What can we prove?

[HarryKeogh]

I understand theories are theories not because they are based on scant evidence but because they cannot be proven and new information can come to light which would require us to alter the theory to suit the new evidence. And from what i've read it seems only mathematics can be proven.

is it correct to say if something is based on observations it can't be proven?

e.g. can i prove the moon revolves around the earth? why or why not? i understand how we can't prove the theories of gravity that keeps the moon revolving around us but can we prove the simple observation "the moon revolves around the earth"?

to me this seems as obvious and testable as 1+1=2.

is there some philosophical element to it (e.g. how can we really know anything) that forces us to acknowledge the observable (no matter how obvious) as theory and not absolute fact?

i think (at least i hope) im stuck on a semantic issue that someone could help clear up for me. thanks!

[Stimpson J. Cat]

HarryKeogh,

is it correct to say if something is based on observations it can't be proven?

Strictly speaking, no.

It is possible to formally prove things based on observations, but only if we make assumptions about our observations. And those assumptions cannot be proven.

This is nothing special, though. All logical frameworks are based on assumptions which cannot be proven.

The problem is that the type of assumptions that would allow you to "prove" things based on observations, aren't very useful.

The scientific method is based on assumptions, but those assumptions do not allow you to prove anything based on observations. Instead, they allow you to gather supporting evidence for a hypothesis, and then establish a confidence level for that hypothesis.

In many cases, like your moon example, that confidence level is so close to 100% that it almost becomes meaningless to say that it is not 100%. But technically speaking, it is less than 100%. In fact, our confidence in any conclusion about the world that we draw from our observations, is necessarily less than our confidence in the scientific method itself. And that confidence is always slightly less than 100%, because we can never formally prove that the assumptions of science are true.

Dr. Stupid

[ceptimus]

You don't even have to observe the things that your theory is about to gather supporting evidence.

Suppose my theory is, 'All dogs bark'.

Then by pure logic, I rearrange this to say, 'Any non-barking object is not a dog'.

If the second version of the theory is correct then so is the first.

So I can go about my daily business, observing as I go any non-barking objects, say my car, the curtains, a paving stone, a lump of coal, etc. And so I gather supporting evidence for my theory.

[patnray]

I disagree. Your observation of non-barking objects is not very useful in supporting the theory that "All dogs bark" because those observations do not rule out competing theories, such as "There is at least one species of non-barking dog". Furthermore, no observsation of non-barking objects that are not dogs could ever disprove your theory. Your theory could be disproven by finding one non-barking dog. Your theory would be well supported, but not quite proven, by observing that every species of dog barks (which would disprove the alternative theory).

That's just the way it is. Things can be conclusively disproven rather easily. Proof, however, is much more difficult. As mentioned above, the best we can hope for is increasing confidence...

[Keneke]

We went round and round this issue a while back. I seem to recall enjoying the debate.

There's always going to be gaps between what we see and what we can say what we see...is. Like Stimpy said, we can never be 100% sure about ANYTHING. Ever. Not realistically.

So, we must backtrack a bit. What is? What is self evident? At what point do things get shunted into the background of your mind because they're almost totally predictable and bound to be true?

It's this leap over the gap, the assumption, which allows us to simplify our lives. It's funny that "always", "never", and even "is" are words that represent abstract values, logically speaking. But in the end, you have to accept some sort of world-view. That's why woo-woo beliefs are so prevalent; it's so easy to have proof of nothing, and therefore believe in everything.

Skepticism and science are simply efforts to shrink the gaps as much as possible. That's why it's not for everyone: it takes a lot of work. But you'll be happy when you don't even have to have a running start to leap over to the other side. ;)

[ceptimus]

I never said my method was a particularly effective way of gathering supporting evidence. But it does nethertheless work, albeit slowly.

Every non-barking object that is not a dog that I observe makes me slightly more confident that my theory is right. Should I ever have the time and patience to examine all the non-barking objects in my universe, and verify that none of them are dogs, then my theory will have been proven.

[fishbob]

It helps if you just remove the word "proof" from your science vocabulary. It is a perfectly useful word in Math and Law (edit to add: and making whiskey), but just does not apply to the scientific process.

[wollery]

Originally posted by ceptimus
You don't even have to observe the things that your theory is about to gather supporting evidence.

Suppose my theory is, 'All dogs bark'.

Then by pure logic, I rearrange this to say, 'Any non-barking object is not a dog'.

If the second version of the theory is correct then so is the first.

So I can go about my daily business, observing as I go any non-barking objects, say my car, the curtains, a paving stone, a lump of coal, etc. And so I gather supporting evidence for my theory.
Sorry ceptimus, but this just doesn't work. As a theory `all dogs bark' is fine, but you simply cannot extrapolate that to 'any non-barking object is not a dog'. This totally misses the possibility that other things bark, which is in no way covered by the original theory. That would be a perfect example of a logical fallacy, not to mention bad science! :(

[Jim_MDP]

Originally posted by ceptimus
I never said my method was a particularly effective way of gathering supporting evidence. But it does nethertheless work, albeit slowly.

Every non-barking object that is not a dog that I observe makes me slightly more confident that my theory is right. Should I ever have the time and patience to examine all the non-barking objects in my universe, and verify that none of them are dogs, then my theory will have been proven.

Never heard (of) a seal, eh?

:p

[Diamond]

A science joke.

An astronomer, a physicist and a mathematician were on a train in Scotland. Suddenly the astronomer exclaims "Look at that field! There's a black sheep! Maybe all sheep in Scotland are black!" The physicist looks and says "No, perhaps most sheep in Scotalnd are black!". The mathematician sighs, rolls his eyes heavenward and says "You are both incorrect. In a place called Scotland there exists at least one field, which contains at least one sheep, at least one side of which is black!"

[HarryKeogh]

Originally posted by Diamond
A science joke.

An astronomer, a physicist and a mathematician were on a train in Scotland. Suddenly the astronomer exclaims "Look at that field! There's a black sheep! Maybe all sheep in Scotland are black!" The physicist looks and says "No, perhaps most sheep in Scotalnd are black!". The mathematician sighs, rolls his eyes heavenward and says "You are both incorrect. In a place called Scotland there exists at least one field, which contains at least one sheep, at least one side of which is black!"

in space no one can hear you laugh.

[Diamond]

Originally posted by HarryKeogh


in space no one can hear you laugh.

Intellectual humor is wasted on nerds. It was to the point of the thread though.....

[ceptimus]

Originally posted by JamesMGMDP


Never heard (of) a seal, eh?

:p You're missing the point. A barking seal is fine and does nothing to stop my gathering supporting evidence. What I am looking for is non-barking objects. Every non-barking object I see, that turns out not to be a dog, adds a little evidence.

I suppose I might find a non-barking object that turned out to be a dead dog - that might invalidate my theory - but of course it equally well invalidates the original theory of "All dogs bark". I'm not going to count a dead dog as a dog for the purpose of my theory anyway.

The two statements:

1. All dogs bark.

2. All non-barking objects are not dogs.

Mean EXACTLY the same thing. They are logically equivalent.

[ceptimus]

Originally posted by wollery

Sorry ceptimus, but this just doesn't work. As a theory `all dogs bark' is fine, but you simply cannot extrapolate that to 'any non-barking object is not a dog'. This totally misses the possibility that other things bark, which is in no way covered by the original theory. That would be a perfect example of a logical fallacy, not to mention bad science! :(
Sorry, you're just plain wrong. See my previous post.

[Martin]

Originally posted by ceptimus
The two statements:

1. All dogs bark.

2. All non-barking objects are not dogs.

Mean EXACTLY the same thing. They are logically equivalentCeptimus is entirely correct, folks. Observe:

If it is a dog, then it barks
It doesn't bark
Therefore, it's not a dog

Simple.

[Diamond]

Originally posted by Martinm
Ceptimus is entirely correct, folks. Observe:

If it is a dog, then it barks
It doesn't bark
Therefore, it's not a dog

Simple.

Yes but a seal barks. Is it a dog?

[ceptimus]

Originally posted by Diamond


Yes but a seal barks. Is it a dog? No. A barking seal does nothing to disprove the theory, "All dogs bark".

As the statement, "Any non-barking object is not a dog" means exactly the same thing, then a barking seal does nothing to disprove that either.

Hmmm... lets look around. I see plenty of non-barking objects: A biro, my computer screen, a piece of paper, my wristwatch. More evidence has been gathered!

[Martin]

Originally posted by Diamond
Yes but a seal barks. Is it a dog?He didn't say that only dogs bark. What he said is this:

IF it's a dog, THEN it barks.

Or, more formally,

A -> B

What you're asserting here is ¬A & B. But then we have

¬A v B -> (A -> B)
¬A & B
¬A
¬A v B
A -> B

so this does not falsify the hypothesis.

[69dodge]

I have a theory that all dogs bark loudly. I see a cat. It doesn't bark loudly and it isn't a dog. So it's evidence in favor of my theory.

You have a theory that all dogs bark softly. You see the same cat. It doesn't bark softly and it isn't a dog. So it's evidence in favor of your theory too.

Oops. :p

How can the same observation be evidence in favor of two contradictory theories?

[davefoc]

For me, I think, S. J. Cat said pretty much everything there is to say about this topic when he said:
This is nothing special, though. All logical frameworks are based on assumptions which cannot be proven.

There are no magic bullets, nothing is knowable to a certainty, maybe not even that.

Still, I spent quite a bit of time musing about this subject around the time of the O.J. Simpson trial. For me, the evidence was well beyond reasonable doubt and approached certainty.

But what did that mean, was I just as certain that Simpson was guilty as that world war II happened. Well I guess not, So there seemed to be degrees of near certainty for me. And how could I be this certain that Simpson was guilty when so many people disagreed wtih me. In the end, my views had to be based on how I expected people to act, perhaps my biases were not letting me see that people will act in very different ways than I expect. Anyway I spent about six months musing about the differences between philosophical certainty and practical certainty and what was provable and as near as I can tell, I discovered nothing of interest and I suppose anybody that has read this far will pretty much agree with that.

[ceptimus]

Originally posted by 69dodge
I have a theory that all dogs bark loudly. I see a cat. It doesn't bark loudly and it isn't a dog. So it's evidence in favor of my theory.

You have a theory that all dogs bark softly. You see the same cat. It doesn't bark softly and it isn't a dog. So it's evidence in favor of your theory too.

Oops. :p

How can the same observation be evidence in favor of two contradictory theories? That's interesting. Our two theories are now:

Your's: All non-loudly-barking objects are not dogs.

Mine: All non-softly-barking objects are not dogs.

The cat that doesn't bark is indeed evidence in favour of both theories.

Imagine we were mad enough to actually try to prove our theories by this long-winded method. After billions of years of effort we have examined all the non-barking objects we can find - grains of sand, coffee machines, everything. None of them turned out to be dogs. Also, of course, none of them turned out to be seals. At this point we have proved at least two theories: 'All dogs bark', and 'All seals bark'.

Now we are in a position to test our competing theories - there are no more non-barking objects left to examine, but there will be a mixture of loudly-barking and softly-barking things out there. To gather evidence for your theory, you will be looking for non-loudly-barking objects. I will be searching for non-softly-barking objects. We might both find seals, audio playback devices, mechanical models of dogs, etc. but eventually, either you will find a non-loudly-barking object that is a dog, and/or I will find a non-softly-barking object that is a dog. At this point, one or both of our theories will have been disproved.

For those that missed it above, I have already admitted that the method I propose is a ridiculous way of going about the research. However, from a logical standpoint every non-barking non-dog observed does add an infinitesimal amount of evidence in support of the theory.

[clusterm2]

Originally posted by ceptimus
You don't even have to observe the things that your theory is about to gather supporting evidence.

Suppose my theory is, 'All dogs bark'.

Then by pure logic, I rearrange this to say, 'Any non-barking object is not a dog'.

If the second version of the theory is correct then so is the first.

So I can go about my daily business, observing as I go any non-barking objects, say my car, the curtains, a paving stone, a lump of coal, etc. And so I gather supporting evidence for my theory.

My gran had a box to warn would be burglars off that barked. 'twas't a dog though

[EdipisReks]

Originally posted by clusterm2


My gran had a box to warn would be burglars off that barked. 'twas't a dog though

that is as irrelavant as the seals.

[BillyJoe]

Wouldn't be much of a burgler if he barked. :cool:

[Diamond]

Originally posted by BillyJoe
Wouldn't be much of a burgler if he barked. :cool:

I suppose that remark was inevitable. But then, so is this emoticon :rolleyes:

[athon]

I see what ceptimus is getting at, albeit rather clumsily.

What he is doing is trying to disprove his hypothesis. The scientific method can be applied in a number of ways, however always amounts to taking a hypothesis and trying to disprove it.

Why? Because as has already been said, you can 'prove' things in maths and law, but in science we explore the weight of evidence.

This can be messy, as there is no quantitative amount of evidence that amounts to proof. A hypothesis becomes a theory if it can be used to correctly anticipate an event. Using this 'dog' example, if you use the hypothesis 'all dogs bark', and you look at an animal and say 'it's a dog, it should bark', and it does, the hypothesis becomes a theory (this barking dog thing is a little barking mad, but I'll play along).

A theory becomes 'robust' if it can be repeated.

Now, a hypothesis cannot truly be proven. There could always be a 'negative' lurking unseen somewhere you haven't looked. It can, however, be disproven. 'All four legged animals are pink' is a hypothesis that can be supported (every four legged animal seen to be pink adds weight) or, in one foul swoop, disproven (oh look! a purple four legged animal!). One way, you could still be wrong. The other, you will have your answer immediately.

Hence 'all dogs bark' can be given the weight of evidence, or disproven. Just find a dog that doesn't bark and your hypothesis has been disproven. The scientific method works best if you can disprove things rather than 'prove' them.

Athon

[xouper]

athon: I see what ceptimus is getting at, albeit rather clumsily.What ceptimus is getting at with the barking dog is also known as Hempel's paradox
http://www.google.com/search?q=%22Hempel%27s+paradox%22

In Hempel's 1937 version, it was black crows, summarized by some un-named smart-ass:

<blockquote>I never saw a purple cow
But if I were to see one
Would the probability ravens are black
Have a better chance to be one?</blockquote>With apologies to Frank Gelett Burgess, author of the original Purple Cow poem.

[BillyJoe]

Originally posted by Diamond
I suppose that remark was inevitable. Yeah well, that's why I was hiding behind the dark specs. :rolleyes:
Originally posted by Diamond
But then, so is this emoticon :rolleyes: ;)