Can You Prove a Negative Statement?

[superwolf]

It's often claimed that you cannot prove a negative. On the surface, it seems to be true: if Person A says “I think Unicorns exist” and Person B says “I don’t think unicorns exist”, it’s pretty clear that Person B is going to have a hard time proving that there isn’t a God. However, if you look a little closer, it actually depends on the nature of the negative statement being made. Here are some negative statements that can be proven very easily:

Five is not equal to four

The ancient Egyptians did not watch Seinfeld

The tsetse fly is not native to North America

Clearly, it’s possible to prove a negative statement. The real problem here is clearly the nature of the positive statement being refuted. When a person asserts that X exists, and he does not specify the nature of X – that is, is X small, large, blue, red? And where is he? Of course it is not possible to prove that X does not exist, if X is a thing that has no definition, no characteristics, and no location. In fact, you can prove just about any kind of negative you can think of – except for (surprise!) the non-existence of mystical beings. When you get right down to it, the statement “you cannot prove a negative” is really just a different way of saying “You can’t prove me wrong because I don’t even know what I’m talking about.”

Logical statements have to abide by certain rules and restrictions. In order for a statement to be logical, it must be falsifiable, which means that it has to be presented in such a way that it could be proven incorrect. A statement is not logical if it cannot be tested to make sure it is true. The statement "X" exists is therefore absurd and nonsensical. No one even knows what X is supposed to be.

 

[ShadowDatsas]

Wow. Is this a scientific way of proving that God does not exist?
Or did you made up this thought in a conversation about God? :P
Regardless, good thinking.
Seems to be a nice way to prove wrong statements that I wouldn't normally mess with.

 

[superwolf]

No, it's not proof that God does not exist. First we'll have to define God scientifically. My real point here is that what scientists use to claim - that you cannot prove a negative - is not necessarily true.

 

[ShadowDatsas]

Ok, sorry. I was just joking.:P
By the way, I don't think anyone could "define God scientifically." It wouldn't be God if he could...
I didn't also knew that scientists claim that you cannot prove a negative so sorry again.
And I agree with you, you can prove a negative with simple examples (like the given ones).

 

[Ivan Seeking]

You can't prove a general negative [I forget the proper terminology here].

One can prove that there is no fly in the jar [for example], but one cannot prove that there are no flies. And it doesn't apply only to mystical ideas. For example, prove that there is no intelligent life in the universe beyond that here on earth.

 

[superwolf]

That's why scientists should not waste their time trying to disprove the existence of God. One can argue philosophically against the existence of such a being, but there's no way of testing it scientifically, even if we had all the technology and instruments we could dream of.

 

[superwolf]

one cannot prove that there are no flies.

Isn't that just because of technological limitations? God on the other hand, is not disprovable, because you have no way of knowing what it would look/hear/smell/feel like if you observed it.

 

[Ivan Seeking]

That's why scientists should not waste their time trying to disprove the existence of God. One can argue philosophically against the existence of such a being, but there's no way of testing it scientifically, even if we had all the technology and instruments we could dream of.

That is, unless God showed up for a test.

 

[superwolf]

That is, unless God showed up for a test.

How would you know it was God?

 

[Ivan Seeking]

How would you know it was God?

You could show evidence that a being meets the definition of God.

 

[superwolf]

But what is that definition?

 

[Ivan Seeking]

It depends on who you ask. Generally, omniscient and omnipotent are considered to be part of the definition, so you could show evidence for this.

 

[f95toli]

Five is not equal to four

The ancient Egyptians did not watch Seinfeld

The tsetse fly is not native to North America

Statement 1 can possibly be proven IF the person you are trying to persuade accepts the fundamental axioms of math.

Statement 2 is impossible to prove. We can't know with 100% certainty that the ancient Egyptians did not have access to time-traveling technology that allowed them to receive broadcasts from the future. It is obviously not very likely, but the point is that you can't prove it.

And I have no idea how one would prove statement 3. Granted, discovering that the tsetse fly IS native to NA would be a sensation; but as far as I know it wouldn't violate any known laws or nature, or even change the way we think of biology and/or the migration of species in any fundamental way. I am not even sure it would be more surprising than e.g. the discovery that Coelacanth is still around (to take just one example).

 

[zoobyshoe]

Statement 2 is impossible to prove. We can't know with 100% certainty that the ancient Egyptians did not have access to time-traveling technology that allowed them to receive broadcasts from the future. It is obviously not very likely, but the point is that you can't prove it.

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

 

[Gokul43201]

You could show evidence that a being meets the definition of God.

It depends on who you ask. Generally, omniscient and omnipotent are considered to be part of the definition, so you could show evidence for this.

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?)

 

[superwolf]

omniscient and omnipotent

It's not possible to find evidence for these.

 

[Ivan Seeking]

It's not possible to find evidence for these.

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.

 

[superwolf]

Omnipotence is impossible. Can God create a stone that is so heavy that he can't lift it himself?

 

[Ivan Seeking]

Omnipotence is impossible.

True or not, that has nothing to do with the discussion. All that you are doing here is arguing that God doesn't exist, which is a violation of the posting guidelines. You asked about proof of a negative.

Can God create a stone that is so heavy that he can't lift it himself?

For a moment he could make himself not a God.

Religious discussions [debates] are not allowed.

 

[junglebeast]

Omnipotence is impossible. Can God create a stone that is so heavy that he can't lift it himself?

That argument does not disprove omnipotence...the usual reply is:

when talking about omnipotence, referencing "a rock so heavy that a deity cannot lift it" is nonsense just as much as referencing "a square circle." So asking "Can a deity create a rock so heavy that even he cannot lift it?" is just as much nonsense as asking "Can a deity draw a square circle?" Therefore the question (and therefore the perceived paradox) is meaningless.

 

[Ivan Seeking]

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?

 

[TheStatutoryApe]

The way I have always understood it is that you can not prove a negative but you can prove a positive which refutes the negative. That is you can show evidence of what is but you can not show evidence of what is not.

 

[superwolf]

Omnipotence leads to paradoxes, therefore it's not possible.

Anyway, why do so many scientists claim that I cannot prove a negative? Is it because of technological limitations, or will it never be possible to prove that pink elephants of measurable size don't exist in the universe?

 

[superwolf]

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?

That's my opinion too. We'll never be able to falsify the existence of such beings, unless we give them a scientific definition.

 

[Moridin]

You can't prove a general negative [I forget the proper terminology here].

One can prove that there is no fly in the jar [for example], but one cannot prove that there are no flies. And it doesn't apply only to mystical ideas. For example, prove that there is no intelligent life in the universe beyond that here on earth.

The lack of rigorous understanding of logic in this statement is appalling. It is entirely possible to prove a universal negative.

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

or

P -> Q
~Q
~P

or

P -> ~Q
P
~Q

http://www.skeptic.com/eskeptic/07-12-05.html
http://www.infidels.org/library/modern/richard_carrier/theory.html

 

[superwolf]

Will you please translate that to human language?

 

[TheStatutoryApe]

It is entirely possible to prove a universal negative.

Excuse my uneducatedness, I am not able to understand the rest of your post.
Reading your links I still have to refer back to my earlier post. One may prove a premise which refutes another but one can not prove a negative premise.

 

[NeoDevin]

Will you please translate that to human language?

Basically what Moridin is saying, is that any time you prove a positive (say P), you are proving the negation of it's negation (~(~P)), hence, you've proven a negative.

Any statement is equivalent to the negation of another (particular) statement.

 

[zoobyshoe]

The lack of rigorous understanding of logic in this statement is appalling. It is entirely possible to prove a universal negative.

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

or

P -> Q
~Q
~P

or

P -> ~Q
P
~Q

http://www.skeptic.com/eskeptic/07-12-05.html
http://www.infidels.org/library/modern/richard_carrier/theory.html

Negative statements often make claims that are hard to prove because they make predictions about things we are in practice unable to observe in a finite time. For instance, "there are no big green Martians" means "there are no big green Martians in this or any universe," and unlike your bathtub, it is not possible to look in every corner of every universe, thus we cannot completely test this proposition--we can just look around within the limits of our ability and our desire to expend time and resources on looking, and prove that, where we have looked so far, and within the limits of our knowing anything at all, there are no big green Martians. In such a case we have proved a negative, just not the negative of the sweeping proposition in question.

http://www.infidels.org/library/modern/richard_carrier/theory.html

Actually, this is pretty unsatisfying, and I think it's clear that when we say you can't prove there are no big, green Martians, it means "in this, or any, universe", and the negative is not proven in the understood sense by having to give up at the practical limits of the search. Same argument with the other link.

The practicalities of day to day living, in which big, green martians continually and consistently fail to show up, are such that it's best not to hold our breaths, but it remains inaccurate to say their non-existence has been proven.

 

[NeoDevin]

Five is not equal to four

You are assuming that math is consistent (thanks Godel). You can never prove the consistency of a (sufficiently complex) theory from within that theory.

There are some things that can never be proven, but to say absolutely that you can never prove a negative is ridiculous.

 

[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