Talk:Raven paradox/Archive 2

Where's the paradox?
Shouldn't it be simple to prove that there is no paradox? There are albino ravens. Thus, all ravens are not black. Thus, not all things that are not black are not ravens. 05:12, 8 April 2008 (UTC)
 * Yes, we know that but that's not where the paradox lies. All that does, is prove that the statement, All Ravens are Black, is false -- which, as I said, we already know. The paradox actually lies in the fact that logic seems to indicate that we can prove the statement false by looking at unblack objects instead of looking at ravens. And a lot of people don't buy that. Hence the use of the word, paradox. -- Derek Ross | Talk 05:58, 8 April 2008 (UTC
 * Yes, for purposes of discussing the paradox it is best to assume that we don't (yet) know whether or not all ravens really are black, so that "all ravens are black" is a plausible hypothesis. Once we know for sure one way or the other, it is a degenerate (special) case and is not as illuminating. — DAGwyn (talk) 19:31, 8 April 2008 (UTC)
 * Alright, but I'm still not seeing a paradox... it is not inductive logic to take a single case and argue from that case for a general rule pertaining to all cases. Actual inductive logic a) would need a larger sample size to make any prediction whatosoever, and b) could at best only argue for a likelihood, not a certainty.  The only way to use inductive logic to prove it for a certainty would be to look at ALL unblack objects, not merely look at a single one, which is of course an impossibility. Jarandhel&#93;&#93; &#91;&#91;User_talk:Jarandhel&#124;(talk) (talk) 02:24, 9 April 2008 (UTC)


 * The single observed case is considered a "confirming instance", and it does not prove the hypothesis; however, it is generally considered to lend some credence to the hypothesis. (I.e. increase the likelihood that the hypothesis is true.)  The paradox is that observing a non-raven doesn't seem like it should have any bearing on the hypothesis, yet it apparently does support the contrapositive, which is logically equivalent to the original hypothesis.  Another way of seeing the paradox is that observing a red apple apparently supports both the hypotheses "All ravens are black" and "All ravens are white", which are mutually contradictory (if any ravens exist). — DAGwyn (talk) 15:45, 10 April 2008 (UTC)
 * To clarify that last thought, observing a red apple supports the general hypothesis, "All Ravens are non-Red", of which the hypotheses, "All Ravens are Black" and "All Ravens are White", are two particular specialisations. I discussed this in more detail earlier on this page (in 2004 and 2005). -- Derek Ross | Talk 16:08, 10 April 2008 (UTC)
 * Then the paradox is that the observation supports (adds evidence for) two contradictory hypotheses, which seems (to some people) to be something that shouldn't be able to happen. — DAGwyn (talk) 23:58, 2 May 2008 (UTC)


 * When you generalize from a sample size which is too small, like a single case, it's called a hasty generalization, which is considered a misuse of induction. How much evidence is enough for the generalization not to be hasty is a question which lacks an objective answer. You're certainly right that induction always involves a loss of certainty. It can get remarkably close to certainty, though - when we drop an object by removing whatever supports it, we are almost certain that it will fall, even though we have seen only a very tiny fraction of unsupported objects. Similarly, with the induction that is imagined to take place in the paradox, we imagine that somebody has seen only a tiny fraction of the ravens, but becomes almost certain that the next raven he sees will be black - just as certain as we are that an unsupported object will fall.


 * When we imagine somebody who has never seen a raven becoming almost certain that all ravens are black, on the basis of the examination of a tiny fraction of non-black non-ravens, then we see that such a person must have made a mistake in his reasoning. And yet he is apparently not using any reasoning which we do not use ourselves when we come to the conclusion that unsupported objects in general fall. Latexallergy (talk) 02:44, 9 April 2008 (UTC)


 * I think this is off the point, but indeed it is a component of the paradox. The observation of a green apple should not lead to the conclusion "all ravens are black" with certainty, but it is a piece of evidence supportive to such a hypothesis. I never thought it was paradox, and I basically agree with the Carpanian approach. People usually equate "a confirmation of truth" to "an evidence for a hypothesis", and when in this problem we have the latter, we think it tries to be the former, and reject it erroneously.
 * Just to quote something from Einstein: "No amount of experimentation can ever prove me right", and compare it to the usual view that "we proved relativity by seeing that bending of lighhhht!". We see that we use certain experiments to reduce the likelihood of theories being false, and although there is often nothing that could grant us absolute certainty, we take the experimental results to be "proofs" of the theories, and it is such a way of thinking that we have to get around, in order to resolve the paradox.129.67.38.26 (talk) 16:17, 2 May 2008 (UTC)

Proof of Santa ?
Can u not use the same reasoning to provide evidence for a statements like -


 * All christmas presents are made in Santa's workshop

Finding non-christmas presents that are not made in Santa's workshop is easy. I think that the article should clarify if this kind of reasoning also applies to statements that are obviously wrong. -- said someone who didn't sign


 * Weirdly enough all Christmas presents are made in Santa's workshop from a formal logic point of view since "All Christmas presents are made in Santa's workshop" is equivelant to "There does not exist an X such that X is a christmas present and X is made in Santa's workshop."  —Preceding unsigned comment added by 58.106.1.101 (talk) 10:58, 22 June 2008 (UTC)


 * That's not quite right. Let's take it one step at a time:
 * All Christmas presents are made in Santa's workshop.
 * means that
 * For all X, either X is made in Santa's Workshop or X is not a Christmas Present.
 * which is equivalent to
 * There does not exist an X such that not (X is made in Santa's Workshop or X is not a Christmas Present).
 * which can be transformed into
 * There does not exist an X such that X is not made in Santa's Workshop and X is a Christmas Present.
 * which can then be transformed into.
 * There does not exist an X such that X is a Christmas Present and X is not made in Santa's Workshop.
 * which is what you meant to say. -- Derek Ross | Talk 18:06, 22 June 2008 (UTC)


 * Sure. But finding a single christmas present which wasn't made in Santa's Workshop isn't hard at all, and disproves it. So while it is true that finding lots of non-Santa made non-Christmas presents reinforces the statement, the amount by which it reinforces the statement is extremely small. Titanium Dragon (talk) 19:08, 22 June 2008 (UTC)


 * Bit like the ravens really. You find black raven after black raven (or white plate after white plate), all supporting the hypothesis, and then you come across one white raven and the hypothesis is disproved at one fell swoop. -- Derek Ross | Talk 04:32, 23 June 2008 (UTC)


 * The correct analogy for the paradox involving Raven→black is not present→Santa but rather Santa→present. DAGwyn (talk) 21:28, 8 July 2008 (UTC)

Why just green apples?
The premise of the article appears to be that the likelihood that a statement is true is increased if we find concrete examples where the statement is true.

Under this premise, finding a white rock increases the likelihood of the statement "all non-black objects are non-ravens", presumably because the statement evaluates as true in light of the new discovery. So what about finding a black rock? The statement evaluates as true under that discovery as well. So it seems that finding any object, of any color, supports the assertion that "all ravens are black", the only exception being the discovery of a non-black raven. 208.33.154.136 (talk) 20:25, 10 April 2009 (UTC)
 * Saying "all non-black objects are non-ravens" is equivalent to saying that "if an object is non-black, it is not a raven." Finding a black object, whether a raven or not, provides no support for that statement. -- Avenue (talk) 21:15, 10 April 2009 (UTC)


 * Huh? Avenue, I don't think your comment is correct.  Look:
 * ~(R ==> B) <==> (R & ~B)
 * Therefore, (R ==> B) <==> (~R or B) by standard elementary logic.
 * And more specifically to the point at hand, we have that (~R or B) ==> (R ==> B)
 * So every time you find either:
 * 1) something that is black, or
 * 2) something that is not a raven
 * you have found evidence to support the hypothesis that all ravens are black.


 * So your assertion that finding a black object, whether a raven or not, provides no support for the claim that all ravens are black is an incorrect assertion. I think the correct comment is the 1) and 2) I stated above: Every time you find an object that either 1) IS black, or 2) IS NOT a raven, you have supported the hypothesis that all ravens are black.  If and only if you find an object that is NOT black and which IS a raven, you will have disproved the hypothesis that all ravens are black.


 * So you could spend your entire life searching for and finding things that are black and/or are not ravens, and you would be doing a valid scientific inquiry (LOL). This is of course a totally ridiculous, worthless way to do a scientific inquiry; no scientist would ever seriously use it ... but nevertheless, it's just old-fashioned logic. Worldrimroamer (talk) 06:26, 17 December 2009 (UTC)

First Appearence?
Did this first appear in 1937? My French is bad:

Theoria

Volume 3 Issue 2-3, Pages 161 - 379 (August 1937)

Le problème de la vérité. (p 206-244)

C. G. Hempel

Madmaxmarchhare (talk) 02:58, 26 April 2009 (UTC)

A false premise
"If an instance X is observed that is consistent with theory T, then the probability that T is true increases"

This is a false premise. Observing a black raven does NOT in itself increase the probability that all ravens are black.

Surprising? Not really. The plausibility of any hypothesis can only be be judged against other hypotheses, unnamed by Hempel. For example, we could be contemplating one world in which there are 100 ravens - all black - out of a total 1,000,000 birds against another world in which there are 200,000 black ravens and 1,800,000 white ravens. Now, let's say that we observe a black raven. This (due to the Bayes theorem) increases by the factor 1,000 the probability that we are living in the second world, in which most ravens are NOT black.

In short, to judge a hypothesis's probability given some evidence, we have to consider the alternative hypotheses as well as their prior probabilities.

The above argument against the "paradox" is due to I. J. Good (1967). I found it quoted by E. T. Jaynes in Chapter 5 of "Probability Theory: The Logic of Science", page 522.

Funny how everyone falls into the trap of thinking about apples ;-) —The preceding unsigned comment was added by 84.129.55.251 (talk) 20:47, 6 December 2006 (UTC).


 * That's a good argument when the only possibilities are the two worlds mentioned. If I knew for certain that one of the two had to be true, observation of a black raven would definitely make me think that I lived in world two (because the chances of seeing a raven at all in world one are so low). Moreover seeing 101 black ravens makes it completely certain that I am living in world two where some ravens are white. However the maths changes depending on how many possible worlds you admit. For instance if you admit a third possible world where there are 200,001 black ravens and 1,800,000 white ravens and a fourth where there are 1,999,999 black ravens and 0 white ravens the factor changes (and 101 ravens is no longer a magic number). Since there is a very large number of possible worlds in the real universe (and an infinite number of possible worlds in the problem universe) which all need to be taken into account to model, "Bayesianly", a statement like "all ravens are black" which makes no comment about the actual numbers of objects/ravens involved, the calculation needs to become a lot more complex then the simple one presented by I J Good. It needs to include all the possible combinations of non-ravens/black ravens/non-black ravens as possible worlds and then show how observation of a black raven affects the chances that you live in one of the worlds where all ravens are black. It would be interesting to see what conclusion it would come to though. Who knows ? It might even show the premise to be true after all (in the real universe at any rate). -- Derek Ross | Talk 00:02, 7 December 2006 (UTC)


 * I think that Good/Jaynes simply want to show that the problem is not specified enough for making any conclusions (as you also noticed). Hempels initial assumption upon which the paradox is built is unfounded. The "paradox" aspect refers to the difficulty of interpreting the non-black non-raven observation. I agree with you that the "two worlds" argument does not quite hit the nail on its head. However, we can easily show the problem is missing information to permit ANY conclusions. Let's just attempt to apply the Bayes theorem to find out the updated odds for the AllRavensBlack hypothesis:


 * O(AllRavensBlack | BlackRavenSeen) = O(AllRavensBlack) * P(BlackRavenSeen | AllRavensBlack) / P(BlackRavenSeen | SomeRavensNotBlack)


 * The likelihood ratio P(BlackRavenSeen | AllRavensBlack) / P(BlackRavenSeen | SomeRavensNotBlack) can be anything you like, depending on the relative number of black and non-black ravens in the (one, actual, our) world. So Hempel's premise that "BlackRavenSeen supports AllRavensBlack" crumbles. He then proceeds to deduce something from his false premise and wonders that deductions can go either way. It seems like a rather embarassing blunder. —The preceding unsigned comment was added by 134.106.27.84 (talk) 11:21, 7 December 2006 (UTC).


 * But Good's "possible worlds" approach actually does gives us a method of working with the hypothesis, "AllRavensBlack". Although the likelihood ratio in our actual world can't be calculated directly because we don't know the numbers, we know that our actual world is one of a finite number of possible worlds in each of which the likelihood ratios are calculable because the numbers of non-ravens, black and non-black ravens are all known.


 * The possible worlds can be enumerated as:


 * There are 0 objects in the universe, 0 are black ravens, 0 are other ravens;


 * There is 1 object in the universe, 0 are black ravens, 0 are other ravens;
 * There is 1 object in the universe, 0 is a black raven, 1 is another raven;
 * There is 1 object in the universe, 1 is a black raven, 0 are other ravens;


 * There are 2 objects in the universe, 0 are black ravens, 0 are other ravens;
 * There are 2 objects in the universe, 0 are black ravens, 1 is another raven;
 * There are 2 objects in the universe, 0 are black ravens, 2 are other ravens;
 * There are 2 objects in the universe, 1 is a black raven, 0 are other ravens;
 * There are 2 objects in the universe, 1 is a black raven, 1 is another raven;
 * There are 2 objects in the universe, 2 are black ravens, 0 are other ravens;


 * There are 3 objects in the universe, 0 are black ravens, 0 are other ravens;
 * There are 3 objects in the universe, 0 are black ravens, 1 is another raven;
 * There are 3 objects in the universe, 0 are black ravens, 2 are other ravens;
 * There are 3 objects in the universe, 0 are black ravens, 3 are other ravens;
 * There are 3 objects in the universe, 1 is a black raven, 0 are other ravens;
 * There are 3 objects in the universe, 1 is a black raven, 1 is another raven;
 * There are 3 objects in the universe, 1 is a black raven, 2 are other ravens;
 * There are 3 objects in the universe, 2 are black ravens, 0 are other ravens;
 * There are 3 objects in the universe, 2 are black ravens, 1 is another raven;
 * There are 3 objects in the universe, 3 are black ravens, 0 are other ravens;
 * etc. (to a very large but finite number for the real world)


 * This is obviously not a Bayesian calculation for the faint-hearted but it is a possible one (and its sum is 1 since one and only one of the hypotheses must be true). However forgetting the difficult calculation for the moment, one can still see that each new observation rules out all possible worlds (ie hypotheses) in which the universe contains less objects than have been seen so far and, in particular, that each observation of a black raven rules out all hypotheses in which less than that number of black ravens are posited. Since each hypothesis has a likelihood associated with it, that means that the overall likelihood for the set of hypotheses where "0 are other ravens" (which is the set that corresponds to the statement, "All Ravens are Black") will change too. It's an interesting question as to exactly how it changes when we see a black raven (or a red apple for that matter). The answer would tell us whether Hempel's premise, "BlackRavenSeen supports AllRavensBlack", is out to lunch or not. -- Derek Ross | Talk 18:28, 7 December 2006 (UTC)


 * Wow. That's a very, very interesting string of logic, there, by both of you. I never even thought about it like that, but after a while, this thought occured to me: that the premise (seeing a black raven increases the odds for the statement to be true) IS true. It has to be true, simply because there is a finite number of objects in the universe. Every object we observe (whether a black raven or a red apple) that is not a non-black raven increases the probability that the statement is true. I think the statement is valid and true on that reasoning alone. Matt Yeager ♫ ( Talk? ) 01:47, 22 December 2006 (UTC)

I came across this article and was astonished to note that it did not include a discussion of I. J. Good's argument or a citation. It should, since Good's argument shows with a clear counter-example that the assertion that observing an instance (e.g., a black raven) necessarily supports the hypothesis that all ravens are black, is simply false. Thus, no paradox can exist since one of Hempel's crucial premises is false.

I believe that some mention of this should appear in the main article. Without an appropriate mention, the article is unbalanced.

The relevant papers are:

Good, I. J., "The Paradox of Confirmation," ''Br. J. Phil. Sci.'' 11, 145-149 (1960)

Good, I. J., "The Paradox of Confirmation (II)," ''Br. J. Phil. Sci.'' 12, 63-64 (1961)

Good, I. J., "The White Shoe is a Red Herring," ''Br. J. Phil. Sci.'' 17, 322 (1967)

Hempel, C. G., "The White Shoe: No Red Herring," ''Br. J. Phil. Sci.'' 18, 239-240 (1967)

Good, I. J., "The White Shoe Qua Red Herring is Pink," ''Br. J. Phil. Sci.'' 19, 156-157 (1968)

Good's first (1960) paper contains an error which is corrected in the second. The Hempel paper is a response to Good's third paper, and Good refutes Hempel's argument in the last paper. Hempel imagines that one can argue in the absence of background information and alternative models, but Good shows otherwise. As far as I know, Hempel did not respond further. Bill Jefferys 19:21, 15 August 2007 (UTC)

Derek's observation that you need to enumerate all of the possible worlds is on the right track but not quite correct as he stated it. When fixed it reveals why Hempel's argument (and also the purported Bayesian calculation in the article) aren't correct.

Derek's idea of enumerating the possible worlds is sound, but he didn't enumerate all of them that are needed. Recall that there have to be some non-black non-ravens in the world, and he didn't list any worlds of that sort. So let i=number of black ravens in a world, j=number of non-black ravens in a world, k=number of black non-ravens in a world and l=number of non-black non-ravens in a world. The possibilities are therefore represented by all quadruples (i,j,k,l) with i,j,k,l integers greater than or equal to zero; we can write the prior probability that the actual world is represented by a particular quadruple by P(i,j,k,l), which is a real number on [0,1]; the numbers so assigned are the prior probabilities of each of these worlds, and they must be assigned so that they add up to 1.

But now we see that observing a non-black non-raven, or even observing a black raven, may decrease, increase, or leave unchanged the posterior probability that we are in a world where all ravens are black. We see this immediately in the simple cases described by I. J. Good in the citations I gave above, as well as the two-world case given at the top of this section. But that's just a particular choice of prior, where the priors on two particular worlds are given positive values and the priors on all other worlds are zero. This is a counter-example to the claim that the article's purported Bayesian calculation makes, as well as a counter-example to the entire Hempel argument. It's clear that whether ones confidence is increased, decreased or remains unchanged depends critically on the assignment of the prior probabilities P(i,j,k,l). Therefore, the problem as stated is simply ill-posed. There is no paradox.

The point really points up two critical mistakes that I have seen frequently in the philosophy of science literature when alleged Bayesian arguments have been made. These are points made trenchantly and convincingly in Jayne's book (cited above). Mistake number 1: You cannot make a correct Bayesian calculation without enumerating all the alternative hypotheses and assigning a prior on them. Here, the alternatives are represented by the mutually exclusive and exhaustive quintuples (i,j,k,l). Mistake number 2: Being vague about what background information is being used. The discussion of Bayesian resolutions in the article is vague about the background information. As we have seen, the background information includes the priors assigned to all the various possible worlds. Without this background information, no conclusions can be reached.

The Bayesian part of the article is wrong and needs to be rewritten. Bill Jefferys (talk) 17:39, 10 January 2008 (UTC)


 * (Guilty as charged, . I didn't explicitly list non-black, non-ravens, (although I did implicitly list non-ravens). Perhaps wrongly, I didn't think that it was necessary to go to that level of detail for the point I was trying to make. But for the point that you are making I fully agree with your approach in extending to a quadruple. -- Derek Ross | Talk 18:41, 3 April 2008 (UTC))


 * Bill, your explanation of how to apply Bayes's theorem to this is correct, but even so, a paradox does remain. It's called a paradox because the application here of logical reasoning, including Bayesian inference, leads to a counterintuitive conclusion with no clear reason why it's reasonable.  In your formulation, you agree it's possible that selection of certain priors (estimates about the frequency of possible worlds) can influence whether "observation of a non-black non-raven" should make one alter his estimate of the probability he assigns to "all ravens are black".  It is this fact that makes it a paradox: Why, we wonder, should an observation of a red apple, have any influence whatsoever, on the probability of the claim "all ravens are black"?  What does apple color have to do with raven color? So, AFAICT, the paradox is unresolved until you can repair the intuition that leads to rejecting the raven/apple color connection, OR you show a relevant way in which "all ravens are black" is unconnected to its contrapositive. MrVoluntarist (talk) 21:56, 2 April 2008 (UTC)

I don't agree. The problem is ill-posed, as Good's example shows, so there cannot be a paradox. Bill Jefferys (talk) 18:04, 3 April 2008 (UTC)


 * I don't know which "problem" you refer to as being posed. The paradox is precisely that a reasonable-sounding line of argumentation leads to an unintuitive and apparently wrong conclusion.  A resolution of that paradox requires showing where the argument went astray. — DAGwyn (talk) 23:53, 2 May 2008 (UTC)

Perhaps this will help: Hempel's argument starts with the fact that the statement "all ravens are black" is logically equivalent to the statement "all non-black objects are non-ravens." But it does not follow from this that observing a black raven (obr) is inferentially equivalent to observing a non-black non-raven (onbnr). That would only be true if the likelihood function P(obr|H) were identically equal to the likelihood function P(onbnr|H) for all hypotheses H under consideration. [Recall that the likelihood function is a function of H given a fixed observation]. But as I. J. Good's counter-example shows, it is in general not the case that those two likelihoods are equal. So Hempel's argument fails.

The "paradox" resides in confusing the logical statement with a statement about what is observed. Even though the logical statement is true, it does not follow that the two possible observations are equivalent or even that they imply that any particular hypothesis is supported or undermined. Thus the resolution of the "paradox" is simply to recognize that Hempel has confused two fundamentally different things. Bill Jefferys (talk) 01:12, 20 December 2009 (UTC)


 * That really helped me. I'd never thought of it from that point of view. Thanks. -- Derek Ross | Talk'' 04:19, 14 March 2010 (UTC)

logicalparadoxes.info
This site is an anonymous mirror of this one, obviously not an RS. Paradoctor (talk) 17:05, 16 June 2009 (UTC)

black raven under doormat as a signal
Something should be added to the article regarding the argument Good (1967) made, that finding a black raven can count as evidence that "All ravens are black" is false, for example, if you and I have prearranged that, if discover "All ravens are black" to be false, then I will leave a black raven under your doormat to relay this information to you.
 * The section, "A false premise" above, discusses Good's argument. -- Derek Ross | Talk'' 00:37, 28 September 2009 (UTC)

There is something left out in the statement of the paradox
In addition to what I'm writing below, please see my comment above (just a couple of posts up) in response to the posting "Why just green apples?" The poster was correct in what he/she said. I cannot find anywhere in this article that the more general statement of the paradox is given.

I think something like the following should be integrated into the article:

__________________________________________________
 * More generally speaking, the following it true:


 * The statement "For all x, if x is a raven, then x is black"


 * is, by elementary logic, equivalent to (see also my posting above):


 * "For all x, either x is not a raven or x is black". (The "or" here is the inclusive or.)


 * Therefore, the paradox can be stated: Every object you find that is either 1) black, or 2) NOT a raven, is evidence in support of the claim that all ravens are black. This is correct logic, but it clearly does not suggest a very fruitful way to conduct a scientific investigation.

__________________________________________________

The point about the green apple in the introduction to the article is, it can be argued, incomplete. The green apple is both not-a-raven and it is not-black. My point is that BOTH of the following are evidence in support of the hypothesis that all ravens are black.
 * 1) Finding a black apple (or a black raven or a black anything) and
 * 2) Finding ANY thing of ANY color that is not a raven.

Of course, finding a non-black raven would disprove the hypothesis once and for all.

So, I'm suggesting this: The article needs to state that (R ==> B) <==> (~R or B). Again, please see my comment posted above under "Why just green apples?"

If no one has a legitimate objection, I will volunteer to add a comment to the article incorporating the above suggestion. I just wanted to post my suggestion in the discussion first, before making a change. Worldrimroamer (talk) 07:26, 17 December 2009 (UTC)


 * If you take a look at the earlier discussion you'll see that we have actually covered this point already. Make sure that you have read the prior discussions before adding anything to the article. -- Derek Ross | Talk'' 18:38, 17 December 2009 (UTC)


 * Thanks for the reply, Derek. You're right, if it's in the discussion I should (try to??) find it (if it doesn't get archived or something before I can read it).  But the question still remains, at least in my mind: Why is the actual logically correct and complete statement of the "paradox" not in the article?  I am stating neither personal opinion nor original research; I'm simply stating Aristotelian Logic 101.  —Preceding unsigned comment added by Worldrimroamer (talk • contribs) 17:43, 19 December 2009 (UTC)


 * Understood. By all means add or expand upon the point if you feel that we haven't made it clearly enough in the article itself. I just meant that we'd already covered it on the discussion page. -- Derek Ross | Talk'' 18:27, 6 January 2010 (UTC)

thoughts
my informal and perhaps incoherent thoughts on the issue, just in case it sheds light on anything not already said:

in the statement that everyhing that is not a raven is not black, "everything" is not actually a closed set. for our purposes, it's a an unlimited open field. observing that the green apple is not a raven is (almost) equivalent to adding a new item to the set on the spot that is a non-black non-raven. if we added a non-black raven to the set on the spot, yes, that would be evidence (against), but we can't actually do that because ravens are defined as black. the statement is inductive, but once you start deriving other statements from it you lose track of its falculty of a non-definition. that's why it seems meaningless to introduce the evidence that a green apple, which is unrelated to ravens, is not black. it's unrelated to whether ravens are black by definition. (*actually, this isn't true.)

"i think it's true that all ravens are black"

if you translate that to "i think it's true that everything that is not a raven is not black", then maybe the green apple is actually evidence.

maybe the open question is whether "i think it's true that all ravens are black" is actually equivalent to "i think it's true that everything that is not a raven is not black." it's already been shown via other paradoxes that not all rules of deduction apply to belief statements.

a further ambiguity is that in "i thnik it's true that everything that is not a raven is not black" it is not clear whether we thnik that we may find a counterexample or that we think that everytihng that is not a raven is not black by definition. furthermore, saying that everything that is not a raven is not black doesn't tell us whether there is anything that is a raven or anything that is black. it also doesn't tell us if all ravens are black. it could be true that some ravens are white, but all non-ravens are also white. if everything is the collection of things in reality, tehre aren't necessarily black non-ravens. if everything is all possible imaginable things, then it includes black non-ravens, but observed things like a green apple are not evidence in that case. 74.186.83.219 (talk) 14:10, 6 January 2010 (UTC)


 * Thank you for your thoughts. Please take some time to read our policies on verifiability and original research. This is not meant to discourage you. If you have any questions, please don't hesitate to ask them here, on my page, or at the help desk. Happy editing, Paradoctor (talk) 17:12, 6 January 2010 (UTC)

(Probabilityislogic (talk) 04:27, 14 May 2011 (UTC)) I would add one (potentially) clarifying view, when you say "all ravens are black" you are basically saying the logical statement "R implies B", or that "R" and "R&B" have the same truth value (R is true if and only if R&B is true). Now this is not equivalent to "all non-ravens are non-black" (this is clearly false - a black cherry or black car or black anything serves as a counter-example to this statement). The equivalent reversal is "non-black means non-raven" or the logical statement "Not B implies Not R". Perhaps the paradox comes about from mistaking "Not R implies Not B" for the actually correct version "not B implies not R".

Paradox in popular culture
Would it be appropriate to add that Raven paradox is referred to in Episode 3 of the VN "Umineko no Naku Koro ni"? — Preceding unsigned comment added by 91.192.70.23 (talk) 11:44, 16 June 2011 (UTC)

nicod's criterion
According to some sources, Nicod's criterion is the obvious thing: A black raven supports the hypothesis, a non-black raven (of which many exist FWIW) falsifies it, and a non-raven says nothing whatsoever about it.

Some sources emphasise just the last part (non-ravens irrelevant to inductive reasoning about raven blackness).

At least one source narrowly defines "Nicod's condition" to be just that black ravens do support the hypothesis. This source calls the latter part (irrelevance of non-ravens) something else, namely "principle 3".

Clearly "Nicod's condition" plus "principle 3" and the "equivalence principle" (that evidence for an equivalent statement supports the original statement) are together inconsistent. Or in other words, the usual form of Nicod's criterion is inconsistent with Hempel's equivalence condition.

The issue is that which definition we pick affects the current article layout as presently titled. The narrower definition conveniently allows distinguishing 3 camps (reject induction from instance, reject equivalence, or reject irrelevance -- notice I've distinguished these just here without mentioning Nicod). Problem is, falsely mischaracterising what Nicod's criterion actually meant is not justified by convenience. Cesiumfrog (talk) 02:59, 29 August 2012 (UTC)

Numbers, please!
Can someone calculate whats the outcome of those nice formulas, lets say with 10 ravens and 10k other objects (or whatever one considers a good size)? — Preceding unsigned comment added by 195.72.132.1 (talk) 05:58, 30 April 2013 (UTC)

Picture
Does this page really need an illustration of objects that are not black and not ravens? If people are really in doubt that such objects exist they can temporarily look around the room they are in and find examples themselves. Also, why apples? —Preceding unsigned comment added by 82.6.96.22 (talk) 19:45, 5 May 2011 (UTC)
 * It absolutely has to be a green apple. If you were to use an example like a red door, you would run into the problems surrounding the Jagger Variation, wherein the individual would desire the example to be painted black, thus hopelessly confusing the raven-or-nonraven issue. As to the pictures, well, they're accurate and make the article prettier, so where's the harm? Milhisfan (talk) 09:36, 23 March 2012 (UTC)
 * In case even more pictures are considered useful, I put some (faked and non-faked) suggestions below; use them if you like - Jochen Burghardt (talk) 11:09, 21 April 2014 (UTC)

failure in Intuitionistic logic
In intuitionistic logic the ravens paradox fails, because the form of Contraposition fails in this logic, but i don't have interesting references for that (it just fails), can somebody add it (with proper references and philosophical meaning )  to the article? — Preceding unsigned comment added by 31.100.167.91 (talk) 10:13, 17 May 2014 (UTC)

Untitled
Perhaps it's a joke. However, it might be a real speculation. A German Hempel in folk language is known as someone who cannot keep things clean and orderly, throwing all - he doesn't need ? - under the couch he's lying on. Or, somehow things thrown move there without anybody noticing it. It well fits certain forms of thinking in Germany.

What's the raven paradox? The same as the black swan phenomenon?

What's wrong with Wikipedia? — Preceding unsigned comment added by 46.115.126.200 (talk) 18:52, 2 February 2014 (UTC)


 * Or should that be "What's non-Wikipedian with non-wrong"? -- Derek Ross &#124; Talk'' 20:53, 2 February 2014 (UTC)


 * "Hempel" is the name of the gentleman who proposed the paradox, as stated in the lead. Paradoctor (talk) 06:29, 3 February 2014 (UTC)

So the red ravens were under the couch all along. — Preceding unsigned comment added by 184.147.137.3 (talk) 03:20, 23 May 2014 (UTC)

Inconsistency with contrapositive article
According to this article the contrapositive of "All ravens are black" is "All non-ravens are non-black", whereas by simply substituting in the given example in the contrapositive article it would appear to be instead "All non-black things are not ravens". I think there needs to be some consistency here i.e. we shouldn't say the paradox involkes logical contraposition and then reference an article which defines it in a different way. 90.199.241.255 (talk) 21:20, 3 April 2015 (UTC)


 * I think you are right, but I couldn't find the location where the article claims the erroneous contraposition. Can you give section and paragraph? - Jochen Burghardt (talk) 22:31, 3 April 2015 (UTC)


 * Paragraph "The paradox", line 3. — Preceding unsigned comment added by 78.15.111.100 (talk) 14:12, 3 June 2015 (UTC)

Why isn't this clearly described as an example of bad logic/logical fallacy?
It's currently causing a lot of confusion on reddit, because this article makes people think it's a real paradox.--109.81.209.137 (talk) 18:18, 28 July 2016 (UTC)