What is proof?

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zenten
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What is proof?

Postby zenten » Wed Aug 22, 2007 8:24 pm UTC

This keeps on popping up in threads all over the place. So I'm creating a thread for it, to point to people when they bring it up (and of course to actually discuss it).

So, to me proof is contextual. If I'm in a math class, it means something different in a physics class, which means something different in an economics class, which means something different to a journalist. This doesn't make any of these types (or other types) "wrong", it just makes them different.

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Postby chaosspawn » Wed Aug 22, 2007 8:36 pm UTC

In most "real life" situations (outside of math and equations) proof seems to mostly refer to statistics. Anecdotal evidence can only prove that an event has happened, but cannot prove trends (e.g. that it happens often). In order to make a more general statement you need more than just isolated incidents. Ideally you'd look at every possible occurrence, and make a judgment based on that. However, a well done study or survey is likely the best you can get.
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Postby Nosforit » Wed Aug 22, 2007 8:45 pm UTC

To me, proof is absolute and therefore confined to the realm of math. I'm of this mind because any discussion having followed logic far enough will conclude that nothing* can be know with absolute certainty and that there is always* room for doubt.


* This is except from affirming one's own existence, that one is in the process of experiencing, and that one is reasoning. These are the axioms which I base my philosophy on as well.
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Postby zenten » Wed Aug 22, 2007 8:48 pm UTC

Nosforit wrote:To me, proof is absolute and therefore confined to the realm of math. I'm of this mind because any discussion having followed logic far enough will conclude that nothing* can be know with absolute certainty and that there is always* room for doubt.


* This is except from affirming one's own existence, that one is in the process of experiencing, and that one is reasoning. These are the axioms which I base my philosophy on as well.


There's room for doubt with math too. You have no way of knowing that this isn't just some shared delusion of mathematicians, where the physical results just happen to usually work out.

Which is why I think narrow definitions that make the word useless are dumb.

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Postby Nimz » Wed Aug 22, 2007 8:51 pm UTC

Within the realm of mathematics, proof is not a difficult concept. Given the assumptions you make, can you logically deduce that the conclusion must happen? If so, it's a proof.

Within the realm of other sciences, proof in the mathematical sense may be impossible. The best you can do in many cases is provide a cogent argument with a strong indication that the conclusion will most likely happen.

Within the realm of justice, instead of trying to see what will happen, you try to see what already happened. Did that person do this dastardly deed? Historical certainty is impossible, as it requires every logically possible piece of evidence to be available. As soon as you aren't an eyewitness, that logically possible piece of evidence is no longer available. Even eyewitnesses can't be certain, as people can have false memories. The best you can do in this case is provide a strong argument, much like the non-mathematical sciences, but for the past rather than the future.

I'll describe one more type of proof - probably the simplest of all to understand. 1/2 % of alcohol (by volume) :lol:

As far as only being able to confirm ones own existence, I don't know that even that can be absolutely confirmed. If you accept a solipsist philosophy, who is to say that your reasoning isn't in the mind of the real solipsist? That said, I am philosophically a realist, but that's another discussion for another thread.
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Postby lorenith » Wed Aug 22, 2007 8:52 pm UTC

Nosforit wrote:* This is except from affirming one's own existence, that one is in the process of experiencing, and that one is reasoning. These are the axioms which I base my philosophy on as well.


How do you know that everything around you including your own body and experiences isn't just an projection of your mind?

Anyway, proof for me is something that can reliably be shown to be true often enough that when it's not true it's because of some weird circumstance, or freak happening. Like generally seat belts will keep you safe in a car crash, but on rare occurrences wearing a seat belt could result in death, where not wearing one would have saved you.

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Postby gmalivuk » Thu Aug 23, 2007 1:23 am UTC

I'm with zenten on this one. Proof (and thus truth) is a contextual thing. There's mathematical proof and mathematical truth, which are the most rigorous kind. (Well, maybe logical is more rigorus. Depends on your view of the relationship between math and logic.)

But there is also scientific proof. Logically, we might say that there is definitely a truth value (though unknowable) to the claim that Bigfoot exists but is completely undetectable. Scientifically, such untestable claims are undecidable. They effectively have no scientific truth value. The upside is that things which do have a scientific truth value can have that value proven (scientifically) in a way that wouldn't count as mathematical proof.

If, for instance, I claim that Bigfoot exists in a stable population size, and is in principle as detectable as any other animal of the same size, a skeptic could scientifically prove that I'm full of shit. They could go about doing this by looking everywhere a Bigfoot might be. Sure, not ever seeing incontrovertible evidence of one doesn't mathematically prove that none exist, it can eventually count as scientific proof.

All we need to do is figure out a probability value: If my claim were correct, with what probability could we expect to consistently fail to find any evidence whatsoever to support it? After all, a stable breeding population would be at least a few thousand individuals. They've all got hair and eat things and take shits and eventually die, so would presumably be leaving evidence all over the place. Given this, how likely is it that we still wouldn't have found any? Pretty close to nil. At which point we can scientifically conclude that Bigfoot doesn't exist.
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Postby Insignificant Deifaction » Thu Aug 23, 2007 2:37 am UTC

Proof is simply the best determination we can make of something based on evidence (which is a collection of observations point towards a certain conclusion, which leads to proof), it is therefore acceptable as fact so long as we have confirmed the evidence (and therefore observations) that make up the proof.

Also, I hate when people go into the "we might have absolutely everything wrong, we could be nothing more than a dream" sort of philosophy. There's no reason to think this might be the case. It might be applying occam's razor to say this, but things are as they seem, even if the reasons and causes are uncertain.
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Postby lorenith » Thu Aug 23, 2007 2:47 am UTC

Eh don't hate me I was just making a joke, I hate mind body problems myself.

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Postby __Kit » Thu Aug 23, 2007 5:41 am UTC

Since 11 I always thought of it as, knowledge being what you know/ have experienced, and information as what you have heard of and are pretty sure is true, but have no knowledge of it.

This is probably wrong, but I would say proof would have to have been recorded and helps if I 'know' it.
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I've also seen this popping up.

Postby grendelkhan » Thu Aug 23, 2007 5:52 am UTC

Forgive me if I assume too much, but I sometimes argue with creationists, and this tends to come up in the context of "all your evidence is based on fallible human knowledge, but I get my capital-T Truth from Jesus himself, which makes it superior".

As I don't have the postcount to post links yet, I can't provide examples, but there are plenty of capital-T Truths that people get by revelation, and they generally tend to suck as a source of knowledge.

On the other hand, pretty much everything we do in this world is based on the best explanation we have for the evidence at hand. This isn't proof in the same sense as mathematicians use it; we could be brains in jars, or a heretofore rather silent Demiurge could start playing cranky games. But this standard of "proof" is enough to sentence human beings to death ("a wizard did it" is not a generally accepted defense when your fingerprints are all over the knife and you're covered in blood); we routinely bet our lives on this sort of proof when we believe that the plane we fly in will stay aloft, that a stick we pick up won't magically turn into a venomous snake, or that trading oral sex with our partners won't cause us to be struck dead by twin bolts of lightning from a cloudless sky.

We do not, of course, bet our lives on capital-T Truth this way, mostly because revelatory Truth is predictably reluctant to act in a convenient way.

So, no, the sort of Proof that's being asked for doesn't exist in the real world... but it doesn't really need to, as what we've got is perfectly good enough to bet your life on.

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Postby Bondolon » Thu Aug 23, 2007 7:50 am UTC

gmalivuk wrote:I'm with zenten on this one. Proof (and thus truth) is a contextual thing. There's mathematical proof and mathematical truth, which are the most rigorous kind. (Well, maybe logical is more rigorus. Depends on your view of the relationship between math and logic.)

But there is also scientific proof. Logically, we might say that there is definitely a truth value (though unknowable) to the claim that Bigfoot exists but is completely undetectable. Scientifically, such untestable claims are undecidable. They effectively have no scientific truth value. The upside is that things which do have a scientific truth value can have that value proven (scientifically) in a way that wouldn't count as mathematical proof.

If, for instance, I claim that Bigfoot exists in a stable population size, and is in principle as detectable as any other animal of the same size, a skeptic could scientifically prove that I'm full of shit. They could go about doing this by looking everywhere a Bigfoot might be. Sure, not ever seeing incontrovertible evidence of one doesn't mathematically prove that none exist, it can eventually count as scientific proof.

All we need to do is figure out a probability value: If my claim were correct, with what probability could we expect to consistently fail to find any evidence whatsoever to support it? After all, a stable breeding population would be at least a few thousand individuals. They've all got hair and eat things and take shits and eventually die, so would presumably be leaving evidence all over the place. Given this, how likely is it that we still wouldn't have found any? Pretty close to nil. At which point we can scientifically conclude that Bigfoot doesn't exist.


I don't think you disagree with the logician/mathematician crowd in this case, as you're just saying that scientific proof is acceptance of abundance of evidence. While this is fine, and perfect for science, as, as I've harped again and again, inductive proof, in the meaningful sense of the word proof, is impossible. That doesn't mean that science can't show things to be likely true, it just can't ever make infallible claims. I'd say that this is a good thing though. To reflect the ever-interesting words of the great Dyson, science needs more heretics. Sometimes, science needs to be questioned *cough*Aristotelian science*cough*, and removing from science the ability to be questioned leads pretty quickly to intellectual bigotry. Can science have proof? Absolutely not. Could this ever be a bad thing? Unequivocally, no.

Science does have its own version of proof, which is acknowledgment of likelihood of truth by way of preponderance of evidence. It is good, in that it sets a reliable standard for showing what is probably the case, while never removing from the field of possibility that what seems overwhelmingly to be the case could very well not be.

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Re: What is proof?

Postby Andrew » Thu Aug 23, 2007 11:57 am UTC

zenten wrote:So, to me proof is contextual. If I'm in a math class, it means something different in a physics class, which means something different in an economics class, which means something different to a journalist. This doesn't make any of these types (or other types) "wrong", it just makes them different.


I don't think there are different "types" of proof (except logical classes like deductive and inductive); just different levels] of proof. Mathematics demands absolute certainty. Science demands absolute certainty but acknowledges that it's impossible and so it always considers the possibility that its proofs are wrong. A court of law demands proof "beyond reasonable doubt". Journalists require a bit of paper they can point to and refer to as "proof".

They're all the same thing: evidence. Just some is more watertight than others.

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Re: What is proof?

Postby zenten » Thu Aug 23, 2007 1:05 pm UTC

Andrew wrote:
zenten wrote:So, to me proof is contextual. If I'm in a math class, it means something different in a physics class, which means something different in an economics class, which means something different to a journalist. This doesn't make any of these types (or other types) "wrong", it just makes them different.


I don't think there are different "types" of proof (except logical classes like deductive and inductive); just different levels] of proof. Mathematics demands absolute certainty. Science demands absolute certainty but acknowledges that it's impossible and so it always considers the possibility that its proofs are wrong. A court of law demands proof "beyond reasonable doubt". Journalists require a bit of paper they can point to and refer to as "proof".

They're all the same thing: evidence. Just some is more watertight than others.


I'm not convinced it's one dimensional like that. Look at civil law versus criminal law. In criminal law, you have that "beyond a reasonable doubt" thing, in civil law it's who is most likely to be true. So being proven guilty in criminal is stronger than civil, but being proven innocent is weaker. There is also the situation of proof that can be changed, to proof that can't, such as an appeal.

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Re: What is proof?

Postby Andrew » Thu Aug 23, 2007 1:51 pm UTC

zenten wrote:I'm not convinced it's one dimensional like that. Look at civil law versus criminal law. In criminal law, you have that "beyond a reasonable doubt" thing, in civil law it's who is most likely to be true. So being proven guilty in criminal is stronger than civil, but being proven innocent is weaker.


You're never "proven innocent" in a criminal court. You are merely not proven guilty. That's why there's no "innocent" plea or verdict; just "not guilty". I believe it's commonplace for a civil case to be brought after a failed criminal one, to try to capitalise on the lower standard of proof required. The defendant in the civil case can't cite the criminal one as precedent.

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Re: What is proof?

Postby zenten » Thu Aug 23, 2007 1:53 pm UTC

Andrew wrote:
zenten wrote:I'm not convinced it's one dimensional like that. Look at civil law versus criminal law. In criminal law, you have that "beyond a reasonable doubt" thing, in civil law it's who is most likely to be true. So being proven guilty in criminal is stronger than civil, but being proven innocent is weaker.


You're never "proven innocent" in a criminal court. You are merely not proven guilty. That's why there's no "innocent" plea or verdict; just "not guilty". I believe it's commonplace for a civil case to be brought after a failed criminal one, to try to capitalise on the lower standard of proof required. The defendant in the civil case can't cite the criminal one as precedent.


Ok, but you're still proven "not guilty". Not, "Well, you might be guilty, but we're not sure". Legally, you did not do it, 100%, no questions asked. Talking about systems based on British law of course, I'm sure there are countries that work differently.

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Postby Yakk » Thu Aug 23, 2007 2:59 pm UTC

A Proof of a Statement X is an sequence of statements that provides sufficiently strong evidence for X.

In general, the Proof should be in some way easier to verify than the statement X itself.

The level of strength of the evidence, and the ease of verification, varies by domain and use of the term Proof.

...

The "ideal" mathematical proof would consist of human-readable simple steps whose connection could be mechanically verified by a proof checker. For the most part, these proofs do not exist. Even proof checker checkbable proofs that aren't human readable tend not to exist for more mathematical beliefs.

The standards of "strength of evidence" and "ease of verification" are much higher in mathematics than in other domains, but they are not absolute.

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Re: What is proof?

Postby Andrew » Thu Aug 23, 2007 3:44 pm UTC

zenten wrote:Ok, but you're still proven "not guilty".


No, you're assumed "not guilty". You're innocent until proven guilty. That's the whole point, surely?

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Postby gmalivuk » Thu Aug 23, 2007 4:24 pm UTC

Bondolon wrote:To reflect the ever-interesting words of the great Dyson, science needs more heretics. Sometimes, science needs to be questioned *cough*Aristotelian science*cough*, and removing from science the ability to be questioned leads pretty quickly to intellectual bigotry. Can science have proof? Absolutely not. Could this ever be a bad thing? Unequivocally, no.

Science does have its own version of proof, which is acknowledgment of likelihood of truth by way of preponderance of evidence. It is good, in that it sets a reliable standard for showing what is probably the case, while never removing from the field of possibility that what seems overwhelmingly to be the case could very well not be.


Perhaps I should have made it more clear that scientific proof is always in some sense tentative. I'm not saying everyone must believe in evolution because that's what Science says happened. I'm just saying that, with the amount of evidence pointing in that direction, you better have one hell of a lot of real counterexamples for me to even glance in your direction when I hear you shouting about how evolution is a lie being perpetuated by some Grand Conspiracy of Scientists who don't allow heresy.

Andrew wrote:
zenten wrote:Ok, but you're still proven "not guilty".


No, you're assumed "not guilty". You're innocent until proven guilty. That's the whole point, surely?


The original point still stands, though: Criminal trial criteria are more strict, so criminal guilt is stronger and criminal "not-guilt" is correspondingly weaker than in a civil case.
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Postby zenten » Thu Aug 23, 2007 4:34 pm UTC

Silly me, I just realized the difference.

In math and science there's a maybe. That maybe could last forever. In law, once the trial is done, it's either yes or no.

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Postby Nosforit » Thu Aug 23, 2007 4:48 pm UTC

Nimz wrote:If you accept a solipsist philosophy, who is to say that your reasoning isn't in the mind of the real solipsist?

Because I am aware, and therefore I AM the real solipsist.

lorenith wrote:How do you know that everything around you including your own body and experiences isn't just an projection of your mind?

I don't. That's the whole point. I have no direct connection with physical reality, as I am not directly aware of the chemical reactions in my brain. There is some sort of black box between physics and awareness that has not yet been explored.

Still I experience certain patterns life, but knowing that they will always be the same requires a priori knowledge of things. Such is only possible in the domain of reason, hence logic and hence math. More on this here: http://en.wikipedia.org/wiki/A_priori_a ... losophy%29
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