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Hempel's Paradox of the Ravens

Surrealism
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2/7/2015 1:02:05 AM
Posted: 1 year ago
This has been an interesting topic to me always, because it makes the notion of "evidence" seem absurd. For those who don't know about it, here's the fast version:

(Based on the assumption that "evidence" for a conditional statement A->B is when you have something that satisfies both A and B)

Premise One: "All ravens are black" is equivalent to "If it is a raven it is black"
Premise Two: "If it is a raven it is black" is equivalent to "If it is not black it is not a raven"
Premise Three: If something is evidence for one statement, it is evidence for any equivalent statements.
Premise Four: A white rock is evidence that "If it is not black it is not a raven"
Conclusion: A white rock is evidence that all ravens are black.

That's just my rushed summary, I'd recommend doing your own research for details. But what I'm asking is, can anyone think of a resolution to the paradox? Because I can't think of anything except that "evidence" doesn't really exist.
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ford_prefect
Posts: 4,143
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2/11/2015 3:23:14 PM
Posted: 1 year ago
At 2/7/2015 1:02:05 AM, Surrealism wrote:
This has been an interesting topic to me always, because it makes the notion of "evidence" seem absurd. For those who don't know about it, here's the fast version:

(Based on the assumption that "evidence" for a conditional statement A->B is when you have something that satisfies both A and B)

Premise One: "All ravens are black" is equivalent to "If it is a raven it is black"
Premise Two: "If it is a raven it is black" is equivalent to "If it is not black it is not a raven"
Premise Three: If something is evidence for one statement, it is evidence for any equivalent statements.
Premise Four: A white rock is evidence that "If it is not black it is not a raven"
Conclusion: A white rock is evidence that all ravens are black.

That's just my rushed summary, I'd recommend doing your own research for details. But what I'm asking is, can anyone think of a resolution to the paradox? Because I can't think of anything except that "evidence" doesn't really exist.

Premise 1 is flawed because albino ravens are white

Nah just kidding. In my opinion, the real problem lies in the definition of evidence. Why is a white rock considered evidence that "if it is not black it is not a raven?" Because it is an example of something that is not black, and therefore not a raven. But in order for it to be proof of the statement "if it is not black, it is not a raven", you'd need to also collect every other non-black object in the universe and show that none of them are ravens.

Similarly, a white rock can be considered evidence that all ravens are black because in order to prove that all ravens are black, you need to sort all the objects in the universe into black and non-black, and then show that the black category contains all existing ravens. The white rock is a tiny piece of evidence in this case, as it is one of the non-black objects that cannot be a raven. If it were a raven, then since it lies outside of the black pile, your proof would fall apart. Thus in a roundabout way, it is evidence.
Surrealism
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2/11/2015 3:30:05 PM
Posted: 1 year ago
At 2/11/2015 3:23:14 PM, ford_prefect wrote:
At 2/7/2015 1:02:05 AM, Surrealism wrote:
This has been an interesting topic to me always, because it makes the notion of "evidence" seem absurd. For those who don't know about it, here's the fast version:

(Based on the assumption that "evidence" for a conditional statement A->B is when you have something that satisfies both A and B)

Premise One: "All ravens are black" is equivalent to "If it is a raven it is black"
Premise Two: "If it is a raven it is black" is equivalent to "If it is not black it is not a raven"
Premise Three: If something is evidence for one statement, it is evidence for any equivalent statements.
Premise Four: A white rock is evidence that "If it is not black it is not a raven"
Conclusion: A white rock is evidence that all ravens are black.

That's just my rushed summary, I'd recommend doing your own research for details. But what I'm asking is, can anyone think of a resolution to the paradox? Because I can't think of anything except that "evidence" doesn't really exist.

Premise 1 is flawed because albino ravens are white

Nah just kidding. In my opinion, the real problem lies in the definition of evidence. Why is a white rock considered evidence that "if it is not black it is not a raven?" Because it is an example of something that is not black, and therefore not a raven. But in order for it to be proof of the statement "if it is not black, it is not a raven", you'd need to also collect every other non-black object in the universe and show that none of them are ravens.

Similarly, a white rock can be considered evidence that all ravens are black because in order to prove that all ravens are black, you need to sort all the objects in the universe into black and non-black, and then show that the black category contains all existing ravens. The white rock is a tiny piece of evidence in this case, as it is one of the non-black objects that cannot be a raven. If it were a raven, then since it lies outside of the black pile, your proof would fall apart. Thus in a roundabout way, it is evidence.

You are confusing evidence and proof. Proof certifies a statement as 100% true. Evidence merely brings knowledge to light that makes a statement more likely to be true.

For me, the point of the paradox is to show that such a thing as evidence can't exist - that it can never be that something is more likely to be true, but that it is true or not.
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ford_prefect
Posts: 4,143
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2/11/2015 3:44:01 PM
Posted: 1 year ago
At 2/11/2015 3:30:05 PM, Surrealism wrote:
At 2/11/2015 3:23:14 PM, ford_prefect wrote:
At 2/7/2015 1:02:05 AM, Surrealism wrote:
This has been an interesting topic to me always, because it makes the notion of "evidence" seem absurd. For those who don't know about it, here's the fast version:

(Based on the assumption that "evidence" for a conditional statement A->B is when you have something that satisfies both A and B)

Premise One: "All ravens are black" is equivalent to "If it is a raven it is black"
Premise Two: "If it is a raven it is black" is equivalent to "If it is not black it is not a raven"
Premise Three: If something is evidence for one statement, it is evidence for any equivalent statements.
Premise Four: A white rock is evidence that "If it is not black it is not a raven"
Conclusion: A white rock is evidence that all ravens are black.

That's just my rushed summary, I'd recommend doing your own research for details. But what I'm asking is, can anyone think of a resolution to the paradox? Because I can't think of anything except that "evidence" doesn't really exist.

Premise 1 is flawed because albino ravens are white

Nah just kidding. In my opinion, the real problem lies in the definition of evidence. Why is a white rock considered evidence that "if it is not black it is not a raven?" Because it is an example of something that is not black, and therefore not a raven. But in order for it to be proof of the statement "if it is not black, it is not a raven", you'd need to also collect every other non-black object in the universe and show that none of them are ravens.

Similarly, a white rock can be considered evidence that all ravens are black because in order to prove that all ravens are black, you need to sort all the objects in the universe into black and non-black, and then show that the black category contains all existing ravens. The white rock is a tiny piece of evidence in this case, as it is one of the non-black objects that cannot be a raven. If it were a raven, then since it lies outside of the black pile, your proof would fall apart. Thus in a roundabout way, it is evidence.

You are confusing evidence and proof. Proof certifies a statement as 100% true. Evidence merely brings knowledge to light that makes a statement more likely to be true.

No I'm not. Evidence is required to prove something. If you only have a little evidence, you can't prove the statement. But as you collect more evidence, the statement becomes more likely to be true, from your point of view. And when you have enough evidence to prove the statement, you accept it as true. So observing that a white rock is not a raven is evidence, not proof, of the statement "all ravens are black." If you were to observe every non-black object in the universe, and none of them were ravens, then you'd have proof that (assuming the existence of ravens) all ravens are black.

For me, the point of the paradox is to show that such a thing as evidence can't exist - that it can never be that something is more likely to be true, but that it is true or not.

It's not a paradox. People just don't understand that evidence can have a small or large magnitude. In this case the magnitude is tiny, but it is still evidence.
Surrealism
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2/11/2015 3:48:48 PM
Posted: 1 year ago
At 2/11/2015 3:44:01 PM, ford_prefect wrote:
At 2/11/2015 3:30:05 PM, Surrealism wrote:
At 2/11/2015 3:23:14 PM, ford_prefect wrote:
At 2/7/2015 1:02:05 AM, Surrealism wrote:
This has been an interesting topic to me always, because it makes the notion of "evidence" seem absurd. For those who don't know about it, here's the fast version:

(Based on the assumption that "evidence" for a conditional statement A->B is when you have something that satisfies both A and B)

Premise One: "All ravens are black" is equivalent to "If it is a raven it is black"
Premise Two: "If it is a raven it is black" is equivalent to "If it is not black it is not a raven"
Premise Three: If something is evidence for one statement, it is evidence for any equivalent statements.
Premise Four: A white rock is evidence that "If it is not black it is not a raven"
Conclusion: A white rock is evidence that all ravens are black.

That's just my rushed summary, I'd recommend doing your own research for details. But what I'm asking is, can anyone think of a resolution to the paradox? Because I can't think of anything except that "evidence" doesn't really exist.

Premise 1 is flawed because albino ravens are white

Nah just kidding. In my opinion, the real problem lies in the definition of evidence. Why is a white rock considered evidence that "if it is not black it is not a raven?" Because it is an example of something that is not black, and therefore not a raven. But in order for it to be proof of the statement "if it is not black, it is not a raven", you'd need to also collect every other non-black object in the universe and show that none of them are ravens.

Similarly, a white rock can be considered evidence that all ravens are black because in order to prove that all ravens are black, you need to sort all the objects in the universe into black and non-black, and then show that the black category contains all existing ravens. The white rock is a tiny piece of evidence in this case, as it is one of the non-black objects that cannot be a raven. If it were a raven, then since it lies outside of the black pile, your proof would fall apart. Thus in a roundabout way, it is evidence.

You are confusing evidence and proof. Proof certifies a statement as 100% true. Evidence merely brings knowledge to light that makes a statement more likely to be true.

No I'm not. Evidence is required to prove something. If you only have a little evidence, you can't prove the statement. But as you collect more evidence, the statement becomes more likely to be true, from your point of view. And when you have enough evidence to prove the statement, you accept it as true. So observing that a white rock is not a raven is evidence, not proof, of the statement "all ravens are black." If you were to observe every non-black object in the universe, and none of them were ravens, then you'd have proof that (assuming the existence of ravens) all ravens are black.

For me, the point of the paradox is to show that such a thing as evidence can't exist - that it can never be that something is more likely to be true, but that it is true or not.

It's not a paradox. People just don't understand that evidence can have a small or large magnitude. In this case the magnitude is tiny, but it is still evidence.

Well, evidence never really becomes proof. As you said, you would need to examine all the ravens in the universe to empirically prove the statement. But there are infinite potential ravens that might exist but don't. We can't examine all of those. 100% proof can only be ascertained in logic or mathematics.

Also, it is a paradox in the sense that common sense tells us that the conclusion - that a white rock is evidence that all ravens are black - is false. And yet the other premises, which by common sense are also true, seem to tell us the opposite.
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dylancatlow
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2/11/2015 9:34:33 PM
Posted: 1 year ago
At 2/7/2015 1:02:05 AM, Surrealism wrote:
This has been an interesting topic to me always, because it makes the notion of "evidence" seem absurd. For those who don't know about it, here's the fast version:

(Based on the assumption that "evidence" for a conditional statement A->B is when you have something that satisfies both A and B)

Premise One: "All ravens are black" is equivalent to "If it is a raven it is black"
Premise Two: "If it is a raven it is black" is equivalent to "If it is not black it is not a raven"
Premise Three: If something is evidence for one statement, it is evidence for any equivalent statements.
Premise Four: A white rock is evidence that "If it is not black it is not a raven"
Conclusion: A white rock is evidence that all ravens are black.

That's just my rushed summary, I'd recommend doing your own research for details. But what I'm asking is, can anyone think of a resolution to the paradox? Because I can't think of anything except that "evidence" doesn't really exist.

Premise four is flawed. A white rock is an example of something that is neither black nor a raven, but it's not evidence in favor of the hypothesis that "If it is not black it is not a raven". Why not? Because reasoning from the specific to the general is not justifiable. At best one could claim that "we have no examples of non-black ravens". Inductive reasoning can only establish degrees of confirmation. And if a white rock is the best you've got, then you have not made a very convincing case.
Surrealism
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2/11/2015 10:16:07 PM
Posted: 1 year ago
At 2/11/2015 9:34:33 PM, dylancatlow wrote:
At 2/7/2015 1:02:05 AM, Surrealism wrote:
This has been an interesting topic to me always, because it makes the notion of "evidence" seem absurd. For those who don't know about it, here's the fast version:

(Based on the assumption that "evidence" for a conditional statement A->B is when you have something that satisfies both A and B)

Premise One: "All ravens are black" is equivalent to "If it is a raven it is black"
Premise Two: "If it is a raven it is black" is equivalent to "If it is not black it is not a raven"
Premise Three: If something is evidence for one statement, it is evidence for any equivalent statements.
Premise Four: A white rock is evidence that "If it is not black it is not a raven"
Conclusion: A white rock is evidence that all ravens are black.

That's just my rushed summary, I'd recommend doing your own research for details. But what I'm asking is, can anyone think of a resolution to the paradox? Because I can't think of anything except that "evidence" doesn't really exist.

Premise four is flawed. A white rock is an example of something that is neither black nor a raven, but it's not evidence in favor of the hypothesis that "If it is not black it is not a raven". Why not? Because reasoning from the specific to the general is not justifiable. At best one could claim that "we have no examples of non-black ravens". Inductive reasoning can only establish degrees of confirmation. And if a white rock is the best you've got, then you have not made a very convincing case.

Again, providing an example was never defined as definitive proof for a claim, and neither was a million examples. It merely makes the idea seem more plausible to us, and we've deemed that "evidence". I would never claim that induction is actually capable of proving anything, and David Hume showed that was a bad way to reason in the 1700s. The whole point of Hempel's Paradox is that the idea of evidence - that an idea could be more likely to be true - isn't actually something that has any solid meaning, and is really just a case of human brains not being able to distinguish between probability and certainty (other examples are those given by Hume in his writings on the problem of induction). But in reality, it might be the case that a statement can't be more or less likely to be true, but can only be true, false, or indeterminate given the related knowledge.
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Garbanza
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2/12/2015 11:52:11 PM
Posted: 1 year ago
I think Hempel's own explanation makes sense, that we already have tacit information about non-black things being non-ravens, so finding a white rock doesn't give us any information we don't have. It would be different for aliens materializing on the earth without prior knowledge of color or birds.

For example, suppose I gave you a bag of buttons and said, all the red buttons have two holes. To confirm my theory, you'd pull out a few to check, and if they're all non-red and don't have two holes, the theory would be supported in the same way as if you pulled out a few and they were all red with two holes.

Although, I think implicit in the statement "all ravens are black" is the concept that ravens exist and even that black ravens exist. These implicit concepts are proven if you find one example of a black raven, but not if you find an example of a white rock.

If you checked the entire bag of buttons and there was not a single red one or one with two holes, technically my theory would be supported, but it would feel like a trick because of the implicit assumption that SOME red buttons with two holes exist.
chui
Posts: 511
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2/13/2015 6:25:28 AM
Posted: 1 year ago
At 2/7/2015 1:02:05 AM, Surrealism wrote:
This has been an interesting topic to me always, because it makes the notion of "evidence" seem absurd. For those who don't know about it, here's the fast version:

(Based on the assumption that "evidence" for a conditional statement A->B is when you have something that satisfies both A and B)

Premise One: "All ravens are black" is equivalent to "If it is a raven it is black"
Premise Two: "If it is a raven it is black" is equivalent to "If it is not black it is not a raven"
Premise Three: If something is evidence for one statement, it is evidence for any equivalent statements.
Premise Four: A white rock is evidence that "If it is not black it is not a raven"
Conclusion: A white rock is evidence that all ravens are black.

That's just my rushed summary, I'd recommend doing your own research for details. But what I'm asking is, can anyone think of a resolution to the paradox? Because I can't think of anything except that "evidence" doesn't really exist.

I must be missing something big here. I see no paradox.

The existence of other objects with different colours is essential if ravens are to be distinguished by colour.

One piece of evidence of course is not a proof of a theory, so any sensible person would then look at ravens in order to develop the black raven theory. I will aside the whole 'can a theory be

So the existence of the white rock is useful because we can point to it and say 'look there are such things as not ravens which are not black'. Therefore I can identify ravens by the property of colour.

This knowledge is not new to any of us, so is seemingly trivial. However imagine a world in which everything is the same colour. The statement "if it is not black it is not a raven" would be on a par with " if its not made of fermions (ie protons, neutrons and electrons...) it is not normal matter". [I am aware that I am referencing the as yet undetected and controversial dark matter]

So where is the paradox? If an object is to be given a value for one of its properties it is useful to know of other possible values for that property. All evidence can be of use, but some is more relevant for a given theory. I fail to see how this 'paradox' makes evidence non-existent.
Amoranemix
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2/15/2015 4:55:34 AM
Posted: 1 year ago
Premise 4 'A white rock is evidence that "If it is not black, it is not a raven"' is false.

Whether or not the white rock is evidence, depends on how it was acquired. The argument suggests a sampling experiment to determine the nature of things. How was the sampling done ?

If you picked a rock and noticed is white, then that doesn't tell you anything about crows.
If you picked something white and noticed it is a rock, then, if there are any white crows, it could have been a crow, but it isn't. So it is evidence that there are no white crows. So it is evidence that there are either no crows or that crows are not white and hence that all crows are black.

I think the reason the white rock looks like evidence in step 4 and not in step 1 is that step 4 is phrased to suggest that the white rock was picked for being white and not for being a rock, which places it in the category of the 'not black' objects, a category that has poor visibility in step 1.

chui
So the existence of the white rock is useful because we can point to it and say 'look there are such things as not ravens which are not black'. Therefore I can identify ravens by the property of colour.
I think the property of colour is assumed to exist.
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Sidewalker
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2/16/2015 6:12:50 AM
Posted: 1 year ago
At 2/7/2015 1:02:05 AM, Surrealism wrote:
This has been an interesting topic to me always, because it makes the notion of "evidence" seem absurd. For those who don't know about it, here's the fast version:

(Based on the assumption that "evidence" for a conditional statement A->B is when you have something that satisfies both A and B)

Premise One: "All ravens are black" is equivalent to "If it is a raven it is black"
Premise Two: "If it is a raven it is black" is equivalent to "If it is not black it is not a raven"
Premise Three: If something is evidence for one statement, it is evidence for any equivalent statements.
Premise Four: A white rock is evidence that "If it is not black it is not a raven"
Conclusion: A white rock is evidence that all ravens are black.

That's just my rushed summary, I'd recommend doing your own research for details. But what I'm asking is, can anyone think of a resolution to the paradox? Because I can't think of anything except that "evidence" doesn't really exist.

It isn't really a paradox so it doesn't actually need to be solved. Hempel was elucidating the difference between inductive logic and intuition as it relates to evidence. Perhaps it could be said that he was demonstrating the difference between application of formal logic and how logic operates practically as it pertains to what is significant and what is incidental.

While the so called paradox is true of formal logic, in practice we don't consider a white rock to be significant or relevent evidence in the question of whether all ravens are black. This doesn't contradict the formal logic of the syllogism, but intuitively we take another logical step in determining the relevence of the type of evidence we will consider significant. We intuitively know that the question pertains to ravens and only so the observation of ravens is significant, and observations of other things is not relevent and can simply be ignored.

So the question is whether or not all ravens are black, it's a problem of inductive logic and application of deductive logic to the inductive process allows a two step process which is not considered in Hempel's syllogism. In practice, we break the question down to first, determining what evidence is significant, the observation of ravens, then we determine what to observe about the evidence set, ravens, which would be their color.

This is just the nature of inductive logic, we can never observe everything, but practically speaking, we can observe enough to get a pretty strong indication of the truth of a proposition, and since we intuitively know that about induction, we also intuitively that it is practical to be selective about what evidence we will consider significant in making that determination.

Scientifically, this is how it works,

There's a very practical little inductive voice inside of us that tells the hopelessly anal deductive voice inside of us when to shut up, So when the question arises, "I wonder if all ravens are black", the automatic response is "I will observe to see", and when Mr. Anal chimes in with his inane considerations about observing everything in the universe, Induction man tells Mr. Anal to "shut the f--- up, because first, we're only going to look at ravens, and second, were only interested in what color those ravens are", when Mr. Anal replies, "But wait, I have a syllogism here I'd like you to consider", Mr. Induction just kicks his a$$.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater