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]

Originally posted by 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?

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

[Tricky]

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.
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]

Originally posted by Tricky
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]

Originally posted by Tricky
[B]
--------------------------------------------------------------------------------
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]

Originally posted by Interesting Ian
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.

Originally posted by Interesting Ian
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?

Originally posted by Interesting Ian
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?).

Originally posted by Interesting Ian
Then arguably it wouldn't be a blue whale by definition.
Again, by your definition. You are ignoring the Metaphysical Blue Whale.

Originally posted by Interesting Ian
They are not the creatures of interest.
To you.

Originally posted by Interesting Ian
Disobeys physical laws.
So do "souls", yet you believe in them.

Originally posted by Interesting Ian
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]

Originally posted by The idea
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]

Originally posted by Cecil
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]

Originally posted by Cecil
Tricky, you're being a little obtuse.
No, I'm being satirical. I obviously don't believe the crap I wrote.
Originally posted by Cecil
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.

Originally posted by Cecil
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.

Originally posted by Cecil
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.

Originally posted by Cecil
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.)

Originally posted by Cecil
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.

Originally posted by Cecil
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]

Originally posted by 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?

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]

Originally posted by 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. ;)

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]

Originally posted by Cecil
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]

Originally posted by Hazelip
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]

Originally posted by Hazelip
"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]

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.

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?

[TheBoyPaj]

"... and it went... wherever I.... did go!"

(10 points await you for the source)

[Oleron]

Originally posted by TheBoyPaj
"... and it went... wherever I.... did go!"

(10 points await you for the source)

'The Meaning of Life'

Do I get the 10 points?

[ceo_esq]

You might want to check out this thread regarding proving a negative:

http://host.randi.org/vbulletin/showthread.php?s=&threadid=22830

[Hazelip]

Originally posted by Abdul Alhazred
Wouldn't a mathematical proof by contradiction be proving a negative? Could you provide an example? I don't mean to be dense, but when I referred to proofs, I was referring to logical proofs. Mathematics has never been my strong suit, so I am unable to come up with a proof such as you ask about off the top of my head...

[Darat]

Originally posted by Garrette
Warning: Unresearched ramblings of a non-philosopher and poorly educated man follow:

...snip...

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

Just my two dinar.

I agree with your stance on this. It's the main reason why I always try to ask what a person means when they use the term "psi". Unfortunately in my experience very few people putting forward a belief in "psi" are willing to define what they mean which means that it isn't possible to debate with them.

[TheBoyPaj]

Originally posted by Oleron


'The Meaning of Life'

Do I get the 10 points?

You do. They are in the cupboard.

[Abdul Alhazred]

Originally posted by Hazelip
Could you provide an example? I don't mean to be dense, but when I referred to proofs, I was referring to logical proofs. Mathematics has never been my strong suit, so I am unable to come up with a proof such as you ask about off the top of my head...

Well, just off the top of my head: Prove that there are no three consecutive integers that add up to 100.

Start by assuming that they exist. Call the middle one x.

(x - 1) + (x) + (x + 1) = 100
3x = 100, which violates the assumption that x is an integer.

Negative proved.

[Interesting Ian]

Originally posted by Garrette


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

[/B]

Psi is only defined negatively. Anomalous cognition simply means obtaining information where normal sensory channels have been eliminated. One can disprove it by simply showing that some ostensibly psi phenomena in fact were communicated using such normal sensory channels.

This generally has been a failure.

[Interesting Ian]

Originally posted by Oleron
[B]

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.



Well I have no idea what arguments these might be. Could you give an example where I have ever made a similar argument?

[Interesting Ian]

Originally posted by Darat


I agree with your stance on this. It's the main reason why I always try to ask what a person means when they use the term "psi". Unfortunately in my experience very few people putting forward a belief in "psi" are willing to define what they mean which means that it isn't possible to debate with them.

See my definition above. BTW psi refers to anomalous perturbation (psychokinesis) as well as anomalous cognition (esp). But they both are only defined negatively ie nothing positive is said about them.

[The Don]

Originally posted by Interesting Ian


Well I have no idea what arguments these might be. Could you give an example where I have ever made a similar argument?
I'm not sure that there was an attack on you here. I think there was merely an attempt to demonstrate how difficult it can be to obtain objective evidence of things particularly when one party is intransigent.

You are sooooo touchy sheesh!

[Oleron]

Originally posted by The Don

I'm not sure that there was an attack on you here. I think there was merely an attempt to demonstrate how difficult it can be to obtain objective evidence of things particularly when one party is intransigent.

You are sooooo touchy sheesh!

True. That is exactly what I was trying to demonstrate.

[Garrette]

Originally posted by Interesting Ian:

Psi is only defined negatively. Anomalous cognition simply means obtaining information where normal sensory channels have been eliminated. One can disprove it by simply showing that some ostensibly psi phenomena in fact were communicated using such normal sensory channels.

For you, perhaps, it is only defined negatively. I don't think everyone agrees with you.

But I'll address your contention. I suggest that it's not just the elimination of normal sensory information that is necessary but also the accounting for probability (or statistics; someone else will know the proper terminology usage).

Further, according to this definition, you're simply saying it's "The Psi of the Gaps." It apparently is a religion to you.

[Interesting Ian]

Originally posted by Garrette
[B]

For you, perhaps, it is only defined negatively. I don't think everyone agrees with you.



Then they are wrong.



But I'll address your contention. I suggest that it's not just the elimination of normal sensory information that is necessary but also the accounting for probability (or statistics; someone else will know the proper terminology usage).



I said obtaining information. By definition that rules out chance.



Further, according to this definition, you're simply saying it's "The Psi of the Gaps." It apparently is a religion to you.

Can't help that. That's how it's defined.

[Garrette]

Interesting Ian:

Then they are wrong.

:D

Interesting Ian:

I said obtaining information. By definition that rules out chance.


Now that you've define it that way, okay.


Interesting Ian:

Can't help that. That's how it's defined.

No. That's not a definition. It's the absence of one.

[Hazelip]

Originally posted by Abdul Alhazred
Well, just off the top of my head: Prove that there are no three consecutive integers that add up to 100.

Start by assuming that they exist. Call the middle one x.

(x - 1) + (x) + (x + 1) = 100
3x = 100, which violates the assumption that x is an integer.

Negative proved. Um...isn't everthing on the right side of the = nothing more than a conclusion?

[Abdul Alhazred]

Originally posted by Hazelip
Um...isn't everthing on the right side of the = nothing more than a conclusion?

Not a fully rigorous proof. The rules of arithmetic and algebra are assumed as axioms.

To continue more rigorously:
3x = 100
x = 33 1/3

and of course 32 1/3 + 33 1/3 + 34 1/3 = 100
but those are not integers.

So I have proven that no three consecutive integers add to 100.

[Hazelip]

Abdul, you have not proven a negative. You have provided evidence of everything but a lack of three consecutive integers producing a sum of 100. You're working backwards from your conclusion.

A conclusion can be reached in light of evidence. If there is no evidence, after repeated accurate (we are talking math here...) attempts to yield a particular result, it is then and only then reasonable to conclude that the opposite of what you have been able to produce does not exist.

In other words, you can prove that three consecutive integers yield a result other than 100 all day and night. After checking your work, and your results, you may then reasonably conclude that there are no three consecutive integers that yield a value of 100. That is a conclusion, it is based on evidence, it is not evidence in and of itself.

[Abdul Alhazred]

Originally posted by Hazelip
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.

OK. What precisely is the is the difference between "conclusion" and "proof"?

In mathematics they are the same.

[Abdul Alhazred]

Originally posted by Hazelip
Abdul, you have not proven a negative. You have provided evidence of everything but a lack of three consecutive integers producing a sum of 100. You're working backwards from your conclusion.


In mathematics, this is known as proof. Working backwards is legitimate. I do not understand what you mean by proof.

[Loki]

Thanx epepke

[phildonnia]

The technique of "perfect induction" can be used to prove a negative. If you were somehow able to observe every blue whale in the universe, and none of them were in your room, then you'd have the proof.

This technique is quite useful for proving things about finite sets, but it doesn't have much application for finite sets, let alone vague philosophy.

The real problem here is that the existence of God is not falsifiable: that is, there is no imaginable phenomenon that would disprove the God hypothesis. This doesn't amount to a proof that God doesn't exist, but it does mean that logic and science are unable to test the matter.

[Hazelip]

Abdul, I did not introduce mathematics, Cecil did. You explain to me what you mean, and then I'll respond. I'm talking about logic and critical thinking. I'm not ducking and weaving, I'm just trying to get a handle on this aspect of the discussion.

I think we're both approaching the same thing from different disciplines. I'm afraid we may be dancing right past one another here...

Now, about my idea as to why "you can't prove a negative" is an acceptable thing to say, even though it cannot be proven? "You can't prove a negative" is a conclusion based upon a preponderance of evidence that only positives can be proven.

[Hazelip]

Abdul?

[Abdul Alhazred]

mistake. see next.

[Abdul Alhazred]

Well gee whiz. I can't be here all the time, but I'm back. :)

To me, logic and mathematics are inseparable. And only in that realm is it reasonable to speak of absolute proof.

But what of non-absolute proof?

To my way of thinking, critical thinking means plausible inference, not proof.

For example, I believe King David was a real person even though I don't believe everything the Bible says about him.

A bit of archaeological evidence combined with what the Bible says leads me to the conclusion that most likely King David actually existed.

The non-Biblical evidence, though fragmentary, is the determining factor. But only in light of the Bible.

This is different from the Biblical "evidence" that Noah existed. In King David's case we have slight corroboration from other sources and no scientific evidence against the nasty dynastic struggles.

Just as the story of George Washington and the cherry tree, though false, is still evidence that George Washington existed. But not proof.

This is much weaker than "proof", but it's good enough for most purposes.

There is also the legal definition of proof "beyond a reasonable doubt". That's stronger than plausible inference as explained above, but weaker than mathemetical proof.

[Hazelip]

Abdul, you're bringing up some other stuff here. Coming close to straw man, but not quite.

Here's the thing about your mathematical example. Stating that no three consecutive integers add up to 100 is a statement of conclusion. You're working backwards from knowledge you already possess.

Somewhere, a loooong time ago, some mathematician, probably Greek, decided to find out if three consecutive integers could add up to 100. He added them up and checked the totals again and again. He could find no evidence that any three consecutive integers would add up to 100. Based upon those findings, he concluded that no three consecutive integers add up to 100.

Thousands of years later, you now present his conclusion, and the calculation as proof. That is wrong.