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Proving a negative

JLam

Proud Skepkid Parent
JLam
Joined
Dec 28, 2004
Messages
4,149
Forgive me if I seem like an idiot in asking this question. I actually AM an idiot, so I have an excuse.

We often speak of the impossibility of proving a negative (for example, asking someone to prove that the Invisible Pink Unicorn doesn't exist) in order to highlight the silliness of an argument.

But it's obviously true that in some cases, it IS possible to prove a negative. For example, if a man was murdered in a London ghetto at 2 a.m. GMT yesterday, it's very easy to prove that Larry King did NOT commit the murder, as he was hosting a television program in Los Angeles at the time.

So, when someone says "Prove Larry King didn't commit this crime," it's quite a simple thing to do.

Is it better to say that it's impossible to prove something doesn't exist, rather than to say that it's impossible to prove a negative? While it's true that it's impossible to prove some negatives, it's not impossible to prove all negatives. OTOH, it does seem quite impossible to prove that something doesn't exist.

Am I making sense here? Or should I just check myself into the nuthouse now?
 
"Prove Larry King did not commit this crime" is different from "prove Larry King committed no crime". The first is dealing with a specific, the second a generality. That would be the same as saying "prove this drug doesn't work for this person", or "prove this drug doesn't work for anyone". It might be easy to prove that the drug doesn't work for a specific person but not that it will not work for anyone.
 
JLam said:
Forgive me if I seem like an idiot in asking this question. I actually AM an idiot, so I have an excuse.

We often speak of the impossibility of proving a negative (for example, asking someone to prove that the Invisible Pink Unicorn doesn't exist) in order to highlight the silliness of an argument.

But it's obviously true that in some cases, it IS possible to prove a negative. For example, if a man was murdered in a London ghetto at 2 a.m. GMT yesterday, it's very easy to prove that Larry King did NOT commit the murder, as he was hosting a television program in Los Angeles at the time.
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That's quite a reasonble question, and it's one of my pet peeves. (I know Randi does this, because I've seen him do it in person.)

What is hard to prove is a distributed assertion.

Now, it just happens to be the case that most negative statements are distributed, but that's as may be.

Try this handy table:

1) Non-distributed positive: Fred L. Jones has a 12-inch nose.
2) Non-distributed negative: Fred L. Jones does not have a 12-inch nose.
3) Distributed positive: All people have 12-inch noses.
4) Distributed negative: No person has a 12-inch nose.
 
Well, he COULD have

You see, Larry King may have some type of Psi powers that he used to force someone to do the dastardly deed by the sheer power of his mind. Alternately, he could have just caused the unfortunate soul to just fall over dead, say from a heart attack.

Can you prove that he didn't?
 
It's very easy to prove a negative just ask for your bank account details the week before your pay check is due !
 
The best explanation I've seen is that it is impossible to prove a universal claim with non-universal evidence. By example, in order to prove that X doesn't exist, you would need essentially a complete (and demonstrably so) list of all things that do exist and show that X isn't on it[1].

On the other hand, even your example of proving Larry King did not commit a certain crime is not really a counter example of the inability to prove a negative. You can prove it was not possible for him to commit the crime, or that someone else, in fact, did. The distinction is small but important: you may not be able to prove that something does not exist, but it may be entirely possible to prove that it can't.

[1] Just to get it out of the way, I know, X does exist, it's right between W and Y.
 
tsg said:
The distinction is small but important: you may not be able to prove that something does not exist, but it may be entirely possible to prove that it can't.
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I don't get the distinction. If you've proven that something can't exist you've proven that it doesn't.
 
Roboramma said:
I don't get the distinction. If you've proven that something can't exist you've proven that it doesn't.
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The distinction is that there is some property or characteristic other than its existence that is being examined. This is different than looking everywhere (literally) and failing to find it. You are not so much proving its non-existence as proving the existence of something else that precludes it.
 
JLam said:
Forgive me if I seem like an idiot in asking this question. I actually AM an idiot, so I have an excuse.

We often speak of the impossibility of proving a negative (for example, asking someone to prove that the Invisible Pink Unicorn doesn't exist) in order to highlight the silliness of an argument.

But it's obviously true that in some cases, it IS possible to prove a negative. For example, if a man was murdered in a London ghetto at 2 a.m. GMT yesterday, it's very easy to prove that Larry King did NOT commit the murder, as he was hosting a television program in Los Angeles at the time.

So, when someone says "Prove Larry King didn't commit this crime," it's quite a simple thing to do.

Is it better to say that it's impossible to prove something doesn't exist, rather than to say that it's impossible to prove a negative? While it's true that it's impossible to prove some negatives, it's not impossible to prove all negatives. OTOH, it does seem quite impossible to prove that something doesn't exist.

Am I making sense here? Or should I just check myself into the nuthouse now?
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Were you actually there at the time? Prove that you're not lying under oath!
 
I think we need to precisely define what is meant by a "negative".

Clearly there are some statements which cannot be tested. Many of these are of the type "X does not exist" , but that need not mean that any statement of the type "X does not exist " is untestable.
For example, the statement "Untestable statements do not exist" is testable.
 
Soapy Sam said:
I think we need to precisely define what is meant by a "negative".

Clearly there are some statements which cannot be tested. Many of these are of the type "X does not exist" , but that need not mean that any statement of the type "X does not exist " is untestable.
For example, the statement "Untestable statements do not exist" is testable.
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Being testable is not the same as being provable. "X does not exist" is falsifiable: simply show that X does exist. But not being able to show X does exist doesn't prove that X doesn't exist.
 
Neither universal positives nor universal negatives can be demonstrated by appealing to non-universal evidence. That's completely true. If I say "All ducks are black, because all of the ducks in this pond are black", that's obviously an invalid argument.
 
Melendwyr said:
Neither universal positives nor universal negatives can be demonstrated by appealing to non-universal evidence. That's completely true. If I say "All ducks are black, because all of the ducks in this pond are black", that's obviously an invalid argument.
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Reminds me of a good (for small values of "good") joke:

An astronomer, a physicist and a mathematician are on a train in Scotland when they see a black sheep in a field out the window. The astronomer says, "Look, Scottish sheep are black!". The physicist corrects him saying, "No, some Scottish sheep are black." The mathematician looks at both of them and says, "In Scotland, there exists a field containing at least one sheep, at least one side of which is black."
 
JLam said:
But it's obviously true that in some cases, it IS possible to prove a negative. For example, if a man was murdered in a London ghetto at 2 a.m. GMT yesterday, it's very easy to prove that Larry King did NOT commit the murder, as he was hosting a television program in Los Angeles at the time.

So, when someone says "Prove Larry King didn't commit this crime," it's quite a simple thing to do.
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There's a simple reason for your confusion. You're thinking that your assertion that "Larry King didn't commit this crime" is a negative assertion. In fact, it is a positive one.

My current English Composition instructor is also the instructor for the college's "critical thinking and reasoning" class, and he had a very simple test to see if something is a provable claim.

If you claim something that requires "universal simultaneous knowledge of the set" it is an unprovable claim.

Stating that something DOES exist can be proved. All you have to do is find one example and it's proved. To prove something does NOT exist requires that you have universal simultaneous knowledge (USK) of the set.

Someone claiming bigfoot exists is making a claim that requires USK. You can narrow down the set, saying that bigfoot exists somewhere on Earth. Even still, you'd have to have USK of the world. Even if you were to narrow down the set to just Canada and have USK of Canada, it's entirely possible that the bigfoot that do exist are all in Washington State.

You can not definitively claim that bigfoot exists until one is found, nor can you claim definitively that bigfoot does NOT exist, because you do not have USK.

Now in scientific terms, your default position must be that something does NOT exist until there is compelling evidence that it does. This default position can be easily changed because all it requires is one proof to change it. If you had a default position that something DOES exist until proven otherwise, that position would never be able to be proven false, because no one could ever have USK to prove otherwise.

This is the flawed reasonsing of the woos and the religious. They believe something exists with no compelling evidence, and ask us to prove that those things do NOT exist. Until we do, they will maintain their beliefs. The counter-argument is that it is impossible to prove that something does NOT exist because we can not have USK. Usually this is simplified by the statement that we can not prove a negitive.

"Larry King did not commit the murder" is a positive assertion. It can be proved.

"Larry King does not exist" is a positive assertion. It can be proved false.

"God exists" is a positive assertion that has no compelling evidence yet, so the default position must be that he does not.

"God does not exist" is a positive assertion that can't be proved because it requires USK.

So you see, the difference between a negitive statement that can be proved or not depends on if the subject of the assertion has any evidence in the positive direction. You can find evidence of Larry King's existance. So far there is no evidence of God's existance.

It's really not about proving a negitive. It's about asking whether the subject of the assertion is able to be proven in the positive.

"Larry King does not exist" can be turned around to "Larry King DOES Exist". both are provable.

"God does not exist" can be turned around to "God does exist". Neither are known, so the default position must be that he does not, and those making the claim that he DOES are required to prove that he does. Turning the argument around and asking those who say he does NOT exist is a trap you should not fall in to.
 
JLam said:
Forgive me if I seem like an idiot in asking this question. I actually AM an idiot, so I have an excuse.

We often speak of the impossibility of proving a negative (for example, asking someone to prove that the Invisible Pink Unicorn doesn't exist) in order to highlight the silliness of an argument.
Click to expand...

Actually it DOES sound like a false argument to me. There ARE negatives that can be conclusively proved. Of course, that depends on what someone means by "conclusive". Depending, it may be that nothing can be proven, either way.

Myself, I prefer to work with reasonable doubt and certainty. So, yes, many negatives can indeed be proved.
 
Melendwyr said:
EagleEye: what would be an example of a negative claim?
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I think that by definition, any claim is a positive claim. Making a claim is making an assertion.

Asserting that something does not exist is easy to DISPROVE if you can provide a single point of concrete evidence.

Asserting that something DOES exist is easy to prove by providing a single example of that thing.

The problem comes when you have an assertion in either direction where there is no concrete evidence either way.

In that case, the default position must be non-existance until there is proof that it does exist.
 
EagleEye said:
I think that by definition, any claim is a positive claim.
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Again: what's a negative claim?

Because if all claims are positive claims, 'positive' is redundant - more than that, it's erroneous, because it implies a duality.

I think you've gotten your arguments wrong.
 
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