# Can one prove a negative?

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.

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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.

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).

Staff Emeritus
Gold Member
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.

Staff Emeritus
Gold Member
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?

Staff Emeritus
Gold Member
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?

Staff Emeritus
Gold Member
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.

Gold Member
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.

Staff Emeritus
Gold Member
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.

Staff Emeritus
Gold Member
It's not possible to find evidence for these.

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.

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

Staff Emeritus
Gold Member
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. :tongue:

Religious discussions [debates] are not allowed.

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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.

Staff Emeritus
Gold Member
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

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."

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

A mystery. Interesting.

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