Is it true?

[Guitarmasterx7]

Draw a circle on the ground. Say aloud, "A cat is not inside this circle."
Have you just proven a negative?.

If you're saying what I think you're saying, no, you have not and CAN not prove a negative, you have only disproved a positive. Before you drew the circle there was nothing to prove that the cat wasn't inside. You can't really prove a negative because there is no such physical thing, and even if you never DREW the circle and said "a cat is not in the circle" the circle would in this case have to be created with your mind beforehand, so you're still disproving a positive.

But if by "prove a negative" you're saying that you can't prove information to be false, then yes, you can.

 

[Grand_Marquis]

Draw a circle on the ground. Say aloud, "A cat is not inside this circle."
Have you just proven a negative?.

As for the cat, what you have proven is merely the fact that you haven't seen a cat inside that circle at that time under that atmospheric preasure, temperature. Alternatively, you would have to prove that the cat isn't invisible. I guess you could say, there is no visible cat (by human eyes) in this circle.

So basically your response to that is "what Grand_Marquis said".

 

[Kaboose the Moose]

I wager a quantum physicist (or our own bodily rhythms [http://www.physorg.com/news132055021.html]) has already found 1 + 1 equals something other than 2, but we still roll with it because it produces results for matters of everyday measurement.

I will say that, in a point that supports math, we have found that there's some interesting correlations to be found in nature in things such as exponential growth (which works for living creatures identically to bank inflation) and plant spirals [http://www.math.smith.edu/phyllo/EXPO/].

However, the bottom line is that you'll never find a number in nature and be able to put it in a jar. It remains a mechanism of measurement. The numbers themselves may be meaningless, but the patterns that emerge as we measure with it, on the other hand, would seem (insofar as we're capable of perceiving) to be very real.

Initially the statemnt was that "things which are removed from reality aren't significant to prove". Which I am more than willing to accept. However, if you consider maths to be a "mechanism for measurement", even if it is not quantifiable in nature, it then cannot be considered as "removed from reality" for it has a physical purpose to serve and its existance directly influences our reality.

Then you say that while it (numbers) may be meaningless, the patterns resulting from these are very real.

Numbers and by proxy mathematics cannot be bent to fit the whims of definitions. It either exists or it doesn't. Numbers, unlike Schrodinger cat , cannot exist in a state of partial reality.

Draw a circle on the ground. Say aloud, "A cat is not inside this circle."
Have you just proven a negative?.

As for the cat, what you have proven is merely the fact that you haven't seen a cat inside that circle at that time under that atmospheric preasure, temperature. Alternatively, you would have to prove that the cat isn't invisible. I guess you could say, there is no visible cat (by human eyes) in this circle.

So basically your response to that is "what Grand_Marquis said".

Bugger me, I hadn't noticed your post before!.

Indeed: what he said.

 

[geldonyetich]

I wager a quantum physicist (or our own bodily rhythms [http://www.physorg.com/news132055021.html]) has already found 1 + 1 equals something other than 2, but we still roll with it because it produces results for matters of everyday measurement.

I will say that, in a point that supports math, we have found that there's some interesting correlations to be found in nature in things such as exponential growth (which works for living creatures identically to bank inflation) and plant spirals [http://www.math.smith.edu/phyllo/EXPO/].

However, the bottom line is that you'll never find a number in nature and be able to put it in a jar. It remains a mechanism of measurement. The numbers themselves may be meaningless, but the patterns that emerge as we measure with it, on the other hand, would seem (insofar as we're capable of perceiving) to be very real.

Initially the statemnt was that "things which are removed from reality aren't significant to prove". Which I am more than willing to accept. However, if you consider maths to be a "mechanism for measurement", even if it is not quantifiable in nature, it then cannot be considered as "removed from reality" for it has a physical purpose to serve and its existance directly influences our reality.

Then you say that while it (numbers) may be meaningless, the patterns resulting from these are very real.

Numbers and by proxy mathematics cannot be bent to fit the whims of definitions. It either exists or it doesn't. Numbers, unlike Schrodinger cat , cannot exist in a state of partial reality.

I dare say I can imagine a number of things, numbers and patterns included, which do not really exist. Understand that my definition of things that exist does not include things that exist only in the mind. As numbers only exist in the mind, so also does their irrefutable nature. This is no Shrodinger's cat enigma.

The patterns we observe from nature, with or without numbers, are just the shadows on Plato's cave. However, that they seem to exist in relatively consistent patterns suggests that there is a fundamental reality that numbers are capable of measuring.

That numbers have proven to be such a versatile and powerful tool (why, the very boxes we're typing this on now run primarily on the theory of numbers) suggests they are sound. However, when push comes to shove, we cannot produce a tangle number, in and of itself, without the loss of fidelity that comes with trying to reduce a real thing into one.

 

[Kaboose the Moose]

I dare say I can imagine a number of things, numbers and patterns included, which do not really exist. This is no Shrodinger's cat enigma.

Understand that my definition of things that exist does not include things that exist only in the mind.

You can spew tautology all you want but it still bears no relevance or sense in this matter.

If you can imaging something, be it real or unreal, it exists for as long as you contemplate it's existence. It may not be physical but it exists in some dimension. If you think about 'dragons' then the dragon exists in your head. It cannot exist in the physical plane as far as we know it, but the dimension that is your head, will hold it's existence. It may not be the Copenhagen interpretation of Shrodinger's Cat theory but the concept of "existing and not existing at the same time" still holds.

 

[McHanhan]

It would be the truth, unless you drew a circle around a cat or if one were to step into the circle in which case it would be false.

you could prove that there is no cat in the circle by one of any dozen scientific or mathematical means, or you could just get some witnesses to verify that there is indeed no cat in the circle.

It isn't about whats true or false in a statement. It's about proving something by means of disproving. There is a vast difference between the two, a difference men (and women..I don't discriminate) with big, long beards like to ponder about on oak tables next to a fireplace.

Draw a circle on the ground. Say aloud, "A cat is not inside this circle."
Have you just proven a negative?.

As for the cat, what you have proven is merely the fact that you haven't seen a cat inside that circle at that time under that atmospheric preasure, temperature. Alternatively, you would have to prove that the cat isn't invisible. I guess you could say, there is no visible cat (by human eyes) in this circle.

All in all it's an utter chore the business of proving a negative. You would have to prove through millions of possible though highly implausible scenarios (intangible cat, invisible cat, submicroscopic cat, cat which exists a half second forward/behind you in the time stream, cat is there but your faith isn't great enough to see it...) that there is no cat there. Basically impossible, since most of those scenarios aren't testable.

Substitute "cat" with "Jesus" or "supreme being". Draw a circle and claim that Jesus doesn't exist there, and you will have people seriously argue with you that Jesus IS in there, and is everywhere- you just can't see, feel, touch, perceive it/him because he doesn't want you to. Possible? Yes. Plausible? not really, but to "prove a negative" you would have to disprove every one of these possible but extremely implausible scenarios.

This is why most rational people claim the burden of proof is on the claimant to prove that the positive claim is true. If I claim there's a cat you can't see inside that circle, I'd better be able to explain how and prove it to you, or the claim isn't worth much.

I deem you to be quite wise. I will forever picture you with a great flowing beard of sorts now.

I'm not sure what you mean. Perhaps if you could give me an example of a universal negative.

I don't know how to simplify the text book definition of a universal negative. It basically is statement of exclusion, where no member of a class is a member of another specified class. In set theory, this corresponds to saying that two sets are ?disjoint?, or saying that the intersection of the two sets is the null set.

A universal negative statement does imply its converse. For example the statement, "no politician is intelligent". It implies that no intelligent people are politicians.

 

[geldonyetich]

I dare say I can imagine a number of things, numbers and patterns included, which do not really exist. This is no Shrodinger's cat enigma.

Understand that my definition of things that exist does not include things that exist only in the mind.

You can spew tautology all you want but it still bears no relevance or sense in this matter.

It has great relevence, but it seems you're not willing to understand it.

If you can imaging something, be it real or unreal, it exists for as long as you contemplate it's existence. It may not be physical but it exists in some dimension. If you think about 'dragons' then the dragon exists in your head. It cannot exist in the physical plane as far as we know it, but the dimension that is your head, will hold it's existence.

In some dimension, eh? Here I thought it merely existed as an abstraction born from the inner functions of my brain matter, no more the thing than the 0s and 1s in our computer's memory are the letters on our screen that have been translated by various processes in between. But my brain is projecting a new dimension of real things now? Goodness, I hope I didn't mistreat them too badly. But do go on...

It may not be the Copenhagen interpretation of Shrodinger's Cat theory but the concept of "existing and not existing at the same time" still holds.

The interesting thing about Shrodinger's Cat is that when you open the box, the cat is always either alive or dead. However, before you open the box, the cat is both alive and dead.

Why?
Because you're imagining it.

Shrodinger's Cat was always a thought experiment, not proof of anything in and of itself. Because it's a thought experiment, it does exist in the realm of the imagination, not the real. Not by a long shot. It's simply something that you can't disprove, and so magic has slipped into the equation.

Spoiler

Interesting how we've come back to attempting to prove a universal negative.

 

[Kaboose the Moose]

It has great relevence, but it seems you're not willing to understand it.

To understand involves explanation. You have given me no explanation for that particular train of thought, so why should I be willing to understand?.

And now before you do take me up on that offer of explanation, I suggest you work on how you intend on explaining the statement, "I am alone when no one is around me" for that is similar to your "understand that my definition of things that exist does not include things that exist only in the mind". Because when you look at it without the unnecessary and rather silly tautology you are saying, "my definition of things is not restricted to that which is in my head".

Well no duh!.

Did you think you were unique in that field?. Everyone defines things/the living world differently and no one is confined to just cerebral processors. If you were, then you would not be human.

So go on, explain to me the relevance of the obvious stated in the intellectual cloak of confusion.

If you can imaging something, be it real or unreal, it exists for as long as you contemplate it's existence. It may not be physical but it exists in some dimension. If you think about 'dragons' then the dragon exists in your head. It cannot exist in the physical plane as far as we know it, but the dimension that is your head, will hold it's existence.

In some dimension, eh? Here I thought it merely existed as an abstraction born from the inner functions of my brain matter, no more the thing than the 0s and 1s in our computer's memory are the letters on our screen that have been translated by various processes in between. But do go on...

Does it require further explanation?. I didn't things so. Allow me to simply using your own "definition of things that exist does not include things that exist only in the mind". What you see as "abstraction born from the inner functions of my brain matter" can be interpreted as a dimension beyond that which we live in. Is that so hard to digest?.

It may not be the Copenhagen interpretation of Shrodinger's Cat theory but the concept of "existing and not existing at the same time" still holds.

The interesting thing about Shrodinger's Cat is that when you open the box, the cat is always either alive or dead. However, before you open the box, the cat is both alive and dead. Why? Because you're imagining it.

Shrodinger's Cat was always a thought experiment, not proof of anything in and of itself. Because it's a thought experiment, it does exist in the realm of the imagination, not the real. Not by a long shot. It's simply something that you can't disprove, and so magic has slipped into the equation.

Spoiler

I think what you have 'cleverly' done here is introduced something that I did not say into the equation. I never used Shrodinger's Cat as a confirmation of exclusion of any theories or beliefs nor did I bring up magic. Why you have decided to again state the obvious to me is rather perplexing.

 

[geldonyetich]

It seems I've used up your patience, Skarin. I'll not waste any more of your time, as it seems your convictions are quite set.

Truth be told, I really can't prove or disprove to you whether or not our brains really do run on a trans-dimensional projection mechanism or not - though it does seem a bit far fetched when we already know how computer RAM works.

[However, I will go this far: if what we imagine is real, then it exists on a reality separated definitively from this one, and so insofar as this reality is concerned, what we contain in our minds is definitively not what exists outside of our mind, and so it's not real to this reality.

Granted, if you're capable of psychic projection, that might well prove me wrong by piercing this apparently unbreakable wall between a mind's reality and the reality that exists outside of our senses. Thus far, there's been no definitive proof anyone has been able to do this, and certainly no lack of people trying to find some given several billion bored apes on this planet.

So, if we can only find numbers in our mental reality as concepts isolated from the physical reality, that in itself establishes that they are not real within physical reality.]

There was all I as ever saying, truth be told -- things which only exist in our mental reality are hardly a chore to prove given that this entire reality is one of our own conception.

[Incidentally, why did you bring up Shrodinger's Cat at all, if not to have me shoot holes in it?]

 

[Kaboose the Moose]

My patience hasn't been used up at all. My curiosity for different convictions is quite immense.

However, I will go this far: if what we imagine is real, then it exists on a reality separated definitively from this one, and so insofar as this reality is concerned, what we contain in our minds is definitively not what exists outside of our mind, and so it's not real to this reality.

There we agree. I, for convenience and for the lack of a better word chose to call it 'another dimension'. By that I don't mean a portal to the Chthulu universe or the spiritual world, rather something which is not based on this plane of existence.

That said however, mathematics (getting back to the start) is not one to exist in the "external dimension" or what have you. Yes, it's basics are based on arbitrary conceptions that we created but it's implications shapes everything. To call the absolute theories of maths insignificant because it's roots are a mad-made construct is in gross error, because man built civilization. We are, in a rather cliched way, bound to maths in reality.

[Schrodiner's cat wasn't to discuss thought experiments but to discuss the duality of existing and not existing at the same time. As in thoughts/dreams/ideas being real (in the head) but unreal (not in the real world)]

 

[geldonyetich]

I really don't have any time left tonight, this will be my last post for at least 8 hours or so, but I'm not sure we're exactly anywhere significant at this point anyway. I think we were just balking over a word, in typical Internet forum snafu sense, in this case: "real."

What you say is in "another dimension" or even what is "not based on this plane of existence" is what I would call "not real." Now, just because it's not real doesn't mean we can't imagine or work with it, or even use it as a valuable tool, but it still isn't what I'd call real.

Therein seems to be the main point of contention. As for why I don't believe being able to imagine is enough to make it real, it has to do with a predisposition with favoring sanity, and finding this to be a good dividing line.

That said however, mathematics (getting back to the start) is not one to exist in the "external dimension" or what have you. Yes, it's basics are based on arbitrary conceptions that we created but it's implications shapes everything. To call the absolute theories of maths insignificant because it's roots are a mad-made construct is in gross error, because man built civilization. We are, in a rather cliched way, bound to maths in reality.

Well, as I said, it's not as though mathematics would seem to be without worth. However, my point was merely that you can't really use mathematical proofs in the same way you would trying to establish a concrete physical proof on the sounds that mathematical proofs do not operate in the same reality.

With that said, perhaps my first post [http://www.escapistmagazine.com/forums/jump/18.161652.4123711] can be grokked, with an understanding of why I made such a big deal over defining what's real and not real.

 

[Kaboose the Moose]

Except that the majority, if not all physical proofs are based on

a) Mathematics

b) Mathematical models.

Excluding religion, which is a major variable in the world of mathematics, the physical world is all about the maths. Which is why I fail to see how you divorce it from reality.

As you say though, both our arguments lie on the loosely strung definition of "real". People for ages have struggled with a philosophical definition for real and without one, we will most likely never see eye to eye on the standing of maths in the physical world.

 

[Kailat777]

I am really interested in philosophy and have been reading about it for a while now. Recently the question cropped about proving universal negatives and if it can be done?. So I was wondering, is it true that you can't prove a negative?. How much truth does this claim carry?
Can one prove a universal negative?

Along with that what is considered proof?. Is inductive reasoning consider sufficient proof? why?.

Is proof by contradiction considered sufficient proof?. why?

If you have another method please provide it.

Discuss and provide examples.

As a mathematician, I'll give my say in the matter. First, what exactly are we getting at when we say "prove a universal negative"? Are we saying "can we prove that the impossible really is impossible?" If that's the case, then yes, we certainly can. As mentioned in a very easy example, we can prove that the square root of two is not a rational number. On the other hand, if we're asking "Is it ever possible to prove the impossible can happen?", then no. In that case, either there is a mistake in your 'proof', thus you've proven nothing, or you've obtained a contradiction, which can prove SOMETHING, but it doesn't prove the contradiction itself (more on that later).

Now, inductive reasoning is not sufficient proof. To explain it as simply as possible, it is an attempt to prove by example, but with a lot of examples. However, it's possible for something to be true an infinite number of times, but not true in general. For another easy example, if we were to live on an island that has only palm trees, we may reason inductively "all trees that I have ever seen are palm trees, thus all trees are palm trees". Note this is very obviously not true, as you can probably prove yourself by going outside and pointing at a tree.

Now, proof by contradiction is generally considered sufficient proof. To explain it simply again, it should seem pretty obvious that if you're trying to prove something and end up with a contradiction, you assumed something that CAUSED that contradiction. That is, if you believe in logic, you also believe things are not naturally contradictory and also that logical statements must be either true or false (otherwise they aren't logical statements). Thus, let's say we start with only things we KNOW to be true (say, A, B, and C are true) and a single assumption of unknown proof value (we assume that, say, P is true). If we get a contradiction (say, A is true and A is false), we know we assumed SOMETHING that wasn't valid. Since there's only one thing we were uncertain on, we know the assumption was wrong. Since all logical statements are either true or false, there's only one way left to go on this (thus, we know P is false).


Oh, and to anyone who wants to complain about how the rational/irrational number argument doesn't matter, you'd be surprised how quickly such things do matter in the physical world. That is, provided you enjoy how all your fancy electronics and bridges seem to work as intended.

Also, a word of warning: it has been proven (surprisingly) that not all things can be proven in any consistent framework. So don't get too excited about the possibility of absolute truth. While you can get "the truth, and nothing but the truth", the drawback is that you can never obtain "the whole truth".

 

[Canadamus Prime]

I'm not sure what you mean. Perhaps if you could give me an example of a universal negative.

I don't know how to simplify the text book definition of a universal negative. It basically is statement of exclusion, where no member of a class is a member of another specified class. In set theory, this corresponds to saying that two sets are ?disjoint?, or saying that the intersection of the two sets is the null set.

A universal negative statement does imply its converse. For example the statement, "no politician is intelligent". It implies that no intelligent people are politicians.

Oh, I see. Well in that case, I would say no. Proof of something usually requires tangible evidence and since a universal negative distinctly describes a lack there of, by it's nature then it'd have to be true until proven false.

 

[geldonyetich]

Except that the majority, if not all physical proofs are based on

a) Mathematics

b) Mathematical models.

Excluding religion, which is a major variable in the world of mathematics, the physical world is all about the maths. Which is why I fail to see how you divorce it from reality.

As you say though, both our arguments lie on the loosely strung definition of "real". People for ages have struggled with a philosophical definition for real and without one, we will most likely never see eye to eye on the standing of maths in the physical world.

Physical proofs, mathematical models. They seem so compelling, evidence that math must be as real as what it is describing. However, these are merely mental framings of things, not the things in themselves. That I can use a language to describe a thing does not make the language spoken as real as the thing. It's a slippery slope to believe it does.

Perhaps Walker Percy described it [http://www.ling.upenn.edu/courses/Fall_1997/ling001/percy.html] better than I could.

 

[ma55ter_fett]

It would be the truth, unless you drew a circle around a cat or if one were to step into the circle in which case it would be false.

you could prove that there is no cat in the circle by one of any dozen scientific or mathematical means, or you could just get some witnesses to verify that there is indeed no cat in the circle.

It isn't about whats true or false in a statement. It's about proving something by means of disproving. There is a vast difference between the two, a difference men (and women..I don't discriminate) with big, long beards like to ponder about on oak tables next to a fireplace.

Draw a circle on the ground. Say aloud, "A cat is not inside this circle."
Have you just proven a negative?.

As for the cat, what you have proven is merely the fact that you haven't seen a cat inside that circle at that time under that atmospheric preasure, temperature. Alternatively, you would have to prove that the cat isn't invisible. I guess you could say, there is no visible cat (by human eyes) in this circle.

All in all it's an utter chore the business of proving a negative. You would have to prove through millions of possible though highly implausible scenarios (intangible cat, invisible cat, submicroscopic cat, cat which exists a half second forward/behind you in the time stream, cat is there but your faith isn't great enough to see it...) that there is no cat there. Basically impossible, since most of those scenarios aren't testable.

Substitute "cat" with "Jesus" or "supreme being". Draw a circle and claim that Jesus doesn't exist there, and you will have people seriously argue with you that Jesus IS in there, and is everywhere- you just can't see, feel, touch, perceive it/him because he doesn't want you to. Possible? Yes. Plausible? not really, but to "prove a negative" you would have to disprove every one of these possible but extremely implausible scenarios.

This is why most rational people claim the burden of proof is on the claimant to prove that the positive claim is true. If I claim there's a cat you can't see inside that circle, I'd better be able to explain how and prove it to you, or the claim isn't worth much.

Since the question of proveing a universal negative is unlikely to get me laid (except by a wise women with big flowing beards) my intrest in it has wained.

 

[Caliostro]

This is a false synecdoche. "Proving something doesn't exist" is only part of the concept of "proving a negative."

Sure, you can't prove Santa Clause doesn't exist because "Santa" has never been clearly defined. For all we know he could be an alien being using alien technology that we've never encountered.

But you can prove that no fraction exists that's equal to the square root of two.

Not necessarily, you can only prove you can't find it yourself.

It's absurd, but it's true. You can't provide irrefutable proof or a negative. You can't prove something something does not exist, didn't happen, or isn't, that's why the burden of proof falls on the claimer, and not the skeptic. That's why people aren't charged of a crime by default and asked to prove they didn't commit a crime. It's first asked for the prosecutor to prove relevant evidence to prove they might have then, then they're simply asked to prove the evidence presented to convict them isn't good enough. It's the prosecutor's job to prove they did.

 

[achilleas.k]

Kailat777 basically ended this thread, but I'll just go on and add a few thingies of my own.

As Kailat777 said, inductive reasoning is not sufficient proof, even though people do it all the time, even scientists. The trick is that scientists will never say that something shown through induction is absolutely true or proven; they will often say something along the lines of "evidence suggests this and that" or "experimental results suggest the existence of ... ". In everyday speech however, most of us go on and say stuff like "the sun will rise tomorrow", when in fact the only indication that this will happen is that it has been true in all past occurrences. Of course, no one expects us say "past evidence suggests that the sun is very likely to rise tomorrow" every time we try to plan something for the next day. Am I off topic here? Let's go back.

A nice example of a proof by contradiction is Alan Turing's proof that the Halting Problem [http://en.wikipedia.org/wiki/Halting_problem][wikipedia.org] is undecidable. Roughly speaking, the proof starts by assuming a solution to the problem and through logical steps arrives at a contradiction, effectively proving that the assumed (abstract) solution cannot exist.

As I understand, what you mean by "universal negative" is something of the sort "no swans are black" (even typing that sentence makes me want to throw up - I had a heated debate with a mate at some point about "empirical evidence" vs "empirical truth" and the swan example came up more than a few times). Of course, in these cases, a single black swan proves the falsehood of the statement. A gazillion white swan observances however, does not prove its truth (not to absolute certainty anyway).

is it true that you can't prove a negative?. How much truth does this claim carry?
Can one prove a universal negative?

Maybe. If you check the swan's DNA and see that it is unable to be black AND you remove from your definition of the word "swan" any species that result from small mutations (which could provide a black swan), I suppose it could be regarded as a proof that no swans are black. You will notice however that in this case, you're exploiting a weakness of natural language to clamp your definition of a word to suit your proof. It doesn't make it any less true though.

Along with that what is considered proof?. Is inductive reasoning consider sufficient proof? why?.

Is proof by contradiction considered sufficient proof?. why?

See above.

If you have another method please provide it.

Discuss and provide examples.

Another proof method I'm sure you're aware of is proof by transposition. If it rains I will be carrying an umbrella. I am not carrying an umbrella, therefore it has not rained. Assuming the italicized statement is true (I always act on that rule), then the fact that I am not carrying an umbrella proves that it has not rained. If you can come up with an absolutely true statement of the form "if p then q" where p is "black swans exist", and you can prove that q does not hold, then I guess you've proven that ~p (not p) is a universal negative, in that "no swans are black".

 

[rokkolpo]

we as humans define the truth, and truth can be different for each person.

so nothing is absolute until we all agree on it. wether it be true or not. it will be considered and therefore validated.

 

[Kaboose the Moose]

This is a false synecdoche. "Proving something doesn't exist" is only part of the concept of "proving a negative."

Sure, you can't prove Santa Clause doesn't exist because "Santa" has never been clearly defined. For all we know he could be an alien being using alien technology that we've never encountered.

But you can prove that no fraction exists that's equal to the square root of two.

Not necessarily, you can only prove you can't find it yourself.

It's absurd, but it's true. You can't provide irrefutable proof or a negative. You can't prove something something does not exist, didn't happen, or isn't, that's why the burden of proof falls on the claimer, and not the skeptic. That's why people aren't charged of a crime by default and asked to prove they didn't commit a crime. It's first asked for the prosecutor to prove relevant evidence to prove they might have then, then they're simply asked to prove the evidence presented to convict them isn't good enough. It's the prosecutor's job to prove they did.

...

Er, yes I know, that's why I said:

This is why most rational people claim the burden of proof is on the claimant to prove that the positive claim is true. If I claim there's a cat you can't see inside that circle, I'd better be able to explain how and prove it to you, or the claim isn't worth much.

on the first page.

Physical proofs, mathematical models. They seem so compelling, evidence that math must be as real as what it is describing. However, these are merely mental framings of things, not the things in themselves. That I can use a language to describe a thing does not make the language spoken as real as the thing. It's a slippery slope to believe it does.

Perhaps Walker Percy described it [http://www.ling.upenn.edu/courses/Fall_1997/ling001/percy.html] better than I could.

I do not have the time to entertain your link for it is unforgivably long and made no sense on the first and second attempt to skim the text. If you wish to summarize the point Mr. Percy Walker was trying to make with his dissecting board, ants, bombs and sonnets, feel free to do so.

However at this point I would like to remind you that we do not yet agree on the definition of "real". Without that our arguments will go nowhere. At any rate perhaps you should read Kailat777's post. As a mathematician perhaps he can be more specific about how maths can prove a negative/the impossible.