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[From my new book "Believing Bullshit".]

Let’s now turn to a variant of “it’s beyond science/reason to decide.” One reason why some suppose science and reason are incapable of establishing beyond reasonable doubt that certain supernatural claims—for example, that fairies or angels or spirit beings exist—are false, is that they assume you can’t prove a negative. Indeed this is widely supposed to be some sort of “law of logic.”

For example, Georgia minister Dr. Nelson L. Price asserts on his website that “one of the laws of logic is that you can’t prove a negative.” If Price is correct and this is indeed a law of logic, then of course it immediately follows that we can’t prove that there are no fairies, angels, or spirit beings, or, indeed, that there is no god. We will have established that the nonexistence of God is indeed beyond the ability of reason and/or science to establish!

The fact is, however, that this supposed “law of logic” is no such thing. As Steven D. Hales points in his paper “You Can Prove a Negative,” “You can’t prove a negative” is a principle of folk logic, not actual logic.

Notice, for a start, that “You cannot prove a negative” is itself a negative. So, if it were true, it would itself be unprovable. Notice that any claim can be transformed into a negative by a little rephrasing—most obviously, by negating the claim and then negating it again. “I exist” is logically equivalent to “I do not not exist,” which is a negative. Yet here is a negative it seems I might perhaps be able to prove (in the style of Descartes—I think, therefore I do not not exist!)

Of course, those who say “You can’t prove a negative” will insist that I have misunderstood their point. As Hales notes, when people say, “You can’t prove a negative,” what they really mean is that you cannot prove that something does not exist. If this point were correct, it would apply not just to supernatural beings lying beyond the cosmic veil but also to things that might be supposed to exist on this side of the veil, such as unicorns, Martians, rabbits with twenty heads, and so on. We would not be able to prove the nonexistence of any of these things either.

But is the point correct? Is it true that we can never prove that something does not exist? Again, it depends. If John claims there’s a unicorn in the tool shed, I can quickly establish he is mistaken by going and taking a look. We could similarly establish there’s no Loch Ness monster by draining the loch. But what of the claim that unicorns once existed? We can’t travel back in time and directly observe all of the past as we can every corner of the tool shed or Loch Ness. Does it follow that we can’t prove unicorns never existed?

It depends in part on what you mean by “prove.” The word has a variety of meanings. By saying something is “proved,” I might mean that it is established beyond all possible doubt. Or I might mean it has been established beyond reasonable doubt (this is the kind of proof required in a court of law). Can we establish beyond reasonable doubt that unicorns have never inhabited the earth? True, the history of our planet has been and gone, so we can no longer directly inspect it. But surely, if unicorns did roam the earth, we would expect to find some evidence of their presence, such as fossils of unicorns or at least of closely related animals from which unicorns might plausibly have evolved. There is none. We also have plenty of evidence that unicorns are a fictional creation, in which case, it’s surely reasonable for us to conclude that there never were any unicorns. Indeed, I’d suggest we can prove this beyond reasonable doubt.

In response, it might be said “But you can’t prove conclusively, beyond all possible doubt, that unicorns never roamed the earth.” This is undeniably true. However, this point is not peculiar to negatives. It can be made about any claim about the unobserved, and thus any scientific theory at all, including scientific theories about what does exist. We can prove beyond reasonable doubt that dinosaurs existed, but not beyond all possible doubt.

Despite the mountain of evidence that dinosaurs roamed the earth, it’s still possible that, say, all those dinosaur fossils are fakes placed there by alien pranksters long ago.

Let’s sum up. If “you can’t prove a negative” means you can’t prove beyond reasonable doubt that certain things don’t exist, then the claim is just false.We prove the nonexistence of things on a regular basis. If, on the other hand, “you can’t prove a negative” means you cannot prove beyond all possible doubt that something does not exist, well, that may, arguably, be true. But so what? That point is irrelevant so far as defending beliefs in supernatural entities against the charge that science and/or reason have established beyond reasonable doubt that they don’t exist.


Alan Arthur said…
I stand corrected. There are some negatives that can be proved beyond doubt and it's not correct to say you can't prove a negative.

My baby child is not eighty years old. Is that a negative? I've got a birth certificate to prove that one beyond any doubt what so ever if the baby lying in the crib doesn't work as proof for anyone.

Depends how you define Martians doesn't it. Are they microbes or complex creatures like us. The information we have about Mars would rule out one, but not the other.

It's possible that a unicorn fossil will be found tomorrow. Though I suspect that it will always be tomorrow and not today. Or given that apparently most species do not leave fossils because they don't die in the right place or the fossils are never found, we may never find a unicorn fossil.

As for gods, I am personally unable to prove beyond any doubt that they don't exist.

I did once start to read what was claimed to be a very technical proof of proving a negative but my eyes quickly glazed over. Your explanation is much more sensible and understandable.

But do I have to prove that gods do not exist? I can look at the factual consequences of using god as an ordering principle to show that god is politically repugnant and socially undesirable and morally unnecessary and we should just ignore it and leave it to contemplate its immaterial navel. If it doesn't like that, then it can pop on down and demonstrate conclusively that it does exist and we might take it seriously. But I wont be holding my breath on that one.
clk said…
I work in finance and sometimes we got to prove to our directors, that a payment was never made to a creditor before approval can be given to make this specific invoice.

How does one prove a payment has never been made? It's like looking for something that shouldn't be there, and once you fail to find it, its proven....
Peter Byrom said…
Stephen, this is just one of the reasons why your debate with Craig is going to be brilliant! No ducking the issues here! :-)
Michael said…
~If this point were correct, it would apply not just to supernatural beings lying beyond the cosmic veil but also to things that might be supposed to exist on this side of the veil, such as unicorns, Martians, rabbits with twenty heads, and so on. We would not be able to prove the nonexistence of any of these things either.~

no, this is where you are wrong. The difference between God versus unicorns, Martians, rabbits with 20 heads and so on is that the latter three are all falsifiable, while God is not. We can add "spaghetti monster" to the latter category since you folks like to use that one a lot two.

In all FOUR of those instances, terms are used which are definable and can be used to disprove the assertion at least within objective terms. (We all agree that ultimately nothing is provable: even science assumes that a proof is not 100% guaranteed, so we have to talk within reason).

For example, we all agree on what a unicorn is: an equine with a horny protuberance in its forehead. If the proposition is made that unicorns once existed, that statement can be falsified because we can devise an objective test that would disprove it, i.e., if we had access to the remains of every single equine, we would be able to test and see if any possessed a genome that would direct the growth of a horned protuberance. Martians are sentient denizens of Mars. Again, to the proposition Martians exist, (or don't exist) we can devise an objective test that would disprove that assertion, i.e., we could go to Mars and investigate it through and through, and if we found no scientific evidence that there were any life on Mars, then the assertion that there are no martians would proved to the degree science can prove a proposition. Twenty headed rabbits are also easy to falsify to the extent that an experiment could be devised that would prove that none existed, insofar as scientific evidence is concerned. And, finally, yes, the same is true of the "spaghetti monster", we all agree as to what spaghetti is, we all agree that a monster is something that generates fear; i.e., in all the four instances, the terms can be defined acceptably that the question can be subjected to falsification.

How do you falsify God? You can't. Simply because there is no agreed upon term to be falsified. God isn't a "thing", God is a conceptual framework.

To say that you can prove God doesn't exist by reference to objective rules of evidence is simply incorrect. One may be able to prove a negative in the material world, but to try and extend that proof, which depends on falsification, to the non-material world, where subjectivity determines the term being discussed, is simply way off.

P.S., I don't believe in God, it's just that I find the constant attempts to suggest that science can prove god doesn't exist beyond a reasonable doubt to be amusing and an exercise in futility.
Anonymous said…
Science has not proved beyond a reasonable doubt that God does not exist, nor can it do so. The most science can do is to state that in material terms there appears to be insufficient evidence to establish beyond a reasonable doubt that God exists. Hence atheism is by its nature dishonest. The logical position for non-believers is to be agnostic.
Nietzsche recommended simply avoiding such debates: "Die historische Widerlegung als die endgültige. — Ehemals suchte man zu beweisen, dass es keinen Gott gebe, heute zeigt man, wie der Glaube, dass es einen Gott gebe, entstehen konnte und wodurch dieser Glaube seine Schwere und Wichtigkeit erhalten hat: dadurch wird ein Gegenbeweis, dass es keinen Gott gebe, überflüssig. — Wenn man ehemals die vorgebrachten "Beweise vom Dasein Gottes" widerlegt hatte, blieb immer noch der Zweifel, ob nicht noch bessere Beweise aufzufinden seien, als die eben widerlegten: damals verstanden die Atheisten sich nicht darauf, reinen Tisch zu machen." ("The historical refutation as the definitive one. Previously, one tried to prove that there was no God, today one shows how the belief that god exists was able to arise, and how this belief obtained its status and importance: thus, the proof that god does not exist became unnecessary. -- Previously, when one had refuted the existing "proofs of god's existence," there remain an uncertaionty about whether proofs could still be found which were better than those just refuted: back then, atheists didn't understand how to be done with the whole business.") -- Morgenroethe, 95th aphorism.

I've mostly taken Nietzsche's advice and avoided arguing with people about such silly ideas as the existence of God. Maybe it's not for everyone -- it's saved me a lot of time and aggravation -- but you do have to set some minimum standards, don't you?
Anonymous said…
“You cannot prove a negative”
Doesn’t this relate to one of the flaws in science? If science could conduct every experiment possible in every way possible, then the basis for a definitive assessment would be in place. If not the infallible ability needed to process the data. Thus to assert that something could not be done may be incorrect. Although any claim that we can currently do it, in the absence of accompanying proof to that effect, is challengeable.

“By saying something is “proved,” I might mean that it is established beyond all possible doubt. Or I might mean it has been established beyond reasonable doubt (this is the kind of proof required in a court of law).”
And we all know how reliable courts of law are. By saying something is “proved,” are we not saying “to my satisfaction”. Since like much of science, its hearsay. Introduce an intentional error into a text book, a see how many pick up on it.

“if unicorns did roam the earth”
They might have been part of an alien genetic experiment. Subsequently thoroughly expunged. (Their housekeeping being par excellence compared to the mess we leave behind). Given Jurassic Park, and genetics. We may yet be those aliens’ apprentices.

“some evidence”
Consider the Antikythera mechanism. A few more years in the sea and that would have been gone for good. Which isn’t the same as never having existed at all. So, would tales of such equipment be deemed mere legend?

“We also have plenty of evidence that unicorns are a fictional creation”
Surely “fictional” means total invention. Whereas misidentification, such as glimpsing Oryx at some distance, is yet another effect.

“I’d suggest we can prove this beyond reasonable doubt.”
Or rather, to a degree we might be prepared to designate reasonable. Until in receipt of a slap in the face from reality.

“We prove the nonexistence of things on a regular basis.”
Math proved conclusively that huge ships almost cut in half, were not victims of freak ocean waves. Eventually a radar satellite showed that the calculated one freak ocean wave every 10,000 years, was in reality 10 freak ocean waves at any one instant in time.

“beliefs in supernatural entities”
might better be investigated by assisting the claimant to share whatever it was that persuaded them. As with scientists who disagree on a conclusion. Both simply need to present to the other the irrefutable proof that convinced them. If unable, what is it they were basing their preferred belief on? Stephen Fry often scolds Alan Davis on Q.I. with regard to the desirability of obtaining information from books. Alan has yet to point out that Stephen doesn’t place credence in the bible. Which, coincidently, is a book.

“If “you can’t prove a negative” means you can’t prove beyond reasonable doubt that certain things don’t exist, then the claim is just false.”
Maybe the question should be: Can anyone prove that “beyond all reasonable doubt” equates to absolute certainty?
Unknown said…
If the test is beyond reasonable doubt (5% of doubt), I agree God cannot meet that test on the mere basis that God is consistent with the existence of the world. The existence of a separate universe may be consistent with the existence of our own, but I would not propose it exists without direct evidence.

However, by the test of absolute certainty as to the absence of another Universe, or of God, I would pass. My approach is that we refine belief by logic until we have reliable knowledge, and if someone says God is beyond knowledge, all I can logically say is "goodbye", as I am seeking knowledge.

Private beliefs are a driver, so I wouldn't crush them entirely, and cannot do so logically (lacks parsimony). However, but I would only operate in the objective public world, and leave private Gods to the people that have them.
Blaise said…
Of course you can prove a negative. How else would you know when you're out of milk?
Emily said…
On Guard:
brenda said…
I know this post is older but I found it by following several links and I feel I must reply.

I am nobody. Stepha Law is a professional philosopher so I have a hard time believing a professional can make so bad an argument as this. It's embarrassing... either that or I have deeply misunderstood everything I have ever read on logic.

"Proof" is well defined and it does NOT mean "mostly true" or "reasonably true" or "beyond a reasonable doubt" or "without evidence to the contrary". Yes, you can prove anything you like as long as you change the meaning of "true" or "proof" and make it sufficiently fuzzy to allow one to to drive a Mac truck through the gap. But that is not the kind of proof people mean when they are talking about god or whatever. What they mean to say is that god's existence is *necessarily* true.

What Stephen is describing is scientific inductive reasoning and NOT logical deductive reasoning. In the case of the latter it most certainly IS true that one cannot prove a negative and that is what people intend when they say we cannot prove negative claims.

If all we have ever seen are white swans we can "prove" that all swans are white as long as we understand that disconfirming evidence may be discovered at any time and render our "proof" false.

As I said I am no one so maybe there is something I missed. Has David Hume been refuted? Is the distinction between inductive and deductive reasoning now obsolete? Has Tarski been superseded by later philosophers? Is the analytic/synthetic distinction no longer valid?

I cannot imagine how this could be.
Buzz Moonman wrote:
"As for gods, I am personally unable to prove beyond any doubt that they don't exist."

Well, I can prove that some gods don't exist, and they are the ones I devised myself----like the one I just thought up two minutes ago. The same goes for any other fiction invented by the human mind. By extension, it is another matter to claim that all gods are the invention of the human mind---although they probably are.
This comment has been removed by the author.
Anonymous said…
First, I enjoyed reading this essay. I'm not sure I fully "get" the arguments for or against it, though, because it seems like there are two (possibly more - but my head is near exploding as it is) classes of "things" that apply to the "testing" of the notion of proving negatives. The one class I think of as boundless, the other (used to disprove the can't disprove a negative) bounded. Examples of proving a negative always seem to require that a boundary be set. To prove that there is no unicorn in the shed requires an implicit "now" be added to the claim. By binding the negative claim, you can pin it to the wall of disproof. But can you prove that there is/was/will never be a unicorn in the shed? Again, only if we continue to bind the claim to the shed. (Or, remove the implicit bounds from "unicorn" as being of visible size, normal speed, etc.) We can build and monitor the shed from its creation to its destruction. So remove the shed. Can we disprove unicorns? Now I feel this is closer to the class of unbound things that cannot be disproved (at least it seems that way to me - I'd honestly appreciate being proven wrong in my thinking, if only to save my head).
brad said…
Seems somewhat disingenuous. Thinking about Spirituality/Divinity here as opposed to religion.
There is no way to disprove the existence of Divinity. To DO that one would need to have the "equipment" and necessary ability to know virtually everything.
When one realizes that the physical component of atomic structure (which manifest on the physical plane from potential and a percentage of probablility from the totally UNOBSERVABLE unmanifest portion of the universe) is one FIVE HUNDRED TRILLIONTH of the total volume, and that as stated: we have no ability to observe or know this unmanifest area. (equivalent to one cubic inch of solid matter electrons/protons/neutrons etc in a volume of more than 35 miles X 35 miles X 35 miles) one realizes the profound LACK of knowledge in this regard.
Does anyone propose to definitely KNOW that something does not exist in there? When there is evidence of spiritual reality in other arenas?
Not convinced on many levels here. The intentional distortion of ludicrous "issues" is a subliminal attempt to denigrate associated non-observed/accepted "scientific" theory.
Unknown said…
The profoundly dishonest position is that of the theist. Asserting the existence of a being that is not only not testable, even in principle, but to claim it has properties (being immaterial) without even being able to demonstrate that immaterial existence is possible, even in principle. 'Immaterial' insofar as I understand it is the theist's explanation for what they do not understand or otherwise think or take to be is explicable by known science. In other words it's no more than an argument from ignorance.
Unknown said…
It shows a fundamental misunderstanding of physics when one talks of "proving" that something about the universe is true. Proofs are for mathematics. (Let's not get into Godel!)

The best we can do is establish a high level of confidence that something is true. And that is how we get through the day: when I plan to get up tomorrow morning, I don't know that the Earth (and I!) will still exist. A quantum fluctuation, alien invaders, or an untracked asteroid might suddenly destroys the world. But I know, given that that hasn't happened in the last 4.5 billion years (or at least 65 million years, in the case of an asteroid), that it's extremely unlikely to occur tomorrow morning.

In the same vein, I've always liked the phrase "extraordinary claims require extraordinary evidence."

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