Hempel’s Raven Paradox

Carl Gustav Hempel presented the argument that observing a green apple is evidence that all ravens are black.

Hempel's Raven Paradox

Suppose you wish to prove that all ravens are black. If you observe one black raven, this does not prove that all ravens are black, but it is one piece of evidence supporting the hypothesis. Observing 10,000 ravens, all of which were black, would still not prove that all ravens are black, though it would again provide some evidence. Meanwhile, observing a single white raven would be absolute proof that not all ravens are black.

In strict logical terms, the statement “All ravens are black” is equivalent to saying “All non-black things are non-ravens.” That is why, if we were to see a non-black thing, such as a white thing, that happened to be a raven, the statement “All ravens are black” would be disproved.

Now, if observing a raven that is black is one piece of evidence for the statement “All ravens are black,” then observing a non-black thing that is a non-raven is one piece of evidence supporting the statement, “All non-black things are non-ravens,” which is its logical equivalent. So, observing a green apple (a non-black thing that is a non-raven), is a small piece of evidence that all ravens are black.

As with other paradoxes, the conclusion seems absurd. Surely observing an apple tells us nothing useful about the color of ravens. However, we must determine what, if anything, is wrong with the argument.

Labyrinths of ReasonFor an extensive look at this paradox, check out William Poundstone’s Labyrinths of Reason.

One attempted resolution to the paradox is to accept that observing a green apple does provide some evidence that all ravens are black, just an exceedingly miniscule amount, given the vast difference between the number of ravens and the number of non-black things. In this view, there is no real paradox, just a disconnect between the logical meaning of the evidence and the fact that it is unlikely to have any real-world significance in determining the color of ravens.

Another approach denies that observing a black raven is evidence that all ravens are black, arguing that hypotheses can never really be proved, only disproved. So observing a black raven disproves the hypothesis that no ravens are black, just as observing a white raven disproves the hypothesis that all ravens are black. Observing a green apple, on the other hand, is consistent with all ravens being black and consistent with no ravens being black.

Some philosophers have pointed out that the nature of the evidence is of crucial importance. (The paradox of the 99 foot tall man illustrates this well.) In the real world, observing the colors of ravens and related species, and studying biology, is simply much more relevant than observing the colors of unrelated things.

Incidentally, white ravens do exist, but they are quite rare.

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