Can you prove a negative?

Question

I am aware that this question has been asked, but I thought it might be good to revisit. If you disagree, well, there's not much I can do about that.
To the topic at hand, keep in mind this is not saying I can prove the nonexistence of God or that I can prove everything negative (if I were able to prove any negative at all). I am simply asking, mathematically and philosophically, can you prove a negative? I have been quick to assert this when asked to prove God doesn't exist, but after looking into it further, it seems quite possible and necessary at times to prove negatives. Your thoughts?

Good thoughts.

Try to think of it this way for a minute (without geting a headache). Can you prove that you can't prove a negative? If you could, would that mean that you have proved a negative, thus making the proof untrue?

Polonium, I am asking if you can prove a negative.
You have not established what you mean by nothing. Having a blank sheet of paper does not mean there is nothing on the paper in the literal sense.

Polon...you're on to something. Although it goes against proper grammar, you can use any proven positive to prove a negative. For instance, say I could prove I am alive. I could also say that I am not not alive. Double negative, but still a proven negative.

Tet, those are good thoughts as well. I think you can prove (in the sense that you can prove anything) a negative by denying things. For instance, and this is borrowed from Professor Stephen D. Hales, here is a situation in which you can prove a negative:
1. If unicorns existed, there would be evidence in the fossil record.
2. There is no evidence of unicorns in the fossil record.
3. Unicorns never existed.

Now, obviously, most will now be saying I must prove my first two statements. I could give evidence supporting them, then you could demand evidence supporting my evidence, and so on. The point is if proving things requires an infinite amount of premises get proved first, we're never going to prove anything one way or the other. At some point we must accept that some evidences are true beyond a reasonable doubt. This is not 100% proof, but does such a thing exist? Most would say that evidence beyond a reasonable doubt amounts to proof.

Answer 1

Overdraft at the bank and I GUARANTEE YOU they will prove your negative.

God can neither be proved nor disproved and that is by His own grand design.

Answer 2

@Ant Bee - that paper is excellent. It would be really helpful if a bunch of the theists here read it. @OP - the writer doesn't actually say that you can't prove a negative without proving the positive first. He explains this statement, the result of eliminating the double negative that results from attempting to affirm that the negative isn't true. And he's not talking about proving something "doesn't not exist." He's referring to the much simpler "prove that X doesn't exist," which is typically what we find requested of us. He goes on to explain why this isn't the best way to decide what's possible and what isn't. --- I can't believe people actually respond demanding to prove wind exists. They've somehow never heard of tornadoes. Anyway, it's not always the case that a negative cannot be proved. If someone proposes the existence of something that is logically impossible then simply demonstrating this proves that it doesn't exist. In my formal logic class the prof used the example of a square circle. Circles, being round, are not square, and vice-versa. The idea being proposed doesn't exist because it is impossible. But these cases are rather rare and if the existence of something coherent is proposed there's little one can do to disprove it. Regardless of whether or not a "negative proof" is possible, common sense (not to mention good manners) dictate that whoever makes the claim has the burden of proof. No amount of mental gymnastics will change the fact that a search to verify something doesn't exist can go on forever without proving anything. A search that is not guaranteed to terminate is a dumb task to take on. The person making the claim has a search with an easy to recognize terminating point: produce the thing they claim exists, or provide sufficient evidence to convince the non-believer, and they're finished. Proof is always defined in such a way that it's obvious when the proof is finished. Searching everywhere in the universe is not a good way to prove something.

Answer 3

Oh FSM, I hate logic...

Yes, it's possible to prove negatives. It's done by disproving the positive. That only applies to binary situations, and even then only if the two statements are mutually exclusive. And where the positive is provable...I think.

"This is a pen", it's either true A or false B...
So if it in fact is not a pen, then A is false, and B is true. Now, B at least appears to be a negative...

unless you want to get philosophical... then you could claim that B is a positive statement of the fact that A is untrue. Nevermind... you can pretty much turn it any way you want if you're willing.

I like to use southpark as an example for proving god:

I say: You killed Kenny, you bastard!

You say you didn't.

In order for me to prove that claim, I'd have to prove Kenny is dead, and that you did kill him. Right?

In order for you to prove your negative statement, you'd have to disprove one of those asumptions, either that Kenny isn't dead, or that you did not do it.

I could prove it by presenting the body, and physical evidence (preferably the murder weapon) that you were the one who killed him.

You would have to produce a non-body, or absolute proof that Kenny didn't exist, and that you did not kill him.

And I'm assuming you couldn't produce a non-body, and a non-muder weapon that woud not have your prints, and prove that it was definately the weapon that was not used to commit the murder that wasn't commited by you.

That's what makes proving negatives in real world quite difficult. And that's why the burder of proof falls to the claimant. ;)

Answer 4

so what your asking is can you prove that God who has never been seen (equaling the negative) be proven? Do you believe in Nothing? Does nothing exist? Of course it does, Nothing even though it can't be seen by anyone exists Space exists, we use space... If we have space which is nothing we can fill that space and make it something. If you have a piece of paper and it's blank, nothing is on it you can draw or write something and then it's not nothing anymore. God can be perceived by people therefore God is something, making him a positive. Just because you can't see God doesn't mean someone else can't.

You can't see many things that actually exist. But they're all around you. It's just a matter of revealing them to the naked eye. Which sometimes requires the imagination. But they are still there... Do you think that The Fabrics of space can be seen, Einsteins theory of space? No they can't be seen by people use that knowledge today to explore space.

O.K.... Well you can prove a Positive right, Well 2 negatives equal a positive which in someway should prove the negatives existed. RIght? I don't know, i'm just throwing some thoughts out there... I love a challenge even if I'm wrong.. at least I try.

Answer 5

Proving a negative is not impossible merely improbable however in this case proving the nonexistence is not the answer it is the inability to prove the existence of god . Simple if you think about it wouldn't you agree ?
OK try this on your pea brain as it is so simple even you should understand the wording this way proving that there is no evidence for the concept is the same as the reverse therefore proving the negative in other-words if the thing does not exist if it isn't positive it must be negative this is called deductive logic .

Answer 6

In some cases you can prove a negative though you can't prove a negative in the general sense.

One can certainly prove that a square circle doesn't exist though because it would contradict itself and one can also prove than an all-good, all-knowing and all-powerful god doesn't exist because it contradicts reality.

Answer 7

Well, you can give a counterexample to an example to make said example false...but that's not proving a negative. There is no way (that I know of anyway) to prove a negative. The burden of proof is on the positive. All the negative can do is to bring forth evidence for the negative, which imay prove it, but so far (once again, to my knowledge) has not happened...

My thoughts...hope it makes sense...lol.

Answer 8

Mathematically you could, if you begin by assuming the positive and working it out until you reach a contradiction. This is the proof by contrapositive.

In logic terms it goes like this. Let's call the positive statement p, and the negative ~p. If p is false, then ~p must be true.

For example, let's say the positive statement is, "There is a fire burning in this room," and your negative statement is, "There is no fire burning in this room." You can prove the negative by saying, "Let's say there were a fire burning in this room. In that case the smoke alarm would go off. But this is not happening. Therefore, the statement, 'There is a fire burning in this room," must be false."

Answer 9

I'd think you can prove a negative only when it involves a situation you are observing yourself. For example, YOU cannot prove that there is not a cat sleeping beside me as I type this. Only I, or anyone who happens to walk into this room and see that there is no cat sleeping beside me, can say for sure that there is not. Philosophically...that's another story, I think.

Like Schrodinger's Cat, observance can prove both sides.