Refresher Course: You can't prove a negative

[Upchurch]

The question of "proving a negative" has come up a couple of times recently when I thought the question trying to be asked was entirely appropriate and possible.

I'm not suggesting I'm going to teach a refresher course. I need one.

Remind me, what is the definition of the "Proving a Negative" logical fallacy and when is it legitimate to ask someone to show that x isn't y?

[drkitten]

The question of "proving a negative" has come up a couple of times recently when I thought the question trying to be asked was entirely appropriate and possible.

I'm not suggesting I'm going to teach a refresher course. I need one.

Remind me, what is the definition of the "Proving a Negative" logical fallacy and when is it legitimate to ask someone to show that x isn't y?

It is not possible to establish a universal negative by examining the universe.

But that's different from disproving a positive, even a specific positive.

For example, I can disprove the positive "there is a bear in my refrigerator" by looking. I can't disprove the positive "there is a bear in someone's refrigerator,' (which would be equivalent to proving that no refrigerators have bears) because I can't look at every refrigerator in the world.

[sphenisc]

It is not possible to establish a universal negative by examining the universe.

But that's different from disproving a positive, even a specific positive.

For example, I can disprove the positive "there is a bear in my refrigerator" by looking. I can't disprove the positive "there is a bear in someone's refrigerator,' (which would be equivalent to proving that no refrigerators have bears) because I can't look at every refrigerator in the world.

Isn't this also true for positives, i.e. "It is not possible to establish a universal positive by examining the universe. "

In which case it would simpler to say

"It is not possible to establish a universal by examining the universe."

[quixotecoyote]

It is not possible to establish a universal negative by examining the universe.

But that's different from disproving a positive, even a specific positive.

For example, I can disprove the positive "there is a bear in my refrigerator" by looking. I can't disprove the positive "there is a bear in someone's refrigerator,' (which would be equivalent to proving that no refrigerators have bears) because I can't look at every refrigerator in the world.

Unless it's an invisible bear.

[drkitten]

Isn't this also true for positives, i.e. "It is not possible to establish a universal positive by examining the universe. "

Yes, but that is generally well enough known that it wouldn't need to be covered in Upchurch's refresher course.



In which case it would simpler to say

"It is not possible to establish a universal by examining the universe."

Simpler, but less useful.

[Upchurch]

Okay, how about an example?

This is from one of the aforementioned times the issue has come up recently.

No sir, you have been here long enough to know that is not the way it works. You do not prove negative claims, such as the UU is not religion.

Is asking someone to prove that Unitarian Universalism is not a religion asking that person to prove a negative?

My instinct now, as then, is that I was not asking The_Animus to prove a negative, but I can't succinctly explain why. Is it that I'm not asking him to prove a universal claim?

[President Bush]

This (http://www.bloomu.edu/departments/philosophy/pages/content/hales/articlepdf/proveanegative.pdf) might help. :)

[Arkan_Wolfshade]

Okay, how about an example?

This is from one of the aforementioned times the issue has come up recently.



Is asking someone to prove that Unitarian Universalism is not a religion asking that person to prove a negative?

My instinct now, as then, is that I was not asking The_Animus to prove a negative, but I can't succinctly explain why. Is it that I'm not asking him to prove a universal claim?
It is not fallacious to ask The_Animus to prove that UU is not a religion. It is entirely reasonable, and doable, to define what elements qualify something as a religion (either dictionary definition, or a commonly agreed upon definition) and examine UU to see if it has those elements. This is no different that proving that a gecko is not a mammal (note: I am making no statement as to whether UU is a religion or not, I am merely providing a analogous example).

This is, of course, fundamentally different that asking The_Animus to prove that no-one considers UU a religion, or something similar.

ETA: I think the subtle problem here is that the statement, "UU is not a religion," is a positive statement in that it can be restated as "UU does not meet the definition of a religion." This is testable.

[JoeEllison]

Okay, how about an example?

This is from one of the aforementioned times the issue has come up recently.



Is asking someone to prove that Unitarian Universalism is not a religion asking that person to prove a negative?

My instinct now, as then, is that I was not asking The_Animus to prove a negative, but I can't succinctly explain why. Is it that I'm not asking him to prove a universal claim?
It isn't a matter of just inserting the word "not" into the assertion, and then calling it a negative, and then saying "you can't prove a negative". "Unitarian Universalism is not a religion" is a statement that can be proved or disproved, the same way that the statement "my car is not red" can be proved or not.

[Jekyll]

It is not possible to establish a universal negative by examining the universe.

But that's different from disproving a positive, even a specific positive.

For example, I can disprove the positive "there is a bear in my refrigerator" by looking. I can't disprove the positive "there is a bear in someone's refrigerator,' (which would be equivalent to proving that no refrigerators have bears) because I can't look at every refrigerator in the world.
Just to clarify, it is possible establish a universal negative from the definitions.
So we can 'prove' the claim that there are no large bears inside any small refrigerators.
This is the same sort of claim as "Unitarian Universalism is not a religion".

[Timothy]

The canard "you can't prove a negative" is commonly trotted out by those who don't understand logic. It stems from their extrapolations of statements that are (almost entirely) true:

"You can't prove aliens don't exist"
"You can't prove ghosts don't exist"
"You can't prove paranormal phenomena don't exist"

whereas

"If I showed you a single example of an alien, I prove it exists"
"If I showed you a single example of a ghost, I prove it exists"
"If I demonstrate a single example of paranormal phenomena, it exists"

without considering *why* those statements are true.

In logic, IF X THEN Y is equivalent to IF NOT X THEN NOT Y. (Equivalent, meaning if the first statement is true, the second statement is true.) The difference in many cases, especially those above, is the magnitude of the search space necessary to prove one versus the other. It's easy to prove the single example case, the search space for proving the nonexistence is too large for all practical purposes.

However, there are plently of "negatives" that can be proven easily, because the search space is more manageable. And "positive" proofs that are (for all practical purposes) impossible

"This petri dish contains the only sample bacteria of this type that exist"

This statement would be impossible to prove, but easy to disprove.

"UU is not a religion"

If you both agree on the criteria that constitute a religion (perhaps large, but by no means infinite) and the properties of UU, then there is absolutely no problem with verifying the truth of a "negative" statement.

[Taffer]

In logic, IF X THEN Y is equivalent to IF NOT X THEN NOT Y. (Equivalent, meaning if the first statement is true, the second statement is true.) The difference in many cases, especially those above, is the magnitude of the search space necessary to prove one versus the other. It's easy to prove the single example case, the search space for proving the nonexistence is too large for all practical purposes.

You really should clarify this. It appears you are suggesting that the argument:

X⊃Y
~X
∴~Y

Is logically valid. It is not.

[Apology]

It also bears noting that, if what you believe is a negative (God does not exist, Bigfoot isn't real, etc.) then you will never be able to prove your premise. You are relieved of the obligation of trying to prove the negative premise, since it's impossible, but you are still making an assertation that you cannot prove. Some people look at this as sort of a get-out-of-jail-free card (I can't prove what I'm saying, and I don't have to because it's impossible) but I see it otherwise (I can't prove what I'm saying and I never will be able to).

All you can do in this case is disprove other people's positive assertions (God does exist, Bigfoot is real) because there is the possibility of proving them with evidence---which has not been met.

[Upchurch]

At its core, then, the "Proving a Negative" is about falsifiability. One would be committing a "proving a negative" fallacy when they ask someone to falsify something that is unfalsifiable.

Is that a sufficient definition?

[drkitten]

Okay, how about an example?

This is from one of the aforementioned times the issue has come up recently.



Is asking someone to prove that Unitarian Universalism is not a religion asking that person to prove a negative?

Not in the fallacious sense, no.... any more than asking someone to prove that 12 is NOT prime, which you can do by factoring it.



My instinct now, as then, is that I was not asking The_Animus to prove a negative, but I can't succinctly explain why. Is it that I'm not asking him to prove a universal claim?

Yes, and you're not asking him to do that by examining the universe for everything that might be a religion.

Presumably any "religion" has certain properties (which can be enumerated). You can easily show that UU does (or does not) have those properties. For example, if "religion" implies "the membership are united by a common belief in God," then UU is demonstrably not a religon.

[blobru]

... In logic, IF X THEN Y is equivalent to IF NOT X THEN NOT Y. (Equivalent, meaning if the first statement is true, the second statement is true.) ...

Small quibble, Tim:

Actually,
IF X THEN Y is equivalent to IF NOT Y THEN NOT X.

IFF X THEN Y is equivalent to IFF NOT X THEN NOT Y, however, where IFF = "if and only if".

[Lucky]

Whenever someone claims you can't prove a negative I ask them to prove it.

[Paul C. Anagnostopoulos]

Is asking someone to prove that Unitarian Universalism is not a religion asking that person to prove a negative?
Seems to me that's just a question of definition.


At its core, then, the "Proving a Negative" is about falsifiability. One would be committing a "proving a negative" fallacy when they ask someone to falsify something that is unfalsifiable.
But then you have to determine what is falsifiable. For example, I can prove that there is no elephant in my living room. However, I would have a hell of a time proving there is no elephant anywhere on Earth. And it would be impossible to prove there is no elephant at all.

But at least I can prove there are no elephants in principle. Imagine someone asks me to disprove something supernatural. That's not even possible in principle, because the definition of supernatural is undoubtedly incoherent. I suppose you could argue that an incoherent definition is falsified from the get-go.

~~ Paul

[Timothy]

Small quibble, Tim:

Actually,
IF X THEN Y is equivalent to IF NOT Y THEN NOT X.


Damn. I knew that. I swear I did. Coffee wasn't strong enough to sufficiently overcome the morning cobwebs.

[Upchurch]

But then you have to determine what is falsifiable.
That's fine. I don't have a problem with that, conceptually. I just lost touch with what "proving a negative" actually meant.

[Paul C. Anagnostopoulos]

Just say, "You can't prove a negativish!"

~~ Paul

[saizai]

Basically: you can't prove that there is no X unless you are able to find all possible evidence for X, and do not find any.

E.g.:
* is there a regular bear in my bedroom?
- no, because I'm looking at it, ergo if there were one I would see it, and I don't see it. So there ain't one.
* is there a regular bear in somebody's bedroom?
- I have no idea, because I can only see my own bedroom
* is there an invisible bear in my bedroom?
- I have no idea, because I can't see invisible things, so even though I'm looking I have no way to know if it's there

Generally:
to prove there exists an X, you need show just one X. simple. :)
to prove there exists NO X, you need to show that X is impossible, OR to show that you have exhaustively searched the space of possible Xs, *would* have found X if there was one, and found none

[blobru]

Damn. I knew that. I swear I did. Coffee wasn't strong enough to sufficiently overcome the morning cobwebs.

I know what you mean, Tim.
For me it's kids' breakfast cereal. Until I get my bowl of Count Chocula, logically I'm pretty much a bat with laryngitis. (Afterwards too actually, except for that brief 15-minute sugar rush, when I can do logic, math, speak in complete sentences, anything...) :)


...Generally:
to prove there exists an X, you need show just one X. simple. :)
to prove there exists NO X, you need to show that X is impossible, OR to show that you have exhaustively searched the space of possible Xs, *would* have found X if there was one, and found none

One normally sees it -- the thread topic -- as a retort to "God doesn't exist."
Logically: there is no x such that x is God.

As you say, empirically this entails checking everything in existence to see if it's God. (Of course in a statistical sense, everything you do check that isn't God is extremely weak confirmation of the proposition: see Hempel's paradox (http://en.wikipedia.org/wiki/Raven_paradox) of induction.)

Since a solely inductive disproof of God seems a longshot, a proof of the negative should also target hypothetical consequences, in this case of God's existence; and try to deduce contradictions from the definition [of God] (as you say, "show that X is impossible").

So I suppose it's strictly true one can't prove a negative; however, by combining induction, hypothesis, and deduction, one may render it very very very likely.

[Soapy Sam]

Isn't saying "It's not possible to prove a negative", itself an attempt to prove a negative?

[Lucky]

Isn't saying "It's not possible to prove a negative", itself an attempt to prove a negative?


I said that!

Whenever someone claims you can't prove a negative I ask them to prove it.

[Soapy Sam]

OH NO YOU DIDN'T!

(Altogether...)

[Upchurch]

(All together...)
Oh, no he didn't.

[Mobyseven]

Isn't saying "It's not possible to prove a negative", itself an attempt to prove a negative?

No, because it is a logical consequence of, well...logic itself.

Playing semantic games isn't very impressive.

[sphenisc]

No, because it is a logical consequence of, well...logic itself.

Playing semantic games isn't very impressive.

It's not a logical consequence of logic itself. It's contingent on a sufficiently large universe for an exhaustive search to be impractical.

[sphenisc]

Oh, no he didn't.

Prove it.









Isn't this where you came in?

[Lucky]

No, because it is a logical consequence of, well...logic itself.

Playing semantic games isn't very impressive.

Although Soapy and I may have sounded flippant, I also meant it seriously and I guess he did. (And it's not at all 'impressive' to accuse someone who's said something you disagree with of 'playing semantic games'.)

Now, I challenge you to logically prove the following:

There exists no negative statement that can be proved.

[Upchurch]

Prove it.

Isn't this where you came in?
Yeah. See, it was a joke from Airplane! (http://www.imdb.com/title/tt0080339/quotes) I was making a funny.

Ted Striker: I flew single engine fighters in the Air Force, but this plane has four engines. It's an entirely different kind of flying altogether.
Rumack, Randy: [together] It's an entirely different kind of flying.

[drkitten]

It's not a logical consequence of logic itself. It's contingent on a sufficiently large universe for an exhaustive search to be impractical.

For a clear example of this, look at the satisfiability problem (sometimes abbreviated SAT). In general terms, the problem is : given a formula in propositional calculus, determine if the forumula is "satisfiable," meaning that there is an assignment of variables such that it is true. It is relatively easy to show that a formula is satisfiable -- you just produce such an assigment.

It difficult (but not impossible) to prove a formula unsatisfiable, because in the general case, you need to look at every element in formula-space. For a small enough space (say, three variables), this is relatively easy, but for a large space (say, a thousand or a million variables), this is impractical to the point of impossibility.

[boojum]

Now, I challenge you to logically prove the following:

There exists no negative statement that can be proved.

The statement above is demonstrably false. There are provable universal negative statements. A lot of it depends on context, of course: the provable universal negative that leaps to mind is from mathematics and has to do with existence of irrational numbers. It can be proven that "There exist no integers p and q such that (p/q)^2 = 2". That's why DrKitten was wise to include "by examining the universe" above when she said, "It is not possible to establish a universal negative by examining the universe".

[sphenisc]

The statement above is demonstrably false. There are provable universal negative statements. A lot of it depends on context, of course: the provable universal negative that leaps to mind is from mathematics and has to do with existence of irrational numbers. It can be proven that "There exist no integers p and q such that (p/q)^2 = 2". That's why DrKitten was wise to include "by examining the universe" above when she said, "It is not possible to establish a universal negative by examining the universe".

Of course in a mod 7 universe, (3/1)^2=2, as you say, it depends on context.

[Lucky]

Now, I challenge you to logically prove the following:

There exists no negative statement that can be proved.
The statement above is demonstrably false. There are provable universal negative statements. A lot of it depends on context, of course: the provable universal negative that leaps to mind is from mathematics and has to do with existence of irrational numbers. It can be proven that "There exist no integers p and q such that (p/q)^2 = 2". That's why DrKitten was wise to include "by examining the universe" above when she said, "It is not possible to establish a universal negative by examining the universe".


I agree it's demonstrably false. My point was that even if you couldn't think of a counter-example it falsifies itself, by being a paradox if proved.

[Mobyseven]

I agree it's demonstrably false. My point was that even if you couldn't think of a counter-example it falsifies itself, by being a paradox if proved.

I don't know why you think the statement has to be proved to be a paradox - it is by virtue of its wording a paradox already. That doesn't mean it's a contradiction.

To make clear what others have already said, "You can't prove a negative," applies when one is examining the universe. Not when one is examining internally coherent systems (i.e. Logic).

[Lucky]

I don't know why you think the statement has to be proved to be a paradox - it is by virtue of its wording a paradox already.
Not quite; it could be false, or true but unprovable. We know, because of counter-examples, that it's actually false, but it's an interesting point that you don't need any counter-examples to show that it can't be both true and provable.

Consider: There exists no negative statement that can be proved.
That is a re-statement of the (invalid) claim that you can't prove a negative. It is also, itself, a negative statement. It's therefore impossible to prove it. It's a more complex variation of Epimenides (he claims: "none of my statements are true"), that includes provability as well as truth and falsity (he tries to prove: "none of my {negative} statements are provable").


To make clear what others have already said, "You can't prove a negative," applies when one is examining the universe. Not when one is examining internally coherent systems (i.e. Logic).
Yes, others have said that, but they're saying the opposite to what you claimed in your previous post:
it is a logical consequence of, well...logic itself.
They're saying that it's not a deduction from the laws of logic, but applies in some circumstances in the real universe, because the real universe is either (a) infinite, or (b) pretty damned big, so any negative claim that would entail searching the universe isn't provable in practice.

Now, this actually does apply to some undeniably important claims and beliefs (... it is impossible to win the JREF challenge by fair means ... nowhere in this universe does there exist a {planet|galaxy|supercluster|sub-universe} where {gravity|time|causality} works backwards ... nowhere on this continent does there exist the perfect partner for me). However probable, they truly cannot be proved, and we just have to live with the uncertainty. However, many negative claims are not of this type. Some instructive examples in this thread, including both purely mathematical/logical and practical ones.

As a supposed law of logic it's just a nonsense.

[UnrepentantSinner]

Just to clarify, it is possible establish a universal negative from the definitions.
So we can 'prove' the claim that there are no large bears inside any small refrigerators.
This is the same sort of claim as "Unitarian Universalism is not a religion".

I often use the example "there are no placental monotremes" since monotremes do not produce placentas during gestation and if they did, by definition, would no longer be a monotreme. Therein lies one of the problems of using definitions though because a literal definition of monotreme only means it has a cloaca. It's the broader definitions that seperate placental mammals from monotremes than the mere word itself.

[JoeTheJuggler]

Obviously you can prove a negative (start with the premise if p then not q--you prove p, then you have proven not q). I think what people mean by "you can't prove a negative" is really something like "you can't prove the non-existence of anything".

Worse yet, that statement is frequently proffered as somehow being support for the case of the existence of something whose existence is unproven.

[Mobyseven]

Not quite; it could be false, or true but unprovable. We know, because of counter-examples, that it's actually false, but it's an interesting point that you don't need any counter-examples to show that it can't be both true and provable.

Consider: There exists no negative statement that can be proved.
That is a re-statement of the (invalid) claim that you can't prove a negative. It is also, itself, a negative statement. It's therefore impossible to prove it. It's a more complex variation of Epimenides (he claims: "none of my statements are true"), that includes provability as well as truth and falsity (he tries to prove: "none of my {negative} statements are provable").



Yes, others have said that, but they're saying the opposite to what you claimed in your previous post:

They're saying that it's not a deduction from the laws of logic, but applies in some circumstances in the real universe, because the real universe is either (a) infinite, or (b) pretty damned big, so any negative claim that would entail searching the universe isn't provable in practice.

Now, this actually does apply to some undeniably important claims and beliefs (... it is impossible to win the JREF challenge by fair means ... nowhere in this universe does there exist a {planet|galaxy|supercluster|sub-universe} where {gravity|time|causality} works backwards ... nowhere on this continent does there exist the perfect partner for me). However probable, they truly cannot be proved, and we just have to live with the uncertainty. However, many negative claims are not of this type. Some instructive examples in this thread, including both purely mathematical/logical and practical ones.

As a supposed law of logic it's just a nonsense.

You're doing a fairly good job as marking yourself as someone who's not going to be convinced of this, so I'm going to try this one more time.

No one said it was a 'law of logic'. It is an important factor in empiricism, and therefore science. It can be easily demonstrated using predicate logic, however I'm not sure if I myself could write a proof for it - or even if a logical proof exists. And yes, it is assumed that the universe is pretty big - you could postulate the existence of a universe no bigger than your bedroom, and then I suppose some negatives could be proven. But unless you know of such a universe where we could all go on our summer vacation, it is a practically useless consideration.

Geddit?

[Lucky]

No one said it was a 'law of logic'.
On the contrary, this is a very common claim. It happens on this forum – Upchurch gave an example of an invalid use. When people state 'you can't prove a negative' as an absolute truth (without reference to the content of the particular negative in question), what on earth do you think they're claiming other than it’s a logical rule?


It is an important factor in empiricism, and therefore science. It can be easily demonstrated using predicate logic, however I'm not sure if I myself could write a proof for it - or even if a logical proof exists. And yes, it is assumed that the universe is pretty big - you could postulate the existence of a universe no bigger than your bedroom, and then I suppose some negatives could be proven. But unless you know of such a universe where we could all go on our summer vacation, it is a practically useless consideration.
It is certainly true that scientific theories and claims are commonly of the 'unprovable' type that would require an infinite (or impractically large) search space. However, this is because they are generalisations about the universe (rather than being specific to a prescribed object or set of objects), and is equally the case whether they are positive or negative. In fact, most scientific theories are framed as positive rather than negative statements.

Negativity/positivity and universality/specificity are orthogonal.

'You can't prove a negative' is actually two different logical fallacies:
1) As in Upchurch's example, when the statement is specific (i.e. the search space is limited). This (very common) use is plain wrong.
2) Even when the statement is the right (unprovable) type, the real point is always that it's universal, not that it's negative. In this case, 'you can't prove a negative' is at best misleading.


To summarise:
Some negative statements can be proved. Some can't, but that's because they are universal, not because they are negative.

[Mobyseven]

To summarise:
Some negative statements can be proved. Some can't, but that's because they are universal, not because they are negative.

Which, if you had bothered doing a moment's research into the subject, is exactly what everyone else here is saying. What you're doing is equivocating the term 'negative' and then declaring that, "You can't prove a negative," is a logical fallacy.

To be clear - you are defining a negative as, "Any statement with a negation in it." (At least it certainly seems like you are.)

When someone says, "You can't prove a negative," the 'negative' they are referring to is a negated existential statement.

Capisci?

[FreakBoy]

It was always my understanding, and I'll be the first to state my understanding isn't always correct, that the "can't prove a negative" issue was more related to the nature of the evidence.

"Prove that there isn't a bull in the room."

It isn't possible to provide evidence that the bull isn't in the room, only to provide evidence in support of an alternate theory.

Ignoring the previously mentioned question regarding negation vs. negated existence....

"Prove that UU isn't a religion"

One can provide evidence that it is. Lack of evidence that it is doesn't mean it isn't, though.

I'm probably wrong though.

[drkitten]

It was always my understanding, and I'll be the first to state my understanding isn't always correct, that the "can't prove a negative" issue was more related to the nature of the evidence.

"Prove that there isn't a bull in the room."

It isn't possible to provide evidence that the bull isn't in the room, only to provide evidence in support of an alternate theory.

Yes, but this framing of the problem is obviously untrue. I can easily provide evidence that there is no bull in my office -- I'm sitting there right now, where the bull would have to be standing, and there is no bull.

Specifically, given what we already know about the properties of bulls (their size, for example), makes it easy to show evidence that there isn't a bull in the room.

What's the "alternate theory"?

Similarly, the dust on the floor of a deserted house is direct evidence that no one has walked across the floor in a while. There's no "alternate theory" that you can phrase.

[FreakBoy]

Isn't that only direct evidence that you are in the room? It certainly allows the deduction that the bull isn't there, but the alternate theory is that you are there.

[drkitten]

Isn't that only direct evidence that you are in the room? It certainly allows the deduction that the bull isn't there, but the alternate theory is that you are there.

Not really. There's no incompatibility between the theories of my being in the room and the bull being in the room (there's room, barely for both of us). Because of that, "I am in the room" isn't really a meaningful "alternate," any more than the theory that "I am an Olymptic gymnast" is an alternate to "I play lead guitar in a garage band." Evidence for the first does not discount the second.

The direct evidence is that there is no bull visible in the room and that there is no hidden area large enough to conceal a bull. Both of those are in fact direct evidence -- and they add up to the conclusion that there is no bull in the room.

[saizai]

Although Soapy and I may have sounded flippant, I also meant it seriously and I guess he did. (And it's not at all 'impressive' to accuse someone who's said something you disagree with of 'playing semantic games'.)

Now, I challenge you to logically prove the following:

There exists no negative statement that can be proved.

I can disprove that pretty easily.

"This sentence does not contain the latter that precedes 'y' in the English alphabet."

[Lucky]

Although Soapy and I may have sounded flippant, I also meant it seriously and I guess he did. (And it's not at all 'impressive' to accuse someone who's said something you disagree with of 'playing semantic games'.)

Now, I challenge you to logically prove the following:

There exists no negative statement that can be proved.
I can disprove that pretty easily.

"This sentence does not contain the latter that precedes 'y' in the English alphabet."

The reason for the challenge was to demonstrate that it can't be done.

There are many ways to disprove it by counter-example, both logical ones like yours, and real-world ones. I was making the point that you don't actually need any counter-examples to see that "you can't prove a negative" can't be proved, as that would be a paradox (therefore there's no reason to believe it):

...
it could be false, or true but unprovable. We know, because of counter-examples, that it's actually false, but it's an interesting point that you don't need any counter-examples to show that it can't be both true and provable.

Consider: There exists no negative statement that can be proved.
That is a re-statement of the (invalid) claim that you can't prove a negative. It is also, itself, a negative statement. It's therefore impossible to prove it. It's a more complex variation of Epimenides (he claims: "none of my statements are true"), that includes provability as well as truth and falsity (he tries to prove: "none of my {negative} statements are provable").

So, that's one reason why "you can't prove a negative" is a fallacy – I wasn't suggesting it's the only one.

[Mobyseven]

Similarly, the dust on the floor of a deserted house is direct evidence that no one has walked across the floor in a while. There's no "alternate theory" that you can phrase.

Order of levitating monks? ;)

[Mobyseven]

The reason for the challenge was to demonstrate that it can't be done.

There are many ways to disprove it by counter-example, both logical ones like yours, and real-world ones. I was making the point that you don't actually need any counter-examples to see that "you can't prove a negative" can't be proved, as that would be a paradox (therefore there's no reason to believe it):



So, that's one reason why "you can't prove a negative" is a fallacy – I wasn't suggesting it's the only one.

Ahem...

Which, if you had bothered doing a moment's research into the subject, is exactly what everyone else here is saying. What you're doing is equivocating the term 'negative' and then declaring that, "You can't prove a negative," is a logical fallacy.

To be clear - you are defining a negative as, "Any statement with a negation in it." (At least it certainly seems like you are.)

When someone says, "You can't prove a negative," the 'negative' they are referring to is a negated existential statement.

Capisci?

"You can't prove a negative," is not a fallacy. The only fallacy being committed here is equivocation - by you.

[FreakBoy]

Not really. There's no incompatibility between the theories of my being in the room and the bull being in the room (there's room, barely for both of us). Because of that, "I am in the room" isn't really a meaningful "alternate," any more than the theory that "I am an Olymptic gymnast" is an alternate to "I play lead guitar in a garage band." Evidence for the first does not discount the second.

The direct evidence is that there is no bull visible in the room and that there is no hidden area large enough to conceal a bull. Both of those are in fact direct evidence -- and they add up to the conclusion that there is no bull in the room.

I stand corrected. Thank you!

[Lucky]

To be clear - you are defining a negative as, "Any statement with a negation in it." (At least it certainly seems like you are.)

When someone says, "You can't prove a negative," the 'negative' they are referring to is a negated existential statement.
No, I am not defining a negative at all. The plain fact is that people commonly do attach the pointless "can't prove a negative" to all types of negative statement, without any clear idea why they think that's the case. We see and hear the claim constantly – there's plenty of evidence of it in this thread!

Look at the post below yours – the poster thought "can't prove a negative" means that, for some reason, negative evidence isn't acceptable. He went on to give an example of a non-universal and plainly provable negated existential (as drKitten showed). Upchurch's example, from a discussion on this forum, isn't an really existential statement at all – it's just a disagreement about a definition.

Whether you like it or not, there are different types of negative statement. The whole point of this thread is to disentangle the types and examine which (if any) are logically unprovable by virtue of the form of the statement (as opposed to its content). Some negatives are universal, some are existential but not universal, some are neither. Types of negative that have been used in this thread as examples of either provable or unprovable statements are:

Logical/mathematical statements, some of which can be formally proved very easily.
Mere definitions, or statements that are in some other way not existential.
Non-universal existential statements with a practicable search space.
Universals (which, as I and others have said, are unprovable because of the associated search space, not because they are negative).

"You can't prove a negative," is not a fallacy. The only fallacy being committed here is equivocation - by you.

The fact is that all the above are types of negative statement, and (other than type 1, the purely mathematical ones) people frequently do claim that they can't be proved. You are using an illegitimate line of argument when you define "negative statement" to include only the type that can't be proved. Obviously, the claim then becomes tautologically true.

[Mobyseven]

Lucky:

Look, we're actually on the same page here - almost. I take objection to your claim that:

You are using an illegitimate line of argument when you define "negative statement" to include only the type that can't be proved. Obviously, the claim then becomes tautologically true.

You claim that I am defining the word 'negative' to only include the type that can't be proved. That is not true - I am using the word as it is meant to be used in this situation. When someone says, "You can't prove a negative," they are referring to a very specific type of 'negative' - that equivocation of the term 'negative' is so common does not change the meaning of the word.

To wit: "You can't prove a negative," is not fallacious, because in that statement the term 'negative' has a very specific meaning. That many people may misunderstand the statement bothers me, but no more than the people who misunderstand relativity or quantum mechanics, and then go on to bastardise those topics with woo.

If a million people commit the logical fallacy of equivocation, it doesn't make them right by consensus. They're still using a fallacy.