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[LoudmouthLee]

Just registered for an account, so, again, take a look at "Hasty Generalization".

Hope this helps, keep me in the loop for possible answers.

-Lee D.

[knightshade]

I was perusing a Martin Gardner book yesterday and he commented on an article he wrote for SA years ago about this same problem. Apparently, it is derived from a famous paradox known as 'Hempel's paradox.' Just figured I'd throw that out.

-k

[muttrox]

Hi all,

I just discovered this thread and have been trying to read through the whole thing. I am the school of thought that Skinny did indeed provide evidence, albiet astonishingly weak evidence.

I wanted to chime in on the randomnes issue. Note that we do not know if Skinny picked the bottle at random or not. Having no other basis to judge, there is certainly a possibility that he "stacked the deck" by pre-choosing the bootle, but that possibility is not a certainty. Therefore, the quality of the evidence is lessened even further, but it does not completely rule out whatever value it has. In other words, unles we know for a fact that Skinny cheated, we cannot completely discount his evidence. Therefore, if you believed that there was some evidence before thinking about the possibility of cheating, you must believe there is some after.

To use the deck of cards analogy -- when I play poker, there is always the possibility that someone is cheating. If someone was dealt a royal straight flush on the first hand, I would certainly suspect foul play. If that person had a history of cheating in the past, I would be darn near certain. However, I could not definitively say there was absolutely zero chance the events hadn't happened on their own with no cheating involved. In the real world (and this part of the puzzle is stated in real world terms), you just don't know one way or the other, and cannot discount the possibility that it was random. Ergo, the event still has some value for evaluating a hypothesis.

[dave10000]

From the official solution:

[Guest]

Pretty clever answer IMO.

David, you say he selected it at random from the universe of all non-black items. However, that is not true. If he is selecting from the universe of non-black items, and there happens to be a non-black raven, then he could pick it. However, he has specifically said that he will not show a raven.

Therefore, he must be picking from a subset of all non-black objects, namely the universe of non-black non-ravens. So when you propose Skinny say "My methodology of picking evidence was that I was going to select a non-black object at random and show it to you.", that is not true. That cannot be his methodology, because that would contradict what Skinny had earlier said, that he would not show a raven.

[muttrox]

The above post is from Muttrox again. Still getting used to this forum!

[dave10000]

[muttrox]

I think your interpretation is conceivable, but not a reasonable one. The common sense interpretation of Skinny's statements and actions is that he intentionally avoided selecting a raven.

How about this one, "I will now point to an object that is not the statue of Jebediah Springfield."

Your interpretation is that I swing my arm around randomly and see where I end up pointing, right?. Odds are good it won't be the statue, so it's a good bet. A more normal interpretation is that I will purposely do exactly what I said I said I would, and deliberately find an object that is not the statue to point at, thus winning the bet.

I can see your point, but I don't think it really follows from the text of the puzzle.

[dave10000]

muttrox --

I disagree, but not because your interpretation *can't* be right. I think it's ambiguous as to what Skinny did and as to how the bet should be interpreted. And Skinny is smart enough (we know), that he would take advantage of *every* possible loophole, so knowing that he had to pick at random from (a suitable universe of) non-black objects, I'm confident he did. It would be a complete non-starter if he didn't, and Skinny is not about to lose *that* easily.

I mean, come on. Skinny once bet $10 that he could do between 1 and 2 thousand pushups in 30 minutes. And then he promptly did 2 and demanded his money, saying "Well, 2 is between 1 and 2000!" So, we know that Skinny does not play by "most reasonable interpretation," he plays by "any interpretation that I can squeeze into the words." I personally think that Skinny's interpretation (as per my previous post) is more reasonable than other interpretations, but at a minimum it is an acceptable interpretation under Skinny's rules as established in the past.

Please note also that Skinny did not say "I will do X," but rather "I bet I will do X." Usually, that implies that there is some chance he would fail at X. Just as "I bet I sink this free throw without hitting the rim" does not mean you promise not to hit the rim (but rather only that you lose if you do), "I bet I will show you an object that is not a raven" does not mean you promise not to show a raven (but rather only that you lose if you do).

Otherwise, what does "I bet I sink this free throw without hitting the rim" mean?

[Celt]

I'm with dave10K on this one.

[muttrox]

I'm starting to come around myself. Being somewhat of a newbie here, I didn't know Skinny played such tricks with language.

It's interesting to me that Skinny almost works against himself. Let's say he picks a non-black object, and lo and behold, it turns out to be a raven. What does he do? Here are the two interpretations.

(1 - the solution's int) He changes his answer. He said he wouldn't point to a raven, so he doesn't. However, the fact that he would perform this action under these circumstances negates the value of pointing to a non-raven object the rest of the time. So by keeping his word, he loses. His actions that he would take in the 1/1,000,000 time that it happens to be a raven lose the bet for him the other 999,999 times.

(2 - David's int) He sticks with the raven. In this case, he loses. He rolled the dice, and unfortunately got the 1/1,000,000 roll. But by taking this chance, he wins the bet the other 999,999 times.

Do I have that right? It's pretty neat. On the basis of what he would have done (even though it almost never occurs) had he initially picked a non-black raven, the bet is decided in all the other cases (overwhelmingly likely) where he picked a non-black non-raven (e.g. a brown beer bottle).

[ewan2]

I think that producing statisticaly significant evidence is practicaly impossible with thwe random non-bacl object aproach.

But the puzzle has one major problem.

evidence is a loosely defined word. legaly speaking he could enter a black raven as evidence that ravens are not black or anything else for that matter

is a statisticaly insignificant survey evidence? can skinny mearly clain to have seen all non-black objects or all ravens? the puzzle relies on a splitting hairs defintion of a word which can mean many things.

However, I still think its a good puzzl becuase it promotes thoguh and discusion about what evidence realy means.

[muttrox]

Statistically insignificant evidence is definitely still evidence. You just mean that's it inconclusive at a certain level (probably p=0.05, the usual standard). However, it is definitely still evidence.

Anyhow, it seems clear to me that it's meant in the sense of logic puzzle evidence, not statistical or legal... it's been discussed quite a bit earlier in the thread.

[lostdummy]

It seems to me that answer to this problem depends on what your definition of evidence really is. If you define evidence loosely as something that can prove or disprove certain statement or theory (which look slike usual interpretation), then I do not think Skinnys argument can hold at all.

Basically, to prove that "All ravens are black" you must really check ALL EXISTING ravens. Therefore seeing ONE black raven is not evidence at all. Not even 'small piece of evidence'. One non-black raven IS evidence, since it will disprove theory. One, 10, milion ... black ravens are not evidence, since they can not prove theory in any way. Oh, they can prove theory that "MAJORITY of ravens are black", but in that case mathematical reversal does not work ... ie you can not say "majority of non-ravens are non-black", nor even "minority of non-ravens are non-black". Only thing involving black ravens that could be considered evidence to original statement is if we can show that we checked all existing ravens and they are all black.

Similary, if we want to prove that "All non-black objects are non-ravens" , we will have to show that really ALL EXISTING non-black objects are not ravens. Again, shoving that only ONE non-black object is non-raven is not evidence at all , while shoving that even one non-black object is raven IS evidence.

And since Skinny showed only one non-black non-raven, it is not evidence at all. Even 10 milions of non-black non-ravens would not be evidence. If we accept that it can be considered evidence, then ANY data related to evidence as a whole is also considered evidence, then few things would be true:
- every possible item on world could be considered 'evidence' - for example 'this is white rock, it is not non-black raven, so consider it evidence' ... and so on
- Skinny would not have to use any logical "All non-black objects are non-ravens" complications to prove his statement. He could just say something like: "this is brown beer bottle, it is not non-black raven, so it is evidence'

[muttrox]

I can't imagine why anyone would define evidence that way. You've equated evidence with proof, which is ridiculous. The whole concept of proof is tenuous at best outside pure mathematics.

[lostdummy]

Well, that was my definition of evidence. If there is another one, please post it, and we can see how it will correspond to this problem. But I still stay at oppinion that 'solution' of this problem is very related to definition of 'evidence'.

And I gave example where , in case we consider 'evidence' in more broader definition that you imply, we can see that Skinny didnt have to use any logic negations to 'prove' his claim. If evidence=any data we collected regarding proving/disproving some case, then he can show any item and say "see, this is chair, it is not raven of some other color, so it does not disaprove my statement that all ravens are black, therefor it is evidence, even if small piece of evidence"

So, to conclude, I admit that my 'definition' of evidence may be wrong, but I still think that this whole problem is connected to such definition, and I also believe that definition that you may have in mind will just prove Skinny right.

[muttrox]

What "evidence" means in this context was discussed a good deal throughout this thread, I don't see any reason to rehash it all in great detail. Your example with the chair is very interesting, since that's the heart of the puzzle -- showing a non-black non-raven is indeed evidence, albiet not proof, in the exact same way that showing a black raven is evidence, albiet not proof.

How do you account for Skinny's statment, "Here is a non-black thing, and it's not a raven, so this is evidence that all ravens are indeed black, though admittedly a very small piece of evidence.", which is completely meaningless by your definition of evidence?

I'm curious why you would think evidence means absolute proof. According to that criteria there is no evidence for relativity, quantum mechanics, evolution, Newton's laws, the sun coming up tomorrow, that there is an internet, etc... After all, we have not checked all possible cases of those theories, so we are akin to showing ten million ravens, when there are more out there. According to your post, that's worthless. So, do you believe there is evidence for those theories?

[Guest]

[lostdummy]

ok, above post is mine ... i forgot to log in again :)

btw, I have some questions about posted solution:

1) In solution it says "How can a piece of evidence support two contradictory claims?", and then proceed to show how that 'problem' can be solved if no raven exists etc. But my question is 'why can not one piece of evidence support two contradictory claims' ? Especially if evidence is defined as most people here imply :)

To give simplified example, lets say that Newton's law and Relativity theory have contradictory claims (as they do, when objects are moving close to speed of light). Now, lets take as one evidence set of data relating speeds, mass ... gathered at normal speeds. Such evidence will support both Newton's law and Relativity theory

2) Rest of solution is based on accepting that evidence can not support two contradictory claims, and then give us 'solution' for that, ie it can be true if 'no raven exists'... so if it is true that one piece of evidence CAN support two contradictory theories, rest of solution is in doubt

3) even if we accept statement about 'evidence can not support two..', proof that Skinny did not show us evidence was explained by Skinny not showing us any non-black raven, ie "Whether or not a non-black raven exists, it's known in advance that Skinny won't be showing it, so showing you the beer bottle does not say anything about ravens at all."

But, in previous part (where it is explained why 'paradox' can exist if no raven exist) it says "can both be true, so long as there aren't any ravens at all!" - Notice that it says any ravens. Therefore, as long as we know that ANY raven exists, Skinnys theory should hold. It is not at all needed to know "Whether or not a non-black raven exists", but "Whether or not any raven exists". And I do think that Skinny is not required to actually show you any raven to prove it exists , because if ANY raven did not exists, you would probably not understand at all Skinny's wager at all. So, assumption that at least one raven exists is by far closer to fact than lot of other assumptions in this solution (like assumption about what is evidence, assumption that evidence can not support two theories....)

To conclude, if we accept all those other 'assumptions', I think that Skinny has indeed provided piece of evidence.

[muttrox]

[lostdummy]

well, I said 'most' of definitions will fall under one of those 2, and yours is closer to #2, as you said, but I did not exclude #3, #4.... My main points were:
1. solution depends on definition of 'evidence'
2. whatever definition you choose, solution can/will be different from posted one


Namely:
a) if you choose definition close to #1, then solution can be simplified (non-thing non-color not needed), but will result is same conclusion : "brown beer bottle is not evidence"
b) if you choose definition close to #2, then posted solution is wrong, and Skinny DID provise evidence, ie "brown beer bottle is evidence".

Now, in your posted example:

[Guest]

Accepting Hempel's paradox can't Skinny showing you the beer bottle be seen as a minute piece of evidence towards the fact that there are no ravnes,thus making the statement "All ravens are black " true?

[CrystyB]

I think that your post can "be seen as" an oversized exaggeration... I mean you say "minute piece of evidence" (emphasis is mine), and a few words later "making the statement [...] true"... What's with that?!?

[Guest]

A minute piece of evidence towards the fact that there are no ravens which fact if true would make the statement "All ravens are black" also true.So evidence towards the non-existence of ravens is evidence towards the fact that all ravens are black.

I think you didn't really try to understand what i was saying.Just found an opportunity to post some half-wit remark.

[CrystyB]

Okay, i guess i didn't realize what you were saying... No ravens means all of them are Whatever-You-Want ([c] mathgrant!), just like a false statement implies anything at all, from the purely logical point of view.

Umm, i think the converse is more true. You seem to have posted without really trying to understand what i was saying... And if you were saying what your second post hints at, then you have clearly missed the "See the Solution" link... : shock :

[ inv ]To clear things up: How is a minute piece of evidence making a statement automatically true? "1=1" is evidence for "n^2 = n^3", but the statement isn't true, is it?[ / inv ]

The above argument is now useless, since you've made it clear that the "thus making" should have been "which would make"