Help with a logic problem?

[Hazelip]

OK. I belong to a mailing list on which the discussion of just how one could disprove the existence of god.

Now, the list doesn't normally deal with this sort of thing, and I expected all sorts of crazy answers. Many were of the "can't prove a negative" variety, and many were presentations of options that could best be described as debunking.

Now, someone on the thread brought this up, and it went right past me as I was engaged in a discussion that wandered into the territory of atheism being a religion (insert groan here), but the point raised has been bothering me for a few days now, and I need some logic assistance here.

"One cannot prove a negative."

How can anyone make such a statement and prove it? I have my own idea on the matter, but it is presenting what I think is a misconception in a very interesting way. But, the statement itself is a negative, so how can one prove that one cannot prove a negative?

 

[Interesting Ian]

OK. I belong to a mailing list on which the discussion of just how one could disprove the existence of god.

Now, the list doesn't normally deal with this sort of thing, and I expected all sorts of crazy answers. Many were of the "can't prove a negative" variety, and many were presentations of options that could best be described as debunking.

Now, someone on the thread brought this up, and it went right past me as I was engaged in a discussion that wandered into the territory of atheism being a religion (insert groan here), but the point raised has been bothering me for a few days now, and I need some logic assistance here.

"One cannot prove a negative."

How can anyone make such a statement and prove it? I have my own idea on the matter, but it is presenting what I think is a misconception in a very interesting way. But, the statement itself is a negative, so how can one prove that one cannot prove a negative?

The statement is patently false anyway. I can prove there's not a blue whale in my bedroom simply by entering it.

 

[Tricky]

Re: Re: Help with a logic problem?

The statement is patently false anyway. I can prove there's not a blue whale in my bedroom simply by entering it.

That easy, huh? Well then I can prove there is no God anywhere I have ever been, because I haven't seen one.

No, Ian, you cannot prove that there is not a blue whale in your bedroom because you cannot investigate every possibility, for example:

• Your room intersects with another dimension. In that dimension, the Blue Whale exists, but you cannot detect it.
• It is the essence of the Blue Whale. Its "self" is in your room.
• It is a very tiny Blue Whale, so tiny as to be as yet undiscovered by science. (Or perhaps rogue scientists have miniturized a whale and hidden it in your room!)
• A new strain of submicroscopic mites has been discovered and they are called "Blue Whales".
• The blue whale leaves as soon as you try to look at it.
• A female blue whale exploded, sending a Blue Whale zygote into the air to be caught by the breeze and wafted into your room.

Silly? Of course, yet I have heard equally silly propositions put forth to explain religious and metaphysical beliefs.

You cannot prove a negative simply because you cannot examine every possibility. Some possibilities (like the alternate dimension) cannot even be tested, yet you can't rule them out.

Oh yes, and the statement "you can't prove a negative" cannot be proven because you cannot examine every single negative. There might be one out there that you can prove.

But really, outside of mathematics, you really can't prove anything, you can only give evidence. There's a great deal of evidence for evolution. There is probably a great deal of evidence that there is not a blue whale in Ian's room.

 

[Yahweh]

Re: Re: Re: Help with a logic problem?

You cannot prove a negative simply because you cannot examine every possibility. Some possibilities (like the alternate dimension) cannot even be tested, yet you can't rule them out.

That scenario might fall into a special variety of possibility called the Empty Possibility.

Empty Possibilities include all unfalsifyable explanation, predictions, and possibilites. All unfalsifyable explanations are perfectly indistinguishable from one another and work just as appropriately for explaning events as all other unfalsifyable explanations.

As long as there is never an experience or test which can confirm or deny any possibility, that possibility is effectively empty as there is no difference between such a world where that seemingly intangible blue whale exists in Ian's bedroom and no blue whales exist in Ian's bedroom.

(I guess thats the more longwinded version of saying "Who gives a flying monkey about things which can never be evidenced"...)

For all intents and purposes, its reasonable to disbelieve in empty possibilities. There are no blue whales in Ian's bedroom.

 

[The idea]

Doesn't a solid alibi prove a negative?

 

[Interesting Ian]

Re: Re: Re: Help with a logic problem?

--------------------------------------------------------------------------------
Originally posted by Interesting Ian


The statement is patently false anyway. I can prove there's not a blue whale in my bedroom simply by entering it.
--------------------------------------------------------------------------------

Tricky
That easy, huh? Well then I can prove there is no God anywhere I have ever been, because I haven't seen one.

If God is defined as being a mind you wouldn't expect to, just like you cannot see other peoples' minds.

No, Ian, you cannot prove that there is not a blue whale in your bedroom because you cannot investigate every possibility, for example:

Your room intersects with another dimension. In that dimension, the Blue Whale exists, but you cannot detect it.

Then it's not in my bedroom, it's in another dimension.

It is the essence of the Blue Whale. Its "self" is in your room.

The blue whale is defined by its physicality.

It is a very tiny Blue Whale, so tiny as to be as yet undiscovered by science. (Or perhaps rogue scientists have miniturized a whale and hidden it in your room!)

Then arguably it wouldn't be a blue whale by definition.

A new strain of submicroscopic mites has been discovered and they are called "Blue Whales".

They are not the creatures of interest.

The blue whale leaves as soon as you try to look at it.

Disobeys physical laws.

A female blue whale exploded, sending a Blue Whale zygote into the air to be caught by the breeze and wafted into your room.

My window is shut.

 

[Cecil]

Tricky, you're being a little obtuse. Using your logic, we can never prove anything. Using tricks like redefining words, positing alternate dimensions, or denying the laws of physics is not useful to us. We can't prove the non-existance of a blue whale in my room in just the same sense as we can't prove that gravity exists (maybe there's a big invisible man with lots of really long arms that pulls everything together). I assume we're talking about proof in the sense that it is reasonable for anyone to believe it. That is, we can prove that the ancient Egyptians did not watch Seinfeld and that penguins are not native to Europe.

In regards to the OP, we have the problem of what constitutes a negative statement. "All crows are black" and "No non-black crows exist" mean exactly the same thing but one seems to be "positive" and the other "negative".

It may help if we separate the two types of propositions, "existential" and "universal". Existential propositions are of the form "There exists an A with property B". Universals are of the form "All A are B". Propositions using "some", "many", or "most" are just specific cases. Now, either type can be negative or positive. The above examples are positive; they can be made negative by prepending "It is not the case that...".

Generalizations about the provability of sets of propositions tend to have no basis in fact. Take the two negative existentials "It is not the case that black polar bears exist" and "It is not the case that one person has lived in 10 different centuries". The first is not "provable" - you would have to examine every polar bear. Maybe there's been a mutation in the hair of the bear, or maybe it was burned. The second is quite "provable" - people do not live that long, and if one did we would know about it.

When people say "you can't prove a negative", they tend to mean "you can't prove a negative existential", or more specifically, "You can't prove that X doesn't exist." While this is true in the strictest sense, there are several methods we can use to show the non-existence of something:

Logical impossibility - there does not exist an integer between 27 and 28.

We would know about it if it existed - there does not exist a Jupiter-sized planet between the orbits of Earth and Mars (its gravitational effects would be obvious).

It conflicts with what we know to be true - There does not exist an ancient Egyptian that watched Seinfeld (We know that Seinfeld did not exist during the lives of the Egyptians).

In fact, the non-existence of nearly anything can be shown as long as the properties of the object can be explicitly and completely defined. In my experience, asking for clarification on the definition of God is futile. All too often, the "you can't prove a negative" is simply a smokescreen for "You can't prove me wrong because I don't know what I'm talking about".

 

[Tricky]

If God is defined as being a mind you wouldn't expect to, just like you cannot see other peoples' minds.

If God is defined as a mind, then a blue whale could be defined so as well. If God is not physical, then God is not anywhere, because a mind is not anywhere.

Then it's not in my bedroom, it's in another dimension.

Why can't your bedroom exist in more than one dimension? From what I have read of your posts, you believe the mind exists in more than one dimension. One which is apart from the physical world and one which interacts with and is affected by the physical world. Why can't Blue Whales get the same break?

The blue whale is defined by its physicality.

According to you. You must accept that unless you can cover every possible definition of "blue whale" then you cannot prove one does not exist in your bedroom. You are only proving that your definition of blue whale does not exist in your bedroom. (Does this argument sound familiar, Ian?).

Then arguably it wouldn't be a blue whale by definition.

Again, by your definition. You are ignoring the Metaphysical Blue Whale.

They are not the creatures of interest.

To you.

Disobeys physical laws.

So do "souls", yet you believe in them.

My window is shut.

How can you prove that it is impossible that someone could enter your room, open a window at the exact instant the Blue Whale zygote floated in, then closed it again and left? You can't. Neither can I prove that it is impossible for the I Ching to work. It is simply very unlikely.

 

[Hazelip]

Doesn't a solid alibi prove a negative?

Nope. It proves your alibi, and then the negative becomes a reasonable conclusion. Be careful of falling into the "working backwards" trap...

 

[Hazelip]

Logical impossibility - there does not exist an integer between 27 and 28.

That is not a proof. That is a conclusion. A proof can only establish the existence of the integers 27 and 28. Once proven, it is then a logical conclusion that there is not an integer between the two.

Conclusions can be negative. Conclusions are different from proof.

 

[Tricky]

Tricky, you're being a little obtuse.

No, I'm being satirical. I obviously don't believe the crap I wrote.

Using your logic, we can never prove anything.

Which is just what I said above. You can't prove anything. You can only give evidence. In some cases, that evidence is so overwhelming that the point is considered "proved", but it is like proving the existence of "infinity". It simply can't be done.

We can't prove the non-existance of a blue whale in my room in just the same sense as we can't prove that gravity exists (maybe there's a big invisible man with lots of really long arms that pulls everything together). I assume we're talking about proof in the sense that it is reasonable for anyone to believe it.

This is my point exactly. We cannot "prove" a negative, but we can show that it is unreasonable for anyone to believe in it. I apply that definition to "God". This is not to say religious people are always unreasonable, but only about their god.

In regards to the OP, we have the problem of what constitutes a negative statement. "All crows are black" and "No non-black crows exist" mean exactly the same thing but one seems to be "positive" and the other "negative".

I think you and I agree, Cecil. Neither statement can be "proven", but by saying "you cannot prove there are no white crows", you are attempting to shift the burden of proof to the person objecting to the unreasonable claim. This shifting of proof is why the term "you cannot prove a negative" came about. It is not technically accurate, but refers to the technique of unreasonable people to shift the burden of proof.

When people say "you can't prove a negative", they tend to mean "you can't prove a negative existential", or more specifically, "You can't prove that X doesn't exist." While this is true in the strictest sense, there are several methods we can use to show the non-existence of something:

Logical impossibility - there does not exist an integer between 27 and 28.

That is simply circular logic. An integer is a whole number. A number that is not a whole number is not a whole number. It is simply a matter of accepting the definitions. However, I did point out in my earlier post that math was one of the few arenas where one actually could prove something (assuming one accepts the definitions.)

We would know about it if it existed - there does not exist a Jupiter-sized planet between the orbits of Earth and Mars (its gravitational effects would be obvious).

It conflicts with what we know to be true - There does not exist an ancient Egyptian that watched Seinfeld (We know that Seinfeld did not exist during the lives of the Egyptians).

Which involves accepting that gravity works and behaves the same everywhere. Cecil, you must understand I am making a point, not actually arguing for these bizarre unliklihoods. The point is, people who ask you to "prove" something doesn't exist do not play by the rules of evidence. That is why they are unreasonable.

In fact, the non-existence of nearly anything can be shown as long as the properties of the object can be explicitly and completely defined. In my experience, asking for clarification on the definition of God is futile. All too often, the "you can't prove a negative" is simply a smokescreen for "You can't prove me wrong because I don't know what I'm talking about".

I agree with you, except that the "you can't prove a negative" is a catch phrase used by skeptics to indicate that you cannot give evidence against something which is essentially undefined. It may not be technically accurate, but it is easy to understand what is really meant.

 

[Suggestologist]

OK. I belong to a mailing list on which the discussion of just how one could disprove the existence of god.

Now, the list doesn't normally deal with this sort of thing, and I expected all sorts of crazy answers. Many were of the "can't prove a negative" variety, and many were presentations of options that could best be described as debunking.

Now, someone on the thread brought this up, and it went right past me as I was engaged in a discussion that wandered into the territory of atheism being a religion (insert groan here), but the point raised has been bothering me for a few days now, and I need some logic assistance here.

"One cannot prove a negative."

How can anyone make such a statement and prove it? I have my own idea on the matter, but it is presenting what I think is a misconception in a very interesting way. But, the statement itself is a negative, so how can one prove that one cannot prove a negative?

There is no water in this glass. Can you prove it? To make it less susceptible to quibbles: "There is no golf ball in this glass." - can you prove it?

One can prove a negative. One cannot prove an ill-defined or undefined negative (or positive).

 

[magicflute]

Ian, please get rid of that Blue Whale in your room already!!! The neighbors are beginning to complain about the smell!! And BTW, I believe you're from another dimension.

 

[Suggestologist]

Ian, please get rid of that Blue Whale in your room already!!! The neighbors are beginning to complain about the smell!! And BTW, I believe you're from another dimension.

Old Chinese Saying: Believe half of what you see, and none of what you hear.

And how much of what you feel?

 

[Garrette]

Warning: Unresearched ramblings of a non-philosopher and poorly educated man follow:

I'm actually in agreement with Ian on this, and it's something I've thought about a bit.

We cannot disprove a negative so long as the negative we are attempting to disprove remains undefined and without specific properties.

It's the same difficulty we run into in things like the book test; the proponents of the existence of something (e.g., "anomolous cognition") must define its characteristics but often or usually fail to do so.

For Ian's blue whale example, Tricky is correct in saying (even though he was joking) that it can't be disproven if there are no stipulations regarding characteristics.

However, if someone says "There is , in your bedroom, a blue whale which follows the normally accepted laws of physics, is not invisible, is corporeal, leaves flukeprints, does not interact with other dimensions, and whose presence will not be affected by your observation of it," then Ian can disprove it simply by looking in.

Similarly, "psi" could be disproven/falsified (insofar as anything outside mathematics can be) if its properties were specifically listed.

Just my two dinar.

 

[TheBoyPaj]

It conflicts with what we know to be true - There does not exist an ancient Egyptian that watched Seinfeld (We know that Seinfeld did not exist during the lives of the Egyptians).

In fact, the non-existence of nearly anything can be shown as long as the properties of the object can be explicitly and completely defined. In my experience, asking for clarification on the definition of God is futile. All too often, the "you can't prove a negative" is simply a smokescreen for "You can't prove me wrong because I don't know what I'm talking about".

The problem is that in this area believers will gladly drag in such issues as alternate universes and smugly give their own smokescreen: "Science doesn't know everything"

There may have been an ancient Egyptian who watched Seinfeld if he saw it in a precognitive vision, for example.

By carefully impregnating their statement with unprovable suggestions, they effectively remove the possibility of being shown to be wrong.

 

[magicflute]

Originally posted by Suggestologist

And how much of what you feel?

ALL the senses can be fooled!

 

[Abdul Alhazred]

That is not a proof. That is a conclusion. A proof can only establish the existence of the integers 27 and 28. Once proven, it is then a logical conclusion that there is not an integer between the two.

Conclusions can be negative. Conclusions are different from proof.

Wouldn't a mathematical proof by contradiction be proving a negative?

 

[epepke]

"One cannot prove a negative."

How can anyone make such a statement and prove it? I have my own idea on the matter, but it is presenting what I think is a misconception in a very interesting way. But, the statement itself is a negative, so how can one prove that one cannot prove a negative?

Well, it's wrong, anyway.

What should be said is that it is much more difficult to show empirical evidence for a distributed claim than a non-distributed claim. Both kinds of claims can come in distributed and non-distributed form:

1) Non-distributed positive: There exists one person who has a 5-inch nose.
2) Non-distributed negative: There exists one person who does not have a 5-inch nose.
3) Distributed positive: Everybody has a 5-inch nose.
4) Distributed negative: Nobody has a 5-inch nose.

It should be obvious these things show affirm/charge/distribution parity (assuming we can call positive/negative "charge" for want of a better word). That is, when you switch all three of affirm/deny, positive/negative, and distributed/non-distributed to the other, it's the same claim. E.g. trying to affirm 1 is the same as trying to deny 4.

It just so happens that most existential positive claims are non-distributed, and most existential negative claims are distributed, which is why people get confused.

 

[Oleron]

Re: Re: Help with a logic problem?

The statement is patently false anyway. I can prove there's not a blue whale in my bedroom simply by entering it.

Perhaps the question is better asked 'Why did you enter the bedroom? To find out if there is a blue whale there?'

OK so what if I said I saw a blue whale in your bedroom, you go and check (finding no whale) and tell me 'There is no whale in my bedroom'.

I then say 'Well it was definitely there, I'm convinced of it. Just because you can't see it right now doesn't mean it didn't happen.'

No matter how much you tell me otherwise I still hold my belief, when, in reality, I am either mad, mistaken or a hoaxer.
Now, according to some, we have real anecdotal evidence for the blue whale/bedroom hypothesis and therefore the claim should not be discounted.
I've lost count of the number of times I have heard similar arguments from believers.

Ian cannot prove a negative completely, all he can do is point out to me the fundamental unlikelyness of my assertion. For his own peace of mind he can put the blue whale/bedroom hypothesis in the mental box marked 'assume hypothesis is not true'. This is legitimate because:
(1) It would be a fundamentally unlikely and difficult thing to get a blue whale into Ian's bedroom.
(2) Ian has researched the evidence and found nothing but a vague anecdote from an unknown source.

BTW Ian, I think the whale is under the duvet, are you sure you've looked hard enough?