Is it possible to prove a negative?
« on: December 19, 2013, 03:51:00 AM »
tl;dr version: every truth claim has a burden of proof.  it doesn't matter whether or not the claim contains a negation.

I feel like I'm derailing the UA vs. gravity thread, so I'm starting a new one.  This isn't strictly about FET, but it comes up a lot.

It's often claimed in various threads by members of both sides that one cannot proves a negative claim like, "There is no x."  This is a popular belief, and it's completely false.  Deductive reasoning is valid if and only if it is impossible for its premises to be true and its conclusion false.  Deductive reasoning is sound if and only if it is valid and its premises are true.  That's all.  It makes no difference if the premises or conclusions contain negations.

First, all truth claims carry a burden of proof.  Consider the following statement: Barack Obama does not exist.  The statement is not relieved of a burden of proof simply because it contains a negation.  Anyone making this claim would be required to offer evidence supporting the truth of its claim.  This is because all truth claims, negative or positive, carry a burden of proof.

Negative claims can also be proven deductively.  Consider the following argument:

1.  If A, then B. (If A exists, then B exists)
2.  Not B. (B does not exist)
3.  Therefore: not A. (A does not exist)

This argument uses a basic rule of inference called modus tollens, and we just used it to prove a negative: not A.  It's logically valid because if the premises are true, then the conclusion cannot be false.  Whether or not it's sound depends on the truth of the premises.

Let's consider a less abstract example:

If Barack Obama exists, then a birth certificate for Barack Obama exists.
A birth certificate for Barack Obama does not exist.
Therefore, Barack Obama does not exist.

This is a good example because it illustrates a point that is often missed in these discussions.  Notice that we can still argue and debate the truth of premises.  A proof can be both valid and not sound.  Obviously the argument I just made is very unsound (the premises are untrue), but if the premises were true, then it would be a logically valid proof of the conclusion (if the premises are true, then the conclusion must be true).

There are obviously a host of other issues that would have to be resolved with the premises (What do we mean by Barack Obama?  Anyone with that name?  The person who is the president?  Does the argument require that the person who is the president be named Barack Obama?).  And, in practice, some conclusions and their associated premises might be too complex in reality for us to resolve; but, the fact that our reasoning includes statements with negatives doesn't make them necessarily irresolvable.

And, we can't just assume that every negative claim is true until proven otherwise.  There's at least one good reason for this: every positive truth claim can be reformulated into a negative one.  It's called double negation.  'x exists' can be rewritten as 'x does not not exist,' or, 'it is not the case that x does not exist.'  If every negative claim is assumed true until proven false, then all claims must be assumed true until proven false.  That is the opposite of skepticism.
« Last Edit: December 19, 2013, 04:02:46 AM by garygreen »
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Re: Is it possible to prove a negative?
« Reply #1 on: December 19, 2013, 03:59:23 AM »
From the gravity thread...

It is true that you cannot empirically prove a negative but all this means is that you should not make such a truth claim to begin with unless you want to make an inductive argument. 

One can prove a negative using deduction in the empirical sense you're talking about.  Whether or not the conclusion or the premises of an argument contain negatives doesn't affect the logical validity of the proof.  We can modify the previous example:

If there is a baseball at location X,Y,Z, then my detector will detect photons as from a baseball at location X,Y,Z.
My detector not detect photons as from a baseball at location X,Y,Z.
Therefore, there is not a baseball at location X,Y,Z.

As before, the proof is valid (conclusion must be true if premises are true) even if it isn't sound (all premises are true).  And, we can certainly debate many aspects of the premises.  P1 can certainly be false for many reasons.  We'd need to better define 'baseball.'  P2 could be false if my detector is bad or faulty or insufficient in some way.  The list goes on.  But, the proof is still valid.

I see what you're getting at, though.  The claim 'there are no unicorns anywhere' would be insurmountably difficult to prove.  But, we could still construct valid deductive arguments in such a proof.  They just almost certainly wouldn't be sound.

1.  If the experiment used proper procedures to eliminate sources of error, then those procedures will be mentioned in documents on that experiment.
2.  Those procedures were not mentioned in documents on that experiment.
3.  The experiment did not use proper procedures to eliminate sources of error.

Alternatively:
3. Proper procedures to eliminate sources of error were used, but not documented.

Just had to toss that in. ;)

But again, that's a problem with truth of P1, not the conclusion.  The argument might not be sound, but it's still valid.  I'm just being pedantic at this point; I know what you're getting at.  It's a good illustration, though.
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Offline spank86

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Re: Is it possible to prove a negative?
« Reply #2 on: December 19, 2013, 12:29:27 PM »
I think there's a difference between the ability to prove a negative and the requirement to prove a negative.

In the case of the specific argument there's only small reason to believe that the controls Tom is requiring were in fact in place, especially as we and by inference they doubt that gravity could affect the calibration of a digital scale after it's set.

Offline bj1234

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Re: Is it possible to prove a negative?
« Reply #3 on: December 19, 2013, 01:14:53 PM »
There is also a huge difference between believing and knowing.

For example, say I flip a coin 500 times.  If they all come up heads, I might be believe that there is no tails on the coin.
Until I physically look at both sides of the coin, there is no way of knowing 100% if there is not a tails on the coin.

However, if my data is limited to just 2 flips, then my belief that there is no tails on the coin really isn't substantiated.

Now say I still claim there is no tails, my opponent asks me why I beloved there is no tails.  The burden of proof lies on me.  I need to show him my data.  I can't just say, "you can't proove a negative, the burden of proof is on you" and walk away.

Now I know this is an oversimplified example, but the premise holds for any claim.

Offline Socker

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Re: Is it possible to prove a negative?
« Reply #4 on: December 19, 2013, 07:11:52 PM »
Isn't the base rule the one making the claim, regardless of whether it's negative or not, has the burden of proof?

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Offline Rama Set

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Re: Is it possible to prove a negative?
« Reply #5 on: December 19, 2013, 07:15:07 PM »
Yes it is. 
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Offline spank86

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Re: Is it possible to prove a negative?
« Reply #6 on: December 19, 2013, 07:32:09 PM »
Isn't the base rule the one making the claim, regardless of whether it's negative or not, has the burden of proof?

yes, however who is making a claim in a long running discussion?

I mean essentially by asking for proof you are making a claim to the contrary of the one posted so there's claims on both sides.

Offline bj1234

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Re: Is it possible to prove a negative?
« Reply #7 on: December 19, 2013, 09:48:12 PM »
Asking for proof is not the same as making a contrary claim.  It is asking the one who claimed it to back up that claim with either evidence or a coherently logical explanation.

For example. 

Person 1 "This coin does not have a tails"
Person 2 "Why do say that?  Please provide proof that it doesn't"

Person 2 did not at all state that the coin must have a tails.  Just asked for evidence to back up the claim.

Now in this case, Person 1 could simply show both sides of the coin to Person 2 to prove the negative claim of the coin not having tails.  Or back it up with some evidence such as "I flipped the coin 500 times and every time it landed heads.  Here is the video with the results of every flip. With eye witnesses testimony." 

However, they cannot just say "Prove me wrong" without supplying some supporting evidence.

Offline spank86

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Re: Is it possible to prove a negative?
« Reply #8 on: December 19, 2013, 09:54:44 PM »
Asking for proof is not the same as making a contrary claim.  It is asking the one who claimed it to back up that claim with either evidence or a coherently logical explanation.

For example. 

Person 1 "This coin does not have a tails"
Person 2 "Why do say that?  Please provide proof that it doesn't"

Person 2 did not at all state that the coin must have a tails.  Just asked for evidence to back up the claim.

Now in this case, Person 1 could simply show both sides of the coin to Person 2 to prove the negative claim of the coin not having tails.  Or back it up with some evidence such as "I flipped the coin 500 times and every time it landed heads.  Here is the video with the results of every flip. With eye witnesses testimony." 

However, they cannot just say "Prove me wrong" without supplying some supporting evidence.

So if the person says I've looked and can't find any evidence online of tails on coins, nor do any articles mention tails on coins.

There would still be a burden of proof on the claimant? Or should you move on/try to find the proof that the  coin does in fact have tails.

Offline bj1234

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Re: Is it possible to prove a negative?
« Reply #9 on: December 19, 2013, 10:35:27 PM »
I would say he needs to supply some of his articles or sources where he looked at.  Not just "well I looked and I couldn't find it"
He needs to say I looked here and here and here.  Supply the sources, then supply a logical argument. 
In the case of the coin.

The data from this video shows 500 coin flips, all coming up heads.
The odds of a single coin(assuming it is a standard issue coin that has both heads and tails) flip coming up heads is 1/2.
We know that each subsequent coin flip is also 1/2.
Therefore the odds of all 500 coin flips coming up heads is (1/2)^500, or a really small number.
The odds of getting 500 heads in a row is such a small chance that this makes me believe that there is no tails on this coin.

He can't just say "prove me wrong" the burden of proof is on you now.
« Last Edit: December 19, 2013, 10:45:17 PM by bj1234 »

Offline spank86

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Re: Is it possible to prove a negative?
« Reply #10 on: December 20, 2013, 01:14:15 AM »
The difference lies in that in the original case that inspired this study the coin flips were being presented as an argument by the other party.


Offline bj1234

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Re: Is it possible to prove a negative?
« Reply #11 on: December 20, 2013, 01:35:04 AM »
Actually, the other side did present their evidence.  It was the gnome experiment and the gravity map.  Tom dismissed this evidence by saying the gnome experiment was not controlled and that the gravity map wasn't true because spaceflight is impossible.  This claim then shifts the burden of proof onto him. 

Quote from wikipedia
http://en.wikipedia.org/wiki/Philosophic_burden_of_proof

Proving a negative

"When the assertion to prove is a negative claim, the burden takes the form of a negative proof, proof of impossibility, or mere evidence of absence. If this negative assertion is in response to a claim made by another party in a debate, asserting the falsehood of the positive claim shifts the burden of proof from the party making the first claim to the one asserting its falsehood, as the agnostic position that "I don't believe that X is true" is different to the explicit denial "I believe that X is false".[8]"


Offline spank86

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Re: Is it possible to prove a negative?
« Reply #12 on: December 20, 2013, 01:40:47 AM »
Actually, the other side did present their evidence.  It was the gnome experiment and the gravity map.  Tom dismissed this evidence by saying the gnome experiment was not controlled and that the gravity map wasn't true because spaceflight is impossible.  This claim then shifts the burden of proof onto him. 

Quote from wikipedia
http://en.wikipedia.org/wiki/Philosophic_burden_of_proof

Proving a negative

"When the assertion to prove is a negative claim, the burden takes the form of a negative proof, proof of impossibility, or mere evidence of absence. If this negative assertion is in response to a claim made by another party in a debate, asserting the falsehood of the positive claim shifts the burden of proof from the party making the first claim to the one asserting its falsehood, as the agnostic position that "I don't believe that X is true" is different to the explicit denial "I believe that X is false".[8]"

I'd agree that the burden of proof was with him on the "no such thing as space flight" claim, but it seems to me the no controls in the gnome experiment is less clear, after all in the first instance he is making a claim directly contrary to what has been stated, in the second he is exposing something that has NOT been stated.

I mean how exactly would you have him go about proving there were no controls?

Short of tracking down the researchers or paying for the full methodology?

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Offline Rama Set

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Re: Is it possible to prove a negative?
« Reply #13 on: December 20, 2013, 02:43:43 AM »
I don't think he can. I took issue with him making the claim and then saying it was valid by citing a Wikipedia page that did not mention the controls, as if that is information that you would expect to find on Wikipedia.
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Offline bj1234

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Re: Is it possible to prove a negative?
« Reply #14 on: December 21, 2013, 06:50:56 PM »
Actually, the other side did present their evidence.  It was the gnome experiment and the gravity map.  Tom dismissed this evidence by saying the gnome experiment was not controlled and that the gravity map wasn't true because spaceflight is impossible.  This claim then shifts the burden of proof onto him. 

Quote from wikipedia
http://en.wikipedia.org/wiki/Philosophic_burden_of_proof

Proving a negative

"When the assertion to prove is a negative claim, the burden takes the form of a negative proof, proof of impossibility, or mere evidence of absence. If this negative assertion is in response to a claim made by another party in a debate, asserting the falsehood of the positive claim shifts the burden of proof from the party making the first claim to the one asserting its falsehood, as the agnostic position that "I don't believe that X is true" is different to the explicit denial "I believe that X is false".[8]"

I'd agree that the burden of proof was with him on the "no such thing as space flight" claim, but it seems to me the no controls in the gnome experiment is less clear, after all in the first instance he is making a claim directly contrary to what has been stated, in the second he is exposing something that has NOT been stated.

I mean how exactly would you have him go about proving there were no controls?

Short of tracking down the researchers or paying for the full methodology?

Well see both his negative claims were disputing evidence that was presented to support a different claim.  It is Tom's responsibility to support his claims. 

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Offline Rama Set

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Re: Is it possible to prove a negative?
« Reply #15 on: December 22, 2013, 01:55:59 AM »

I mean how exactly would you have him go about proving there were no controls?

Short of tracking down the researchers or paying for the full methodology?

But this is the crux of the matter. He asserted a truth he had no support for and cannot easily find the support for unless he wants to start sorting through the published appears which are behind paywalls at $40 each. In this case you should not make the claim in the first place unless you are willing to do the work or be exposed for lazy research work.
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Offline Tom Bishop

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Re: Is it possible to prove a negative?
« Reply #16 on: December 28, 2013, 12:22:50 AM »
Who said it was impossible to prove a negative?

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Offline markjo

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Re: Is it possible to prove a negative?
« Reply #17 on: December 28, 2013, 12:43:32 AM »
Who said it was impossible to prove a negative?
Does this mean that you admit that you must now start supporting your negative claims?
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Offline Tom Bishop

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Re: Is it possible to prove a negative?
« Reply #18 on: December 28, 2013, 01:13:20 AM »
Who said it was impossible to prove a negative?
Does this mean that you admit that you must now start supporting your negative claims?

Negative claims already have supporting evidence of absence by virtue of an absence of evidence.

Offline bj1234

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Re: Is it possible to prove a negative?
« Reply #19 on: December 28, 2013, 02:19:31 AM »
Who said it was impossible to prove a negative?
Does this mean that you admit that you must now start supporting your negative claims?

Negative claims already have supporting evidence of absence by virtue of an absence of evidence.
Only if you have looked in the most likely places.  Otherwise, it is just an argument from ignorance.

http://en.wikipedia.org/wiki/Evidence_of_absence

Quote
in the absence of evidence rendering the existence of some entity probable, we are justified in believing that it does not exist, provided that (1) it is not something that might leave no traces and (2) we have comprehensively surveyed the area where the evidence would be found if the entity existed...[5]

Note the bold.  In other words, if you haven't looked in the most likely places, you cannot use absence of evidence to claim it does not exist.
« Last Edit: December 28, 2013, 02:24:16 AM by bj1234 »