You CAN prove a negative

[Dorian Gray]

Who says you can't? Well, you're wrong.

There are many negative statements that can be proven.
This text is not white.
I am not a turnip.

See?

This says it better than I do.
http://www.graveyardofthegods.net/articles/cantprovenegative.html

Thirdly, the statement that “you cannot prove a negative” is simply false. On the surface, it seems to be true: if Person A says “I think God exists” and Person B says “I don’t think God exists,” it’s pretty clear that Person B is going to have a hard time proving that there isn’t a God. However, if you look a little closer, it actually depends on the nature of the negative statement being made. Here are some negative statements that can be proven very easily:

Five is not equal to four
The ancient Egyptians did not watch Seinfeld
The tsetse fly is not native to North America

Clearly, it’s possible to prove a negative statement. The real problem here is clearly the nature of the positive statement being refuted. When a person asserts that God exists, he does not specify the nature of God – that is, is God small, large, blue, red? And where is he? Of course it is not possible to prove that God does not exist, if “God” is a thing that has no definition, no characteristics, and no location. In fact, you can prove just about any kind of negative you can think of – except for (surprise!) the non-existence of mystical beings. When you get right down to it, the statement “you cannot prove a negative” is really just a different way of saying “You can’t prove me wrong because I don’t even know what I’m talking about.”

 

[Skeptical Greg]

A good explanation, but I think it boils down to the elements of the negative statement being made..


The statement:

The tsetse fly is not native to North America


Contains verifiable positive elements.. i.e. tsetse flys and North America ...


The statement:

There is no God.

Contains no such elements..

 

[Andonyx]

Who says you can't? Well, you're wrong.

There are many negative statements that can be proven.
This text is not white.
I am not a turnip.

See?

This says it better than I do.
http://www.graveyardofthegods.net/articles/cantprovenegative.html

While the general sentment of those arguments is correct, what your missing is the steps in the process. And Diogenes hinted at it by discussing positive verifiable elements. But it's more than that. It's that the first step in any of those proofs is actually a positive proof.

"This text is not white"

The first step to proving that is to say what color the text IS, I.E, Black. Then to determine that Black is not equal to white, therefore logically the text is not white.

Likewise, you ARE a human being, human beings are not equal to turnips, therefore you are NOT a turnip.

And it breaks down into finer distinctions for examples not as obvious. In the turnip case, we could say what evidence do we have of your qualities? Well you can obviously type. Turnips cannot type, nor have they ever in history been observed to have typed, therefore, you must NOT be a turnip.

Again there has to be a positive definition to your qualities and that definition must be exclusionary to the condition we are testing for in order to make a negative statement of verifiable truth.

In the case of proving complete negatives you cannot if there is no positive verifiable element to work from.

 

[LW]

The whole "can't prove a negative" thing refers only to questions of form:

There EXISTS some entity X with properties Y.

To prove such a claim false you have to search the whole domain of the problem. If such a complete search can be made, then you can prove negative. For example, in mathematics you can prove that there doesn't exists a rational number q such that q is the square root of 2.

Unfortunately, you can't do that in Real Life. Here also comes the additional problem that the word "proof" has two meanings. The strict mathematical and the common sense one, where a thing is considered proven if it is extremely unlikely to be false.

Of the claims present in the first post:

I am not a turnip.
The ancient Egyptians did not watch Seinfeld
The tsetse fly is not native to North America

can be considered to be provable in the common sense way, but even they cannot be proven in mathematical way.

The ancient Egyptians might have had access to time machines and use them to watch Seinfield. The tsetse fly might be originally native to North America but all of them spontaneously decided to migrate to Africa, and you might be a super-intelligent turnip in disguise about to conquer the world.

Of course, the probabilities of the three alternative explanations are diminutive and the original propositions can be said to be proven in the everyday sense. But not in the mathematical sense.

 

[LW]

This text is not white.

By the way, the truth value of this proposition depends on the user browser settings. For example, before I followed the "quote" link, the text was white on my screen but now it is blue. So, it most definitely can't be proven in either direction.

 

[ceo_esq]

This must be one of the least well understood logical concepts to crop up (repeatedly) on the forum.

(I'm quoting myself from another thread below).

It's certainly possible to prove a negative, although proving a negative historical proposition can be particularly challenging. The things to be wary of are not proofs of negative propositions but negative proofs, as they can lead to what is sometimes called the Fallacy of the Negative Proof:

It occurs whenever a historian declares that "there is no evidence that X is the case," and then proceeds to affirm or assume that not-X is the case. . . . [A] simple statement that "there is no evidence of X" means precisely what it says – no evidence. The only correct empirical procedure is to find affirmative evidence of not-X – which is often difficult, but never in my experience impossible.

(Source: David Hackett Fischer, Historians' Fallacies: Toward a Logic of Historical Thought 47-48 (1970))

 

[slimshady2357]

LW is correct.

The phrase refers only to negative existential statements. It's too bad it's been short formed to the point where it confuses people now.

Adam

 

[LW]

The phrase refers only to negative existential statements.

Though, a similar condition also applies to positive universal statements such as "all ravens are black".

 

[mummymonkey]

Caw!

 

[Checkmite]

When dealing with an object whose properties are known fully, you can prove "negatives". If I lose a pen, look for it, and find that it is not under my living room couch, I can say that "The pen is not under my living room couch" is a negative statement that has been proven true.

When dealing with objects whose properties are not known, you cannot prove a negative. "There is not an alien spaceship parked on my front lawn" cannot be proven, because invisibility may be a property of the alien spaceship. Since I do not fully know the properties of the alien spaceship, I cannot prove any negative hypothesis involving it.

 

[Tricky]

When dealing with objects whose properties are not known, you cannot prove a negative. "There is not an alien spaceship parked on my front lawn" cannot be proven, because invisibility may be a property of the alien spaceship. Since I do not fully know the properties of the alien spaceship, I cannot prove any negative hypothesis involving it.

(or it may be veeeery tiny.)

But it does appear we need a better phrase than the one we have been using. I recommend,

"You cannot prove the non-existance of anything"

 

[Dorian Gray]

I remind you of the bold type: Of course it is not possible to prove that God does not exist, if “God” is a thing that has no definition, no characteristics, and no location.

And the invisibility argument can be used for anything, as can the time machine argument or the gremlin argument.

Just because those arguments are USED, however, doesn't mean we have to accept them.

It is equally impossible to prove God exists. We can refute this using arguments spiritually similar to the invis, time machine or gremlin argument, only not so weaselly.

All I am saying is that the statement "it is impossible to prove a negative" is a false statement in an absolute context.

 

[Skeptical Greg]

It is equally impossible to prove God exists.

With the currently available evidence, I would agree..

 

[Tricky]

All I am saying is that the statement "it is impossible to prove a negative" is a false statement in an absolute context.

And gramatically, you are absolutely correct (which is why I recommend the change). But I doubt that the wording confuses many people. If we were to follow this out grammatically, it would be impossible to disprove a double negative.

 

[jan]

The whole "can't prove a negative" thing refers only to questions of form:

There EXISTS some entity X with properties Y.

To prove such a claim false you have to search the whole domain of the problem. If such a complete search can be made, then you can prove negative. For example, in mathematics you can prove that there doesn't exists a rational number q such that q is the square root of 2.

Unfortunately, you can't do that in Real Life.

If we had an idea what the term "god" means, and if we could prove that this definition is self-contradicting, we could prove he doesn't exist. For example, if we agree that god is responsible for the existence of time, and on the other hand has a personality, and if we could somehow show that both traits do not mix well (since having a personality would require to be subjected to time, or something like this), we could prove a negative. But of course it is unlikely that this will happen, since there is no official, canonical definition of god, and since such a proof of impossibility would probably be very unreliable and dubious, since it would have to deal with quite outlandish, not well known things.