Proving a Negative: or, Is Hillary Clinton Chinese?

Great Debates
41

Hmmm… I don’t follow, but this is interesting.

In case I’ve been unclear about the topic (which maybe I have, given that Libertarian up to the end was still talking about conditions necessary for proof, when I thought it was clear we were only discussing situations when proof was unavailable)… when I say the question exempts purely theoretical or paper ideas, I mean we’re not concerned w/ conditions necessary to assume the falsity of abstract propositions such as the discussion of sets and axioms Libertarian introduced in the thread’s second post. I intended the OP to consider only assertions made about the real world, such as “Hillary Clinton is American {or Chinese}”, “Bush intentionally misled the public about WMD in Iraq”, “Tiger woods has won more PGA tournaments than any other golfer”, or “I already looked in the hall closet, honey, and I’m telling you it’s not in there”.

I don’t mean that the conditions themselves won’t ever be abstract. In fact, they’d have to be, wouldn’t they, to a certain extent at least?

So with that in mind, I don’t see how I’d be free to assume any conditions I want when dealing with real-world claims. That is, if you’re using the term “conditions” in the same way I’ve been using it. I mean, obviously, the condition “The claim is made by my brother” is not sufficient to assert that the claim is false. By contrast, I do think the condition Libertarian proposed, if even indirectly, that “The claim is false if it violates known fact” holds water.

I also agree with Colibri’s ideas – it’s difficult not to – but they seem to deal rather narrowly with propositions that can be tested and judged against possibilities of random chance.

For instance, if someone says “I believe that leprechauns exist”, it’s hard to see how Colibri’s standards could even apply.

You could apply the principle more generally, but then we’re left with the unsatisfying proposition of accepting that, somehow, by asserting the falsity of the claim “leprechauns are real”, we’re making a leap from “this is highly unlikely” to “this isn’t true” at some very low but still arbitrary level of probability.

Fact is, there is no probability that leprechauns exist, and we come to that conclusion not by observation of the entire world to check and see if they’re there, nor by resorting to classroom logic.

We can safely say that this claim is false (not just highly unlikely) because of certain conditions of rational thought. E.g.:

  1. The origins of the tales of leprechauns are mythic.
  2. The only area in which they were ever asserted to exist has been very thoroughly explored, and no such thing is there.
  3. There has never been any direct evidence that creatures of this sort (not just leprechauns, but fairies, ogres, gnomes, and the like) ever existed.
  4. The existence of leprechauns would require an overhaul of our understanding of the physical world.
  5. The conditions necessary to believe that this is a possibility stretch common sense so far as to be ridiculous.

That’s what I mean by conditions necessary to reject a non-abstract claim in the absence of direct proof to the contrary.

42

My personal policy regarding such statements is to smile and nod, since proving them wrong requires more effort than is justified.

43

Yeah, I’m also with Bippy in nixing that one, but for different reasons. The consequences of being wrong about the claim “My Bible is to the left of my copy of The Silmarillion on the bookshelf, rather than to the right of it” are trivial. That don’t make it false, though.

44

Same here. I’m only using statements like these b/c everyone will agree they’re false (see the PS in the OP).

But what about “There is no god”?

This was one of the questions (as Zagadka alluded to above) that got me started on this. It’s been asserted on SDMB that the existence of God cannot be disproved. Yet I believe that enough conditions pertain so that the existence of a god may be positively rejected as a false idea.

Then there was also the thread asking “Is there objective evidence that the Bible is to be prefered over other scripture?” Seems to me the answer is simply “Nope”. Yet the thread goes on. After all, how can I be sure? Can’t prove a negative, right?

So I thought it’d be interesting, and of some real import, to ask if it could be asserted that there were conditions under which it’s safe to call bullshit on an idea that can’t be directly disproved.

The issue doesn’t seem trivial to me.

45

Uh-huh. [smiles and nods and backs away slowly]

46

Maybe we are heading towards a new concept I might call it ‘False for all intents and purposes’ something that though not provably false has the state that the probability of it being true is so low as to be safely considered zero.
As with all things to do with probability, if you give enough chances for something to happen it becomes likely to happen. So we must also limit the scope of the statement of falseness to ensure the likelyhood of the false statement being wrong to remain close enough to zero to be safely considered zero.

ie the statement ‘No Leprechaun exists on this planet at this time’ would be ‘False for all intents and purposes’ from my perspective.
Since the probability that ‘One or more Leprechaun exists on this planet at this time’ is sufficiently close to zero from my perspective to ignore.

But there is always a subjective element of what is close enough to zero probability to be ignored.
Unfortunately randomness in the quantum state of matter means that anything that is not self conflicting has a non zero probability of existing.
It is a philisophical question as to whether a four sided triangle could exist. But solid quantum physics will give you a probability limit for a 3’ tall green skinned humanoid that talks with an Irish accent spontaneously coming into existing. That probability can be shown to be >0 but also very very small.

This all boils down to the fact that without brute force or other proof of falsehood any statement that a negative is false will need some bounds on the probability you accept that the statement of falsehood is itself wrong.

<BANG!> sorry that was my head exploding.

47

Oh, Bippy! Not you, too!

That’s it, I give up. If everyone here can talk themselves into believing that patently ridiculous statements are somehow remotely possible, then there’s no hope.

At least I learned something.

And by the way, the cat is either dead or alive.

48

There has to be a certain level of arbitrariness involved since you agree that there is no actual proof one way or the other. If there is no proof, it is left to the individual to decide what constitutes enough evidence to make them believe one way or the other. For you, the fact that nobody has ever found a leprechaun, that they are found only in myths, and that nothing even remotely like them has been found, etc, etc, is enough, but that might not be enough for every reasoning/sane person. Thus, I said choose your own conditions.

49

Thingol remember patently obvious was the idea that the sun moves round the earth.

I’m affraid quantum mechanics gives us a mechagnism where you could turn into a Leprechaun. (OK it is debatable whether the Leprechaun could still be you, but …)

The quarks making up your body could rearange themselves into a 3’ tall Leprechaun, and since I guess there would be mass left over a small bag of gold would be possible as well.

It can be shown that this is more likely than you turning into an Elephant (less quarks would need to move) but both have a probability of greater than zero.

Can we ignore the probability of Thingol becoming a Leprechaun? Well we can find the bounds of the probability being discussed and see that the chance of even one of the quarks currently part of Thingol rearanging itself to a position suitable for being a Leprechaun is very small. In fact the probability of a single Thingol to Leprechaun transformation to occur within an imaginary universe full of nothing but Thingols and existing for the entire current age of the real universe is still very very close to zero.

So we can say of the chance that it won’t happen within the visable universe with assurity.
Unfortunately the universe may be bigger than the visible part of the universe by a very very very great amount. If it is true that the Universe is insanely big, then insane things are very likely to be happening in some places in that universe, such a big universe will contain a Thingol who will change into a Leprechaun as soon as they next type a message on a computer message board. Luckily the chance of this happening anywhere near the Bippy typing this is close enough to zero for me to ignore.
Insane things do not have zero probability of existing so long as their existance is not self contradictory
So I can only ever say about something non self-contradictory that it is not going to happen in the visable universe.

For Leprechauns if you only define them as small green men then I wouldn’t like to say categorically that small green men don’t exist in this universe.
If you define them as small green men living on this planet with an Irish accent and a long history. I would say ‘Not in this Universe’
As for Mrs H.Clinton (Chinese) I can only say with certainty enough to please myself ‘Not in this Universe, govener’.

50

Thingol;

I think you would like Karl Popper’s book, “The logic of scientific discovery.” He talks about all this stuff (separating BS from reality) in more detail then you would probably ever want to know. Still leaves some room for uncertaintly though.

FWIW, I don’t have a problem calling a lot of ideas BS. In spite of uncertainty it’s often times it’s pretty clear when the odd are in your favor.

51

If two things are mutually exclusive, then proving one to be true means that the other is false. For instance, I could effectively prove the negative claim “Hillary Rodham Clinton was not born in the People’s Republic of China” by producing solid evidence that she was born somewhere else. She couldn’t have been born in two places at once!

Now, proving that she is not Chinese is a little trickier, as “Chinese” could be defined in various ways. One could apply some sort of one-drop rule to the definition and consider someone “Chinese” if they have any ethnic Chinese ancestry at all. This would not be mutually exclusive with being a blonde American WASP. It’s unlikely, but not completely impossible, that a person who looks like HRC could be descended from the offspring of an unrecorded relationship between, say, a white frontierswoman and a Chinese railway worker. However, if one uses a stricter and more reasonable definition of “Chinese”, it probably wouldn’t be too difficult to show that all of HRC’s recent ancestors weren’t Chinese because they were something else.

52

This doesn’t fit your own original definition of the problem since that proposition can be positively disproved.

This one would make me tweak my proposal, since, if there’s nothing you can do about it the difference between the consequences of being wrong or being right about rejecting the claim as false would be trivial. If there is something you can do about it then the objection is the same as my objection to Thingol’s attempted rebuttal.