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[mith]

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[Celt]

[You have not lost the wager.
"All ravens are black" is not equivalent to "all non-black things are non-ravens".
The fact that the bottle is not black provides no relevant information.

To elucidate...
In order to prove that all ravens are indeed black, it would be necessary to prove that there are no non-black ravens. The only way to do this is to gather all ravens together and show that they are all black. The only evidence therefore, that can be proffered, would be something that concerns the colour of a raven. An artist's impression of a strand from the feather of a single raven would provide some corroborating evidence but the fact that other objects have a colour, black or otherwise, is irrelevant.]

[Guest]

[But what if you gathered all non-black things in the universe, and observed that none of them are ravens? Surely, that must be relevant somehow.]

[Burning]

[The statements "All ravens are black," and "All non-black things are not ravens," are logically equivalent, but I do think there are two flaws with considering non-black non-ravens as evidence.

First the statement "All ravens are black," implies the existence of ravens. This is not part of the logical content of the sentence, but it is a reasonable interpretation based on how language is actually used. Gathering all non-black objects will prove the non-existence of a non-black raven, but it will not prove the existence of any black ravens.

Second, the number of ravens in the universe is presumably finite, so gathering a large but finite number of black ravens provides reasonable evidence for the blackness of all ravens. The number of non-black things is presumably infinite, so gathering a finite set of non-black non-ravens only provides an infinitesimal amount of evidence for the non-ravenness of non-black things.

I think the first is the stronger objection, because I think producing the brown beer bottle would still be strange as a way to provide evidence for the statement "All the ravens in this room are black."
_________________
"Space is blue, and birds fly through it."
Werner Heisenberg

[Celt]

I've changed my mind. Silly of me to think this was a trivial puzzle.
[Earlier I said that '"All ravens are black" is not equivalent to "all non-black things are non-ravens"'. The statements are logically equivalent if they are both true but since we are trying to prove the first statement, I thought the "fuzziness" of the logic must be taken into account.
However...
If "All ravens are black" then "all non-black things are non-ravens".
If "all non-black things are non-ravens" then, assuming ravens exist, "All ravens are black".
If some thing exists which is non-black and is not a raven then it lends a miniscule amount of credence to the statement "all non-black things are non-ravens" which in turn, adds a tiny degree of credence to the statement "All ravens are black".
That ravens exist is a given in much the same way that the colour black exists. Incidentally, this would also have worked for "All unicorns are green".]

[dave10000]

As with many -- but not all -- of Skinny's bets, it turns on a question of interpretation. What does the word "evidence" mean?

I believe that under most reasonable definitions of "evidence," Skinny has lost the bet. For example, the first definition at dictionary.com:

"A thing or things helpful in forming a conclusion or judgment"

I think that almost no-one would believe that a brown bottle is *helpful* in forming a conclusion as to whether all ravens are black. Thus, I believe that Skinny has failed under this definition. (If you disagree, consider that the brown bottle equally supports the conclusions that all ravens are white, all ravens are red, all ravens are blue, etc. Thus, it is not *helpful* in forming a conclusion as to whether all ravens are black.)

Under *any* definition of "evidence" used in court (and I am, after all, a lawyer), Skinny's proffer would fail miserably.

No doubt, though, there are definitions of "evidence" that would support Skinny's position.

Thus, whether Skinny wins or loses depends upon what "evidence" means. And, likely, it depends on who decides that question. When you and Skinny dispute whether he has won one of his bets, who decides? If it is someone beholden to Skinny, then you're bound to lose.

A bigger question is: Why did you take the bet in the first place? Surely Skinny could have shown you a book (which is not a raven) that says "all ravens are black, or offered the testimony of an expert on the issue (which might even rise to the level of admissible evidence in a court). Certainly anyone who takes the bet as Skinny offered it *deserves* to lose. But, IMHO, they do not lose based upon the purported "evidence" that Skinny actually offered.

[cha]

The bet is not about providing proof, just a piece of evidence, and no single piece of evidence needs to be conclusive. "Conclusions" can be reached when enough cumulative evidence is presented, and in this situation if all possible non-black objects are presented, it becomes proof.

[dave10000]

[Zygon]

Skinny states that the statement “All ravens are black” and said it is the logical equivalent of “All non-black things are non-ravens”.

The only way that this makes sense is to remove the double-negative form of the second statement – then all black things become ravens. This is tempting but must surely be wrong. Perhaps, then, Skinny would be trying to introduce the logical episode of trying to show additional pieces of evidence; there are a lot of non-black things out there that are not ravens, and therefore there is a weight of evidence of contrary proof. This is simply silly. Even if you were to exhaust the entire universe of things that aren’t Ravens and aren’t black, you’ve still said nothing about black ravens.

The problem here is one of distribution. In the first case, the universe of things is limited to those which are black. Within this universe, there are ravens.

In the second case, the distribution is much larger: All non-black things. In this universe exist things, it is assumed, but all of the things will be non-ravens, which is the equivalent of none of the things being ravens. But wait a second here! The statement says that something will exist, it is written in the positive form. They will be non-ravens. But non-ravens are non-things. Non-things are nothing. Therefore all non-black things are nothings? I think we have to rewrite the premise. Rewritten, the statement becomes: All things that are not black are not ravens, and we can find a multitude of items that contradict this proposal.

[Zygon]

The subject of this last proposal is distributed: There are things that are black, and things that aren’t, and this covers the entire universe of things. Ravens are a subset of “things that are black”

The predicate of the premise is not distributed as equally: There are things in the universe that aren’t Ravens, and there are things that are. One is not a subset of the other, but actually a distinct set.

[Icarus]

Skinny has lost this wager. The statements may appear to be equivalent, but they are not absolute.

If you agree the statements are equivalent, then you have to agree the following also to be equivalent:

'all ravens are black' = 'all non-black things are non-ravens' = 'all black things are ravens'

My computer is black - is it a raven ?

Also, if you agree with the statement 'all ravens are black' is equivalent to the statement 'all non-black things are non-ravens', then by the same logic you can substitue cat for raven, you now get:

'all cats are black' is equivalent to the statement 'all non-black things are non-cats'

I'm sure you have all seen a non-black cat in your lifetime. I know I have.[/i]

[dave10000]

[Zygon]

Hi Dave,

If x, then y doesn't seem to me to imply the correlative, if not x then not y. It would seem insufficient.

If I strike a match, then I get fire. If I don't strike a match, then I won't get fire leaves-out that if I use a spark-generator in fron of an oxy-acetylene torch I will still get fire.

Again, I ask that we look at distribution of terms.

[Zygon]

Sorry Dave,

I am as guilty as many here of not reading attetively before I post. I see now that I raised the same point as you.

Forgiveness?

[dave10000]

Forgiveness.

[Speeder]

Hi All,

I would say that the most conclusive way to prove the proposition 'all ravens are black' is to find all the ravens in the universe and check what colour they are. If they are all black then the proposition is true. If you find a non-black raven then you can stop as the proposition is false.

Alternatively we could find all the non-black things in the universe and if we don't find a raven then the proposition is true providing that there exists such a thing as a raven. If we find a raven among the non-black things then we can stop as the propostion is false. This would take much longer than the first option as there are much more non-black things than there are ravens.

However, obviously neither of the above is practical, and the question is to provide evidence rather than proof. Skinny's brown bottle is obviously not conclusive evidence, but it is arguably evidence nonetheless. If Skinny were to produce more and more non-black objects then this would be further evidence, eventually becoming conclusive if he got as far as producing the last non-black object and it turned out not to be a raven.

If Skinny were to produce a brown bottle as evidence that all ravens where white, then I think we would still lose our bet because the more things he produced that were neither white nor ravens, the more evidence he would have that ravens are white - until he found a black raven.

It may be all down to how we *use* evidence. Crop circles may be used as evidence of extra terrestrial shennanigans, or of meteorological phenomena, or of sad pranksters, depending on what case we are trying to prove.

Ultimately I believe evidence is fact that apparently supports a proposition. Unfortunately if this is true it would mean Skinny would win the bet.

Speeder.

[dave10000]

Speeder --

Even if you take that general position (which I concede that some philosophers have taken and thus is *a* valid view but not the only one), it does not address point 2 in my previous post about randomness.

In order for a sampling to be evidence of "all-ness" or "none-ness" it must be random. Again, for example, suppose I take a new deck of cards and say that I will show you evidence that there is no Ace of Spades. If *I* show you 51 of those cards, carefully chosen by me to exclude an Ace of Spades, that is no evidence at all that the Ace of Spades is missing. However, if *you* select 51 cards at random and the Ace is not among them, that might be viewed as evidence that the Ace is missing.

Thus, even if a *random* selection of a non-black object that hapens to be a nonraven is evidence, it does not follow that an object specifically selected by someone, nonrandomly, as a "confirming instance" must also be viewed as evidence. And, thus, the fact that Skinny himself chose the bottle as a purportedly confirming instance, and there is nothing to suggest that he did so randomly, I think he still loses.

[Speeder]

Hi Dave,

I don't think Skinny needs to prove that only black ravens exist; the puzzle only requires him to give evidence, and as long as the evidence he gives can indeed be termed evidence then he wins the bet. I think he might have pulled it off.

I can't decide on your card example. In reality I agree, even after 51 cards I would discard the so called 'evidence' as rubbish because I'd expect the last remaining card to be the Ace. But then again the 51 drawn cards technically support the argument that there is no Ace of Spades in the pack because they don't disprove the hypothesis.

Although, I am beginning to wonder if there is a falacy in the double negative logic. And I would like Skinny to fail for once.

Speeder.

[Oscar]

Hempel's paradox has long been a favourite of mine.
It seems to me that it turns, as dave10k suggests, on the interpretation of the terms used, and also by the nature of the method by which the 'evidence' is sought.

I think it's clear that the 2 theories are equivalent and that a confirming
instance for one is a confirming instance for the other. What is important
though is whether the proffered 'evidence' for the theory has any chance of disproving it; if not, then it is not evidence.

For example if my search method for finding evidence is to examine all
non-black things and see if they are ravens, then if I find the thing is a
raven it disproves the theory; hence if I discover it is not a raven then
it is some (tiny) evidence in favour of both theories.

If, however, my search method is to search for all non-ravens and see what colour they are, then I am never going to disprove the theories, hence the 'evidence' is no such thing. Since Skinny's 'proof' implies that his evidence was guaranteed to be a non-raven he has clearly been using this method, and he doesn't win his bet. Unfortunately, since the actual bet was 'I can produce evidence that all ravens are black without showing you any ravens' you don't win the bet yourself. If he could demonstrate that the search method was valid and the first result of this search was a non-raven then he would still win, although validating the method might prove difficult. (especially in a court of law, with Dave opposing!)
If the search for non-black things is conducted in an area which
is known to be free of ravens then again the theories cannot be
contradicted, hence no valid evidence for them can be counted.

Conversely a search which was limited to black things only would not prove the theories either, no matter how many ravens were produced, since this 'evidence' could never disprove the theories.

On the whole my inclination would be to accept the beer and declare the bet void.

Incidentally I have actually proved that all ravens are black - look it up
in dictionary.com:
raven:
'A large bird (Corvus corax) having black plumage and a croaking cry.'
i.e. if it's not black, it's not a raven

[/i]

[Zygon]

I think this may help.

When one makes a statement "All S are P" one relies on having knowledge of at least one S that is in fact P.

All men are mortals would only be stated after the discovery of at least one man who has died.

When one makes the statement "All S are not P", one again makes that statement after finding at least one instance of proof. Even though the predicate is in negative form, there would be one instance at least proving the negative instance, the thing not having the predicated quality:

All mice are not men.

But in this example, we are asked to posit a proposition where we cannot find a first instance - we're being asked to reverse the onus of truth.

Sure, you can find a non-black thing that is not a raven, you ca in fact find many. But the first instance in the premise "All ravens are black" is much more confirming. We know that we are adding directly related evidence to the entire class of objects being referred to.

This is why if an single instance of the opposite - finding a non-black raven, would destroy the argument that all ravens are black AND the argument that all non-black things are not ravens. It has more logical force simply due the fact that it has at its beginning at least one demonstrable instance. Proving something exists by showing any number of contrary evidences can never have this force.

Pay up, Skinny!

[ewan]

is it just me or are these puzzles getting easier?

inorder to provide evidence for 'all non black things are not ravens' skinny needs to show you all non-black things. just showing you a subset of non-black things such as a beer bottle only gives evidence for the statement 'some non black things are not ravens' and thus is not evidence that ravens are black

[Speeder]

Ewan,

Okay, we agree showing all non-black things is conclusive evidence (assuming that there are no ravens among the things).
Showing all non-black things except one would be pretty conclusive evidence.
Showing 99% of non-black things; still pretty convincing evidence.
Showing 50% of non-black things; evidence but not quite as convincing.
25% of non-black things; less convincing evidence, but arguably evidence nonetheless.
Extrapolating this; 1 non-black thing is still arguably evidence, though highly unconvincing.
However, Skinny doesn't need to *prove* all ravens are black, just produce evidence.

Speeder.

[ewan]

ahh but anything less than 100% is only evidence that _SOME_ non black things are non ravens. not evidence that _ALL_ non black things are non ravens.

since skinny can never produce all non black things he can never offer evidence that all non black things are X. some non black things are not evidence about all non black things just as some red cars are not evidence that all cars are red.

however, perhapse skinny could look up the ravens genes and show that the raven genome requires it to have black feathers, since _all_ ravens have the raven genome by definition this would be evidence that all ravens are black.

[ewan]

just read about the random selection. I guess this would be evidence as long as it was statisticaly significant, you would need to produce quite a few random 'non black things' before you got a statistical significant sample of non ravens. I dont think skinny can do it before lunch

[Celt]

ewan,

I think you are mixing up proof and evidence. Skinny does not have to prove anything. He merely needs to begin the process of proving "all ravens are black". He could equally have offered the bottle as evidence that all ravens are blue.

[ewan]

not at all, you have to remember that evidence has to imply the thing you are trying to demonstrate. a non black non-raven dosnt imply ravens are black.

a significant random selection would be evidence becuase you could say statisticaly the chance of picking your all non-black non raven set if some ravens were non-black.

to go back to the card example, say my hypothosis is all aces are black. if i specificaly pick one non-black non ace and show you, this is not evidence, as we all ready know that some cards are non-black non-ace, it implies nothing.

if i pick 1 random card and its non-black non-ace, its not evidence becuase its not statistical significant.

if i pick 50 random cards and none are non-black non-ace that is good evidence as the chance of picking such a large sample without picking a non-black ace is low

if i choose all the non-black cards and they are all non-aces then this is conculsive evidence.

in the all ravens case, the set of non-black objects is arguably infinite or near infinite, thus skinny can not get a statisicaly significant sample unless hes got an infinite sample,

[get a clue]

ewan,

grasp that stick firmly at the wrong end and hang on!
_________________
Password is lowercase and has no spaces or punctuation.

[sfoenixb]

Skinny did not prove his point. One non-black thing does not show that all non-black things are not ravens.

If you paid him you've been conned

[Burning]

[Celt]

The fact that a husband takes out a large insurance policy on his wife shortly before she dies in a freak accident is evidence of murder, even if it proves nothing.
Surely the brown bottle can be considered in the same vein. It is merely flimsy circumstantial evidence supporting a proposal while proving nothing.

[Burning]

[dave10000]

[impossibleroot]

[dave10000]

I suppose I could have said the last part clearer. I meant that in an analogous but somewhat opposite way, just as Tall Bob could be evidence but not a confirming example, the brown bottle could be a confirming example but not evidence. (Note that the first does not imply the second -- the fact that something can be a quadrilateral without being a square does not mean that something can be a square without being a quadrilateral -- but my point was that the two concepts were not coextensive, and thus if one successfully argues that the brown bottle is a confirming example, that does not automatically mean it is also evidence.)

My view of "evidence" is that it must be "persuasive," even if to only a tiny degree. In the law, that generally means that evidence of a fact, in order to count as evidence of a fact (or, more precisely, to be "relevant"), must make a recipient more likely to believe the ultimate fact is true. Thus, somewhat oppositely to the Tall Bob situation, I am (almost) willing to allow that the brown bottle is a confirming example of "all ravens are black," but since I do not believe it has any actual "persuading" power (none, not even a tiny, tiny bit) as to the issue of "all ravens are black," I do not think it is evidence.

Of course, those with different definitions of "evidence" might come out differently. That's why I suggested, in my first post on the topic, that Skinny's fate depends upon what one means by "evidence." But if *I* were ruling on the bet, I would not count the brown bottle, produced by Skinny in a non-random way, as evidence supporting the proposition that "all ravens are black." *Maybe* if he got me when I was tired, I might agree that the brown bottle was a confirming example. But the bet was over whether he could produce "evidence," and in my view the brown bottle does not get there. (Of course, Skinny might still win because the bet was whether he *could* produce evidence, and I'm sure he can. But the brown bottle is not that evidence.)

[Celt]

[ralphmerridew]

[dave10000]

[Austin]

The way I see this problem, its entirety relies on the definition of "evidence." Mathematically (or logically), skinny did nothing, because he did not show that ALL non-black things are non-ravens. Statistically, he also did very little. First off, there is no reason to give him the benefit of the doubt in that he selected a random item. Even if he had, the chances of it being non-black are pretty good (say, 1 in 8). What skinny provided was not at all helpful in reaching a conclusion, in order for him to make that method of proving something at all useful, he would have to show a large percentage of non-black things in the universe are not ravens, and he would have to do it at random selection.

The fact that what skinny did was useless can be demonstrated by this idea. Pretend you knew nothing at all of ravens (for all you know, they could resemble trout and are red). Does skinny showing you a random item help you reach the conclusion that ravens are black? Not at all... if you came to that conclusion from that 'evidence,' it was entirely a matter of luck. For all you know, ravens could still be red. In fact, assuming skinny didn't chose items at random, I argue that he would have to show you every non-black thing in the universe and assure you that it is not a raven before he would have given you any evidence that all ravens are black.

[ewan]

definitions of evidence

"EVIDENCE - In law, various things presented in court for the purpose of proving or disproving a question under inquiry. Includes testimony, documents, photographs, maps and video tapes.

Trial evidence consists of:

1. The sworn testimony of witnesses, on both direct and cross-examination, regardless of who called the witness; 2. The exhibits which have been received into evidence; and Any facts to which all the lawyers have agreed or stipulated."

so perhapse all skinny has to do is present his brown bottle or literaly _anything_ in a court, all he has to do is assert that it is evidence and it becomes evidence.

[dave10000]