Proving a Negative: or, Is Hillary Clinton Chinese?

[Thingol]

I’ll try to pipe down on this thread… I’m interested in what the board has to say.

The question is essentially this:
Under what circumstances is it safe to conclude the falsity of a proposition which cannot be positively disproved?

Examples:

1. I can positively disprove the claim that there’s a grown elephant in my front yard.
2. I’d also say I can positively disprove the claim that there exists a species of elephant which spends its life-cycle inside the bowels of living rodents, without actually having to investigate the world’s rodent population.
3. I can’t positively disprove that a leprechaun exists somewhere, but I’m willing to reject the idea for other reasons.

The reason I ask is that I have seen it proposed on several SDMB threads that one must accept certain propositions as plausible simply because one can’t produce positive proof to the contrary, despite what appears to me sufficient reason to dismiss the claim on other grounds.

I love this board. But I’m almost tempted to believe that if I posted the proposition that Hillary Clinton is actually Chinese, I’d get a debate. “How can you say absolutely? Have you personally investigated the authenticity of her birth certificate? Isn’t it at least possible that her murder was covered up by performing plastic surgery on a body-double who happened to have been born in China, and therefore the person we all now accept as being ‘Hillary Clinton’ is, in fact, Chinese?”

PS: I hope folks don’t get sidetracked by that admittedly frivolous example. I am genuinely interested in the question at top.

[Liberal]

Under what circumstances is it safe to conclude the falsity of a proposition which cannot be positively disproved?

It’s a matter of epistemic scope. If you are unable to examine the entire set, or every element in the set, you are unable to conclude anything general about the set. Therefore, you can prove that there is no pink elephant in your front yard, but you cannot conclude from that information that there is not one anywhere on earth.

Note, however, that that does not stop us from making rather reasonable assumptions and stating them as premises. The Induction Axiom, frex, presumes that every natural number has a successor. But the set of natural numbers is too large to examine, so it cannot be proved.

[Thingol]

@Libertarian

If you are unable to examine the entire set, or every element in the set, you are unable to conclude anything general about the set.

I’d like to propose up front that this logic cannot be accepted for real-world applications. To do so would mean that I have to accept as plausible the notion that leprechauns exist, or that there may be rodents with elephants living in their digestive systems. Yet these are clearly foolish ideas.

[Zagadka]

Well, one element of any debate is defining terms. When you say “anywhere,” do you mean anywhere on this planet, or anywhere in the universe?

For instance, in your not-so-thinly veiled reference to the god debate, one can ask, “on what plane of existence?” If one person is insisting that god has a physical form, and thus, must exist somewhere tangible, and another person is arguing that god is a metaphysical force, these two people will be using two uncomparable forms, and will never see eye-to-eye.

For your leprechaun argument, you have to, first of all, define what a leprechaun is. If you use the word “magical creature” in your description, you have to define what “magical” is. If you simply say, “a little person wearing a green hat,” it is certainly possible that there is a little person wearing a green hat somewhere on the planet - what we popularly term, and what you may thing of, as a leprechaun is not necessarily what a leprechaun is. We see this all the time with words like “race.”

Assumptions are fine, as long as it is understood on what terms the assumptions are made. For your assumption about elephants living in rodents, if you are to state than an elephant is qualified as, “Either of two very large herbivorous mammals, Elephas maximus of south-central Asia or Loxodonta africana,” which is a rather reasonable definition, further define the rodent, then yes, I think it would be a safe assumption to make.

However, making a broader assumption that there are no living creatures living in furry mammals, could easily be waved off.

[ultrafilter]

It is possible to prove a negative by showing that its negation is logically impossible, or by perfect induction (i.e., brute force). Other than that, you’re stuck.

[ultrafilter]

@Libertarian

Note, however, that that does not stop us from making rather reasonable assumptions and stating them as premises. The Induction Axiom, frex, presumes that every natural number has a successor. But the set of natural numbers is too large to examine, so it cannot be proved.

Are you proposing an alternate set theory where the union axiom does not hold?

[Thingol]

Boy am I gonna regret omitting this…

I meant to apply this question to real-world situations exclusively, and not to purely logical, mathematical, or abstract propositions.

For real-world questions, stating a premise and drawing a general conclusion about every member of a group are equivalent notions.

E.g., to say “I accept the premise that elephants can’t live inside rodents” is non-different from saying “Every rodent on the planet has no elephant living in its bowels.”

[Thingol]

@Zagadka

Well, one element of any debate is defining terms. When you say “anywhere,” do you mean anywhere on this planet, or anywhere in the universe?

Zag, please… We’re not actually debating these examples.

And if you wish to propose that leprechauns are real, you’re simply trolling.

Again, here’s the issue:
For non-abstract questions, under what conditions can an idea be safely rejected in the absence of direct proof to the contrary?

[Zagadka]

@Thingol

Zag, please… We’re not actually debating these examples.

You can use examples, but I can’t?

And if you wish to propose that leprechauns are real, you’re simply trolling.

O_o Where did I propose that leprechauns are real? Why are you cherrypicking my posts instead of addressing my points?

Again, here’s the issue:
For non-abstract questions, under what conditions can an idea be safely rejected in the absence of direct proof to the contrary?

As I said, it is dependent on the issue and the definitions at hand. I’m apparently not allowed to use examples, or I would give one.

[John_Mace]

If someone asks you to prove that HRC is not Chinese in an actual debate, they are using a Logic Fallacy called Burden of Proof. “That which is not proved false must be assumed to be true”. It is his/her responsibility to prove that HRC is Chinese, not your responsibility to prove that she is not.

[Captain_Lance_Murdoch]

The burden of proof also applies to the leprechauns. One cannot disprove the existence of leprechauns, but the burden lies on those who propose they are real to prove they are real. Minus that evidence, one cannot claim that he knows leprechauns exist.

The same thing could be said of Big Foot, the Loch Ness Monster or the WMD.

[toadspittle]

@John Mace

If someone asks you to prove that HRC is not Chinese in an actual debate, they are using a Logic Fallacy called Burden of Proof. “That which is not proved false must be assumed to be true”. It is his/her responsibility to prove that HRC is Chinese, not your responsibility to prove that she is not.

Did you even read that link you posted? Both you and Capt. Lance just violated it! The burden of proof fallacy is NOT that “extraordinary claims require extraordinary proof” or that “the burden of proof automatically lies on the person making a positive assertion (i.e., leprechauns exist)”.

The burden of proof fallacy means that NEITHER SIDE is allowed to assert that the burden of proof is on the other side. Re-read your link.

[Liberal]

@Libertarian

It’s a matter of epistemic scope. If you are unable to examine the entire set, or every element in the set, you are unable to conclude anything general about the set. Therefore, you can prove that there is no pink elephant in your front yard, but you cannot conclude from that information that there is not one anywhere on earth.

Note, however, that that does not stop us from making rather reasonable assumptions and stating them as premises. The Induction Axiom, frex, presumes that every natural number has a successor. But the set of natural numbers is too large to examine, so it cannot be proved.

@Thingol

I’d like to propose up front that this logic cannot be accepted for real-world applications. To do so would mean that I have to accept as plausible the notion that leprechauns exist, or that there may be rodents with elephants living in their digestive systems. Yet these are clearly foolish ideas.

As you can see, I did not say that you must accept any notion whatsoever. In fact, I explicitly said that you can conclude nothing general from insufficient observation.

@Libertarian

Note, however, that that does not stop us from making rather reasonable assumptions and stating them as premises. The Induction Axiom, frex, presumes that every natural number has a successor. But the set of natural numbers is too large to examine, so it cannot be proved.

@Ultrafilter

Are you proposing an alternate set theory where the union axiom does not hold?

Do what? That’s a rabbit out of a hat. As you can see, I said that such axioms are reasonable.

[Colibri]

@Thingol

I’d like to propose up front that this logic cannot be accepted for real-world applications. To do so would mean that I have to accept as plausible the notion that leprechauns exist, or that there may be rodents with elephants living in their digestive systems. Yet these are clearly foolish ideas.

The scientific take on this would be that hypotheses in general are not actually proven or disproven, but rather that they have been shown to be probable or improbable to a particular degree.

(The exception would be the “brute force” approach, in which one has examined all possible cases.)

For a scientist, “statistically significant” results are those which have less than a 5% probability of having resulted from chance; “highly significant” results are those which have less than a 1% probability.

It is essentially an arbitrary decision at what level of improbability to consider something to be “implausible” or “impossible.”

(Of course, it is going to be pretty difficult to assign an actual probability figure to the proposition that Hilary is or is not Chinese.)

[John_Mace]

@toadspittle

Did you even read that link you posted? Both you and Capt. Lance just violated it! The burden of proof fallacy is NOT that “extraordinary claims require extraordinary proof” or that “the burden of proof automatically lies on the person making a positive assertion (i.e., leprechauns exist)”.

The burden of proof fallacy means that NEITHER SIDE is allowed to assert that the burden of proof is on the other side. Re-read your link.

I beg to differ. The Burden of Proof is on the guy who makes the claim. By asking you to prove a claim (either negative or positive) without first offering your own proof for your claim, you have shifted the “burden of proof”.

In the OP’s situation, he is talking abouts someone saying: “Prove that HRC is not Chinese”, to which the proper response is : “You must first state your case that HRC is Chinese”.

[Bippy_the_Beardless]

@John Mace

I beg to differ. The Burden of Proof is on the guy who makes the claim. By asking you to prove a claim (either negative or positive) without first offering your own proof for your claim, you have shifted the “burden of proof”.

In the OP’s situation, he is talking abouts someone saying: “Prove that HRC is not Chinese”, to which the proper response is : “You must first state your case that HRC is Chinese”.

But if they do not state a case for HRC being Chinese, it does not follow that HRC is necessarily not Chinese. This is the fallacy.

For instance if I say HRC is American, but then give my proof ‘because I think she looks American’ the weakness of my proof dose not mean that she is not American, only that I have not given you any reason to believe she is American.
It would be a fallacy to claim that my lack of good proof is enough to discount the idea that she may be American.

[Loopydude]

For the Real World, I agree heartily with Colibri and Mr. Mace: Remarkable claims require remarkable evidence, and the best method for approaching such claims is the scientific one. Thusly, you avoid engaging in protracted arguments about frivolous, fatuous, and outlandish subjects; and you also cover your ass by not stating anything absolutely, only so far as one can reasonably conclude.

Using pure logic is great heuristics, but often damn tedious in real life.

[Thingol]

@Bippy the Beardless

if I say HRC is American, but then give my proof ‘because I think she looks American’ the weakness of my proof dose not mean that she is not American, only that I have not given you any reason to believe she is American.
It would be a fallacy to claim that my lack of good proof is enough to discount the idea that she may be American.

Thank you, Bippy!

Do keep in mind that the OP concerns specifically the conditions under which a claim may safely be rejected as false even if direct proof to the contrary is absent.

I am willing to accept ultrafilter’s condition: “showing that its negation is logically impossible”.

However, failure to prove is clearly not a sufficient condition for rejecting a proposition as false.

[John_Mace]

@Bippy the Beardless

But if they do not state a case for HRC being Chinese, it does not follow that HRC is necessarily not Chinese. This is the fallacy.

For instance if I say HRC is American, but then give my proof ‘because I think she looks American’ the weakness of my proof dose not mean that she is not American, only that I have not given you any reason to believe she is American.
It would be a fallacy to claim that my lack of good proof is enough to discount the idea that she may be American.

Exactly. Merely making the statement does not burden the other party with disproving the statement. And offering crappy back-up evidence doesn’t either. One can dismember each piece of evidence and the burden is still on the person making the original statement.

[Ilsa_Lund]

@Thingol

The question is essentially this:
Under what circumstances is it safe to conclude the falsity of a proposition which cannot be positively disproved?

Examples:

1. I can positively disprove the claim that there’s a grown elephant in my front yard.

I have often wondered about this. It would seem that within set parameters, proving a negative would be easy.

I will now prove that there is not an elephant in my lap.

1. Elephants are defined as large mammals with trunks and thick grey skin.
2. My lap is defined as the mid portion of my thighs to my navel.
3. There are not any gray mammals in the vicinity of my navel in my frame of reference.
4. There is not an elephant in my lap.