# Not being able to prove a negative.

The statement “you cannot prove a negative” is self-contradictory.

Now who said it was possible to prove a positive!?

A double negative, eh, Libertarian? What about, “you cain’t not prove no damned negative?”

Seriously, though, I’m surprised that nobody has yet brought up the simple yet annoyingly difficult to “prove” four-color map theorem. Part of Appel and Haken’s “proof” relies on checking a list of representative models so vast it must be verified by a computer.

Some still argue this doesn’t constitute a proper proof, but nobody and nothing that I know of has been able to provide a contradictory example.

“Some still argue this doesn’t constitute a proper proof, but nobody and nothing that I know of has been able to provide a contradictory example.”

Could, ah, someone help me out of this tar pit, please?

Proving a positive: “This thing is right here. Proved.”
Proving a negative: “This thing is not right here. Proved?” No, not in such cases where the nature of “thingy-ness” is not tied to a specific location/time. Proving a negative requires enumerating all the possible areas and saying, “See? The thing isn’t anywhere, because I’ve just showed you everywhere.”

But we can’t show people everywhere, so we can’t prove the negative.

Accepting certain axioms of existence, physical laws, and so on, make it possible to prove certain negatives.

IOW, it is not possible to prove a negative when it is not possible to completely enumerate all possibilities.

It is not accurate to assert that “you can’t prove a negative”. Given a formal system which permits negative statements to be phrased, they are as susceptible to proof as any other statements within that system. “I am not French” is as susceptible to proof as “I am English”.

A simple syllogism will suffice:

1. English people are not French people.
2. I am English.
Therefore: I am not French.

However, it is usually the case that when people say “you can’t prove a negative” they are alluding to a perfectly sound principle of rational thinking, but expressing it in a kind of shorthand which leaves out some of the fine detail.

Usually, they are referring to the fact that a single counter-example can disprove a negative, but no number of counter-examples can prove a negative.

Example. I say “No white ravens exist”. The opposite of this would be “White ravens exist” (a positive statement). If I can produce even one single instance of a white raven, I can prove the positive statement, and thereby disprove the original.

Now, suppose I assert “White ravens exist”. The opposite of this would be “No white ravens exist” (a negative statement). Even if I can produce a million instances of ravens, and they all happen to be black, and no white ones seem ever to have been found, I have not proved that “No white ravens exist”. I can produce lots and lots of counter-examples, but it remains logically possible that white ones exist, but just haven’t been found or noticed yet. Hence I can never prove the negative, and the original assertion remains undetermined.

So, the more long-winded but accurate version of “You can’t prove a negative” would be “Argument by counter-example can only apply to statements of existence, not statements of non-existence”.

Okay, I’ll shut up now.

It isn’t any old negative that is impossible to prove, it is the universal negative case that is impossible to prove.
*
There are no ghosts.

No one can run 110 miles per hour
*

Specific negative assertions, on the other hand, can be proven given sufficient and appropriate evidence:

The sun is not larger in circumference than the earth’s orbit

The patient in room 703 is not dead
*

Now let’s consider universal postulates :

*There are ghosts.

All people eventually die.*

Universal postulates stated in the positive are not open to falsification, and this may be what somebody originally meant when they said “you cannot prove a negative”.

The scientific tradition regarding theories is that you formulate your research premise to be falsifiable, and success consists of failing to falsify your premise. (This is why “theories” do not get upgraded to “facts”. Theories are not proven–they can only be disproven). This construct relies on the inverse rule about proving universals: it only takes one discordant fact to disprove one of them if the universal is worded as a negative. Find me one ghost or one sprinter who hits 100 mph and you can say goodbye to your negative universals that deny their existence. Failing to find these examples, however, does not prove the theories, it merely means that you have failed to falsify them. You can’t do that with positive universals–you can’t say “Behold, the nonexistence of ghosts”, nor can you even say “Aha, here is a 400 year old guru and he hasn’t died yet, so that disproves your statement that all people eventually die”.

So while it is not accurate to say that you cannot prove a negative, it is accurate to say that you cannot falsify a universal positive by presenting its negative.

Say it this way:

"It’s hard to tell the difference between ‘extremely rare’ versus ‘nonexistent.’ "

If you claim to have witnessed a rare event such as
Ball Lightning, yet I am skeptical that it ever occured, you
can say “ha ha, you can’t prove a negative.”

But the issue is REALLY about whether eyewitness reports
of rarely-occurring strange events are fradulent.

It all boils down to placing the burden of proof on the person
who makes the claim. If you say that you saw space aliens
in a UFO, I can say “that’s nice, but it’s up to you to provide
some good physical evidence if you want people to believe

It is a perfectly sound principle of rational thinking, but that’s not how I’ve seen the shorthand “you can’t prove a negative” used. It’s often used like
Person A: Ex p(x)
Person B: -Ex p(x)
Person A: Prove it!
Person B: You can’t prove a negative. I win by default, nyah, nyah!
That’s just my experience; YMMV.

erislover, it can be proved, for example, that the open interval (0,1) has no maximal element, even though the set is uncountable and so cannot be enumerated.

It can be used to weasel out of any argument! Imagine:

Person A: Ex p(x)
Person B: -Ex p(x)
Person A: Since you can’t prove a negative, you can’t prove that. I win by default, nyah, nyah!

This is true. The method I listed works only if the two mutually exclusive conditions are the only possible conditions, something I explained, albeit poorly, later in my post.

Thus, say we have two statements:

A. Room 10 has six desks in it.
B. Room 10 has no desks in it.

These conditions are mutually exclusive, meaning they cannot both be true at the same time, but they can both be false, for example if there were six desks in room 10.

However if the two conditions are the only possible conditions, disproving one does validate the other.

A. Room 10 has no desks in it.
B. Room 10 has at least one desk in it.

Proving a or b invalidates the other, and disproving a or b validates the other.

The problem in the OP, the existence of God, is a problem of the first type in that one cannot postulate a mutually exclusive condition to the existence of God that is provable and is, within a logical framework, the only alternative.

Wrong definitons. There is no such thing as ‘hard’ or ‘soft’ atheists. (In particular, by your definition, ‘hard’ atheists would belong to a religious sect (and therefore not be atheists). Only your ‘soft’ atheists are really atheists.) But we’ve hashed this out ad nauseum in The Pit, so this is not the place.

This is all I have to say.

You’re like a friend I use to have who liked to argue for argument’s sake. You know what I mean, and the point I’m trying to make, but you argue about the details anyway. Oh well, whatever floats your boat.

:o Didn’t even see that; guess I oversimplified. Usually IME it’s B who claims “victory.” More “with it” B’s will follow up with “The burden of proof is on he who alleges” or somesuch, which is perfectly valid. In fact, it makes redundant the nonsense about not being able to prove a negative. Of course, if B were going first, the burden of proof would be on him and the supposed negativity of his position could be (mis-)used by A as you say.

The whole thing smells to me like some Internet-spawned logic UL. ianzin, are you sure about how it originated or was it an educated guess? Does anyone know where “you can’t prove a negative” first appeared?

Wow. Every time I start thinking that I am pretty smart, I stumble across a thread like this…