Saturday, October 26, 2013

You can prove a negative

It is widely claimed that you cannot prove a negative, but Steven D. Hales rebuts this:
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.


Randy Smith said...

But you aren't proving a negative. You are turning the question around so that you no longer have to, then proving a POSITIVE. This is harder to do with general statements than it is with such a specific (and lets face it, unrealistic) example. Who tries to claim the impossible like an elephant in their room? This is also very dangerous thinking. Because, in the REAL world, you get things like THIS:

Prove that you have never killed anyone. Or that you have not committed treason. Or that you have never committed, say bestiality. You have a video of you entire life sitting around, to prove your innocence?

This is NOT just an academic exercise- people have died over their inability to prove a negative (The Salem witch trials are an example).

Roger said...

A criminal charge usually specifies a particular time, place, and instrument. Many people do indeed prove their innocence in court by proving a negative.

The Salem witch trials were not caused by an inability to prove a negative. They were caused by mass hysteria, misconceptions, lack of due process, etc. That was 300 years ago. Our ability to prove a negative has not changed since then, but we do not have any more witch trials.