I have heard the following statement one time too many and want to know "Why can't you prove a negative?"

Question

Examples would be welcomed, for example, it may be difficult to prove God exists beyond a shadow of a doubt, but impossible to prove He does not exist.

Answer 1

In the early days of the comedy weekly take off on tabloids, the World Weekly News ran a headline, "Invisible Aliens Among Us." I pointed it out to my wife and said, "It's true, I have seen them."

That was the humor of that mag. It was a joke, and you could not really prove them wrong. (I caught them once....One cover had "John Wayne reincarnates into baby. They had an interview with a 12 hour old baby, and then slowly it lost the power to speak. Then, a few weeks later, they ran a story John Wayne's Ghost Haunts the Alamo) One of these stories is obviously false.)

On a more serious note, one of my parents was Catholic and the other Jewish. I once asked the difference and was told the Jews do not believe that Jesus was the son of G-d. One of my parents was wrong. That led to the conclusion that both might be wrong.

You can justify a positive, i.e. I pray to G-d and my prayers have been answered. If you then say, there is no G-d, because I prayed and they were not answered, the obvious reply is that he did answer and it was no. You can still justify.

Last thought, can some negatives be proved? Up to a point. Higher and P.I. to follow your spouse around to prove she is not cheating on you. However, that negative only works so long as you have her followed.

Answer 2

Yes, people seem to take this phrase as th holy truth. Actually, there is little reason to think you can't prove a negative.

For one thing, "you can't prove a negative" simply contradicts itself. "You can't prove a negative" is saying that "no situation will exist where it is possible to prove a negatve." This is claiming a negative, and if there is proof for it, then you have a contradiction, and if there is not proof you have an arbitrary proposition.

You can prove negatives in logic. If we accept that "If P, then Q" and we accept "not Q," then we have proven "not P." If the weatherman was right, it would rain today. It did not rain today. Therefore the weatherman was not right. A similar form of reasoning is used in philosophy of religion (since you brought up the God thing.) It is the problem of evil: If an all-powerful, all-good, all-knowing God exists, there would be no evil. Evil exists. Therefore such a God does not exist. This proof works, provided we accept the premises. If you don't think it works, its not because you think its impossible to prove a negative, its because you reject one of the two premises.

"Proving a negative" can also apply to scientific theories. But even here, I think there is good reason to think a negative can be proven. Scientific theories, for example, are widely thought to be ONLY able to be disproven, never proven. This was the insight of Karl Popper and is widely accepted in science. The reasoning behind it is, if a theory predicts something to happen, and that thing does not happen, we know the theory is wrong. (To what degree it is wrong is a different question, it may only require minor tweaks or may have to be abandoned altogether.) If a theory makes a prediction that turns out to be right, however, this doesn't prove that the theory is correct, only that it made one correct prediction. Many false theories have made a lot of correct predictions.

With purely empirical proof, it is possible to prove a negative too. This is usually what people are thinking of when they say it is impossible to prove a negative. If we have evidence that something is the case, however, that logically implies that its contradiction is not the case. So if we accept that science "proves" that it is the case that the earth orbits the sun, this logically implies that science has proved a negative - science has proven that it is not the case that the earth is stationary. If we want to say that we can prove "positives," and we accept the law of non-contradiction, then we must conclude that we can also empirically prove negatives. Proof that something is the case counts as proof that its contradiction is not the case, and this is a negative.

The only time it is correct to say that we cannot prove a negative is when we make sweeping universal statements based on empirical evidence. The type of statements along the lines of "unicorns do not exist" or "indetectable aliens do not live among us" would be examples. But these types of statements aren't very common, or, I think, very interesting. In any case they form only one small subset of types of proof in a sea of possible proofs.

Proving a negative is a key part of logic, is thought to be the key defining characteristic of scientific theories, and is logically implied by any empirical proof of a positive. So why people insist that you can't prove a negative is beyond me.

Answer 3

How would you prove that a horse exists? The best way would be to track down a horse. The same goes for anything you want to prove exists - even something as elusive as a unicorn - one example and you're done.

Now... how do you prove that NO unicorn exists? You can't show someone a no-unicorn. You might try looking in places where unicorns are supposed to be, but all you will prove is that they're not where they're supposed to be, not that they don't exist anywhere. To conclusively prove the complete absense of unicorns in the universe, you would have to do no less than search every place in the universe where a unicorn could conceivably be, and do so in such a way that you can demonstrate it's not just being moved from places you haven't yeat searched to places you've already searched when your back was turned.

In other words, it's pretty much impossible by the strictest of standards.

Of course, most of us accept more generous standards. In the strictest sense, if you see hoof-prints, a pile of horse-apples, and have an eye-witness who saw a horse walk by, it could all still be a fraud. But most of us would consider it satisfactorily proved.

Thus when two people argue about whether something is 'proved' or not, they are probably using different standards. Nobody has strictly proved the non-existance of unicorns, but their complete and utter absence is convincing enough for most of us.

Answer 4

If something exists then one day someone might prove it by getting the something and running tests on it and showing it to the world. This may be highly unlikely, but it is possible. For example, maybe one day God might come down to earth in the middle of the World Cup and reveal himself somehow that will prove that He exists to all the people of the world who are watching.

However, if God doesn't exist, there is no way to prove that because there is nothing that you can show. You can't prove that nothing is there because you would have to investigate and examine everything that exists and that is impossible since existance is infinite.

This is a particularly extreme case since God is a big subject. For a better understanding, apply this principle to something else. For example, I can prove that dinosaurs once existed. I can show you the fossil record. But I can't prove that bigfoot never existed. There is no evidence to support that he existed, but maybe the evidence is hidden, make we haven't found it, maybe it once existed but has sense been destroyed- there is just no way to prove it.

Answer 5

It's not like there's absolutely never any provable negatives, its just that in general it's the criteria for proving a positive, i.e. one solid example, is so much easier than proving a negative, i.e. scan for absence anywhere and everywhere it could possible be, that we just say "You can't prove a negative."

The two proofs are not in the same class.

Prove you at least have $20. Easy - show me a twenty. Prove you don't have $20. Now I have to check every bank account in the world for both your name and any alias you might use. The pockets in jacket, shirt and pants you own.
etc.... I seriously could type all day places and ways a person could hide $20.

So if you say to me: "Prove you have a twenty." and I reply "Prove I don't." It's not really a valid answer, because it's easy to prove a positive, and difficult, if not impossible, to prove a negative.

Answer 6

well tahts right, because a lack of evidnece is not proof that you havent missed something. if you coudl check every single molecule in time and space for god, and you didnt come up with him, then i guess you could say he doenst exist. but its impossible to prove a negative, because yo ucan never be sure you didnt miss a small proof of a positive

Answer 7

I can not prove that I do not exist nor that I exist. What ever acceptable level of proof is necessary to 'prove' mandates the level of success.
You can not prove anything if the level of proof necessary is too high.

Answer 8

Actually, you can -- but it depends on the negative. The matter is a bit too complex to address here; it is (of necessity) discussed in my paper "A proof of the theory of evolution", which will be sent to anyone requesting it who provides an e-mail address. For a specific discussion of god, see:

Answer 9

You can't prove a negative because you can't prove whether something isn't real, you can only prove whether it is.