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?

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    This is simply highlighting the fundamental problem of induction. It's not unusual for inductive logic to violate intuition, which is exactly the position taken by the "young man". – Cody Gray Aug 19 '11 at 8:33
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    @Cody So if I'm not mistaken, what you are saying is that this question boils down to whether you believe in Inductive reasoning or not. Hence if I believe in induction I'll support the ornithologist's argument, if not I'll tend to support the young man. The answer to this question is merely a matter of opinion. Is that what you are trying to say? – Green Noob Aug 19 '11 at 11:42
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    @Green noob - no, it is not about whether you "believe" in inductive reasoning or not. Everyone does and must in order to function at all in this world. Gravity, for example, is an inductive hypothesis. That I am the one controlling my arm when it moves is an inductive hypothesis. The vast majority of claims/arguments are based off premises derived from inductive reasoning or are inductive in logical form themselves. The argument in your passage is about the weight of inductive reasoning, not whether it is valid. It IS valid; the strength of an inductive claim lies in the evidence for it. – stoicfury Aug 19 '11 at 15:48
  • Your problem here is in assuming that one of them is correct just because they oppose each other. It is possible that both are incorrect. In the final case the the blue jacket and gray pants simply agree with the statement that non black things are non ravens. It is a compositional fallacy to assume that a part indicates the truth of the whole. – Chad Aug 19 '11 at 20:28

This question is much more interesting as a statistics problem than a logic problem. Yes, of course, there could be a bird that is genetically a raven except for one mutation that happens to make its plumage some non-black color, and we would of course call that a raven also. So in some sense the young man is right; you don't know for certain that every raven is black unless you have (at least via proxy) inspected every raven. The ornithologist only knows that ravens he has seen are overwhelmingly black (with no counterexamples), and hence it is a reasonable approximation for him to say that they "are black" (assuming that he's seen a representative sample).

But then the question is: given that the ornithologist has seen, say, 300 ravens, and they've all been black, if he finds another raven at random, how confident should he be that this new raven will be black, even if pragmatically we agree that he should say "ravens are black" based on past experience? And thus begins a long detour through Bayesian statistics and priors (which are probably not uniform given what we know about coloration of bird plumage).


the statement 'All ravens are black' is logically equivalent to the statement 'All non-black things are non-ravens.'

This is logically valid, but it is not necessarily true. The equivalent statement ('All non-black things are non-ravens.') can only be as true as the antecedent statement ('All ravens are black').

"Hence, all these colorful, non-black non-ravens also support the generalization." ... "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."

This reasoning is valid, but only in a finite system. So if you were to take the universe as finite, then technically, yes, this is correct. But it would only provide very weak support for the argument, given that our universe (even if it is "finite") is very very big. As Rex pointed out, this has everything to do with statistics.

For example:

I have a jar of 10 marbles. I've seen 3 black marbles and they all have a red dot on them. "Therefore," I say, "all black marbles have a red dot." This statement could be true or false. There are still 7/10 marbles in there which we don't know, so there's a 70% chance we could be wrong. The remaining ones could all be black with a red dot, or they could be other colors, or black with no dot — we just don't know. But if I were to start taking out other marbles and I pull out, say, two green marbles, even though they are not black with a red dot, I know now that there is now a slightly greater chance that my claim is true (statistically), because there are only 5 marbles left instead of 7, which means there is only a 50% chance that I could be wrong (instead of 70%).

So you can see why the ornithologist is correct in principle. That said, our universe has a lot more than 10 marbles, so a more appropriate analogy (though still far off) would be filling a jar the size of the Empire State building with sand, each grain of sand representing a possible "marble" (anything) in the universe. The knowledge that 2 grains of sand (blue jacket, gray pants) are NOT black ravens does not significantly strengthen your claim about all ravens being black...

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