Without getting into a huge debate…
Can you prove that something doesn’t exist, definitely? I’ve heard, “you can’t prove a negative”…but I’m fairly confident that there are no elephants, lions, or bears in my apartment.
Yeah, it all depends on what you want to prove
I can prove that there exists no integers greater then or equal to 2 and less then or equal to 16 that can be divided into 17 without leaving a remainder.
the trick is to successfully eliminate all other possibilities. That however is extremely difficult for certain problems, and pretty impossible for non-mathmatical ones.
Yeah, I have no idea where that came from. It is a simple matter to prove that Not A is true by proving that A is false. Typically, people confuse the scope of an assertion with its predication. There is a big difference between proving that there are no unicorns in your bathtub and proving that there are no unicorns in the universe.
This whole idea of being unable to prove a negative might have been started on the Internet by strong atheists!
More usually this line is used against atheists.
No, actually, it’s the atheists (the strong ones) who invoke it when asked by the theists to prove there is no God. “[Gasp!] You know I can’t prove a negative!”
If you check the link, it raises the amusing notion of a strong atheist arguing with a weak atheist. Often, the strong atheist will say to the theist, “Hey, you’re the one with the burden of proof, because you’re the one who claims God exists. My claim that He doesn’t exist is simply disbelief, and not belief in anything.” But against the weak atheist, the strong atheist finds himself in the embarassing position of being the one making the assertion “Not A”, while the weak atheist is making no claim one way or the other! Precious!
People forget that Fermat’s Last Theorem was also a negative, and that was proved in 1995.
Refresher: There is no whole number N greater than 2 that satisfies the equation x^N + y^N = z^N
(I’d use superscripts if I knew how)
X[sub]2[/sub]
X[sup]2[/sup]
cool, I know know how now, here’s how. I’ll use {} instead of so it isn’t recognized
What I just did was
X{sub}2{/sub}
X{sup}2{/sup}
There are lots of negatives that are easy to prove:
[ul]
[li] Your neighbor is not the president of North Korea.[/li][li] The earth is not larger than Jupiter.[/li][li] The third item in this list is not a greeting to Opal.[/li][li] You do not have three eyes.[/li][/ul]
OK - I look forward to your proofs of any of those bullet points.
I think you will find that anything that depends on perception will fail to prove the negative (not that I can prove that either!). Numerous philosophers have gone over this ground - which suggests this is destined for the GD board.
I tend to support the idea that only in mathematics can you yield proofs of a negative.
What’s the difference between proving a negative and disproving a positive?
Okay…
[ul]
[li] My neighbor is a farmer in the U.S. Two different people are not the same person. Therefore, he is not the president of North Korea.[/li][li] The earth is 12,760 in diameter. Jupiter is 142,800 km in diamter. Therefore, the earth is not larger than Jupiter.[/li][li] The third item was a proposition. A greeting is not a propostion. Therefore, the third item was not a greeting.[/li][li] I have two eyes. 2 != 3. Therefore, I do not have three eyes.[/li][/ul]
Jab:
If I understand your question, the first is a compound predicate, and the second is a simple predicate. But they are interchangeable as propositions so long as the predicative associations are unchanged.
For example:
If A, then B. Not B, therefore Not A. — Correct
If A, then B. Not A, therefore Not B. — Fallacy
The problem with “you can’t prove a negative” is that it’s an abbreviated statement. Within a sufficiently limited logical system, you can of course prove or disprove any statement allowed by the sysytem. However, most logical systems are not simple. In particular, the actual, physical universe is rather complex :).
What people are really trying to say is “It is not always possible to prove that the statement ‘X is globally impossible (or absolutely nonexistent)’ is true with respect to a logical domain consisting of the physical universe.” It can be said in various even more convoluted fashions, but that demonstrates why people tend to give the short, imprecise version as a stand-in for the above idea. In particular:
YOu must first establish with abolute certainly that Kim Jong-Il is not an impostor or pretender. You must establish that he is not secretly taking orders from your neighbor. You must establish beyond any doubt that you are not deceived about the preceding. YOu must establish that **I ** am not deceived about any of the above propositions before I can be certain your reasoning is correct (see where this is going?
[quote]
[li] The earth is not larger than Jupiter.[/li][/quote]
[quote]
[li] The earth is 12,760 in diameter. Jupiter is 142,800 km in diamter. Therefore, the earth is not larger than Jupiter. [/li][/quote]
Similar objections: you must prove beyond any doubt that these measurements are correct, and that they are not derived from error, deception, scientific conspiracy, or unknown fallacies in our system of remote planetary measurement. Then you must prove that you are not deceived about the above… (et multiple cetera)
[quote]
[li] The third item in this list is not a greeting to Opal.[/li][/quote]
This is a question of grammatical structure, which certainly falls under bit about “limited logical systems” above. I cannot help but point out, however, that your proposition can contain a greeting, as yours does; thus you are in fact wrong 
[quote]
[li] You do not have three eyes. [/li][/quote]
[quote]
[li] I have two eyes. 2 != 3. Therefore, I do not have three eyes.[/li][/quote]
Hopefully you can see where I would go with this one re: possibility of deceit, etc. Furtheremore, since a person with three eyes also certainly has at lest two, it is not sufficient to cite that you have two eyes as a means of proving that you do not have three.
The point of the above was not to accuse you of weak logic, or to exercise my sophistry muscles- the point is, within the domain of the universe, it is not generally possible to say “X is not possible” (or, especially, there is no X, anywhere, since an infinite number of scenarios of the for “X is possible because Y” can be formulated. Since it is not possible to answer with every possible disproof, it is not possible to prove the negative case absolutely : the elephant in your apartment may have stepped out for a smoke, he may be disguised as a lamp-stand, etc.
HTH.
I am an amateur in these matters, not even a dilettante. Still, may I ask: Is it always the case that (A or ~A) is true? I think not*.
[sub]If you like, we could talk about “barbers who shave only those men who don’t shave themselves” or we could consider “heterological and autological” words.[/sub]
The statement “You can’t prove a negative” as it is commonly used means “You can’t prove the non-existence of a non-existent object.”
People often assert beliefs in things of which there is no tangible proof (God, UFO’s, second gunmen, yeti, compassionate conservatism, etc). When it’s pointed out that there’s no evidence these things exist, they argue that they do exist but the evidence of their existence is concealed.
However it is possible to prove a negative; ie to prove a non-existent object doesn’t exist. You assume the existence of the object in question. You then determine what observable consequences would have to exist if this object existed. You then investigate whether these consequences exist. If they do not, you’ve proven that the object does not exist.
The problem with the above is that while the logic is undeniable, it is not overwhelmingly obvious. And people who are fuzzy-minded enough to believe in non-existent things in the first place are usually guaranteed to not have the requisite brainpower to follow the argument to its inevitable conclusion. At some point, they’ll go “huh?” and stop listening.
Even if we accept that Libertarian proved that his neighbor is not the President of North Korea, that was not the proposition he set out to prove. He was trying to prove that “your neighbor” was not the President of North Korea. Although I doubt that Kim Jong-Il’s neighbor read the post, that possibility cannot be ruled out completely, so the proposition may be false.
Regarding the thread’s question, the phrase “you can’t prove a negative” is usually encountered when someone is challenged to prove that an object cannot exist or an event cannot happen under any possible set of circumstances, even ones not conceivable by the challenger or the challenged. Such challenges are most often encountered in discussions about the supernatural.
A: There are fairies in my garden.
B: I was just there. I didn’t see any fairies. Or trip over any.
A: They’re invisible, insensible, silent, and odorless.
Can anybody prove that you can’t prove a negative, though?
Surprised no-one else had asked that.
:adds new entry to log of smartass comments:
:burps:
I’d say no, but then I’d have to prove it, wouldn’t I?
What can make an assertion difficult to prove, whether it is phrased as A or Not A, is its scope, not its predication.
When I said that a greeting is not a proposition, I meant a proposition in the sense of logic (i.e., a statement that is either true or false, but not both true and false, nor neither true nor false), which ought to have been clear from the context of this topic.
If neither A nor Not A is true, then A is not a proposition.
The protest about my proof that my neighbor is not the president of North Korea holds even if the proposition is stated as “Kim Jung-II is the president of North Korea”, except that then you greatly increase the scope of your protest, e.g., you must prove that Kim Jung-II is not secretly taking orders from everybody else on earth, and possibly beyond!
The protest about my proof that the earth is not larger than Jupiter still holds, even if the assertion is predicated in the affirmative: Jupiter is larger than the earth.
The protest about my third item not being a greeting is misguided, as explained above.
The protest about your not having three eyes is a red herring, but I will concede the point that I don’t know whether the protestor has three eyes, though the truth of the proposition would be easy enough to test by looking at him. Perhaps he could refer us to his photograph. Still, I should have said that I (or Tris, whom I’ve met) do not have three eyes.
Note that any of the proofs we discuss here are contingent upon our taking the validity of logic itself as axiomatic, or else we’ll find ourselves begging the question.
There is a negative you can prove if and only if there is
something you can prove.
Proof:
(=>) If you can prove (not A), then (not A) is something
you can prove.
(<=) Suppose you can prove A. Then immediately it follows
that not(not A) is true. So you can prove the negative
not(not A).
I haven’t seen the answer I was looking for in this thread (yet). The statement “you can’t prove a negative” applies when it’s talking about a “falsifiable” proposition. I’d like someone more knowledgeable about formal logic to elaborate, but the way I understand it is this.
In formal logic, a statement has no meaning unless that statement is falsifiable, meaning that if the statement is indeed false, it can be proved false. The assertion that you can’t prove a negative has to do with this idea.