Does a negative claimant have a burden of proof?



I have often heard it said that the burden of proof is on the positive claimant but not on the one making a negative claim. A person claiming, "God exists" has a burden of proof but not a person claiming, "God does not exist."

If I assert, "Object A does not exist" then this assertion implies a weaker assertion that is a positive claim. Namely, "There exists at least one universe in which Object A does not exist." Since the latter claim is a positive assertion then the burden of proof follows.

All claims of nonexistence can be reformulated into a claim of existence using the trick, "There exists at least one universe in which...."

Thus the burden of proof falls to claims of nonexistence, right?


Posted 2011-07-01T03:49:38.643

Reputation: 609

All claims are positive, regardless. Claim: Meaning "to maintain as true, assert a belief or opinion" is from 1864 ("A common use, regarded by many as inelegant" - Century Dictionary, 1895); claim properly should not stray too far from its true meaning of "to demand recognition of a right."

– Bread – 2018-09-15T22:06:39.517

Claim: Meaning "to maintain as true, assert a belief or opinion"; Assertive: "declaratory, positive..."

– Bread – 2018-09-15T22:33:29.430

7How are you gonna check out that universe? – Raskolnikov – 2011-07-07T17:05:11.910

2+1. I'm pretty sure people who say "the Holocaust did not happen and Auschwitz did not exist" have a burden of proof. – Twilight Sparkle – 2014-04-27T10:05:22.680



I would say that generally, the burden of proof falls on whomever is making a claim, regardless of the positive or negative nature of that claim. It's fairly easy to imagine how any positive claim could be rephrased so as to be a negative one, and it's difficult to imagine that this should reasonably remove the asserter's burden of proof.

Now, the problem lies in the fact that it's often thought to be extremely difficult, if not actually impossible, to prove a negative. It's easy to imagine (in theory) how one would go about proving a positive statement, but things become much more difficult when your task is to prove the absence of something.

But many philosophers and logicians actually disagree with the catchphrase "you can't prove a negative". Steven Hales argues that this is merely a principle of "folk logic", and that a fundamental law of logic, the law of non-contradiction, makes it relatively straightforward to prove a negative.

In practice, I think the truth lies somewhere in the middle. Hales seems to be making the argument that it's possible to assemble a formal logical proof of a negative statement. He doesn't guarantee the possibility of conclusively proving all of the premises of such argument. That is all well and good, but the average person rarely finds formal logic proofs very persuasive. The real problem is that negative claims often make assertions about things that we are in practice either unable to observe altogether, or that are difficult to observe in finite time.

Consider, for example, I make the claim that "there is no intelligent life on other planets". Certainly it seems intuitive that I possess the burden of proof for such a statement. But as discussed, it would be extremely difficult, if not impossible, for me to actually provide a compelling proof of this claim, because it's impossible to conclusively examine the entire contents of this and every other universe, looking for intelligent life (even putting aside such technical issues as what barometer we use to measure "intelligence", or even "life").

Certainly, following Hales's example, I could make the following "logical" argument:

Premise A: If intelligent life were to exist elsewhere in our, or any other, universe, we would be able to make contact with it.

Premise B: We have been unable to make contact with any intelligent life in our, or any other, universe.

Conclusion: Therefore, intelligent life does not exist in our, or any other, universe.

But I guarantee that anyone reading that argument is immediately going to object to the first premise. Some would probably even quibble over the second. In a strictly logical sense, my argument is sound: if the premises hold, then the conclusion follows. But that doesn't mean it will manage to convince very many people. The reality is that because negatively-phrased statements often make such sweeping claims, it's very easy to conceive of potential counter-examples or poke holes in the premises of those proofs.

But I don't think it's accurate to say that the burden of proof falls only on those who claim non-existence, either. Consider that I were to make the argument that Santa Claus exists. Why should the burden of proof be on you to disprove that argument? Certainly in making a claim, I should possess at least a minimal burden of proof to substantiate that claim, right?

So my general rule, and one widely followed in philosophical debates, is that the person who is making a claim always holds the initial burden of proof. Once that claim is made and the burden of proof is overcome, the burden of proof falls to any challengers of that argument, because what is a challenge to an argument but a claim to the contrary?

The way I see it, it's logically disingenuous to allow people to get away with making any type of argument without providing some sort of proof for that claim. For what it's worth, I've never heard the premise that you lead with in your question, and it strikes me as downright specious. A person who claims that "God exists" should have just as much burden of proving that assertion as a person who claims that "God does not exist". Why should I be free to spout nonsense just because I rephrase it as a negative?

Cody Gray

Posted 2011-07-01T03:49:38.643

Reputation: 5 059

I agree that the burden of proof falls on the claimant, If I were to make a claim and they you say no you are wrong you would then have a burden of proof on your own counter claim. – Chad – 2011-07-01T12:57:09.583

I like what Stephen Hales said with regard to folk logic. I have heard the "positive claimaint = burden of proof" claim spouted by researchers of mathematics (not in mathematical logic), lay philosophers and have even seen this spouted on websites of philosophers at minor universities. It has always seemed unsatisfying to me.

I suppose the true question becomes when does the burden of proof exist? Can such a rule be formed or must it be always on a case by case basis?

Thank you for your response. – sykh – 2011-07-01T13:09:00.173

Your answer contradicts several generally accepted premises of philosophy of science. Would you like to expand on in what way for example Karl Poppers "The logic of scientific discovery" in your opinion is wrong? – Lennart Regebro – 2011-07-05T16:42:55.237

@Lennart: No, not really. I haven't read any of Poppers work, so there's no way that I could compare between the two. I don't even know how it is that what I said contradicts that. Feel free to provide that answer, though. – Cody Gray – 2011-07-05T23:57:51.630

1I think that the problem with this answer is that it runs counter to how the concept is deployed in informal logic. If I claim my new drug is know to be safe and the regulatory authority claims that it is not know to be, this answer implies that both I am the regulatory authority have a burden of proof. But, the point of the concept is to articulate that often in the face of such competing claims one side or the other faces the burden or obligation to substantiate their claim. If I claim playing chess cures cancer, it isn't up to you to show it doesn't; it is for me to substantiate my view. – vanden – 2011-07-06T02:44:09.430

@Cody: I did provide that answer. I also downvoted all others, including this, as they simply are incorrect. Seems that the misunderstandings on this topic is greater than I anticipated. :-) – Lennart Regebro – 2011-07-06T05:29:00.817

@YequalsX: "I have heard the 'positive claimant=burden of proof' claim spouted by researchers of mathematics" . As far as math goes, lay, research, applied, or otherwise, I have only ever seen that any claim, positive or negative, requires proof. Negatives seem harder to prove, but that doesn't dispel the need to prove it. Do you have any examples that might show where burden of proof on positive math-like claims are encouraged but not for negative ones? – Mitch – 2011-07-06T13:50:43.500

@Mitch: I'm sorry, they were all incorrect. I wouldn't have done so normally, but the combination of everybody being wrong, and nobody recognizing this required it. Perhaps it could serve as a kick in the butt to get this question up to the level it deserves. – Lennart Regebro – 2011-07-06T14:27:58.960

1@Lennart: I think your answer is wrong, but it earned my upvote since it is a) well reasoned, b) well researched, and c) well written. Good philosophical questions will not likely yield obviously right or wrong answers in my opinion, so the correctness of an answer seems a poor criteria for judging it. – Jon Ericson – 2011-07-06T19:14:08.867

@Jon: Normally you are of course completely correct. In this case though I am of the opinion that there is a correct answer. I feel as such as the answers here mostly cloud the issue, and aren't helpful. – Lennart Regebro – 2011-07-06T21:30:38.097

@Lennart: I rather suspect that if you consult any standard informal logic / critical thinking text, you will see that my answer is pretty orthodox. That doesn't preclude that it is wrong, of course. But, my claim here, if true, surely shifts the burden onto you to defend the claim that the answer is wrong. – vanden – 2011-07-07T05:19:39.127

@Lennart: Negative claims can be proven in certain situations. I can prove there is no largest natural number. – sykh – 2011-07-07T18:12:54.110

@Mitch: What I meant with my comment about mathematicians (I'm a mathematician by the way) was that I've heard it mathematicians say that as a matter or principle only a positive claimant has the burden of proof. Usually this being in the context of belief in God. My contention is that all positive claims imply a negative claim and thus it is absurd to believe that only a positive claimant has the burden of proof in every situation. – sykh – 2011-07-07T18:16:22.097

@vanden: I don't believe that any claimant always has a burden of proof. My contention is that it is incorrect to have a blind rule that only a positive claimant has a burden of proof. I would certainly require a negative claim that I don't exist have proof. I wouldn't require the positive claim that I exist to have proof. Sometime positive claimant should prove the claim, sometimes the negative claimant has the burden of proof. – sykh – 2011-07-07T18:18:15.510

@YequalsX: OK, I see what you're saying. I still don't think mathematicians say that (that the burden of proof is on the positive claimant), but then I agree with you that it is absurd to have the burden rely on positivity. – Mitch – 2011-07-07T20:08:49.940

@YequalsX: This is a good example of why "proving a negative" is a red herring. It is a negative statement, but the claim is a positive one, namely: For every natural number X there exist a natural number X+1. – Lennart Regebro – 2011-07-08T05:10:04.707

7@Lennert: It's interesting that you down vote people who have a different opinion than you. You said you did this because they are wrong. This is interesting because your basis for believing they are wrong is Popper's book. Implicitly you are claiming Popper's book is correct. This is a positive assertion. You haven't demonstrated that Popper's book is correct and contains no flaws in reasoning. – sykh – 2011-07-08T12:41:01.467

@mixedmath: Several of the above comments have stopped discussing the issue, and started discussing me. It also does so by claiming things that are untrue, like saying that I have not provided arguments, or by misrepresenting my position in ways I find directly insulting. I believe all comments starting with and after "It's interesting that you down vote people who have a different opinion than you" should be deleted, as the comments later are nothing but personal attacks on me, and does not belong on this site. – Lennart Regebro – 2011-07-11T06:49:49.363

Yes, the attacks on individuals (rather than ideas) and the interweaving of comments about (down-)voting are unproductive and need to stop. Discussing ideas is perfectly acceptable, but I fear that's not what is happening here anymore. For the record, there is absolutely nothing wrong with Lennart voting down answers for whatever reasons he feels are acceptable. Downvotes are meant to be anonymous, and though he was willing to "fess up" to his downvotes should not be taken as an indication to attack his choice(s) to do so. Folks, I impore you to please stop obsessing over downvotes. – Cody Gray – 2011-07-11T08:10:42.417

My advice is to start a new question if you want to learn more about Popper's thoughts on formal logic. There aren't enough questions asked here on the site as it is. That is a far more productive forum in which to have this discussion than the comment threads. It also keeps things less focused on personal attacks and the decision whether or not to downvote answers. – Cody Gray – 2011-07-11T08:11:44.053

This is a little late in the day, but there seems to be a problem with this approach: what counts as a "claim"? Doesn't this answer suggest that it would be reasonable for me to go through my life believing whatever I want, as long as I never make a "claim" about it? – senderle – 2014-04-30T00:03:15.637


Not necessarily tied to philosophy, but in formal debates the sides agree on a proposition to make arguments about. One side will assert the proposition and assume the burden of proof while the other side will refute the proposition. But the structure of the proposition may be anything the two sides can agree to debate. Using your example, the proposition could be that God exists or that he doesn't. Whichever side takes up the affirmative side assumes the burden of proof.

In practice, it's often useful for the proposition to be one that asserts the existence of God, since a person making that assertion has specific properties and definitions of the concept in mind. Meanwhile, the person rejecting the assertion presumably isn't in a position to propose a definition of God. A similar situation occurs in court trials: the prosecution takes on the burden of proof because it would be impractical for the defense to show the defendant is innocent of all possible crimes. (There are other, very good, reasons for this procedure in addition when it comes to the legal system.)

Notice that while the burden of proof is a powerful advantage in a debate, it isn't decisive. The affirmative position has control over the definition of terms, which is critically important. Suppose, for instance, that Sir Issac Newton were in a debate over his Second Law of motion:

F = ma

If his opponent pointed out that we observe centrifugal force if we rotate a body around an axis. For instance, a bucket full of water will not spill even if it's upside down, but there is no acceleration a opposing the gravitational acceleration.

Since Newton has taken the affirmative side, he is free to argue that a represents both linear and angular acceleration. Usually when we think of acceleration, we mean linear acceleration like what happens when a body is free to fall to Earth or when a body is pushed across a surface. It might seem like Newton is changing the meaning of words, but that's one of the rights of the person making a claim.

Here we touch on Karl Popper's falsification criteria for scientific inquiry (as introduced in Lennart Regebro's answer). Traditionally, science was seen as an application of inductive reasoning. However as David Hume (and others) have pointed out, it isn't possible to show that inductive reasoning is valid without relying on inductive reasoning itself, which begs the question. Popper's solution was to suggest that we should not attempt to pursue inductive solutions to scientific questions, but to propose solutions that are most likely wrong (often because they make very specific predictions) and try to find evidence they are wrong. According to Popper, falsification rather than induction is the goal of science. For this reason, rather than the practical reasons I suggest above, the burden of proof is on the person making positive claim such as "Newton's Second Law holds always and everywhere."

Thomas Kuhn responds directly to Popper in The Structure of Scientific Revolutions:

Clearly, the role thus attributed to falsification is much like the one this essay assigns to anomalous experiences, i.e., to experiences that, by evoking crisis, prepare the way for a new theory. Nevertheless, anomalous experiences may not be identified with falsifying ones. Indeed, I doubt that the later exist. As has repeatedly been emphasized before, no theory ever solves all the puzzles with which it is confronted at a given time; nor are the solutions already achieved often perfect. On the contrary, it is just the incompleteness and imperfection of the existing data-theory fit that, at any given time, define many of the puzzles that characterize normal science. If any and every failure to fit were ground for theory rejection, all theories ought to be rejected at all times.

In summary, there's no reason to say that the "negative" side of an argument does not have a burden of proof, but in practice propositions are usually formulated in a "positive" mode in order to narrow the scope of a debate. But other times a negative proposition may be necessary. For instance, in a parole hearing the burden of proof is reversed from the trial rules: it's necessary to prove to some level of burden that the prisoner will not violate their parole if released. In a philosophical debate, it's likely the burden of proof would fall on the person claiming that the material world does not exist, but is an illusion.

Jon Ericson

Posted 2011-07-01T03:49:38.643

Reputation: 6 843


The heuristic that the burden of proof is on the affirmative side of a dispute is intended to be broader than just claims of existence and non-existence. It is also one of a number of different (sometimes conflicting) considerations that go into the determination of the burden of proof. I said 'heuristic' as there is no algorithmic way to determine where the burden of proof lies.

Imagine that we observed some phenomenon for which cannot account, say the diminished bee populations. Were I to suggest that the population decline was caused by cell phone transmissions, you might well accept that this is the sort of thing which could conceivably be involved but might still reasonably demand to know why I think this. 'Well, why do you think it isn't cell phone transmissions?' would be a wholly inappropriate reply on my part. As I am offering the positive account, all else being equal, the burden is on me to establish that my account is correct, not upon you to impeach it.

Another consideration is initial plausibility. Say that we were to arrive at my apartment and observe that the door frame was splintered, the door was open, all my electronics and other portable valuables were gone. You offer the theory that I have been robbed; I offer the theory that a highly localized meteorological phenomenon tore through my apartment. We both are offering affirmative claims, but since yours is quite plausible and mine is not at all plausible, the burden is on me rather than on you. Indeed, we would reasonably take the inability of proponents to mount a serious case for alternative explanations to count as a reason to accept your account.

Neither of these are fool-proof. One can often reformulate a claim to change whether it seems affirmative or negative (often with a transformation that seems less like a cheap trick than the one your offer). And, erroneous beliefs will adversely affect the extent to which our judgments of plausibility are reliable. (It takes a fair bit of knowledge of 20th c. science to find it plausible that the chair on which I sit is made mainly of empty space.)

Some conflict between these two considerations can help explain why "all else being equal" is needed. If you have the view that dogs exist and I've the view that they do not, the fact that your claim is affirmative hardly means that the burden of proof is on you; my claim is so implausible that that implausibility swamps the affirmative nature of your claim for purposes of finding where the burden of proof lies.

A third consideration is the costs of error on each side. Consider two drugs developed by pharmaceutical firms, one intended to help with acne, the other to help patients with advance terminal cancer. The burden of proof to establish safety of the drugs is higher on the firm that developed the acne medication than it is on the firm with the drug targeting the cancer patient as the cost of error in the acne case is much higher.


Posted 2011-07-01T03:49:38.643

Reputation: 1 614

I like the initial plausibility angle. In the case of "god exists" and "god does not exist" we see that this is in the eye of the beholder. I suppose this is as good an explanation behind the endless debates people have on this topic as any. It also explains why people are so intractable in their beliefs on theological matters. – sykh – 2011-07-01T13:31:02.713

On re-reading it, I agree that your answer is not incorrect. I will withdraw the -1 if you make an edit so I can. :-) – Lennart Regebro – 2011-07-07T06:44:22.113


All claimants have a burden of proof. If I were to make claim that the earth is round I would have a burden to provide proof at least if asked. In physics we spent several weeks confirming the laws of motion experimentally. When we are taught about the laws of motion it is backed up with centuries of experimental data and confirmation.

The only claims that do not necessarily require a burden of proof are claims of opinion, "BBQ sauce tastes better on burgers than A1." While arguementitive it is clearly a statement of opinion even though it is not worded as such. However a statement of "Many people prefer the taste of BBQ sauce to A1 on their burgers" may fall in a grey area. It is a statement of opinion but it has a indefinate amount of quantification. Any demand of proof is expected to have a reasonable allowance. It is concievable that there are people who prefer condiment sauce to another. However if the statement were more specific with words like Most, or a specific percentage then there would be a burden of proof to show a study or studies that agree with the statement.

As for religion. There is a burden of proof here. The priest says I can not prove god. I can educate you to his teachings, I can provide counsel to you in your times of need. I offer you a promise of eternal life for believing. So while there is a burden of proof on the theologian you can choose not to require it. Or you can choose not to accept it. This is the case with all claims. You can accept "Global Warming" but that does not absolve the claimants burden of proof to anyone else other than you.


Posted 2011-07-01T03:49:38.643

Reputation: 1 512

I agree that claiming a nonexistance should require a proof and that you shouldn't need to find a counterexample for something that was not proven and only stated. – Niklas R. – 2011-08-17T04:07:24.883


I think Cody's answer is absolutely correct (which is not to say that other answers are incorrect). To come at this from a different perspective, consider the negative claim:

No two people share the same fingerprint.

This is a generally accepted piece of wisdom, but it has not been proven to be true. Quite the contrary, there are several scientists who doubt the veracity of this claim.

To disprove this claim, all one has to do is find two people with the same fingerprint. To prove it, however, one has to take biometric information of everyone in the world (which might eventually happen, mostly), but even then once someone new is born (about 4.5 per second, currently), the claim must be proven all over again.

Now, consider using your trick. Instead of asking them to prove the negative above, you ask them to prove that

There exists at least one person who doesn't have the same fingerprint as anyone else in the world.

On its face, that initially sounds like an easier task, and it is–slightly. Instead of doing n * (n - 1) comparisons (where n is approaching 7 billion), one merely has to do n - 1 comparisons. However, one still must do n measurements, of course. Even in this case (as with yours) there exists a more positive version of this:

This person has the same fingerprint as that person.

That claim is comparatively easy to prove. (Assuming one doesn't go down certain bunny holes.)

Ben Hocking

Posted 2011-07-01T03:49:38.643

Reputation: 1 022

1Actually Ben just because it is un provable does not mean that you do not have a burden of proof if you make the claim. As far as the fingerprint thing goes, the idea is that one or more fingerprints are found at the scene of a crime. The more of them that match you that are found and if you have opportunity to be at the scene the greater the likelyhood that you were there. There are partials found that kind of match other people quite regularly. A quick search of the justice project will turn up people who were wrongly convicted with partial fingerprints. – Chad – 2011-07-05T20:28:47.803

@Chad: In acknowledging Cody's answer as being correct, I was tacitly agreeing with Cody's point that your first sentence echos. Of course the person making the first claim has a certain burden of proof. In court cases, such as you mention, the burden of proof is "beyond a reasonable doubt" (which is actually less rigorous than a mathematical proof). My point was that it is much easier to disprove it conclusively than to prove it conclusively. And, as the links I provided suggest (as well as your examples), we've come quite a good distance towards disproving it, if not there already. – Ben Hocking – 2011-07-06T12:20:31.050


I don't think the burden of proof is on positive or negative versions. I think it is with respect to the existing claims. If you are in a society that is generally atheistic, then the burden of proof is on claims that there is at least one god (of course it goes both ways, that is why it is appropriate for the burden of proof to be placed on atheists in a god-believing society).

The difficulty sometimes is in figuring out what the socially acceptable norms. Skepticism is a trend contrary to this which is to take the burden of proving any side (putting doubt on an accepted claims).

Also, sometimes there is no clear standard, say with a new concept which may have alternatives. Whichever direction, it is the new statement which needs to have energy spent on justification.


Posted 2011-07-01T03:49:38.643

Reputation: 3 173

3I think I agree mostly with where your answer is going here. But a persuasive argument could certainly be made that just because your claim is one consistent with common societal beliefs does not actually mitigate your burden of proof as the claimant. Rather, it merely implies that the proof can be minimal or elided for convenience in most cases, as the people to whom you are speaking will infer their own proofs. – Cody Gray – 2011-07-02T04:53:40.700

1It would certainly be reasonable for someone who did not adhere to the community norms to press you to warrant your argument on the basis that, as the claimant, you hadn't met your burden of proof. That is to say, it's not their duty to insert or imply their own justification(s). The burden of proof is not necessarily shifted entirely to your opponent. – Cody Gray – 2011-07-02T04:54:38.627

If I understand you aright, you're effectively saying the burden of proof lies with the claimant in all cases except where the claim is one which is generally accepted to be true (or would be, if it were publicised). Thus The moon is made of milk requires proof, whereas The moon is NOT made of milk doesn't require such (I hope!). – FumbleFingers – 2011-07-02T23:01:22.037

@FumbleFingers: I'd have to say yes to that (though it sounds like a setup to a 'gotcha' (which of course may be appropriate)). This burden of proof' method ('you only need to prove/argue claims that aren't already generally accepted') leads to confirmation bias, which skepticism attempts to dispel. – Mitch – 2011-07-04T21:56:35.080

No it wasn't a setup, though I see where you're coming from. In some hypothetical fairyland maybe The moon is NOT made of green cheese might be said to attract the burden of proof. All I'm saying is that if there are two opposing arguments, and if one of them is overwhelmingly accepted as true by those we might suppose to be experts in the matter, the burden of proof quite rightly lies with whoever is championing the minority position. The possibility of confirmation bias on the part of the majority could legitimately form part of his argument. – FumbleFingers – 2011-07-04T22:42:03.590

@FumbleFingers: Yes, that is exactly it, and why skepticism is sometimes welcome to get at the truth (which is to say, this 'social constructivist' version of responsibility of burden of proof isn't necessarily truth-preserving or even truth-interested. But ti keeps people happy. – Mitch – 2011-07-04T22:58:09.280

Looking at many of the questions asked on, I'm increasingly thinking all this hoohah about 'social constructivism' isn't going to advance the sum of human knowledge much either. But as you imply, ti keeps us/them off the streets! :) – FumbleFingers – 2011-07-04T23:26:18.433

@FumbleFingers: I think social constructivism is more of a descriptive theory of epistemology rather than normative. That is, it is beng more honest about how things work rathe than trying to get people to do it that way. It's not 'anything goes', and it allows progress just not exactly in the classical pattern. – Mitch – 2011-07-06T13:17:47.617

I think I understand that. I just meant that insofar as sites like wikipedia and are manifestations of 'popular social constructivism', I'm not sure we actually advance the totality of 'things known'. We just (hopefully) spread the already known things more widely. – FumbleFingers – 2011-07-06T15:00:40.973

@Cody: so you're saying that, in a rewording of my answer, the burden of proof is on everybody, but the current socially accepted claim can have its proof minimized, referred to, or elided altogether? But (to go into word play) that sounds to me like a mitigation or lessening or even removal of the burden. A reasonable oversimplification of that would be that the new claimant is the one with the burden of proof (or to weaken it, much more of a burden). Does that sound right? – Mitch – 2011-07-07T14:10:06.340

Well, I disagree with the restatement or oversimplification, but Lennart's comments have made me question whether I really know enough about this to provide the correct answer. Most of my understanding of logic comes more from a philosophy of debate perspective than a philosophy of science. – Cody Gray – 2011-07-08T05:47:06.980


The problem is that negative claims that are only provable by enumeration in a (quasi-) infinite solution space are impossible to prove. What I mean here are claims that require proofs like the following: "Inspect everything in the universe, compare each object with God, decide if one was found".

Other classes of negative claims (I'm not sure if these apply to your question) may have proofs, e.g., by reductio ad absurdum.


Posted 2011-07-01T03:49:38.643

Reputation: 31


Proving a "negative" is a red herring, as the claim "X is a red" also means "X is not blue", which is a negative. Also, factual claims are completely different from theoretical claims.

In the question itself you refer to existence and non-existence, and since existence can be proven (while non-existence can not), the burden of proof is on existence. This can be extended to positive factual claims in general, as they can be proven. Therefore the burden of proof lies one the one who is making a factual claim, like:

  • Aliens are intensely interested in our behinds.
  • Black swans exist
  • Homeopathy works
  • A majority of people in the US want universal/public/whatever health care
  • The moon is made of rock
  • The continents are moving


However when it comes to explanations of the facts by making theoretical claims on how these facts fit together, these can never be proven. This is because theories by necessity are a type of induction. But the problem with induction is that it doesn't lead to knowledge. You can not from a set of facts (which are all about the past or present) induce anything about the future (which is what the explanatory theories do).

Karl Poppers famous solution to this is "falsification", i e that theories does not need to be proven, they need to be falsified. Therefore the burden of proof in these cases rest on the person who claims they are false. This concerns things like:

  • Capitalism causes poverty
  • The diversity of life is an effect of speciation by evolution
  • Mountain ranges are created when continents crash together very slowly
  • The earth is flat, it just looks round because of optical illusions
  • It is impossible to go faster than the speed of light


The proving here can be either to show that the facts or assumptions in the theory is wrong, or that the logic doesn't work, or most commonly, by coming up with a better theory. "Better" generally means either more accurate or simpler, with less assumptions (like Ockhams razor).

The original posts "there exists at least one universe where A does not exist" is a claim of existence, so in that case, you have to prove that this universe exists. However, it is not as you say a claim of non-existence, because it allows A to exist in other universes. Therefore it is not a reformulation of the negative claim. The negative claim is either "There exists NO universe where A exists", or just "A does not exist in this universe". Both interpretations of "A does not exist" are reasonable and in practice equal, as we can't know anything about other universes.

Lennart Regebro

Posted 2011-07-01T03:49:38.643

Reputation: 3 378

"majority of people in the US want health care" -- did you meant to add 'universal' (or 'affordable') here? Presumably most of us do want some healthcare at some point :) – Joseph Weissman – 2011-07-01T12:17:58.017

I was not making the argument that <b>"there exists at least one universe where A does not exist"</b> is a claim of non-existence. I'm claiming that the bold statement above is implied by the statement <b>"A does not exist"</b>. That is, a nonexistence claim always implies an existence claim. – sykh – 2011-07-01T13:22:45.793

-1 for your "Facts" these are conclusions of science of or some pseudo science. Something like laws of motion have been proven over time and accepted as laws. Even the theory of evolution has new claims supporting this. You do not hear about new claims about the laws of motion because they have been accepted as true. I will give you a +1 if you want to change the "Facts" to actual factual examples like the sky appears blue because of defraction of light... etc. – Chad – 2011-07-01T13:37:38.253

@Chad: The facts are intentionally half correct, half incorrect. Geez, man. The laws of motion are not facts, they are theories. So is your "the sky appears blue because of defraction of light". That is not a fact, it is a theory. "A clear sky is blue", that is a fact. So as usual, you have everything completely backwards. – Lennart Regebro – 2011-07-01T13:53:27.700

1@Joseph: Hah! Yeah, I did mean universal health care. Not that it matters, the point is it is a factual claim that can be proven by asking them. :-) – Lennart Regebro – 2011-07-01T13:54:35.030

@YeqalsX: Same thing. All you are really saying is that the claim "A does not exist" implies the existance of non-existance, which is true, but changes nothing. You still can't prove it. – Lennart Regebro – 2011-07-01T13:57:00.037

@lennart - If i were to claim that "Capitolism Causes Poverty" is false then yes i would have a burden of proof. But that does not absolve you of your burden of proof to show that it does. And a clear sky appears blue because of light defraction... It is actually colorless. – Chad – 2011-07-01T14:09:12.543

@Lennart: Since I have not stated what A is then how can you conclude that I "can't prove it"? There are people who believe that a positive claimant has the burden of proof but not a negative claimant. Since a negative claim always implies a positive claim then this reasoning is flawed. Well, in my opinion it is flawed. I was wondering what experts or others thought about this. – sykh – 2011-07-01T14:45:51.697

@YequalsX: Because you can't prove non-existance. It's a fundamental fact of science. @Chad: No, you are confused. @both of you: Read the book I linked to. Really. This is not a trivial issue I won't be able to explain it in a comment. The book is very good (but far from a light read).

– Lennart Regebro – 2011-07-01T22:25:30.473

1@Lennart: I think it is possible to prove that there isn't a blackhole in the center of the Earth large enough, right now, to devour the planet. Non-existance can be proven in some cases. – sykh – 2011-07-02T02:00:08.950

1@Lennart: Your arguement boils down to : 'If someone else does the work to show something I have no burden to show any proof at all.' I strongly reject this notion. At a bare minimum you have the burden to show this work as your support. – Chad – 2011-07-05T13:25:50.807

@Chad: No, that has absolutely no resemblance to anything I have said at all, ever. Neither would I never say anything so fundamentally daft. – Lennart Regebro – 2011-07-05T16:34:42.950

@YequalsX: That is not a claim of non-existence. A claim of non-existence would be "there are no black holes". Your claim is "the center of the earth consists of something else than a black hole". Honestly, read the book. It's good. – Lennart Regebro – 2011-07-05T16:38:15.630

@Lennart that is exactly how I read what you are saying. – Chad – 2011-07-05T16:42:21.853

@Chad: Yeah, well read it again, more carefully. There is no way what I said can be interpreted in that way if you actually read it. Of course I can be unclear too, but not THAT unclear. We can have another chat session again to figure out what your fundamental misunderstand is this time, but since the last ended up with you refusing to talk to me, I doubt its usefulness. – Lennart Regebro – 2011-07-05T16:47:10.303

1I guess I'm another one of those people who doesn't understand. First, I'm not entirely clear on how your answer contradicts what mine says. Second, I'm not sure that I understand intuitively why the claimant who says "Capitalism causes poverty" would not possess the burden of proof. You say that this statement concerns merely an "explanation of the facts", which "can never be proven", but your answer doesn't explain why that's the case. If you made the claim that capitalism causes poverty I would certainly expect you to go on to prove that, and argue you hadn't met your burden otherwise. – Cody Gray – 2011-07-06T09:08:54.607

@Cody: OK, I need to improve the explanation of why, apparently. I didn't make that much of an effort to do so, as the question was who had the burden of proof, not why. :-) It is basically a result of the problem of induction. There is no way you can induce that just because gravity seems to be 9.81m/s2, there is no way you can prove that to be true all the time, everywhere.

– Lennart Regebro – 2011-07-06T10:51:12.373

@Cody: OK, updated. – Lennart Regebro – 2011-07-06T11:36:12.257

How would you respond to criticisms such as Thomas Kuhn's that falsifying data is usually explained away or ignored until the evidence becomes overwhelming and causes scientific revolution? A key quote from The Structure of Scientific Revolutions: "On the contrary, it is just the incompleteness and imperfection of the existing data-theory fit that, at any given time, define many of the puzzles that characterize normal science. If any and every failure to fit were ground for theory rejection, all theories ought to be rejected at all times." – Jon Ericson – 2011-07-06T18:04:53.027

@Jon: Kuhn misunderstands Popper completely. Popper talks about the problems of knowlesge and how science should be done as a result of this. Kuhn's criticism basically boils down to "But that's not how it actually is done", which of course is completely besides the point. – Lennart Regebro – 2011-07-06T21:33:45.410

One could argue that the best way to study science is to use the scientific method itself. More difficult, it's hard to see how Popper's theory itself could be falsified if "how science is actually done" is beside the point. But I see you are a Popper man as I am a Kuhn man, so I will let the point drop. – Jon Ericson – 2011-07-06T22:29:44.537

@JonEricson: I think your Kuhn quote is a very good one and perhaps deserves to stand alone as an answer. As these comments are now far longer than the answer itself, there is clearly additional information to be given. – davidlowryduda – 2011-07-07T03:35:36.797

4The claim that one cannot prove a negative is a harmful falsehood. Here are some things that I can prove: there is no largest prime, there is no recursive procedure to decide whether a give first-order logic sentence is a logical truth, there are no Ojibway words in this comment, there is no detectable unicorn standing on my head, there is no married bachelor, there is no hope of making progress on these issues until, in the face of such examples, we abandon the canard that one cannot prove a negative. (That last one is perhaps exaggerated.) – vanden – 2011-07-07T05:34:15.490

@vanden: Which is why I said non-existence not "negative". And no, you can not prove that there is no detectable unicorn on your head. You can only fail to detect it. – Lennart Regebro – 2011-07-07T06:29:12.080

@vanden: Clarified this in the answer. – Lennart Regebro – 2011-07-07T06:34:55.460

1@Lennart: The changes help, but several of the items on my list are both non-controversially provable and claims of non-existence (e.g., there exists no recursive procedure ...) The unicorn example, with its inclusion of "detectable" runs the risk of triviality, but also because of that inclusion can be defended as provable. However, I do concede that the view that, despite that inclusion, the claim is not provable isn't without merit, either. – vanden – 2011-07-07T14:59:38.260

Rather than: '"X is a red" also means "X is not blue"', it would be better to say: '"X is red" also implies "X is not blue"'. Proving "X is not blue" does not prove "X is red". – Jon Ericson – 2011-07-07T17:28:01.943

2@Lennert: A statement of the form: "There does not exist...." is a claim of nonexistence. Saying: "There does not exist a black hole in the center of the Earth large to destroy the planet in the next 10 seconds" is a claim of nonexistence. – sykh – 2011-07-07T18:12:09.447

@YeualsX: No it's not a claim of non-existence. It claims the center of the earth exists, and is made up of something. It is as much a claim of non-existence as saying "My cat is not a dog". – Lennart Regebro – 2011-07-08T05:13:34.593

@vanden: First of all, mathematics is purely abstract and can, as all systems like this, only be provable within itself. You can't prove mathematics at all. Hence you can not prove any mathematical statement. And secondly, no, the unicorn example is not provable. See above. – Lennart Regebro – 2011-07-08T05:17:45.683

@Lennart: Well, I really don't know how to respond to that. It is unclear to me that you are using the word 'prove' in a manner in keeping with its meaning in English. – vanden – 2011-07-08T05:27:20.570

@vanden: Hah. I definitely use the word prove in exactly the same way as you and everyone else. About the provability of maths, see

– Lennart Regebro – 2011-07-08T07:09:20.283

@Lennert: Any statement of the form, "A exists" implies a negative assertion. Similarly any statement of the form "A does not exist" implies a positive assertion. All you have done is reformulate the statement I've made. That's great but the original claim is a claim of nonexistence. And it is easily provable that there is no black hole in the center of the Earth large enough to consume the planet in the next 10 seconds. Reformulate it all you want. All claim can be reformulated. It's still a claim of nonexistence. – sykh – 2011-07-08T12:36:15.543

@Lennert: I am afraid that you do not. If one says "you cannot prove any mathematical statement," then language has gone on holiday. You appear to be citing Gödel's Incompleteness Theorems as demonstrating that mathematical claims cannot be proved. This is perhaps the most bizarre misunderstanding of Gödel's results that I have encountered. They are results in mathematics that Gödel proved that show the non-existence of formal systems with certain desirable properties. If wikipedia supports your claim, shame on it. Try

– vanden – 2011-07-08T13:54:29.330

@Lennert: Godel proved that no recursively enumerable set of axioms was strong enough to prove all true statements about the natural numbers. But the second order Peano axioms are strong enough to prove all true statements about the natural numbers. Of course the second order system is not recursively enumerable though. Mathematical statements can be proven. As vanden mentioned, Godel proved his famous result. Thus there is at least one proof of a mathematical statement. – sykh – 2011-07-08T22:08:37.383

@YequalsX, @vanden: I'm sorry, but the fact (hehe) is that mathematics is all theory, and none of it can be proven without first assuming several mathematical axioms. It is as such not fact in the same sense that "I have an apple in my hand" is a fact. Sorry. You all both talk about proofs within the mathematical framework, which is an abstract theoretical framework, not fact. – Lennart Regebro – 2011-07-09T06:05:11.687

@Lennart - This is what I mean by your logic and my logic disagree. Mathmatics is a series of rules. These rules bear scrutiny of the ages. IE A+B=B+A, (a + b)c=ac+bc... These are known as properties of mathmatics. They are not theory they are rules. Using these rules we can further prove other rules. These are not theories they are mathamatical fact. Science has theories because they have not been proven. Once they have been proven they are referred to as laws because they always prove true. This is the accepted logic. – Chad – 2011-07-10T23:36:42.863

1@Lennart Continued - In theory you have an apple in your hand. Because it appears to be an apple, and it came from the branch of a tree that has provided a certian unknown number of apples previously and has never produced anything other than apples. However what if this time it is infact a pear. They are similar in that they are both basically rounded objects from trees. In order for you to say that you have an apple in your hand is a fact you must first prove that it is an apple. Once you have proven it then it becomes a fact. – Chad – 2011-07-10T23:40:42.563

@Chad: I'm not saying mathematics is wrong. I'm saying it is not factual, but a theory. Your argument about apples/pear is completely correct, and supports my standpoint. When claiming that the object I claim is an apple in fact is a pear, you acknowledge the objects existence. QED. – Lennart Regebro – 2011-07-11T06:44:12.710

Math is not theory nor is it factual. Math is a set of rules that relate to numeric values. It is a method of proving fact but not itself theory or fact. There are mathmatical theorys, in that they have not been proven. However once proven they become another rule as opposed to a fact. – Chad – 2011-07-11T10:24:49.883

@Chad: We agree it's not facts, and that means my standpoint holds. Also please note that "Theory" does not mean "Not proven". A theory can be proven, it is still a theory.

– Lennart Regebro – 2011-07-12T07:36:14.383


“Proof sketch“ is: assume that something exists, deduce a contradiction and you've proven a non-existence.

So I agree that non-existence can be proven: e.g., "There is no possibility that the statement A is false"; statement A is: "Paris is the capital of France". We can assume there is a possibility that the statement A is false and soon we find that the negation is true and a logical consequence. You just use existence elimination.

Assume ∃x, derive a contradiction and you're done. It leads to the conclusion ¬∃x(¬P(A)), which is a negation that there exists an x such that there is no probability for A; since assuming ∃x(¬P(A)) leads to a contradiction that P(A) could be false. When checking with reality, the simple fact that Paris is the capital of France logically rules out all other cases.

Hence: All other cases have been proven non-existent and non-existence (¬∃x) has been proven.

Niklas R.

Posted 2011-07-01T03:49:38.643

Reputation: 570


"Burden" is an artificial construct: a notion of a social responsibility. It's tautological that demonstration of a claim's truth requires there to be a demonstration - but if someone is fine with making assertions sans justification or support then they are free to do so. The only issue is that others are likewise free to dismiss or ignore such assertions - and of course people are free to dismiss and ignore well-established assertions just as well, but then are they being rational? It all boils down to this: in a civil, meaningful discussion where participants seek to understand each other and make advances towards greater truth, there is a need for constructive input, otherwise people are not participating in the spirit of the discussion. So when openness and transparency are community standards, there is indeed a burden of making available the resources for better gauging an idea's plausibility or credibility.


Posted 2011-07-01T03:49:38.643

Reputation: 269

The 'burden' is artificial if establishing some kind of truth is. In a civil, meaningful discussion, there is trust, but of what? That work (a burden) has been done. – Mitch – 2011-08-26T02:57:15.037


A burden of proof falls under the auspices of speech acts. Anyone disrupting a conversation by bringing disagreement to it has an obligation to make things right, as it were, and explain one's self. It is completely a social construct. This is the principle of "onus probandi", be the application in general conversation or in a legal setting.

A burden of justification befalls all beliefs that anyone has that can at least in theory be justified. It is what rational people do; it is not a construct. That the content of some proposition may be expressed negatively is irrelevant. One's belief or doubt in the verity of such propositions is what is being justified, not the proposition itself. It would then be absurd to suggest that "I am justified to believe 'there are no elves' because I cannot justify the proposition 'there are no elves'." Obviously, we are justified to believe there are no elves given facts of the matter into which no elf appears. (See negative facts and justification: B. Russell, On Propositions, pg 5-6, 25, 39-40)

With your example, one is justified to believe "There are no deity" just in case deity are defined as transcendent. This is axiomatically true, true by definition. Such deity exist outside of our measurable experience. Reality is a term denoting all that is within our measurable experience. To exist is to be "real"; "manifesting in reality". Hence, deity do not "manifest in reality" and then do not "exist". A second justification is that deity manifest in the same way as "nothing" and then any other sense applied to "God" and "exists" is irrelevant and incoherent. Third, given what folks claim about deity, we can via experience (formally, "enumeration") empirically determine that no such deity exist.

Just a couple of thoughts.

Steven Hoyt

Posted 2011-07-01T03:49:38.643

Reputation: 133


1) The burden of proof is borne by whoever makes the claim that is easiest to prove.

Absolute non existence of something is impossible to prove, but please notice how your rephrasing into :

"There exists at least one universe in which Object A does not exist."

also narrowed the conditions. If you were to narrow it further into:

"A glass of water does not exist on this table."

then this negative claim could easily be proved.

2) In case (1) is disputed, Occam's Razor can be used. And Occam's razor tends to favor the non existence of things as it makes the world simpler.

Manu de Hanoi

Posted 2011-07-01T03:49:38.643

Reputation: 394


Beware of any claimant that can not do the following:

Bob says "There is at least one dog on planet earth."

Larry says "Prove it."

Bob shows him a dog and says "HA! HA! I win!"

Contrast this with the following claim.

Bob says "There is at least one man over 100 feet tall on planet earth."

Larry politely says "Prove it."

Bob says "Theories can never be confirmed, only falsified. FALSIFY IT! Prove there is not a man over 100 feet tall on planet earth!"

It is as simple as this. Every single thing you can not see, touch, hear, taste, smell, or assign mathematical quantification to does not exist UNTIL you can do so. The emotions you feel do not exist until we develop a ruler to measure them with.

Negative existential claims such as "There are no black swans." can only be falsified, not confirmed.

Positive existential claims such as "There are black swans." can only be confirmed, not falsified.

Abercrombie Dorfen

Posted 2011-07-01T03:49:38.643

Reputation: 174


Not all negative claims can be validly reformulated into positive claims. To reformulate a negative claim about god's lack of existence into a positive claim about a universe in which god does not exist, you need meaningfulness, else the conversion fails.

The positive claim about god's existence roughly claims that there exists something in the universe that corresponds to that person's concept of god, outside just the concept itself. The negative claim about god's nonexistence roughly claims that the person has no such concept that is capable of corresponding to anything outside the concept itself. No matter how you convert it, it still is at root that the person has no concept that is capable of corresponding.

So while some negative claims can be converted into positive claims, negative claims based on non-conceptuality cannot be converted. They are fundamentally negative claims. The burden is always on the person who wants to employ a concept to give that concept content and you cannot formulate a positive claim without a well-defined concept.

To put it simply, fundamentally, any positive claim about god requires a well-defined concept of god. A purely negative claim does not ('my concept of god is incapable of denoting anything that exists'). So you cannot convert a pure negative claim into a positive one.

David Schwartz

Posted 2011-07-01T03:49:38.643

Reputation: 1 010


To demand that someone prove a negative statement is always irrational! Why? Because if somebody says "X does not exist?" he/she is saying "I know of no reason to even suspect in the least that X exists". So what are you going to say to the person who says that? Surely not "Prove that you don't know of any reason to suspect that X exists"!! What could be more irrational than "Prove that you don't know something that I know!" or "Prove that you are ignorant of something". What could be stupider?


Posted 2011-07-01T03:49:38.643

Reputation: 61

A negative claim is "X does not exist". All that is saying is "I know of no reason to believe that X exists". So to say he has a burden of proof, you are demanding that he prove that he is ignorant of any reason to believe that X exists! So it is always irrational to demand that a negative claimant prove that he is ignorant of any reason to believe something. You just cannot rationally say to somebody "Prove your ignorance!". – user8159 – 2017-11-30T19:37:36.167


Answering to the claim: "I have often heard it said that the burden of proof is on the positive claimant but not on the one making a negative claim. A person claiming, "God exists" has a burden of proof but not a person claiming, "God does not exist.""

It has nothing to do with making a positive vs. a negative claim.

The first claim "God exists" is not falsifiable. It is impossible to prove "god does not exist", because whatever proof you find, one could claim that you only found that proof because an almighty god wanted you to find it. "God does not exist" is falsifiable. If there was a god, and it decided to prove me wrong, that should be an easy thing to do (hasn't happened yet, though).

Not being falsifiable makes a claim not only unscientific, it makes it quite pointless.


Posted 2011-07-01T03:49:38.643

Reputation: 3 297

I would reject the last sentence. You cannot prove to me that you're not a lying scoundrel (i.e. it is not falsifiable), but it's pretty purposeful that you have others believe you're not. – virmaior – 2014-07-05T01:12:09.753

Actually, I don't care what you think. But what you state is indeed falsifiable (and insulting) unless you take a very strange definition of "lying scoundrel". – gnasher729 – 2014-07-08T16:10:10.663

1Your feeling insulted helps prove my point (though I'm sorry you're taking it personally. It's hard to judge what if any background someone has in philosophy). Even though you "don't care what [I] think", I'll explain anyway. You can't falsify the claim, because I can ignore everything you say on the basis of my premise. But it surely (and you demonstrate this is so) matters to you (meaning it is not pointless) whether this claim is true. – virmaior – 2014-07-08T23:28:42.620