Discuss Nevermore here

[groza528]

How about this?

[impossibleroot]

Sounds like Skinny waited until the white raven *didn't* exist anymore...

[Guest]

Ok, so assuming we've gotten over notion that anything _could_ be considered evidence, and also assuming there is no preconceived notion that ravens are black:

1. So he has a box with every raven in existence in it, and grabs one, right? Well, its definately evidence that _some_ ravens are black, but statistically it doesn't prove much. If he grabbed 3, 4, or even 100 ravens and they were all black, it would then become evidence that all ravens are black because you have eliminated to a large extent that the raven was picked by chance, and that there are not in fact ravens of all colors.

2. even less-so evidence than #1, because there is no element of chance involed: skinny picked whatever raven he wanted. It could be the only black raven in existence and all others are white.

3. Nope, once again the statistics thing. And whats a representitive universe? Anything even close will still be huge, so one element out of say 15 billion is insignificant.

5. Although my answer was the same for both, I would say that #1 is much closer to being evidence that all ravens are black than #3 is, mostly because there are far fewer ravens than non-black objects (even in a representitive universe), so any raven will be statistically more significant.

6. Actually its the opposite (seeing one card out of a full deck and knowing it is red actually increases the probability that the second card will be black. While the first card has a probability of being red = 50%, the second will have a probability being 26/51 ~50.9%). _BUT_ this requires knowing something about decks of cards to be relevent, so that argument is invalid.

8. I disagree. Firstoff, these statements (p->q, ~q->~p [the contrapositive]) are being looked at as mathematical comparisons, but in the context they are invalid. Showing that some non-black objects are non-ravens is not the same nor is it evidence to the statement "all non-black objects are non-ravens." Going back to the argument that we only need evidence and not proof, 'evidence' (by your definition) is not established until some statistically significant number of 'non-black non-ravens' or 'black ravens' have been presented.

I go back to the very simple argument that if I have you guess what color a glurtz is and show you a non-glurtz (of any color), there is no way that you can tell me what color a glurtz is nor can you tell me that they are all the same color. Because what I showed you does not help you decide what color a glurtz is nor does it give you any reason to assume they are all the same color, it is not evidence.

[austinap]

The above was my post, and the probability given for the second card (~50.99%) is the probability for the next card being _black_. the probability for it being red would be 25/51, ~49.01% instead of 50%.

[dave10000]

[dave10000]

[dave10000]

How about the following? I'm curious to see what people think. (Assume no trickery, such as color-changing cubes, language tricks, forcing your choices so that they're not really random, etc.)

I have a box with 2 items in it. They are enclosed in plastic spheres, so you can't tell them apart by touch. You feel inside that there are indeed 2 items. I then put a red cube (in a similar plastic sphere) into the box. I claim that all cubes in the box right *now* are red. You know, because you saw, that the box contains at least one red cube.

Q1. You pull an item from the box, and it is a red cube. Does that increase the strength of your belief, to any degree, that all cubes in the box when I said "now" were red? Why or why not?

Q2. Now, with 2 items remaining in the box, you pull another item out of the box. It is a blue pyramid. Does *that* increase the strength of your belief, to any degree, that all cubes in the box when I said "now" were red? Why or why not?

[Guest]

[dave10000]

[Guest]

You still missed the point.

The point was that you can tell me nothing about the object even after I showed you a different object and made some claim that something about it wasn't the same as a glurtz. If it were evidence, you could form some sort of conclusion (or at least, an inkling of an idea) of some property of a glurtz, but obviously you cant. I could say something like "all glurtz' are round," show you some sort of non-round object and promise it wasn't a glurtz, and you still would have no idea what shape a glurtz was. The only idea you'd have would be my word that all glurtz' are round. The fact that I showed you a non-round object that wasn't a glurtz is completely insignificant. A glurtz could still be round.

Also, there was nothing in the passage to indicate that the object shown was chosen at random. Given those circumstances, skinny could show you 99.9999% of all non-black objects in the universe and still not have given evidence that all ravens are black, because all objects were shown at his discretion. The biggest part of this is that the item was not chosen at random. Had the item been chosen at random, I suppose by some twist of the imagination the item _could_ be conceived as evidence, though I still would argue that because you could make no useful conclusions from that 'evidence.'

[austinap]

I keep forgetting to log in again

[austinap]

Correcting myself here:

We can make no deduction at all from what skinny gave us. Again, let p='it is a raven' and q='it is black.'

skinny's statement was "all non-black things are non-ravens" (~q->~p). (~q) is true, but we still can't conclude anything about ~p. For all we know, he could be lying. Reducing this statement, we get (~q->~p)<=>(q or ~p) or "it is black or it is not a raven." Because q is false, this reduces simply to ~p. What skinny said wasn't necessarily true, it is only true if all ravens are indeed black but doesn't force them to be any more likely to be black. He proved it to you as much as saying "all ravens are black" would prove it to you.

[dave10000]

[austinap]

Well, your post 46 questions were pretty obvious, but they don't fall along the same lines as the puzzle does. And as far as stating that the object wasn't chosen randomly, I was referring to the original puzzle.

BUT, I did give a mathematical proof which applies even to randomly chosen objects (assuming you follow the along the lines of the puzzle and chose only 1 object).

stating again (letting p = "it is a raven" and q="it is black"), and we are given q = false and asked to solve for p (in the equation ~q->~p), so we have:

~q -> ~p <=> q or ~p

and since q = false, we have

q or ~p <=> ~p.

We can make no conclusion about p in this equation given what we are given.

Now, your comeback to this would be that we're given ~p = true, so therefore this is a true statement, and you would be correct. This also means nothing. Because this is a true statement, we can re-arrange things again and again, only to find out that what skinny showed us is not a raven. This is because anything he is telling us is about this object alone, not non-ravens or non-black objects in general.

[dave10000]

[Oscar]

[dave10000]

[austinap]

First off, here's my answer to your two questions:

Q1: This could probably be considered evidence, though still weak evidence given that there is a 1/3 chance it is the same cube I just saw you throw it. However, due to the limited number of objects and the fact that is saying something about what it itself is (a red cube), it doesn't much apply to the ravens problem.

Q2. Obviously it increases the strength of my belief that all items in the box are not red cubs. It only takes one counter-example to disprove a statement.

[dave10000]

I asked:

[dave10000]

I think this is as stark as I can make it:

The 1000 ravens experiment.

Given: I have exactly 1000 ravens in this box.

Given: I have exactly 1000 nonblack things in this box.

Note that those groups can overlap. Perhaps the box contains exactly 1000 white ravens. Or perhaps it contains 500 white ravens, 500 black ravens and 500 red ballons. Or perhaps it contains 1000 black ravens and 1000 blue balloons. You get the point.

Q1: If I pull an item out of the box and it's a black raven, that gets me 1/1000 of the way to the statement "all ravens in the box are black." If I did that 999 more times, I'd be sure of the statement. Let's call that a milliconfirmation. Is a milliconfirmation "evidence" that "all ravens in the box are black"?

Q2: If I pull an item out of the box and it's a green shoe, that gets me 1/1000 of the way to the statement "all nonblack objects in the box are nonravens." If I did that 999 more times, I'd be sure of the statement. So, it's a milliconfirmation of "all nonblack objects in the box are nonravens," according to our definition of "milliconfirmation" in Q1. Is it "evidence" that "all nonblack objects in the box are nonravens"?

Q3: If your answers to Q1 and Q2 are different, why? (Be specific)

Q4: If your answers to Q1 and Q2 are different, then is the green shoe of Q2, which is by definition a milliconfirmation of "all nonblack objects in the box are nonravens," also a milliconfirmation of "all ravens in the box are black"? If not, why not? (Be specific)

Q5: If your answers to Q1 and Q2 are the same, and if Skinny can prove that he picked a brown bottle at random from all things within 100 miles of him (he was picking at random from all things -- not all ravens, or all nonravens, or all nonblack things), then did Skinny win the bet? If not, why not? (Be specific)

[Guest]

[dave10000]

[Celt]

[Rio]

This has been a very interesting thread. Taking a slightly different approach, consider the following situation:

You and Skinny are walking around town, many miles from home. It begins to rain. As you duck into a coffee shop you wonder aloud whether all of your cats are inside your house. Skinny says "So you're wondering whether all of the cats that belong to you are inside your house? I have evidence that they are!" You are delighted. "What evidence?", you say. "Well," says Skinny triumphantly, "this cup of coffee isn't in your house!" You feel so relieved...

Basically, the problem is that the information provided by Skinny does not differentiate between the two possible states of affairs that might obtain: (P1) that all your cats are in your house, and (P2) that at least one of your cats is outside. P1 and P2 are contradictory - they cannot both be true. Skinny's information, if it were evidence for the one, would be evidence against the other. Since this is not the case, Skinny's information cannot be construed as evidence for either scenario.

The same holds true for (R1) All ravens are black, and (R2) at least one raven is non-black. The existence of a brown bottle, by itself, constitutes neither confirming nor disconfirming evidence for either scenario, and hence Skinny must lose the bet.

[dave10000]

Celt --

I tend to agree.

In the original puzzle, though, it is pretty clear that Skinny did *not* pick the bottle at random from all things within 100 miles of him. Rather, he (1) picked an object from inside the bar, where he presumably knew no ravens existed, and (2) presented you with an item, after he examined it and knew that it was a nonblack nonraven. In that event, I firmly believe that the brown bottle, in the original puzzle as given, did not qualify as evidence that "all ravens are black" (or of "all non-black objects are non-ravens"). I expect you agree. Do you?

* * *

And a request to the poster of the official solution, when it is posted:

PLEASE address the fact that Skinny intentionally picked an object he knew not to be a raven -- he did *not* pick an object at random that had some chance of falsifying the claim. Since that is the case, what Skinny chose did NOT qualify as evidence.

To see why, consider that if we allow Skinny to intentionally pick an object that is consistent with the claim, then he could provide evidence of almost anything. For instance, suppose he made the bet "I can produce evidence that all people named Joe have red hair." If he then went out and searched until he found a guy named Joe with red hair, THAT would not be evidence, since the purported evidence was not selected at random. (Joe *might* be viewed as an intentionally selected "confirming example," but a confirming example that is not selected at random is not evidence.) Unless the official response addresses the fact that Skinny's selection was not at random and was designed so that it was incapable of being inconsistent with the claim, then the solution will be incomplete at best (and wrong at worst).

[Celt]

[dave10000]

[Celt]

I understand what you mean, but I don't think anyone else will.

It appears we are in agreement then, other than the random selection thing.

[Guest]

I had another idea. Say a man's wife has been missing for some time, and he is on trial for her murder. If the prosecution shows only that the man had purchased a large life insurance policy on her a week before, this would not be considered evidence that a crime was even committed. If however the prosecutor produced additional information (blood stained carpet, her blood on his clothes, history of violent fights,etc.), then the insurance policy would be evidence - but only when considered in context with the other facts. Skinny's situation is similar. The beer bottle only becomes evidence when considered along with all (or most?) other non-black objects. Since no other facts were presented, Skinny loses.

Of course, this ignores all the evidence I've seen so far that indicates Skinny never loses.

[cha]

Forgot to log in above...

[pob14]

I think the difficulty lies in a definitional problem.

The term "evidence" is a legal, and ordinary English, word with meaning that relates to those arenas. We use "evidence" in court to mean "anything that makes a disputed fact more or less likely to be true" (actually, that's the definition of RELEVANT evidence, but never mind for now).

However, the proposition (A>B)>(~B>~A) is one of formal logic. While formal logic is often useful in legal or everyday situations, it isn't the SAME. For example, we don't use the term "proof" in its formal sense in court. We don't, and can't, "prove" things in court the same way we prove them in symbolic logic.

So Skinny is mixing terms; he's offering inductive proof of a syllogistic proposition. And, though I'm not a logician nor a mathemetician, I think I can quote Hank Hill here: "That ain't right."

I think Skinny loses for cheating.

POB

[Highest Prime]

[dave10000]

HP --

You certainly hit on the right line of reasoning in your post above. I agree that if it was unlikely but not impossible that the object chosen could be a raven, the object might still be viewed as "evidence" under an appropriately broad definition. (It would have a flaw upon a flaw, but that would still be nonzero which might be good enough for some definitions, though none that I personally would pick.)

The greater problem with Skinny's choice, I believe, is that -- as far as I can tell -- Skinny intentionally chose the brown bottle KNOWING it was not a raven. That is, he did not choose a non-black object at random to give to you, but rather chose a non-black object -- made sure it was not a raven -- and then gave it to you. That's not explicitly stated in the original puzzle, but in my view is a more reasonable interpretation of what Skinny did than assuming that he chose an item wholly at random from all non-black objects in the area. (I think Celt and I disagree on this, but I have no big quarrel if someone thinks Skinny *did* choose at random from objects in the bar. The original problem does not makes this clear.)

Thus, if I claimed that all 100 jelly beans in this jar were red and I pulled one out at random and it was red, that would be (slight) evidence supporting my claim. But if I looked in the bag and made sure the one I pulled out was red, that would not be any evidence at all supporting my claim. In my view, Skinny's bottle was more like the latter than the former, and thus in my view not evidence. For those who believe Skinny's bottle was more like the former, I have no problem with calling it "evidence" under a very broad interpretation of that word. The problem does not specify what "evidence" means, so that is another ambiguity leading to different possible results. Under most -- and perhaps all -- definitions that I would give to the word "evidence," the brown bottle would fail. But I recognize that under some sufficiently broad (and, in my view, philosophical and not particularly useful) definitions it could succeed.

[dave10000]

[Rio]

Dave10K:

The jelly bean example is nice, and while I recognize that you've moved from "Nevermore" on to an interesting discussion of the relationship between probability and evidence, I'd like to pose the following for your consideration:

B1: "All beans in the bag are red"

is equivalent to

R1: "all ravens (in the world) are black"

except that you've nicely shrunk the world down to the size of the bag. The most straightforward contrapositive of B1 is:

B2: "all non-red things in the bag are non-beans."

Let's assume for simplicity's sake that there are some beans in the bag, as well as some non-red things, but that beyond that, you have no knowledge of what's in the bag. (Nothing hinges on this assumption - it's just easier to talk about.)

If Skinny reaches into the bag and pulls out a silver coin, he has demonstrated something from the bag that is non-red and a non-bean, satisfying B2. But my question for you is this: has the production of the coin given you any more reason to believe that all beans in the bag are red than you had before the coin was produced, whether or not the coin was grabbed at random or intentionally?

In other words, how does the production of the coin help you decide whether B1 is more likely to be true or false?

From my perspective, it doesn't, because the production of the coin cannot, even probabilistically, distinguish between the case where all beans in the bag are red, and the case where none of them are.

On a completely different note, one could also make the following independent argument:

Evidence, whatever that is, is non-transitive. That is, if information I is evidence for proposition P, and P entails Q, I does not thereby become evidence for Q. Why? Well assume it were transitive. Then, since any arbitrary proposition entails a true proposition, it follows that , e.g., fossils, which surely constitute evidence for something, constitute evidence for the claim my computer has more RAM now than it did 3 years ago, which is absurd. Therefore, we must reject the hypothesis that the evidentiary relationship is transitive.

Note that Skinny's claim cannot be made unless evidence is transitive. Since it is not. Skinny's out of luck.

What do you think?

[dave10000]

[Rio]

[dave10000]

[LoudmouthLee]

New here, but as a Philosophy minor (and as an English Teacher), I feel I can shed some light onto this issue.

This issue is a famous logical fallacy called "Hasty Generalization"... Here's another example:

(1) LoudmouthLee, the New Yorker, stole my wallet. Therefore, all New Yorkers are theives.

(You, obviously cannot say that...)

or:

(2) I asked six of my friends what they thought of the new government restraints and they agreed it is a good idea. The new restraints are therefore generally popular.

(Too small of a sample, right?)

Someone who is more in-tune with their mathematics (unlike me) can write a fromal mathematical prrof when it comes to probability theory. I'll just leave you guys to it.

Hope this helps, if you need more info about the logical fallacy, I'll be happy to post.

Best regards,
Lee D.

[Guest]

1: All ravens are black ==> According to Skinny
2: All non black are non-ravens ==> Based First Statement
3: Something is non black only prove that Something is not raven since all ravens are black, according to the first statement. Afterall the first statement is the FACT we used in the puzzle, to prove other statement.
4. Now assume the bottle is black. Is it prove that the bottle is raven? No. Because we need the statement of "ALL BLACK IS RAVEN".

So, Skinny lost because he simply didn't prove all ravens are black from the bottle.