catsittingstill | On the impossibility of proving a negative

On the impossibility of proving a negative

So I was having an argument the other day, and a phrase popped up:

"It is impossible to prove a negative."

At the time I just let it go by. This phrase pops up a lot in discussions of this type (anything touching on atheism) and it's generally accepted as true and it didn't occur to me to think more deeply about it. But I was puttering around this morning sweeping the floors and I started thinking about it.

It is impossible to prove a negative.

Let's move it out of knee-jerk territory (at least for many people atheism is knee-jerk territory) and think about some other negatives.

"My plates are not trying to murder me."

"There is not a green unicorn sitting in my lap as I type this."

"The floor will not open up and swallow me when I get up off this chair."

Is it seriously not possible to prove any of these things? Does the fact that my plates have never tried to murder me before; that I have never heard of plates murdering anyone, that plates have never, in fact, been observed to move of their own accord before as far as I know, much less to move with intent--do those things mean nothing about my plates' current plans with regard to murder?

Well, hmm. Sometimes something that never happened before happens. Someone writes a song that never existed before, someone invents something that never existed before... I guess one can make a case that just because there is no evidence whatsoever that plates have ever murdered anyone or even moved on their own doesn't mean it absolutely can't happen.

So, one could be "aplatistic" on the subject of plates: "I am certain my plates are not trying to murder me." One could be "platistc" on the subject of plates "I am certain my plates are trying to murder me." Or one could be "ambiplatistic" on the subject of plates "My plates may be trying to murder me; there is no way for me to be certain."

I suppose one could, technically, make the argument that the ambiplatitisic stance is the only truly correct one. I mean, if you can't prove that your plates aren't trying to murder you, and you have no evidence that your plates are trying to murder you, then the stance that your plates may be trying to murder you covers both possiblities.

But which one produces more reasonable behavior in real life? The aplatistic stance would produce the behavior most people (I think) exhibit around plates--we behave as if it never crossed our mind that our plates might try to murder us; we take no precautions whatsoever; we walk through the kitchen without a care, and turn our backs on the plates without a second thought, and handle them with causual, indeed contemptuous, lack of concern. The platistic stance? I'm guessing it would involve smashing plates, or possibly banning them from the house. The ambiplatistic stance--I guess one would tiptoe through the kitchen only when necessary, keeping a wary eye on the plates the whole time. Or possibly simply ban them from the house, to be on the safe side--though that might be seen as unjust, since there is no evidence that the plates are planning to murder you.

So is it unreasonable to think that a person who smashes her plates to keep them from trying to kill her is...well, psychologically unusual? Arguably to the point where her ability to live a normal life is compromised? Is it unreasonable to say that being ambiplatistic--tiptoeing through the kitchen and never turning one's back on one's plates--is silly?

And if not, does that mean that sometimes it doesn't matter whether or not one can prove a negative?

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My plates are trying to murder me. They made a concerted attempt to burn me only this morning but I was too quick for them.

Seriously, the word "prove" is misused all the time. There may not be proof for a universal negative (there can be proof for negatives confined by time or space, such as, "My plates are not jumping out of the cupboard just now,") but there is evidence. Reasonable people usually live their lives based on evidence rather than proof anyway; most things in real life are difficult to prove in formal mathematical terms.

The problem when one tries to translate this into discussions about atheism and religion is that many people do have sensory evidence of the divine. Not necessarily accurate sensory evidence, mind you; but from whatever cause, their brains interpret certain neural firings as a physical sensation of Something There. It's really hard to argue against what someone's own senses are telling them -- just try to explain to a hallucinating person that their skin isn't covered with bugs when they see them and feel them. It's not unreasonable to point out the bugs aren't actually there, but it's a real uphill battle because your empirical sensory evidence and theirs do not match. And most people, not really unreasonably, go by their own in case of conflict.

Exactly why most people's brains do this is unclear; the material I've read on the subject seems to suggest it's probably genetic, but what it was an adaptation for is the subject of much scientific speculation. There are people who are apparently just born without it -- I'm one of them. I come from a line of five generations of atheists on both sides, and as far as I can tell, whatever it is which constitutes a "spiritual sense" in most people is something I don't have. Even in the times of my life when I've tried to be religious, I didn't have the wiring for it.

It can be really hard to talk successfully about a lack of external evidence to someone whose own senses are telling them there is evidence, though.

All of our experiences are experienced through our bodies, and in essence, through our neurons. And all are interpreted culturally. With at least half of people experiencing "God" one way or another, it's hard to say, empirically, whether that's an illusion or whether that faculty is simply not available to all people.

As to proof, except in specific defined academic areas, "proof" is simply enough evidence to convince someone that the assertion is true. This makes it very very subjective.

Even moreso when it comes to religion, where there are many people to whom "faith" means believing no matter what evidence might be presented to the contrary. I've also met atheists who would check themselves into mental institutions (or so they have said) before believing even blatant proof like a burning (but unconsumed) bush, should one appear before them.

Lawyers prove negatives in court all the time.

Prove that Virgil Timson didn't murder his wife! 1. Virgil Timson has been on the other side of the planet for the last three months; 2. I have here a signed confession from Peanuts Malloy; and 3. If that doesn't convince you, here's Mrs. Timson alive and well. Peanuts Malloy must be even nuttier than the prosecutor.

Of course, the real elephant in the room, from the perspective of a Defendant or an atheist, is that the one asserting the positive tends to have the burden of proof, BECAUSE proof of a negative is more difficult.

Whenever I hear that trope, I hear it as "You can't *dis*prove a negative".

Which, honestly, I never really cared about the details of the logic arguments, because no matter how much someone sets up logic examples (like your plates), the examples never seemed to hold up to me. Of course I can prove your plates aren't trying to murder you. Can I prove they'll never try to murder you? Sure I can. Anything that tries to get into the nitty gritty of a detailed logical argument has to ignore the surrounding facts (plates don't have brains, for example). Those logic puzzles are all well and good, but they're not real-world, they're just us turning over some neurons in our brains in fun ways.

What it comes down to is this: In all areas, there are some things that are provable and testable, and some things that aren't. Some are positives, some are negatives. In theology, it turns out that I can't prove that there's a God or that there isn't a God. All I can do is find evidence, or fail to find evidence, that one of his so-called actions can be caused by natural and observable phenomenon. That's got nothing to do with proving a negative, it's got to do with whether or not I'm testing the existence of something that can't be tested.

Okay, let's have a go...

What you are describing is not proof as I understand the term to have been used in this kind of discussion in my experience, but something more like "the application of common sense," which--as far as I know--is not the same thing. Also, the negative statements you list are not universally recognised as being of the same order as the statement "I sense the existence of an entity I characterise as God," since they are deliberately selected for ease of disproof (plates, being man-made things, demonstrably possess no consciousness, perception or volition; the floor around your chair is susceptible to examination for instability; if you had a green unicorn in your lap you would probably not be able to reach the keyboard).

There are other, less absurd negatives that you might have cited, such as "there is not an Earth-sized planet occupying the opposite position in Earth's orbit," "there is no Eldritch Temple of Starry Wisdom in Zander's home street," or "John Lennon is not dead." Clearly, if it makes any sense at all, the statement "it is impossible to prove a negative" cannot apply to this kind of proposition.

So what kind of proposition does it apply to? Universal propositions, perhaps, rather than particular ones, and those whose converse is not excluded from possibility on the ground of absurdity. "There are no left-handed Indonesian prostitutes." "There are no other life-bearing planets in the universe." "There are no problems that cannot be solved by the application of common sense."

It may be arguable that it does not matter whether or not one can prove these negatives either, but that, I think, is a subjective judgment and not in any way equivalent to "the negative is automatically true." And to reason from "I do not need to prove that my plates are not trying to kill me" to "I do not need to prove that the sense you have of an entity which you characterise as God is an illusion" is, I think, faulty reasoning based on an incorrect assumption.

Note: as previously stated, I have no such sense.

How's that?

Absolute logical proof is only possible in the abstract mathematical realm where we precisely state and agree on the rules ahead of time. In math-land, I can absolutely prove that 2+2=4. I can absolutely prove that there are no even prime numbers larger than 2. It has also been rigorously proven that no map can be drawn that can't be colored with only 4 colors, or that no integers a, b, c, and n, a, b, and c > 0 and n > 2, such that a^n + b^n = c^n (though those proofs are way beyond me). In the realm where it's truly possible to prove anything, it is possible to prove a negative, though it may be more difficult than disproving a negative by providing a counterexample.

In the real world, there are no axioms. There are only working hypotheses and heuristics that we generally agree on, and we often find that when we try to state them exactly we don't agree on them. And there is no truly absolute evidence; all observational data is subject to fallible perceptions and fallible memory. If I interview your plates and they speak and tell me that yes, they are in fact trying to kill you, that doesn't actually prove the platist proposition -- they could be lying, or I could be nuts.

Much more vexing, though, is the fact that human beings don't evaluate and maintain their beliefs through pure logic. We filter evidence that is offered to us based on how it fits with what we already believe and how much we want it to be valid. The more emotionally invested we are in a position, the less likely we are to honestly consider something that appears to contradict our position. And there are few questions that we're more emotionally invested in than the existence and nature of a deity.

I actually like what Richard Dawkins has said on the subject; specifically when it comes to the existence or non exixtence of non-corporeal deities. Since you can neither prove nor disprove, empirically, the existence of such things, it ceases to become a question of proof. It then becomes a question of probability. When you work out the likelihood of life on any planet, the odds are stacked well out of favor of living things. However, when all the required conditions are met, life happens. Then work out the likelihood of developing sentient life and the odds become slimmer still. Again, when the need arises in an organism, sentience arises. After that, we reach a point where the odds are so very unlikely it becomes as close to impossible as makes no odds. Ergo, the existence of deities becomes nothing more or less than a question of faith. At this point we are beyond ration, reason or logic. I wouldn't be betting my life on the existence of such deities. It is just too big a gamble.
When we come to the questin of your plates, what do you think would be the likelihood of your plates having invisible brains? If this were the case, I shouldn't be surprised if they had a psychotic need to take out a hit on their owners. I'd be a little nuts, too, if all I had to do was sit in a cupboard and wait for someone to pile hot food in my face.

"It is impossible to prove a negative."
At the time I just let it go by.

Yes, this is one of those preposterous assertions that are stated as fact in many contexts, including accusations of corruption in high office. It's a tiresome fallacy, sometimes used as shorthand for a different, but valid argument, and sometimes in the absence of a valid argument.

We behave as if it never crossed our mind that our plates might try to murder us; we take no precautions whatsoever; we walk through the kitchen without a care, and turn our backs on the plates without a second thought, and handle them with causual, indeed contemptuous, lack of concern.

What a wonderful first sentence for a story!

To a large extent there seems to be a bizarre misunderstanding in the assertion that claims the only kind of proof acceptable is deductive proof. It is true that most of those statements are not deductively provable. The inductive evidence, however, is overwhelming.

Several recent conversations with a client came to mind that are somewhat relevant. Consider the rumour that someone is pregnant. (Or in my case, that someone has head lice). Truth and evidence have nothing to do with proving that either of these rumours is in error. It's all about _belief_. If the whole school believes that Susy Cheerleader is pregnant, then nothing will break that belief, even the passage of time with no evidence of a pregnancy. Rumour will then believe that the pregnancy was terminated because, after all, EVERYONE knows that Susy was pregnant. No more can we prove that my student doesn't have, and never did have, head lice. EVERYONE knows that she had it and gave it to everyone else. Proof is immaterial.

And that is what you are talking about: a matter of belief as opposed to a matter of proof. The ability of humans beings to hold beliefs in the face of any logic or reason, let alone fact, is quite astounding. It has also been a source of some of the seamier episodes of our past, present and, no doubt, future.

Leave aside the application of the issue to specific philosophical questions.

The problem is that in trying to assert the correctness of a negative statement, most people will use the absence of evidence as the "proof".

1) Absence of evidence is not evidence of absence.

Now, this being said, the statement itself is not absolute. Just because you can't prove the negative doesn't mean you can't state that the probability of the negative is low. Your plates are very probably not trying to kill you, this can be induced from the fact that in the recorded history of humanity of which we are aware no one has ever discovered a sentient plate masterminding a criminal plot to murder a person. However, while the probability is so small as to be practically nil, it is not technically nil.

2) Low probability is not logical proof.

3) Lack of logical proof does not imply any level of probability.

Finally, what is considered "evidence" by some is not "evidence" by others. Using your green unicorn as an example, the proper statement would be that I have no way to prove to you that there is not a green unicorn sitting on your lap. If you are under the influence of drugs, paint fumes, or stacks of closing documents that need signing, you might very well see that green unicorn plain as day, and I have no way to prove to you it is not really there.

On a base level, evidence is of itself only a probability - depending on the independent verifiable existence of the evidence (and the acceptance of the independence of the verification) it can be weighted on a scale from true to false.

4) Absolute evidence isn't.

And, lest anyone think that this applies only to abstract philosophical and/or religion/non-religion arguments, I deal every day with people who want me to prove that my products are NOT causing a problem out in the network somewhere. All I can do is prove what my products ARE doing, I can't prove what they don't do without using evidence internal to the product which is, by any definition, biased.

It is curious that this seems to be highly associated with theological discussions. I had always heard it discussed in either pure philosophical terms or as a point of law.

Mind you, I'm not disputing that this argument could arise a lot in lay discussions about religion.

The weird part, to me, is that proof has nothing to do with religion, at all. Religion is all about *faith,* which by definition is to believe in something for which there is no proof (or at least, it hasn't been discovered, yet.)

If it's proven, then faith isn't involved. Merely recognition.

[Edited for clarfication]

Gotta watch those cups and saucers, the Bowl of the Sentient Chili, and the Plate of the Flying Spaghetti Monster.

The "project" of theism in many ways resembles on a much larger scale the "project" of artificial intelligence. There have been many interesting by-products, but central questions--in fact some of the same central questions--remain untouched. This might suggest to sensible people that arguing over the central questions is perhaps less important than engaging the related fields that come from the central questions. And fighting wars over unanswered central questions is right out.

[This is the added part] The problem is that if, after all these long centuries, theists haven't proven their case, saying that it hasn't yet been disproven is disingenuous. It hasn't been disproven, of course, but if their theism were valid, surely by now they'd have a better case. And yet the thought and actions thought to be peripheral to the philosophical claims of theism. All the art, all the music, the genuine caring for people, the support for ethical philosophy: these are things worth having and doing. So perhaps a useful attitude to theistic belief is to allow the central problem to remain unsettled.

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