I know. That's why I think it's a good example.
You asked what's the difference between my logic and your logic, and why I called yours "terrible." It's because your logic leads you to infer that there are no black swans, a conclusion that subsequent observation proves false. False is the opposite of true.
The logic I outlined, on the other hand, inferred only that the likelihood of seeing a black swan is somewhat less than that of several alternative hypotheses that would explain why Joe claimed to have seen one, given the facts as we know them. And strictly speaking, this inference is true. Note that conclusions drawn from such reasoning are contingent, subject to amendment given further evidence. And that's why science works.
We have to examine WHY we think this is improbable, though. Because we have not observed ANY black swans.
And the strength of any inference we draw from this lack of black swan sightings is directly proportional to the overall number of swan sightings. If we had only ever seen one swan, and it was white, we would be in a poor position to predict the color of the next swan we see. If, on the other hand, we had seen millions, and all were white, we would be inclined to bet money that the next one will be white, also.
Then it has led you to conclude something false.
If, on the other hand, the absence of non-white swans leads us to assign a high degree of probability to the sentence, "the swan is white," then we are just being reasonable.
I had a strong feeling you did. Thus the dialectic.
Exactly.
I don't see how. The old theory is that all swans are white. The new theory on offer is that Joe saw a black swan; therefore, some swans are black. This would indeed explain why Joe would say he saw a black swan, and would tend to falsify the old theory. But it seems unlikely given that millions of swans have been seen, and none were black.
Now you have a choice: lean toward the theory that swans are white, which is based on millions of observations, or lean toward the theory that some swans are black, based on one observation. This alone tends to cast doubt on Joe's theory, but we would need to offer likelier alternatives that might explain Joe's behavior. If the incidence of human error, hallucination, or lying is greater than one in millions (and I think it is), then it is reasonable to suppose that the fault lies with Joe's statement, not with the idea that swans are white.
So perhaps we investigate further and find that some farmer across the lake, unbeknownst to Joe, reports seeing a black swan in the same place at the same time. Since it is highly unlikely that two witnesses would independently see the same hallucination or make up the same lie, we might consider the lying and hallucination hypotheses falsified.
Furthermore, suppose that the only aquatic bird known to inhabit the region is the swan, and that Joe saw the bird swimming on the lake. This would cast severe doubt on the hypothesis that Joe mistook another bird for a swan, leaving us only the hypothesis that both Joe and the farmer literally cannot tell black from white.
But a defender of the white swan theory comes to the rescue, saying that the migration patterns of the Greater Curmudgeon have recently shifted because of wetland habitat destruction, and that Greater Curmudgeons have been documented only recently in areas not far from Joe and the farmer. Greater Curmudgeons are big black aquatic birds with long necks. Now we might plausibly explain why two separate witnesses saw a big black bird on a lake and thought it was a swan. The white swan theory is preserved; we have failed to falsify it...
...until scientists discover a whole flock of black swans on L'Isle des Chaussettes.
That's how it really goes in science, I'm afraid.
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