Do negative assertions require proof?

Question

A negative proposition is a proposition which asserts what something is not. A negative claimant is someone who makes a negative proposition.

The "burden of proof" is commonly said to be owed by the maker of a positive proposition. Since they are asserting something which is not certain, one can only believe such a thing if an argument is provided, for that thing.

Whereas, the burdeon of proof is often taken to not be necessary, for negative claims which are the default and opposite of an unjustified positive one.

For example, a person claiming, "God exists" has a burden of proof, and a person claiming, "God does not exist", does not. This implies that belief in God is less of a default than absence of belief in God. God's existence would require justification; in its absence, we would by default assume the negative (or the "null hypothesis", that there is nothing to believe).

However, this notion may be paradoxical, because it depends on how you designate what is or is not a "positive claim". For example, if I assert, "Object A does not exist", then while according to the above definition this would be a negative claim, this assertion actually does contain a positive claim; it implies, 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: we must prove the existence of such a supposed world, or otherwise, assume the claim as void.

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

What does this tell us about the idea of a "burden of proof"?

Answer 1

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?

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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.)

Answer 7

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

etc.

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

etc.

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.

Answer 8

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.

Answer 9

"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.

Answer 10

“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.

Answer 11

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.

Answer 12

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.

Answer 13

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.

Answer 14

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.

Answer 15

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?

Answer 16

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.