a negative.
First of all, YOU would know if you did the dishes or not, she should not have to prove it to you. LOL Anyway, maybe you did do the dishes but the kids left more in the sink.
She proved to herself that I didn't do the dishes. She even has evidence that I didn't do the dishes.
The point is that proving a negative can be done. Through proof of impossibility, or evidence of absence.
Proof of impossibility is what my wife used to prove that I didn't do the dishes.
It is impossible to do the dishes yet there be piles of dishes still in the sink.
Therefore, I didn't do the dishes.
Evidence of absence is looking for evidence where it would be most likely to be if it existed.
Wife asks me if the mail came.
I check the mailbox, it is not there.
I just proved that the mail did not arrive.