How does “You can’t prove a negative” work?

In: Mathematics

Prove that I don’t have an invisible, intangible, undetectable teapot hidden inside my ass. You can’t. Even proving I don’t have a perfectly normal teapot in my ass is impossible, because I can just continue claiming that I do, and that you simply haven’t located it yet.

Proving something exists is easy, you find it, and then you point at it.

Proving something *doesn’t* exist requires that you eliminate all possible cases in which it could exist and you would not perceive it. Which is impossible in any practical sense.

This is a refrain used in debates to indicate when your opponent is making an argument that can’t be proven due to its construction. They generally have to do with concepts that are unknowable, like the truth value of a religion, but they could be about a knowable subject that there isn’t adequate information to prove.

For example, if I ask you to prove that you haven’t committed any murders, or else I will throw you in jail, it would be hard for you to prove your innocence that way. In order to prove it, you would have to provide evidence of every activity you’ve ever done. It’s unlikely that you could provide enough information to prove your innocence due to my construction of the inquiry.

Burden of proof requires evidence. (Proving something is what you say it is)

Any evidence that it does exist would prove it true but failure to find any evidence would not prove it false, it would only prove that you have failed to find evidence.

It doesn’t, because it’s a paradox. The statement “You can’t prove a negative” is, itself, a negative, so if you cannot prove it you have to disregard it, while if you can prove it, you have disproven it by proving it.

In reality, some negatives can be proven. For example:

* relativity can prove the statement “No object with mass can move as fast as light moves in the vacuum”

* Newtonian physics can prove the statement “There is not a counter-Earth behind the Sun”

* Genetics can prove the statement “There can be no hybrid organism between Homo sapiens and Musca domestica”

The correct procedure to follow is: “Whoever makes a statement, must prove it, or else it is worthless.”

“You can’t prove a negative” is an adage typically said when accusing a person of trying to shift the burden of proof, particularly involving an unfalsifiable claim. As a famous example, if I were to claim there was a small teapot in space (too small to be detected by our current instruments) and asked you to prove me wrong, you might reply that you can’t prove a negative as there is no practical way for you to scour all that space to prove there are no teapots there, while I could easily prove there is by showing some evidence, such as a photograph or the teapot itself.

As with most adages, it is not always accurate. For example, there is a medical blood test called a d-Dimer that is sometimes useful for testing whether a patient has a blood clot, which sometimes can be deadly. The d-Dimer can prove you don’t have a clot with a negative result, but it does not prove anything with a positive result, so it is an example of a situation in which you can prove a negative but not a positive.

“There is an alien in my house.” This is a positive. I can prove it by finding one alien in my house one time.

“There is no alien in my house.” This is a negative. I can’t prove it. Even if I check every square inch of my house, maybe they are really small and I can’t see them. Maybe they are invisible. Maybe they know how to stand directly behind me at all times. There is always a chance that an alien exists, even if it’s the tiniest chance imaginable.