Got the Memo Yet? You Can Indeed Prove a Negative!

[Mock Turtle]

I always figured that if I wanted to prove a negative, I
would just first convert the negative into a positive.

So while I might not be able to prove that unicorns don't
exist, I would instead try to prove that the absence of
unicorns does exist.

Okay this is making me dizzy....

Well, if you multiply two negatives together, they do make a positive ... hence you can get two for the price of one.

 

[sayak83]

Things must've greatly changed in the world of mathematics since my day.
We never used an exclamation mark do denote inequality.
For one thing, there was the perfectly standard, useful, & unambiguous
equality sign with line thru it.
And we see the confusion caused by its also denoting factorial.

! Is used as the symbol for NOT operator. Hence can be used independently of the = sign. Like NOT AND (NAND) can be written as ! & etc.

 

[Revoltingest]

! Is used as the symbol for NOT operator. Hence can be used independently of the = sign. Like NOT AND (NAND) can be written as ! & etc.

Well, that's just terrible.
When I become dictator, things will change.

 

[Skwim]

If I prove that the butler killed my dinner guest, I have also proved that the gardener did not. Is this confusing to people?

Nah, the gardener also had a hand in it.

.

 

[PureX]

Comments? Rave Reviews? Observations? Deranged Rants?

You cannot prove a universal negative.

You can prove that "X" does not exist within the parameters of "A through W". But you can only do this by defining "X", and by defining the parameters within which "X" can or cannot be determined to exist.

"God", however, is not definable in that way. And neither is "existence" as a singular whole concept. Both of them are infinite possibilities. And we can't specify the infinite.

 

[Bob the Unbeliever]

"God", however, is not definable in that way.

That is, actually, a definition. Thus your claim is proven false, because it is internally inconsistent.

In simple terms, you cannot have a square-circle, because of the understanding of what a square is, and what a circle is. The two are mutually exclusive.

The term "god is undefinable" renders the statement meaningless, and thus, a null statement.

Even worse, it means the word "god" has absolutely no useful meaning at all-- may as well replace it with "foo" or "zalarkfarb".

Who believes in things without meaning anyway?

 

[shunyadragon]

On the contrary, I proved that no elephants exist in my room. That is a proof of a negative: the non-existence of elephants with a certain property.

The 'confirmation' is one of non-existence of such elephants.

On the contrary as far as I am concerned this qualifies as an empirical question, which may be worded also as a positive question, which like the example I gave before. It does not qualify for a proposition that argues for the fallacy of proving the negative.

True propositions that qualify for the fallacy of proving the negative can be worded as a positive question and cannot proven either way such as; Prove God does not exist, versus prove God exists.

 

[Curious George]

On the contrary as far as I am concerned this qualifies as an empirical question, which may be worded also as a positive question, which like the example I gave before. It does not qualify for a proposition that argues for the fallacy of proving the negative.

True propositions that qualify for the fallacy of proving the negative can be worded as a positive question and cannot proven either way such as; Prove God does not exist, versus prove God exists.

Prove that.

 

[Politesse]

Nah, the gardener also had a hand in it.

.

If so, there should be some tangible evidence for that as well.

 

[Skwim]

If so, there should be some tangible evidence for that as well.

You just have to look harder. Try the garden shed under the bag of potting soil.

.

 

[Sunstone]

If I prove that the butler killed my dinner guest, I have also proved that the gardener did not. Is this confusing to people?

You'd better rephrase that, "If I prove that the butler alone killed my dinner guest, I have also proved that the gardener did not." Otherwise people will pretend not to understand you. I know I would.

 

[Sunstone]

First, the examples provided using a negative statement are not truly proving a negative. Second, I am waiting for an example of actual proving a negative that is not a fallacy other than a contradiction and a factorial.

There are many negative statements in hypothesis that are falsifiable in science such a hypothesis might be word worded as a negative statement: Falsify that these fossil bones do not belong to species x. The results would a positive answer whether the bones belong to species x, or an unknown or known species y..

My advice is to read the articles linked to in the OP and quit speaking from outraged ignorance. Please take it.

 

[Sunstone]

Aha! if we're not careful this could be one of those tricky, self-referential paradox thingies.

I agree with the examples in the OP. That said, I can't think of any other examples outside the domain of logic and math. Can you?

There are many examples in the articles linked to in the OP. I especially recommend the first two articles. I think the second is better written than the first.

 

[Polymath257]

You cannot prove a universal negative.

So the claim that there is *universally* no thing x with x =/= x isn't proving a negative?

Why not?

You can prove that "X" does not exist within the parameters of "A through W". But you can only do this by defining "X", and by defining the parameters within which "X" can or cannot be determined to exist.

In other words, you make it meaningful to ask whether X exists. OK.

"God", however, is not definable in that way.

In what way *is* God definable?

And neither is "existence" as a singular whole concept. Both of them are infinite possibilities. And we can't specify the infinite.

I'm not quite sure what you mean here, but I specify infinite sets all the time. For example, N+{1,2,3,4,5...} is the set of natural numbers. It is a very specific, determined, set that is also infinite.

 

[Polymath257]

First, the examples provided using a negative statement are not truly proving a negative. Second, I am waiting for an example of actual proving a negative that is not a fallacy other than a contradiction and a factorial.

There are many negative statements in hypothesis that are falsifiable in science such a hypothesis might be word worded as a negative statement: Falsify that these fossil bones do not belong to species x. The results would a positive answer whether the bones belong to species x, or an unknown or known species y..

Which means that you did, in fact, prove a negative.

Maybe the question is what you mean by the phrase 'prove a negative'. For me, it simply means a statement of the form

'¬p'

where p is some statement. Or, potentially,

¬ ∃x Φx

Both of which I have given examples of.

Since *every* statement of the first can be rewritten in the form

∀x ¬Φx

this also shows a universal statement negation of some sort.

 

[Polymath257]

False, you are not truly proving a negative proposition that an unknown x exist does not exist.

Sorry, did you leave something out by mistake? This statement didn't parse for me.

Unless you are going to be specific you are dealing with a known x. You need to word this in actual example of an unknown like God, and try to prove God does not exist.

Why would I need to do that? If the properties are unknown, how is it even meaningful to talk about existence?

No better at all.

This fails, because you are not trying to prove that African elephants do not exist, ie the 'black swan fallacy.' You are simply confirming whether the elephant is in the room or not. If the unknown animal in the room does not have peanut breath, it is proven not to be an elephant.

And I managed to prove the negative statement:

No elephant exists in my room.

I agree, I am confirming whether or not an elephant exists in my room. I confirmed the negative statement.

A true proving the negative cannot be equated to empirically or mathmatically determining the presence of a known object nor a given known math variable such as one designated as x

Sorry, again I am having trouble making sense of what you wrote. Could you be more clear?

If you propose to prove a purple elephant with pink strips does not exist. You have a true fallacy on your hands.

Why is that? I certainly know that no such thing exists in my room, right?

 

[PureX]

In what way *is* God definable?

Only in a limited and subjective way.

Does 'Bigfoot' exist?

If we can define what we mean by a "Bigfoot", and we can define what we mean by it's "existing" (as an ideological entity?, as a living organism?, as a human experience?, etc.), then we can determine if such exists. But we cannot define "God" this specifically. And we cannot define the parameters of God's existence, either. So we cannot determine if God exists or not.

I'm not quite sure what you mean here, but I specify infinite sets all the time. For example, N+{1,2,3,4,5...} is the set of natural numbers. It is a very specific, determined, set that is also infinite.

These ideological infinities exist only in the imagination, where they cannot be verified except by their own logic. Like words before they have been applied to reality.

 

[shunyadragon]

Sorry, did you leave something out by mistake? This statement didn't parse for me.



Why would I need to do that? If the properties are unknown, how is it even meaningful to talk about existence?



And I managed to prove the negative statement:

No elephant exists in my room.

I agree, I am confirming whether or not an elephant exists in my room. I confirmed the negative statement.



Sorry, again I am having trouble making sense of what you wrote. Could you be more clear?



Why is that? I certainly know that no such thing exists in my room, right?

Let's put it bluntly. The fallacy of proving the negative applies to logical questions that do not have an empirical resolution, and NOT propositions nor questions that can be solved or answered empirically!

 

[Polymath257]

Only in a limited and subjective way.

Does 'Bigfoot' exist?

If we can define what we mean by a "Bigfoot", and we can define what we mean by it's "existing" (as an ideological entity?, as a living organism?, as a human experience?, etc.), then we can determine if such exists. But we cannot define "God" this specifically. And we cannot define the parameters of God's existence, either. So we cannot determine if God exists or not.

That, to me, simply says that the whole question is meaningless because the terms haven't been defined well enough.

These ideological infinities exist only in the imagination, where they cannot be verified except by their own logic. Like words before they have been applied to reality.

And applied to good effect. I'm not sure why you call them 'ideological'. They are infinities and we have a consistent theory of such things that works quite well.

 

[Polymath257]

Let's put it bluntly. The fallacy of proving the negative applies to logic, and NOT propositions or questions that can be solved or answered empirically!

You haven't shown why that might be the case.