Myth: You Can’t Prove a Negative
March 2, 2008 by Bob Patterson
Martial Development has an interesting post on James Randi. I’m not weighing in on Randi but I will weigh on the myth that you cannot prove a negative. From MD:
They cannot hope to prove a negative, that no “paranormal, supernatural, or occult power or event” exists…
Here’s the comment I left over there. I thought it worth posting here, too:
MD -
I’ll leave Randi to defend himself and his organization if he so chooses.
However, I will point out that you CAN prove a negative beyond a reasonable doubt and assign a probability to it.
There really isn’t such a thing as a “purely” negative statement, because every negative includes a positive, and vice versa. Thus, “there are no psychic monks in my closet” includes “this closet contains something other than monks” (in the sense that even “no things” is something, e.g. a vacuum).
“Something” is here a set restricted only by excluding monks, such that for every set S there is a set Not-S, and vice versa. In almost-English: Every negative entails a positive and vice versa.
To test the negative proposition one merely has to look in my closet: Since psychic monks being in my closet (p) entails that we would see monks when we look in my closet (q), if we find q false, we know that p is false. Thus, we have proved a negative.
Of course, we could be mistaken about what we saw, or about what a psychic monk looks like, or things could have changed after we looked, but within the limits of our knowing anything within reason, and given a full understanding of what a proposition means and thus entails, we can easily prove a negative in such a case.
This is not “proof” in the same sense as a mathematical proof, which establishes that something is inherent in the meaning of something else (and that therefore the conclusion is necessarily true–often 100% true based on numbers), but it is proof in the scientific sense and in the sense used in most courts of law. So my monk example holds because when p entails q, it means that q is included in the very meaning of p. Whenever you assert p, you are also asserting q. In other words, q is nothing more than an element of p.
Thus, all things being as we expect, “Bigfoot is in my kitchen” means if you look in my kitchen you will see Bigfoot, so not seeing him means the negative of “Bigfoot is in my kitchen.”
Negative statements often make claims that are hard to prove because they make predictions about things we are in practice unable to observe. For instance, the statement “there are no psychic monks” means that “there are no monks in this universe,” and unlike my closet, it is not possible to look in every corner of this universe, thus we cannot completely test this proposition. All we can reasonably do is look around within the limits of our ability and our desire to expend time and resources on looking, and prove that, where we have looked so far, and within the limits of our knowing anything at all, there are no psychic monks.
In such a case we have proved a negative, just not the negative of the sweeping proposition in question, and we can assign a probability to it. Obviously the probability of me seeing a psychic monk in my closet is quite low. On the other hand, assigning a probability to the existence of a psychic monk “somewhere” in the universe might be ill advised, because we do not have the ability to look “everywhere”. So, in that example I might suspend my judgment.
So, the Randi test or just about any other scientific test which has tested for “paranormal powers” has proven a negative, in my opinion.
Also see Shermer’s You Can Prove a Negative:
So why is it that people insist that you can’t prove a negative? I think it is the result of two things: (1) Disappointment that induction is not bulletproof, airtight, and infallible, and (2) A desperate desire to keep believing whatever one believes, even if all the evidence is against it…
If we’re going to dismiss inductive arguments because they produce conclusions that are probable but not definite, then we are in deep manure. Despite its fallibility, induction is vital in every aspect of our lives, from the mundane to the most sophisticated science. Without induction we know basically nothing about the world apart from our own immediate perceptions. So we’d better keep induction, warts and all, and use it to form negative beliefs as well as positive ones.
You can prove a negative — at least as much as you can prove anything at all.
Update: This is an updated based on a recent comment I just received concerning the invisible elf that may or may not live in my fridge. See my comment and also take a look at Dawkins explaining it. Granted, Dawkins is talking about “God” and is not my favorite person. That having been noted I can’t deny his logic. In fact, you can replace “God” with elf, chi, ki, or just about any other supernatural idea and you’ll get the point I’m trying to make. At least I hope you do…
~BCP
(Note: This post might change on this blog as I look back at it, review and reflect upon my logic, etc. )
I agree with you in some particular instances, but there are many things I don’t think are possible to disprove.
One simple example would be:
Did you know that when you open your fridge, that tiny invisible elf turns the light on. This elf by virtue of being tiny and invisible can not be seen, touched, heard, or in an way studied through man made means. This elf also leaves absolutely no trace of it’s being in your fridge, and your fridge is “designed” to look at if electricity is being used in conjunction with a small switch to turn on the light.
Obviously this argument is complete bullshit, but can you PROVE definitively that it is bunk?
In your example by leaving your closet door open, you might be able to prove that specific thing to be false, but most of the time when people refer to not being able to prove a negative, they are referring to more supernatural phenomena which for one reason or another can not be studied directly and accurately by science.
Just because James Randi proves that Sylvia Brown and a host of other “psychics” are frauds does not and can not prove that nobody is psychic. While you and I may believe that all psychic’s are frauds or delusional, this can’t be proven unless EVERY PERSON on the planet is tested, and even then, perhaps Edgard Kasey (sp?) or some other dead person or some other person yet to be born may have “the gift”.
First, if the supernatural cannot be studied by natural means, then how can we study it objectively? If, only a few people have this “gift”, then that’s problematic for people like me who appear to not have supernatural insight.
Second, you need to re-read my post and the Shermer link.
A criminologist can study a percent of all inmates and based on his or her observations make a prediction that, say 40% of certain type of person will commit a certain crime. It’s not certain at the 100% level and it’s not even looking at the entire population but it is a prediction based on probability.
It happens all the time in fields such as psychology, sociology, marketing, economics, finance, physics, biology, etc.
As for your elf example, well, no I can’t prove with certainty that it does not exist. Being certain and being probable are TWO different things which is my point.
Or, as Bertrand Russell famously said in his essay “Is There God?”
“If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes.
But if I were to go on to say that, since my assertion cannot be disproved, it is an intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense.”
~BCP
I completely agree that there are no elves, no psychics, no teapot in the sky, and no god.
My point is only that while we can say the existance of something is highly improbable, and we can say that the likelihood of something is so small as to be legitimately ignored as a possibility, we can not in all honesty say that something specifically is false under all circumstances (primarily depending on the definition of that phenomena excluding it’s ability to be measured).
Take for example Richard Dawkins, who is one of the most outspoken atheists around, and one of the harshest critics of theism, religion, and blind faith. Even Dawkins puts his certainty of there being no god at 95% leaving a 5% chance that god does in fact exist (personally I think he is being a bit too generous giving it that high a likelihood, but that’s another argument).
While we can say with as much certainty as we are capable of that the biblical account of the creation is false ,we can not PROVE that god did not in fact create the universe 5 minutes ago, and all of our memories, all of our science, all of everything that happened more than 5 minutes ago is an illusion designed to fool us into a false belief. I don’t believe this is true, as I am sure you would agree with me, but I can never PROVE 100% that this is not the case.
Proving beyond all reasonable doubt, and proving 100% are not the same thing.
No, but believing something that has, say, a 5% certainty of being true is foolish. Which, again is my point. On those instances I would suspend my judgment or deny it outright.
On psychic phenomena among humans I’m comfortable denying. On psychic phenomena in the known Universe I’d have to suspend my judgment and claim agnosticism.
I agree, we should treat these things as if they do not exist, but this does not mean that they have actually been proven false.
The ONLY reason that I bring this point up so strenuously is that religious people will often times ask for “proof” of something (or lack of something), and it’s better to start with the understanding that “proof” is not something we can scientifically do. What we CAN do however is to show that the preponderance of the evidence leads in a direction, and that deviation from this direction is highly suspect and almost certainly wrong.
BTW, I’m not sure if you’d be interested in the discussion or not, but I have a good one going on at the moment on my blog (230+ comments so far) that I’d like to hear your opinion on if you’ve got the time and interest in the topic.
http://potomac9499.wordpress.com/2008/01/30/an-open-question-to-all-believers/
That’s exactly the point I’m trying to make! Related to that is just because they have not been proven false does not mean we need to believe they are true, either.
Unless new evidence comes to light that, after thorough evaluation, causes us to reassess our hypothesis.
I’ll follow your link - no promises that I’ll post, however.
~BCP
It seems we agree, the only difference is language I guess.
By default my default position is to NOT believe without evidence, or a consensus of opinion by scientists or another group who should be “experts” on the subject.
However a lack of belief is not the same as “knowing” something to be false or untrue.
I think we both agree, but we used different wording, which perhaps caused a misunderstanding…
Oh, and thank you for your reply on my blog, it’s a long one, so it may take me a bit to respond.
I think we just said it differently. Anyhow, that’s why I *mostly* try to avoid these discussions these days. The language of science and philosophy are hard enough to understand for those who have to use it. It gets even worse when you try to explain it to other folks who get their “science” from the popular news. The popular news on science is usually what twinkes are to healthy food.
In the end it becomes one long argument.
~BCP
If only you had been able to tell this to Hume!
Of course, we live our lives predicated on the conclusions of inductive reasoning - but that hardly constitutes an argument for their truth - merely their practicality.
Wittgenstein might have a few notions on your private definition of the word “proof”.
You also create a strawman [well, borrow Russell's] about faith when you claim that it is necessarily intolerant of doubt. The concept of faith, in fact, has no meaning without doubt. Try some Kierkegaard.
Personally, I think there’s no absolute to be known - either through analysis or analogy. Of course, I’ve no proof for that - but I will myself to live anyway [c.f. Nietzsche].
Nevertheless, I always enjoy reading people’s statements of faith, like:
“By default my default position is to NOT believe without evidence, or a consensus of opinion by scientists or another group who should be “experts” on the subject.”
cheers
Hi Meanjink -
Thanks for your insightful comments.
1. On inductive reasoning. Re-read (or actually read) the link to Mr. Shermer’s page. If you have issues send him an e-mail.
“The very nature of an inductive argument is to make a conclusion probable, but not certain, given the truth of the premises. That is just what an inductive argument is. We’d better not dismiss induction because we’re not getting certainty out of it, though.”
Again: Big difference between certainty and probable.
2. I never claimed faith is intolerable of doubt. I laid out an analogy based on probability. Try some statistics and the scientific method. As for Russell, he’s dead. However feel free to contact Dr. Dawkins.
3. 2+2 is 4. I am absolutely sure.
4. I always enjoy red herrings but when you mix them with equivocation they give me gas. From Webster, faith:
(1): firm belief in something for which there is no proof (2): complete trust3: something that is believed especially with strong conviction; especially : a system of religious beliefs
If I observe 365 sunrises 365 days in a row it’s not “faith” (i.e., firm belief in something for which there is no proof”
to predict that the sun will rise tomorrow and assign a probability to it. Nor, is it “faith” if I add to my prediction the consensus of several dozen astronomers who have made the same observation, taken measurments, video recordings, etc.
Final comment: This discussion is going beyond the scope of my humble martial arts blog. Your post is exactly why–for the most part–my time is better spent self-actualizing through the martial arts than debating how many angels can (or cannot) fit on the head of a pin.
The last word is yours.
Cheers,
Bob
“my time is better spent self-actualizing through the martial arts”
Admirably enough so, though you certainly don’t need me to tell you that.
Nevertheless, you may enjoy reading some Hume (who says that if you think the sun will rise on the 366th day, you are doing nothing more than guessing - useful guessing, but guessing nonetheless). As for 2+2=4, you’ve no way to be sure you’re not being deceived by an evil genius as to the nature of mathematics (Descartes said this). And my final comment was to suggest that belief in some objective validity regarding quantification and the scientific method is, of course, belief - and therefore faith.
Thanks to you for your thoughtful response, interesting post, and lovely blog.
cheers
Scooped yet again! I’d hoped mine would be the first martial arts blog to discuss Hume and Wittgenstein.
Yeah like I need one more thing to look like a geek!
You know, we are going at it all wrong. Considering how much energy this topic seems to create we should start our own opposing viewpoints show.
We just need a suitable title…
“Did you know that when you open your fridge, that tiny invisible elf turns the light on. This elf by virtue of being tiny and invisible can not be seen, touched, heard, or in an way studied through man made means. This elf also leaves absolutely no trace of it’s being in your fridge, and your fridge is “designed” to look at if electricity is being used in conjunction with a small switch to turn on the light.
Obviously this argument is complete bullshit, but can you PROVE definitively that it is bunk?
”
quote from rodibidably
yes i can disprove it, just put a camera in the fridge
“tiny invisible elf”
How is a camera going to help with something that is INVISIBLE?
“This elf by virtue of being tiny and invisible can not be seen, touched, heard, or in an way studied through man made means.”
By using this wording, it essentially becomes the same as the argument for god or a number of different pseudosciences. As we know, any time that somebody “proves” a specific aspect of “god”, psychic powers, etc is untrue, the believers use the old argument that “science is not capable of studying this.
While their argument is not intellectually honest, it becomes an unfalsifiable position.
I’d use my invisible camera.
~BCP
Does that use invisible film?
I’m not sure. I keep losing the camera.
~BCP