Hempel's ravens (The Confirmation Paradox)

[Haiming]

While taking a group of benefactors on a tour through the new aviary they had just helped to build, a noted ornithologist commented, "And here we have two of the finest examples of ravens that I have ever seen. Notice the lustrous black plumage for which all ravens are famous." The ornithologist continued his lecture, commenting on the corvine feeding and nesting habits as well as on the birds' legendary role as harbingers of ill fortune.

When the ornithologist had finished, a young man said, "Sir, excuse me, but did you say that 'All ravens are black'?"

"I don't know if I said exactly that, but it's true. All ravens are black."

"But, how do you know that - for certain, I mean?" asked the young man.

"Well, I've seen a few hundred ravens in my day and every one of them has been black."

"Yes, but a few hundred are not all. How many ravens are there, anyway?"

"I would guess several million. As for your question, many other scientists, and non-scientists for that matter, have observed ravens over thousands of years and so far the birds have all been black. At least, I don't know of a single instance in which someone has produced a non-black raven."

"That's true, but it's still not all - just most."

"True, but there is other evidence. For example, take all these lovely multicolored birds we have seen today - the parrots, toucans, the peacocks -"

"They're lovely, but what do they have to do with your claim that all ravens are black?"

"Don't you see?" asked the ornithologist.

"No, I don't see. Please explain."

"Well, you accept the idea that every new instance of another black raven that is observed adds to the support of the generalization that all ravens are black?"

"Yes, of course."

"Well then, the statement 'All ravens are black' is logically equivalent to the statement 'All non-black things are non-ravens.' This being so and because whatever confirms a statement also confirms any logically equivalent statement, it's clear that any non-black non-raven supports the generalization 'All ravens are black.' Hence, all these colorful, non-black non-ravens also support the generalization."

"That's ridiculous," chided the young man. "In that case you might as well say that your blue jacket and gray pants also confirm the statement 'All ravens are black.' After all, they're also non-black non-ravens."

"That's correct," said the ornithologist. "Now you're beginning to think like a true scientist."

Who is reasoning correctly, the ornithologist or the young man?

[WitchOfDoubt]

Let's suppose that there were only 1,000 ravens in the whole world, and you saw 999 of them chosen at random, and those were black. That would be very STRONG evidence that all ravens are black.

Let's suppose there were 1,000,000 ravens, and you saw 999 chosen at random, and all were black. Well, that'd still be pretty good evidence to intuit that blackness is a general property of ravens, though the existence of albino members of other species should probably make you qualify that 'all.'

Now, how many "non-black" objects are there? Waaaaaaaaay more. You COULD prove that all ravens are black by checking every single non-black object in the universe. But a random sample of non-raven objects is so non-representative of that huge set that it is ridiculously weak evidence. Induction works best when you have entities that could reasonably be expected to be similar to each other on some level. It's easier to make generalizations about "dogs" than it is to generalize about "things represented by words that begin with d" or "things that are not cats."

This doesn't mean that "all ravens are black" is 'easier to prove' than "all non-black things are not-ravens". The two statements really are logically equivalent. But it's more efficient to look at the ravens than it is to sample the the rest of the universe.

Edited June 5, 2012 by WitchOfDoubt

[flamebirde]

And all black things must be ravens, by your reasoning of logic equivalence. which is ridiculous because I'm wearing black pants right now.

[joshuagenes]

The bird guy claims that blackness is included in the definition of what a raven is and without it a raven is not a raven. A little white spray paint can change a raven into a non-raven by his definition. A proper definition would consist of defining characteristics that do not change like portions of the DNA, and a fuzzy set of defining characteristics for rapid identification. However the bird guy cleverly changes the argument from hinging on the world ALL and converts it into a generalization. The young man is a logically correct and the scientist is a sneaky bastard.

[bonanova]

Who is reasoning correctly, the ornithologist or the young man?

Well they both have a point. It's a matter of magnitude.

Can we assume that if you eliminate everything that is false, all that remains is the truth?

That seems reasonable.

But if everything is a very large set then that is a daunting task.

Especially if the truth is a very small subset of everything.

Daunting or not, if we complete the task we have completed the proof.

1. Conceivably we could assemble all the ravens and note their color.

   Say we did that and they all were in fact black.

   Q.E.D.

2. In a fairy tale world, we could also assemble everything that is not black.

   It would take a while, but conceivably we could note each item's identity and confirm none of them were ravens.

   Q.E.D.

So they are both right.

It's just that the second proof [to a very much lesser extent the first proof] is in practice carried out to such a miniscule extent that it adds infinitesimally to the proof. There is nothing inherently wrong with examining things that are not remotely related to ravens in order to prove something about ravens. It's just that we have to examine everything, all things, possible ravens or not, that are not black in order to prove something about the blackness of ravens.

Only their blackness, and nothing else. It's specious to point out that a white picket fence has nothing to do with ravens. It's more to the point that a white picket fence has something to do with things that might be black.