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Nevermore

Skinny's bet is a variation on Hempel's Paradox, discovered by Carl Hempel in 1946.

Suppose you want to know whether all ravens are black. You could start by investigating all the ravens you can find. As soon as you find even one raven that is not black, you have disproved the hypothesis. However, if you don't find any counterexamples, every black raven you see adds a bit of weight to the hypothesis. Without checking all ravens in existence, you can't prove the hypothesis, but if you check a large number, you can conclude that it is very likely.

Hempel's belief was that evidence could also be provided by looking for non-black objects. As Skinny points out in the wager, the statement "All ravens are black" is logically equivalent to its contrapositive, "All non-black objects are non-ravens." Either is disproved by finding a single non-black raven, but likewise, if you check enough non-black things and don't find any ravens, you can conclude that the hypothesis is likely.

Here's the catch. While finding a non-black non-raven does indeed provide evidence to support the hypothesis to a very small degree, it might also support other statements. For example, our brown beer bottle is also a non-white non-raven. How can a piece of evidence support two contradictory claims?

The "out" is that "All ravens are black" and "All ravens are white" are not, in fact, contradictory claims. They can both be true, so long as there aren't any ravens at all! And, of course, as soon as you have observed at least one raven, you know that if all ravens are the same color, it has to be that one.

So has Skinny won the bet? No, he hasn't, not even if we accept Hempel's argument that non-black non-ravens provide (a very small amount of) evidence to support the statement. In the wager, Skinny stated that he would provide evidence without showing any ravens. Whether or not a non-black raven exists, it's known in advance that Skinny won't be showing it, so showing you the beer bottle does not say anything about ravens at all.

You meet him for lunch the following day and explain your logic. "Alright, alright, you win this time," he says. "Double or nothing?"

(note: The puzzle has been modified to read "will provide evidence today" instead of "can provide evidence".)

Images created by Matthew Van Atta.

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