Can You Prove a Negative Statement?

[zoobyshoe]

~P -> Q
~Q
~(~P)

or

P -> Q
~Q
~P

or

P -> ~Q
P
~Q

Incidentally, is this the origin of the admonition: "Mind your P's and Q's."

 

[NeoDevin]

Incidentally, is this the origin of the admonition: "Mind your P's and Q's."

http://www.phrases.org.uk/meanings/248000.html"

 

[superwolf]

Can one prove anything at all? Isn't it all a matter of finding probabilities?

 

[superwolf]

So I cannot prove that 5 does not equal 4?

 

[zoobyshoe]

http://www.phrases.org.uk/meanings/248000.html"

A mystery. Interesting.

 

[Gokul43201]

Well, how about if he made the heavens cease to exist?

Any number of tests could be done to test for knowledge that couldn't possibly be had. For starters, it could be as simple as "what's in my hand?" From there, predict the time and location of the next nova or solar flare.

I don't understand your objection.

None of these are tests of omnipotence or omniscience. They are only tests of some potence and some science! What did Clarke say about a sufficiently advanced technology?

And your last test is reminiscent of the manner in which clever ancients with some knowledge of astronomical and/or weather patterns used this as a tool to claim Godship or at least priesthood (ability-to-talk-to God-ship).

How would a test-God demonstrate that it is omniscient or omnipotent? (Besides, is there even a definition of these terms that is logically consistent within some axiomatic framework?)

If we really had a God to test, you would not be able to falsify the claim based on the definition. Isn't that that the limit of science no matter what the subject may be?

I'm not sure if (and if you are, then how) you are answering my question. Could you clarify?

 

[Moridin]

Can one prove anything at all? Isn't it all a matter of finding probabilities?

Self-refuting, since that statement cannot be proven if it is true.

 

[Moridin]

I think it is clear that the people in the "you cannot prove a negative" camp has that position because of ideology, rather a result of any rational investigation.

 

[superwolf]

Self-refuting, since that statement cannot be proven if it is true.

Interesting. So it's actually idiotic to claim that nothing is for sure? Ergo, something is?

 

[NeoDevin]

Interesting. So it's actually idiotic to claim that nothing is for sure? Ergo, something is?

No. If "nothing is for sure" then you can't prove it (or you can prove both it, and it's negation).

 

[zoobyshoe]

I think it is clear that the people in the "you cannot prove a negative" camp has that position because of ideology, rather a result of any rational investigation.

From your first link:

So why is it that people insist that you can’t prove a negative? I think it is the result of two things: (1) Disappointment that induction is not bulletproof, airtight, and infallible, and (2) A desperate desire to keep believing whatever one believes, even if all the evidence is against it. That’s why people keep believing in alien abductions, even when flying saucers always turn out to be weather balloons, stealth jets, comets, or too much alcohol. You can’t prove a negative! You can’t prove that there are no alien abductions! Meaning: your argument against aliens is inductive, therefore not incontrovertible. Since I want to believe in aliens, I’m going to dismiss the argument no matter how overwhelming the evidence against aliens, and no matter how vanishingly small the chance of extraterrestrial abduction.

Faced with the kind of people described in reason (2) it is, indeed disappointing that no airtight argument against the existence of various things can be constructed.

 

[Moridin]

It can and has been done. No square circle exists anywhere in the universe, is one, for instance.

 

[WhoWee]

The ancient Egyptians did not watch Seinfeld because he is Jewish. For comedy they liked Malcom In The Middle of all things.

Or maybe the $10,000 Pyramid?

 

[WhoWee]

It can and has been done. No square circle exists anywhere in the universe, is one, for instance.

Unless of course it's made out of a piece of string that can be molded into various patterns/forms...then it could also be a triangle?

 

[zoobyshoe]

It can and has been done. No square circle exists anywhere in the universe, is one, for instance.

Yes, but prove there are no ghosts.

 

[zoobyshoe]

Or maybe the $10,000 Pyramid?

You'd think, but for game shows they liked Cash Cab.

 

[WhoWee]

You'd think, but for game shows they liked Cash Cab.

You got me...what is Cash Cab?

 

[Loren Booda]

I am reminded that maintaining a theorem is a lot harder than disproving one; the former eventually needs to satisfy a near infinity of data, whereas the latter is achieved by one fact.

 

[Moridin]

Yes, but prove there are no ghosts.

Ah, but now you seem to have made the weaker claim that there exists some negatives that cannot be proven, rather than the statement that all negatives are fundamentally unprovable. In any case, here is a quick and dirty attempt. It is very sketchy for sure, but it outlines a general way in which something like it could be done in theory.

1. Ghosts are commonly defined as an immaterial entity that interacts with parts of the physical world (and other features which are of less relevance here)
2. Everything that interacts with some part of the physical world must by definition be physical (how could it otherwise interact?)
3. Therefore, there cannot exist anything immaterial that can interact with the physical world (from 2).
4. Ghosts cannot exist (from 1&3)

Alternatively, we can derive internal contradictions from the concept of ghost. Ghosts can walk through walls, but do not fall through floors and so on.

 

[zoobyshoe]

You got me...what is Cash Cab?

You're in NY City. You hail a cab and get in. Suddenly bells, buzzers, and whistles go off, and the ceiling errupts with flashing lights. The cabbie turns and announces "YOU'RE IN THE CASH CAB! It's a TV game show that takes place right here in my cab!"

The United States' version of Cash Cab (stylized as CA$H CAB)[1] airs on the Discovery Channel, and is hosted by comedian and licensed New York cab driver Ben Bailey. The cab takes passengers as normal fares, and once they agree to play the driver asks a series of questions of increasing difficulty and cash value. Incorrect answers earn a "strike," and if contestants accumulate three strikes they lose the game, lose any money they have won to that point, and the cab pulls over and drops the contestants on the street. Contestants are given two "shout-outs," in which they can ask for help to answer a question, either by placing a mobile phone call or by asking a passerby on the street. Contestants can earn an addition $250 in a "Red Light Challenge" if the cab stops at a traffic light when they have earned $200 or more. To win the challenge, contestants must provide multiple answers to the question within thirty seconds; incorrect responses in the Red Light Challenge are not penalized in any way. Upon arriving at the contestants' destination with fewer than three strikes, the driver offers contestants a choice: a single "Video Bonus Question" for double or nothing.

http://en.wikipedia.org/wiki/Cash_Cab

 

[zoobyshoe]

Ah, but now you seem to have made the weaker claim that there exists some negatives that cannot be proven, rather than the statement that all negatives are fundamentally unprovable.

That's true, I see that some negatives can be proved, (which weakens the last refuge of the illogical, thank goodness). Your links had a better point, I think, which is that in cases where you can't disprove a negative, the positive form of the statement also cannot be proven: "There are ghosts" cannot be proven. This, at least, takes away any implication that your inability to disprove a thing helps to prove it. Mexican standoff.

In any case, here is a quick and dirty attempt. It is very sketchy for sure, but it outlines a general way in which something like it could be done in theory.

1. Ghosts are commonly defined as an immaterial entity that interacts with parts of the physical world (and other features which are of less relevance here)
2. Everything that interacts with some part of the physical world must by definition be physical (how could it otherwise interact?)
3. Therefore, there cannot exist anything immaterial that can interact with the physical world (from 2).
4. Ghosts cannot exist (from 1&3)

Alternatively, we can derive internal contradictions from the concept of ghost. Ghosts can walk through walls, but do not fall through floors and so on.

Well, that's not bad, but in practice your average ghost believer will start offering speculative propositions about ghost physics, how ghosts probably don't operate on the same principles as matter and energy known to Science, and you'll get assertions that Science doesn't know everything, or assertions that quantum physics supports ghosts, and so forth. If you are not debating with someone who is aware of formal logic and doesn't subscribe to it, you can't prove or disprove anything they choose to assert.

 

[TheStatutoryApe]

Ah, but now you seem to have made the weaker claim that there exists some negatives that cannot be proven, rather than the statement that all negatives are fundamentally unprovable. In any case, here is a quick and dirty attempt. It is very sketchy for sure, but it outlines a general way in which something like it could be done in theory.

1. Ghosts are commonly defined as an immaterial entity that interacts with parts of the physical world (and other features which are of less relevance here)
2. Everything that interacts with some part of the physical world must by definition be physical (how could it otherwise interact?)
3. Therefore, there cannot exist anything immaterial that can interact with the physical world (from 2).
4. Ghosts cannot exist (from 1&3)

Alternatively, we can derive internal contradictions from the concept of ghost. Ghosts can walk through walls, but do not fall through floors and so on.

I've read that a long time ago a small town sent a box of rocks to a university explaining that they had fallen from the heavens and pelted the town. The scientists laughed and explained that this was quite absurd. There was no scientific evidence that such a thing could ever possibly occur. And I'm sure that the townspeople who sent the rocks were very likely unable to produce a scientifically valid description of the phenomena.
Even today it is extremely rare that meteorites are found that were actually observed to fall and only a handful of meteorites are turned in per year though it is estimated that hundreds fall to Earth per year.

There are any number of examples of phenomena, creatures, and objects that science heavily refuted until the day they were proved true. Would you say that any negative statements made regarding these things were proved? at least until reality got in the way of the proof?

 

[zoobyshoe]

There are any number of examples of phenomena, creatures, and objects that science heavily refuted until the day they were proved true. Would you say that any negative statements made regarding these things were proved? at least until reality got in the way of the proof?

I've read of a few similar things and it seems to entail the scientists making assertions, only; not offering proofs. IIRC during the series of shark attacks on which the movie Jaws was based an icthyologist or marine biologist was quoted as saying sharks don't ever attack people. (This was something like 1911.)

In your story the rocks were probably ordinary rocks, not meteorites, and this was probably an instance of strange things falling from the sky, as when fish and frogs suddenly rain down. The book Mysteries of the Unexplained contains quite a few examples of this from all over the world. There is a proposed mechanism, which is that tornados suck these things up, shoot them high into the atmosphere, and they come down many miles away from the original site. I suspect the University that received the rocks saw instantly that they were not meteorites and dismissed the claim they fell from the sky.

 

[TheStatutoryApe]

I've read of a few similar things and it seems to entail the scientists making assertions, only; not offering proofs. IIRC during the series of shark attacks on which the movie Jaws was based an icthyologist or marine biologist was quoted as saying sharks don't ever attack people. (This was something like 1911.)

In your story the rocks were probably ordinary rocks, not meteorites, and this was probably an instance of strange things falling from the sky, as when fish and frogs suddenly rain down. The book Mysteries of the Unexplained contains quite a few examples of this from all over the world. There is a proposed mechanism, which is that tornados suck these things up, shoot them high into the atmosphere, and they come down many miles away from the original site. I suspect the University that received the rocks saw instantly that they were not meteorites and dismissed the claim they fell from the sky.

I had believed I read it in The Book of the Damned by Charles Fort. Either I read it elsewhere though or I just can't find it in his scatter shot style of writing but I found this article...
http://www.meteorite.com/nininger/nininger-moments-20.htm
At one time it was not at all scientifically accepted that stones of any sort could fall from the sky. Due to the mythological thunderstone phenomena and the rarity of observed meteor strikes it is fairly reasonable for the scientists to have been skeptical. I believe that the articles cited by Moridin and his own argument regarding ghosts would likely accept lack of scientific records regarding a phenomenon and a more plausible and scientifically recorded alternative explanation as good enough to prove a negative. Even if it is only based on assertions that may or may not be accurate. Certainly being skeptical is fine but obviously believing in a "proven" negative does not seem proper when negative proof is often found in error.

 

[zoobyshoe]

I had believed I read it in The Book of the Damned by Charles Fort. Either I read it elsewhere though or I just can't find it in his scatter shot style of writing but I found this article...
http://www.meteorite.com/nininger/nininger-moments-20.htm
At one time it was not at all scientifically accepted that stones of any sort could fall from the sky. Due to the mythological thunderstone phenomena and the rarity of observed meteor strikes it is fairly reasonable for the scientists to have been skeptical.

I am pretty surprised the phenomenon of meteors wasn't recognized at any time in History. The further back you go the more people watched the night skies, and shooting stars are so frequent you'd think more actual crashes would have been observed and recorded. However, they may be recorded as magical events from the Middle Ages back, and not recognizable as reports of meteors crashing. Hard to say.

I believe that the articles cited by Moridin and his own argument regarding ghosts would likely accept lack of scientific records regarding a phenomenon and a more plausible and scientifically recorded alternative explanation as good enough to prove a negative. Even if it is only based on assertions that may or may not be accurate. Certainly being skeptical is fine but obviously believing in a "proven" negative does not seem proper when negative proof is often found in error.

In general, one man with a rock and a story shouldn't be enough for you to revise your conception of how Nature works, though. It can, and usually does, go the other way: the chupacabra corpse turns out to have common canine DNA, the Lake Monster you shot yesterday washes up as a huge sturgeon with a bullet in it today.

 

[TheStatutoryApe]

I am pretty surprised the phenomenon of meteors wasn't recognized at any time in History. The further back you go the more people watched the night skies, and shooting stars are so frequent you'd think more actual crashes would have been observed and recorded. However, they may be recorded as magical events from the Middle Ages back, and not recognizable as reports of meteors crashing. Hard to say.

I know, its a bit odd. Lack of evidence though would be a major concern. The more common description of thunderstones (or thunder axes) which supposedly came down to Earth in lightning and which are a bit of a legendary phenomena are likely to have made meteor strikes seem similar and even the stones seem to have a similar cause, as discussed in the article. Since they had to have seen "shooting stars" and someone at some point must have observed one through a telescope I wonder if they simply thought that a meteor could not make it to the surface of the Earth before burning up.

In general, one man with a rock and a story shouldn't be enough for you to revise your conception of how Nature works, though. It can, and usually does, go the other way: the chupacabra corpse turns out to have common canine DNA, the Lake Monster you shot yesterday washes up as a huge sturgeon with a bullet in it today.

I certainly understand skepticism and that many myths are really myths.
Now that I have thought about it more and reread one of Moridin's articles I think the issue is with logicians and mathematicians and their mindset (or ideology). They like to work with definites. Any self referencial and self defining system is going to maintain consistency and if it does not then it will be fixed so that it will. The ability of these systems to model reality is not in their purview. That is an issue for physicists, chemists, doctors, ect. Those same sorts of persons who the author of that article mentions are the ones who state a negative can not be proven before he goes on to claim that no logician would support that statement.

 

[zoobyshoe]

I know, its a bit odd. Lack of evidence though would be a major concern. The more common description of thunderstones (or thunder axes) which supposedly came down to Earth in lightning and which are a bit of a legendary phenomena are likely to have made meteor strikes seem similar and even the stones seem to have a similar cause, as discussed in the article. Since they had to have seen "shooting stars" and someone at some point must have observed one through a telescope I wonder if they simply thought that a meteor could not make it to the surface of the Earth before burning up.

I googled and found the "lightning strike" thunderstones, but also this very different story of the thunderstones:
http://www.cscs.umich.edu/~crshalizi/White/antiquity/thunder.html

I certainly understand skepticism and that many myths are really myths.
Now that I have thought about it more and reread one of Moridin's articles I think the issue is with logicians and mathematicians and their mindset (or ideology). They like to work with definites. Any self referencial and self defining system is going to maintain consistency and if it does not then it will be fixed so that it will. The ability of these systems to model reality is not in their purview. That is an issue for physicists, chemists, doctors, ect. Those same sorts of persons who the author of that article mentions are the ones who state a negative can not be proven before he goes on to claim that no logician would support that statement.

Clearly, anyway, some kinds of negatives can be proven or demonstrated: "there is no elephant in this jar", and if a positive can be disproven it's negative can be proven. Those aren't the tricky ones, though. Usually when a guy shows up with a rock and a story there's nothing to get any traction on one way or another.

 

[millitiz]

Hmm, very interesting. Yes, it is possible to prove negative. And I think there are many examples above.
However, for those statements that you could not prove negatively, those are the statements that does not restrict the domain.
In math, the statement is always, "if A, then B"
And most of the time, one would also say what domain you are talking about (Real space, etc).
So for instance, proving that there is no life form, creature other than those on earth.
Yes, you can prove it, except you need to restrict the domain and the definition. For instance, you can pick a cube in the space, and test if there is any creature/life form of any sort in that cube. See, it is really easy to prove local property. But to prove a global one, well, even the mathametician would pull off their hairs ;)
In fact, there is not way to prove a "global property" in the sense that you can always shrink your domain, and there is a limit to it (ie, a point). But you can keep expanding your domain, and there is no REAL end point (yes, it suppose to end at infinity, but if you can reach it, then it is not infinity by definition).

 

[millitiz]

Just very quickly, even in math, there are things that you cannot prove it nor disprove it (yet, I hope). For instance, whether there are other "infinity" in between the "size all Reall number and the size of natural number."

 

[NeoDevin]

Just very quickly, even in math, there are things that you cannot prove it nor disprove it (yet, I hope). For instance, whether there are other "infinity" in between the "size all Reall number and the size of natural number."

Even in math, there are some things which are fundamentally impossible to prove/disprove.