# Yes, dammit, one CAN prove a fucking negative

The most absurd assertion on the planet is frequently seen, for example here:

Stop fucking saying that. Yes, dammit, one CAN prove a negative. And sometimes, it’s trivially easy. For example, one can prove that an equilateral triangle has no right angles. Or, one can prove that 1 + 1 is not equal to 3. In fact, one of the most common methods of proof, reductio ad absurdum, requires proving the negative of your premise.

How the stupid assertion got started is unclear. As best I can tell, it originated on Usenet sometime in the 90s. Certainly, it appears nowhere in classical or modern logic or philosophy. I’ve never even heard of a logical system in which a negative cannot be proved, and there are a boatload of weird-ass logical systems out there.

If one cannot prove a negative, then one cannot prove that one cannot prove a negative, so why assert it? Here’s an excellent article on the topic from Infidels Dot Org.

So please, in the interest of Straight Dope’s mission to stamp out ignorance, stop spreading that ridiculous myth.

Thank you.

I thought the point is that you can’t prove an empirical negative. For example, you can’t say “There aren’t any green cats,” because there’s no way to be absolutely sure that you’ve gone and checked every cat.

However, you can use logical proofs to prove “a priori” negatives.

Or such is what I remember from freshman Philosophy class.

That’s a matter of scope, not negation. There are no green cats on my fork.

My theory is that this idea arises from the legal arena, where one can provide documentary, physical or eyewitness evidence that this, that or the other thing happened, but cannot provide such direct evidence that the other thing, that or this did not happen. Proof of a negative can only be indirect, via the absence of positive evidence, and the inferences that can be drawn from that.

That’s my theory, anyway. I cheerfully invite our legal **eagles to swoop in and prove me wrong.

Could be. Don’t know much about law. But it’s a damn fool thing to say in the context of Magellan’s statement to FinnAgain: “The other has to do with the rules of logic…”.

Whenever someone tells me “You can’t prove a negative,” I just say, “Sure I can! Nothing is in my pocket.” I turn my pocket inside out. “Hey, I just proved a negative!”

My thought is that such claims might result from a misunderstanding of the idea of falsifiability, a la Karl Popper. I’m sure we’ve all heard the story of Popper and the swans.

You see a white swan.
You conclude that some swans are white.
You keep seeing white swans.
You infer that all swans are white.

But this last inference can never be fully tested, unless you can be sure that you have seen every swan in existence.

Of course, once you see even a single black swan, you can made the statement, "Not all swans are white. Thus, you have falsified the “all swans are white” statement.

Of course, this could be wrong; but it’s the only thing i can think of when trying to work out why anyone would think that you can’t prove a negative.

Nah, that’s easy. You can prove events didn’t happen. And there is even a rule for testimony by civil servants about the non-existence of documents:

http://www.law.cornell.edu/rules/fre/rules.htm#Rule803

Though it certainly is sometimes more difficult to prove that an event did not occur. It would sometimes be quite tough to prove that you didn’t rob a bank; or as the Kevin Spacey character put it in American Beauty, “Can you prove that you didn’t offer to save my job if I let you blow me?” http://www.imdb.com/title/tt0169547/quotes. But the prosecution frequently has to “prove a negative.” *E.g. * http://www.lawskills.com/case/ga/id/57601/ (Prosecution must disprove alibi and all other affirmative defenses beyond a reasonable doubt).

This seems like the general idea (a much weaker claim; and one entirely inconsistent with the way it is used)

and then there is this strand:

Of course, since induction itself is based on the presumption that the future will be like the past, http://en.wikipedia.org/wiki/David_Hume#The_problem_of_induction, this may not be all that significant an issue.

Hmmmmm… Even in the rules you cite, though, isn’t that indirect rather than direct evidence, in that you’re inferring a fact from the absence of something?

1. Event X would normally be recorded in Memo Y.
2. Records kept in the usual course do not contain Memo Y.
3. Therefore, Event X did not occur.

Also, to disprove an alibi, the prosecution must produce proof of facts which contradict the matters alleged in the alibi. For example:

1. Defendant: I was bowling at Candlepin Heaven at 10:30 that night.
2. Prosecution: Candlepin Heaven closes at 10:00 p.m. every night.

But maybe what I’m arguing here is the difference between direct and indirect (circumstantial) evidence rather than proof of a negative per se.

http://boards.straightdope.com/sdmb/showthread.php?p=6351455&highlight=gfactor#post6351455 (Wherein yours truly deals with the related theory: I can’t prove it because it is counterfactual, therefore, I’m right)(posts 290 and 291).

Proving once again that my memory of Intro to Philosophy is sketchy, what I meant to say is akin to what everyone quoted from Popper – absolute, existential negatives can’t be proven empirically.

Like Liberal said, I guess it is an issue of scope. For example, you can’t empirically prove the statement “X does not exist” because you can’t check all of X, or be sure that you have managed it if you try. More limited empirical statements can, I see now, be demonstrated (“X does not exist in this space.”)

Anyway, I think this misconception arises, as everyone has said, from people who, kinda like me, remember half of what they learned in Phil class and forget the other half…

Yes. The example I chose involves drawing a negative inference from a lack of a record. That’s really the only time you need a special rule. Direct proof is easy:

a. “I saw the defendant approach the intersection. He arrived at the stop sign, but did not stop.”
b. “The defendant says he was on the Omnibus bound for Clapham at 8:30. He wasn’t though. I know because I was raping him just then.”
c. But the most recent controversial example is this one: “Terri Schiavo is not in a persistent vegetative state. I know this because I saw her do X.” While this claim is similar to the others, it involves a different regret matrix. The rules of induction say that the claim has been considered and rejected by authoritative bodies, and disagreed with by others who had better knowledge, and therefore is less credible. But the principle remains the same.

Let me give a f’r instance, if I may:

Several years ago, I lived in an apartment complex. The ceiling was leaking in the living room when it rains, and I told my landlady about it. She stated that it cannot be fixed while it’s raining. I can understand that.

A few weeks later, I mentioned again to my landlady that the ceiling would still leak. She stated that they were not going to fix it, since it wasn’t raining at the time, therefore no leak existed.

I called the local Tenants Association, who advised me to send the landlady a certified letter stating that, if repairs were not made, I would withhold rent until such time as it was fixed. I mailed said letter, and withheld the rent, as no repairs were ever made.

The landlady then filed for eviction on the grounds that I didn’t pay rent. It went to court. The judge was shown my copy of the letter I sent, along with the signed receipt.

However, prior to the court hearing, there had been a different hearing where an arbiter would listen to both sides, and rule accordingly. A notice for THAT hearing was left on my apartment door, and a copy was mailed to me.

I NEVER saw them.

I suspect that the landlady took the notice off of the door before I could see it, and also removed the copy from my mailbox (I, of course, cannot prove this).

At the hearing (the first one I mentioned), the police officer who put the notice on my door testified that the notice WAS left.

I can’t prove that I never saw it. I signed an affidavit stating I’d never seen it (which is true), but, since the police records show that it was delivered, the judge had no choice but to find in favor of the apartment complex, and I was summarily evicted.

I’m not sure what that proves. At work was a legal presumption: constructive notice.

http://dictionary.law.com/default2.asp?selected=319&bold=||||

The beauty of service by posting: It doesn’t matter whether you actually read the notice. All that they have to prove is that they posted it. Does it get abused? You bet. That’s why service by posting is insufficient if there is a way to serve you personally. In a case such as yours, you have a right to prove that you didn’t receive notice. Unfortunately, the other side has documents prepared earlier that tend to prove that you did get notice–and a claim of lack of notice is a common tactic, used even when the defendant really did get notice. Because of this, courts have developed a presumption that a document that was mailed was received. In other words, the cards were stacked against you. Courts tend to take claims of lack of notice with a grain of salt. Hence, you could have proved that you didn’t get notice, but you weren’t believed.

When they tell me that, I like to say, “Prove it.”

Here’s how SentientMeat managed to get this point through to me:

Clear and poignant, I think.

Bzzt! In spherical geometry an equilateral triangle has three ninety degree angles.

I’d like to prove that Liberal’s statement about how one is unable to prove a negative is untrue is untrue, but you can’t prove a negative.

Just kidding. I’ve fallen into that trap myself. OK, nobody should say, “you can’t prove a negative.” When people use it, they are saying “it is unreasonable or impossible to prove such a thing does not exist anywhere in time or space, but since none have been shown to exist in time or space, please show me that such a thing does exist.”

Bzzt! In spherical geometry an equilateral triangle MAY have three ninety degree angles; depending on the size of the triangle relative to the sphere it certainly doesn’t have to.