An oft repeated truism is,”You can’t prove a negative” by which people usually mean that it’s impossible to prove that something does not exist. This is a retooling of another old saying: absence of evidence is not evidence of absence. Many people believe it is a law of logic.

It’s not. And it isn’t true outside of logic, either.

In most legal systems a form of this principle exists, though it’s usually expressed as a burden of proof argument: the defense doesn’t have to prove that their client didn’t do it, they just have to show that the prosecution hasn’t conclusively proven that the client did do it. However, that doesn’t mean that the defense isn’t allowed to go the extra mile. If the defense can prove that another person actually committed the crime, for instance, or if they prove that it was physically impossible for their client to have done it, they have proven a negative.

In mathematics we have proof by impossibility, which is another form of proving the negative. And in logic you can use a rule of inference called “denying the consequent” to prove other kinds of negatives.

So the next time someone accuses someone of something horrid with little evidence, and replies to any arguments by saying, “you can’t prove it didn’t happen!” Point out that they have the burden of proof wrong: the accuser is the one who has something to prove. The rest of us just have to raise reasonable doubts…